STAR 2 QAUG13198. 

5101-258 

Flat-Plate 

Solar Array Project 

) 

lj-'" 

DOE/JPL-1012-103 

Distribution Category UC-63b 

:;i~Proceedings of the Flat-Plate Solar 

Array Project Research Forum on 

High-Efficiency Crystalline Silicon 

Solar Cells 

(NASA-CB-1760.47) P~OCEEDINGSOI' THE 

Fl.AT-J?LAXE SOLA£. lBBAY P.BCJ~CT :RESEARCH 

FORU!! ON H.lGH-EFF.lC.IENCl CBlf1AI..L.INE S.IUCON 

SOLAR CELLS (Jet PropulsioD Lab.) 498 p 

HC A21/HFAOl CSCL lOA G3/44 

May 15, 1985 

Prepared for 

N85-31615 

THRU 

N85~31643 

Unclas 

21837 

U.S. Department of Energy 

Through an Agreement with \ 

National Aeronautics and Space Administration 

by 

Jet Propulsion Laboratory 

California Institute of Technology 

Pasadena, California 

JPL Pl)blication 85-38 

! 
5101-258 

Flat-Plate 

Solar Array Project 

DOE/JPL·1012-103 

Distribution Category UC-63b 

Proceedings of the Flat-Plate Solar 

Array Project Research Forum on 

High-Efficiency Crystalline Silicon 

Solar Cells 

May 15,1985 

Prepared for 

U.S. Department of Energy 

Through an Agreement with 

National Aeronautics and Space Administration 

by 

Jet Propulsion Laboratory 

California Institute of Technology 

Pasadena, California 

JPL Publication 85-38 
I 

. '~ 

1 

j 

I 1 

! 

i 

-i 

! 

! 

~l 

I II 

j 

n 

, 

f 

I 

! 

H 

! 

Prepared by the Jet Propulsion Laboratory, California Institute of Technology, 

for the U.S;'Depi!ortment of Energy through an agreement with the National 

Aeronautics and Space Administration. 

: '.,. , .~: 

The JPL FIat-Plate Solar Array Project is sponsored by the U.S. Department of 

Energy and is part of the National Photovoltaics Program to initiate a major 

effort toward the development of cost-competitive solar arrays. 

This report was prepared as an account of work sponsored by an agency of the 

United States Government. Neither the United 'States Government nor any 

agency thereof, nor any of their employees, makes any warranty, express or 

implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process 

disclosed, or represents that its use would not infringe privately owned rights. 

Reference herein to any specific commercial product, process, or service by trade 

name, trademark, manufacturer, or otherwise, does not necessarily constitute or 

imply its endorsement, recommendation, or favoring by the United States 

Government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States 

Government or any agency thereof. 

This document reports on work done under NASA Task RE-152. Amendment 

66, DOE/NASA lAA No. DE-AIOI-76ET20356. 
ABSTRACT 

The High-Efficiency Crystalline Silicon Solar Cells Research Forum was 

held on July 9-11, 1984, in Phoenix, Arizona. The Research Forum addressed 

high-efficiency concepts, surface-interface effects, bulk effects, modeling 

and device processing. These topics were arranged into six interactive 

sessions, which focused on the state-of-the-art of device structures, 

identification of barriers to achieve high-efficiency cells and potential ways 

to overcome these barriers. The Forum arrangement was intended to enable and 

encourage interaction and discussion among participants. Promising technical 

areas of future research are presented in these Proceedings. 

iii 
~i 

I 

j 

FOREWORD 

The High-Efficiency Crystalline Silicon Solar Cells Research Forum 

was held at The PointA Hotel in Phoenix, Arizona July 9 through 11, 1984. It 

is my pleasure to introduce to you the papers contained in these Proceedings. 

All of the papers were invited (not submitted) from the best of a wealth of 

suggestions put forward and discussed by experts in the field and the 

Organizing conwittee. 

The objectives of the Forum were to address theoretical solar cell 

conversion efficiency limitations, the state of the art of device structures, 

identification of barriers to achievement of high-efficiency cells, and 

potential ways to overcome the barriers, and to provide the opportunity for 

unrestricted technology exchange among those attending. The format used to 

achieve these objectives involved six intensive sessions. 

The discussion sections have been edited with the intent of 

enchancing the clarity and continuity of each discussion. This procedure 

makes these Proceedings a most valuable reference document containing 

definitive work by some of the best solar-cell experts in the world. 

Forum it 

people. 

author's, 

work and 

This excellent collection of pspers, and the success of the Research 

reports, result from the efforts of a large number of dedicated 

I wish to record my gratitude to the Organizing Committee, the 

the session chairmen, and many other supporting people for their hard 

friendship. 

Ram Kachare, 

Chairman of the Forum 

and Proceedings Editor 

PRECEDING PAGE BLANK NOT FILMED 

v 
»m: 

PARTICIPANTS 

FLAT-PLATE SOLAR ARRAY PROJECT 

HIGH-EFFICIENCY CRYSTALLINE 

SILICON SOLAR CELL RESEARCH FORUM 

ADDIS. F. William 

Joint Center for Graduate Study 

100 Sprout Road 

Richland. WA 99352 

(509) 375-3176 

ANNAN. R. H. "Bud" 

U. S. Department of Energy 

Forrestal Building. CE 333 

1000 Independence Ave .• SW. 5E066 

Washington. DC 20585 

BACKUS, Charles E. 

Arizona State University 

Director, Engineering Research Center 

Tempe, AZ 85287 

(602) 965-1725 

BELL, Richard o. 

Mobil Solar Energy Corp. 

16 Hickory Drive 

Waltham, MA 02154 

(617) 890-0909 

BICKLER, Donald B. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 512/103 

.Pasadena, CA 91109 

(818) 577-9219 

BURGER. Dale R. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 512/103 

Pasadena. CA 91109 

(818) 577-9374 

CALLAGHAN, William T. 

Jet Propulsion Laboratory 

4800 Oak Grove Driv~. M.S. 502/422 

Pasadena, CA 9ll0~ 

(818) 577-9517 

CAMPBELL, Robert 

Westinghouse Electric Corp. 

P.O. Box 10864 

Pittsburgh, PA 15236 

(412) 892-5600, X 5364 

vii 

CHADI. D. James 

Xerox Palo Alto Research 

3333 Coyote Hills Road 

Palo Alto, CA 94304 

(415) 494-4136 

CHENG, Li-Jen 

Jet Propulsion Laboratory 

4800 Oak Grove Drive. M.S. 238/343 

Pasadena, CA 91109 

(818) 354-3068 

CISZEK, Ted 

Solar Energy Research institute 

1617 Cole Blvd. M.S. 16/3 

Golden, CO 80401 

(303) 231-1769 

COLEMAN, Michael G. 

SOlavolt International 

P.O. Box 2934 

Phoenix, AZ 95062 

(602) 231-6455 

CROTTY, Gerald 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 238/343 

Pasadena, CA 91109 

(818) 354-6294 

CULIK, Jerry 

Solarex Corp. 

1335 Piccard Drive 

Rockville, MD 20850 

(301) 948-0202 

DAUD, Taher 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 238/343 

Pasadena, CA91109 

(818) 354-5782 

DYER, Larry D. 

Texas Instruments 

P.O. Box 84 

Sherman, TX 75090 

(219) 892-5351 

P..RECEDING PAGE BLANK NOT FILMED 

~,,~-- -" ~~-'------"'------
FLOOD, Dennis 

NASA Lewis Research Center 

21000 Brookpark Road 

Cleveland, OH 44135 

(216) 294-6303 

FONASH, Stephen 

Penn State Univerrsity 

Engineering Sciences Programs 

University Park, PA 16802 

(814) 865-4931 

GRUNTHANER, Frank 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, 198/231 

Pasadena, CA 91109 

(818) 354-5564 

HA.~OKA, Jack 

Mobil Solar Energy Corp. 

16 Hickory Drive 

Waltham, HA 02254 

(617) 890-0909 

ILES, Peter 

Applied Solar Energy Corp. 

15251 E. Don Julian Road 

City of Industry, CA 91749 

(818) 963-6581 

JOHNSON, Scott M. 

Solarex Corp. 

1335 Piccard Driv~ 

Rockville, MD 20850 

(301) 948-0202 

KACHARE, Ram 

Jet Propu1si.on Laboratory 

4800 Oak Grove Drive, M.S. 238/343 

Pasadena, CA 91109 

(818) 354-4583 

KARIUS, Siegfried 

National Research Council 

Montreal Road 

Ottawa, Ontario, CANADA K1A OR6 

(613) 993-2730 

KAZKERSKI, L."L. 

Solar Energy Research Institute 

1617 Cole Blvd. 

Golden, CO 80401 

(303) 231-1115 

viii 

KEA\f"NEY, Chris 

Spire Corp. 

PatL"iots Park 

Bedford, HA 01730 

(617) 275-6000 

KESLER, Matt 

Solavo1t International 

P.O. Box 2934 

Phoenix, AZ 85062 

(602) 231-6434 

KING, David L. 

Sandia National Laboratories 

Kirtland AFG Base - East 

P.O. Box 5800, Div. 6224 

Albuquerque, NK 87185 

(505) 844-8220 

KOLIWAD, Kris 

Jet Propulsion Laboratory 

4800 Oak Grove Dri've, M.S. 238/343 

Pasadena, CA 91109 

(818) 354-5197 

T.AI, Stefan 

Intel Corp. 

3065 Bowers Ave., M.S. SCl-277 

Santa Clara, CA 95051 

(408) 987-5655 

T ... AMBE, John 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 122-123 

Pasadena, CA 91109 

(818) 354-8238 

LAMORTE, Michael F. 

Research Triangle Institute 

P.O. Box 12194 

Research Triangle Park, NC 27709 

(919) 541-6477 

LANDSBERG, Peter T. 

University of Southampton 

Southampton, England SOG 5N4 

(011 44 703) 559122 

LEIPOLD, Martin H. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, K.S. 507/228 

Pasadena, CA 91109 

(818) 577-9267 
LESK. Arnie 

Solavolt International 

P.O. Box 2934 

Phoenix. AZ 85062 

(602) 231-6458 

LINDHOLM. Fredrik A. 

University of Florida 

4406 SW 17th Terrace 

Gainesville. FL 32608 

(904) 392-4929 

LINDMAYER. Joseph 

Solarex Corp. 

1335 Piccard Drive 

Rockville. MD 20850 

(301) 948-0202 

LOFERSI<.I, Joseph J. 

Brown University 

Prof. of Engineering 

Box D 

Providence, RI 02912 

(401) 863-2870 

MILSTEIN, Joseph 

Solar Energy Research Institute 

1617 Cole Blvd. 

Golden, CO 80401 

(303) 231-7299 

MINAHAN, Joseph A. 

Spectrolab, Inc. 

12500 Gladstone Avenue 

Sylmar, CA 91342 

(SIS) 365-4611, XS72 

MOACANlN, Jovan 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 122-123 

Pasadena, CA 91109 

MOKASHl, Anant R. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 238/343 

Pasadena, CA 91109 

(818) 354-6017 

NATESH, Ram 

Materials Research, Inc. 

790 East 700 South 

Centerville. UT 84014 

(801) 298-4000 

ix 

NEUGROSCHEL, Arnost 

University of Florida 

Electrical Engineering 

Gainesville, FL 32611 

(904) 392-4949 

OLSEN, Larry C. 

Joint Center for Graduate Study 

100 Sprout Road 

Richland, WA 99352 

(509) 375-3176 

PEARCE, Charles W. 

AT&T Technology Systems 

555 Union Blvd., 323800 

Allentown. PA 18103 

(215) 439-7711 

PHILJ .. lPS, Mary J. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 502/422 

Pasadena, CA 91109 

(818) 517-9096 

PRINCE, Dr. Morton 

U. S. Department of Energy 

Forrestal Building, CE 333 

1000 Independence Ave., SW, 5E066 

Washington, DC 205S5 

(202) 252-1725 

PRYOR, Robert 

Solavo1t International 

P.O. Box 2934 

Phoenix, AZ 85062 

(602) 231-6454 

RAl-CHOUDHURY, P. 

Westinghouse Electric Corp. 

1310 Beulah Road 

Pittsburgh, PA 15235 

(412) 256-1891 

RALPH, Eugene L. 

Hughes Aircraft 

6445 N. Willard Ave. 

San Gabriel, CA 91775 

(213) 647-8855 

RAO, Hari 

Mobil Solar Elergy Corp. 

4 Suburban Park Dr. 

Billerica, MA 91821 

(617) 893-8826 
ROHATGI. Aj eet 

Westinghouse Electric Corp. 

1310 Beulah Road 

Pittsburgh. PA 15235 

(412) 256-1905 

ROSE. Ben 

Sandia Rational Laboratories 

Kirtland AFG Base - East 

P.O. Box 5800. Div. 6224 

A1buquerque,NM 87185 

(505) 846-4516 

SAH, C. Tang 

C. T. Sah Associates 

403 Pond Ridge Lane 

Urbana, IL 61801 

(211) 384-5205 

SAKIOTIS, Riek 

Solavolt International 

P.O. Box 2934 

Phoenix, AZ 85062 

(602) 231-6449 

SALTZMAN, Dennis 

Solavolt International 

P.O. Box 2934 

Phoenix, AZ 85062 

(602) 231-6441 

SCHMIDT. Wilfried 

Telefunken Electronic GmbH 

Theresienstr. 2 

Heilbronn, West Germany 7100 

(07131) 882-665 

SCHMIT. Rusty 

Sob.volt International 

P.O. Box 2934 

Phoenix, AZ 80562 

(602) 231- 6436 

SCHRODER. Dieter K. 

Arizona State University 

Electrical Engineering Department 

Tempe, AZ 85287 

(602) 965-6621 

SCHUMACHER. Joseph C. 

J. C. Schumacher Co. 

580 Airport Road 

Oceans ide. CA 92054 

(619) 433-1663 

x 

SCHUYLER, Terry W. 

Solar Energy Research Institute 

1617 Cole Blvd. 

Golden, C) 80404 

(303) 231-1106 

SCHWARTZ, Richard 

Purdue University 

Electrical Engtg Department 

West Lafayette, IN 47907 

SCHWUTTKE, G.H. 

GHS Research & Development 

8162 East Del Pico Drive 

Scottsdale, AZ 85258 

(602) 951-0422 

SCOLARO, Anthony 

U. S. Department of Energy 

Forrestal Building, CE 333 

1000 Independence Ave., SW, 5E066 

Washington, DC 20585 

(202) 252-5548 

SCOTT-MONCK. John A. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 125/231 

Pasadena, CA 91109 

-(818) 354-7625 

SHIMADA, Katsunori 

Jet Propulsion Laboratory 

4800 Oak Grive Drive, M.S. 50717.28 

Pasadena, CA 91109 

(818) 577-9626 

SIRTL, Erhard Heliot~onic GMBH 

Johannes-Hess-&trasse 24 

8263 Burghausen, West Germany 

08677-83-2580 

SMOKLER. Melvin I. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 507/201 

Pasadena, CA 91109 

(818) 577-9238 

SOPORI, Bhushan 

Solavolt International 

f.,0. Box 2934 

Phoenix, SZ 85062 

(602) 231- 6446 
I 

I 

I 

I ,1 

~ ! ,t 

[\ 

I 

I 

SPITZER, Mark 

Spire Corp. 

Patriots Park 

Bedford, MA 01730 

(617) 275-6000 

SUREK, Thomas 

Solar Energy Research Institute 

Program Office Henager 

1617 Cole Blvd. 

Golden, CO 80401 

(303) 231-1371 

SWANSON, Richard M. 

Associate Professor 

Stanford University, Stanford Elec. Labs 

McCullough 204 

Stanford, CA 94305 

(415) 497-0804 

TAN, Teh Y. 

IBM Corp. General Technology Div1sion 

Z-40E 

Hopewell Heights, NY 12533 

(914) 894-3140 

TODOROF, William 

Alternative Energy Systems, Inc. 

20442 Sun Valley Drive 

Laguna Beach, CA 92651 

(714) 494-9433 

TURNER, Gary B. 

ARCO Solar, Inc. 

P.O. Box 4400 

Woodland Hills, CA 91365 

(818) 700-7159 

TUSTIN, David G. 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 502/422 

Pasadena, CA 91109 

(818) 577-9096 

VANN, Hank VB 

ARCO Solar, Inc. 

P.O. Box 4400 

Woodland Hills, CA 91365 

(805) 489-7981 

xi 

von ROOS, Oldwig 

Jet Propulsion Laboratory 

4800 Oak Grove Drive, M.S. 512/103 

Pasadena, CA 91109 

(818) 577-9994 

WEINKEISTER, Roger 

Solavolt International 

P.O. Box 2934 

Phoenix, AZ 85062 

(602) 231- 6427 

WOLF, Martin 

Unive~sity of Pennsylvania 

304 Moore, D-2 

Philadelphia, PA 19104 

(215) 898-4822 

YOO, Henry 

ARCO Solar, Inc. 

P.O. Box 4400 

Woodland Hills, CA 91365 

(805) 484-7981 
CONTENTS 

SESSION I 

OVERVIEW 

(H. Prince, U.S. Department of Energy, Chairman) 

Historical Perspective of Barriers to 

Achieving High-Efficiency Silicon Solar Cells 

(J. Lindmayer, Solarex Corp) ..•...•• 

Some Aspects of the Hinority Carriers Lifetime 

in Silicon 

(P. Landsberg, University of Southampton) 

Review of Recombination. phenomena in 

High-Efficiency Solar Cells 

(C.T. Sah, C.T. Sah Associates) 

SESSION II 

HIGH-EFFICIENCY CONCEPTS 

(H. Wolf, University of Pennsylvania, Chairman) 

Silicon Solar Cell Efficiency Improvement: 

Status and Outlook 

(H. Wolf, University of Pennsylvania) 

Some Practical Considerations for Economical 

Back Contact Formation on High-Efficiency 

Solar Cells 

3 

7 

13 

37 

53 

(A. Lesk, Solavolt International) . • . . . . . . . . . • • .. 77 

High-Efficiency Cell Concepts on Low-Cost 

Silicon Sheet 

(R. Bell, Mobil Solar Energy Corp.) 

High Lifetime Silicon Processing 

(R. Swanson, Stanford University) 

Silicon HINP Solar Cells 

(L. Olsen, Univer·sity of Washington, 

Joint Center for Graduate Study) 

DINNER SPEAKER 

High-Efficiency Solar Cell Research for 

Space Applications 

(D. Flood, NASA Lewis Research Center) . 

P.RECEDING PAGE BLANK NOT FILJ.\1ED 

xiii 

87 

107 

123 

147 
SESSION III 

SURFAce-INTERFACE EFFECTS 

(L. Kazmerski, Solar Energy Research Institute, Chairman) 

Atomic structure of the Annealed 

si (111) Surface 

(D. Chadi, Xerox Palo Alto Research Center) 

Surface and Interface Characteristics 

. . . . . . . . . . 

(L. Kazmerski, Solar Energy Research Institute) 

Nitridation of Si02 for Surface 

Passivation 

(S. Lai, Intel corp.) . 

Surface Passivation and Junction Formation 

Using Low-Energy Hydrogen Implants 

(S. Fonash. Pennsylvania state University) 

Analysis of Interface Parameters 

(C. Bates, Stanford University) . 

Chemical Structure of Interfaces 

(F. Grunthaner, Jet Propulsion Laboratory) 

SESSION IV 

BULK EFFECTS 

(E. SirU, Heliotronic GmbH, Chairman) 

structural Defects in Crystalline Silicon 

(E. Sirtl, Heliotronic GmbH) . . . . 

Oxygen and Carbon Impurities and Related 

Defects in Silicon 

(C. Pearce, AT&T Technology) ..... . 

Current Understanding of Point Defects and 

Diffusion Processes in Silicon 

(T. Tan, IBM Corp.) ......... . 

Defects in Web Dendrite Silicon Ribbon 

Crystals and Their Influence on Minority 

Carrier Lifetime 

(G. Schwuttke. Arizona State University) 

EBIC Characterization and Hydrogen 

Passivation in Silicon Sheet 

(J. Hanoka, Mobil Solar Energy Corp.) 

Measurement of Electrical Parameters 

and Current Components in the Bulk of 

Silicon Solar Cells 

(A. Neugroschel, University of Florida) 

xiv 

163 

189 

209 

221 

239 

241 

243 

257 

279 

299 

311 
SESSION V 

MODELING 

(R. Schwartz. Purdue University. Chairman) 

Current Status of One and two Dimensional 

Numerical Models: Successes and Limitations 

(R. Schwartz. Purdue University) ..•. 

Application of Closed-Form Solution 

Using Recursion Relationship in 

Silicon Solar Cells 

(H. Lamorte. Research triangle Institute) 

Phenomena Simulation for Heavy Doping 

and Surface Recombination Velocity 

(F. Lindholm. University of Florida) 

SESSION VI 

HIGH-EFFICIENCY DEVICE PROCESSING 

(P. Rai-Choudhu~y. Westinghouse Electric Co .• Chairman) 

High-Efficiency Large-Area Polysi1icon 

Solar Cells 

(S. Johnson, Solarex Corp.) ..... 

High-Efficiency Solar Cell Processing 

(F. Ho, Applied Solar Energy Corp.) . 

Process and Design Considerations for 

High-Efficiency Solar Cells 

(A. Rohatgi, Westinghouse Electric Co.) . 

Processing technology for High-Efficiency 

Silicon Solar Cells 

(M. Spitzer, Spire Corp.) ....... . 

texture Etching of (100) Silicon 

for Solar Cells 

(L. Dyer, texas In~truments, Inc.) 

SUMMARY AND DISCUSSION SESSION . . . . . . . 

xv 

331 

351 

371 

403 

419 

429 

447 

471 

485 
INTRODUCTORY REMARKS 

KOLIWAD: My name is Kris Koliwad. I am from the Flat-Plate Solar Array 

Project. It is my pleasure this morning to welcome you all to this Forum 

on High-Efficiency Crystalline Solar Cells on behalf of the FSA Project 

at the Jet Propulsion Laboratory, and of the Department of Energy. If 

you go through the agenda, you will notice that this is indeed an 

impressive gathering, and we are fortunate to have you at this meeting. 

I will say a few words about the driving force for this Research Forum 

and the other Research Forums we have held covering different subjects 

relevant to our Project objectives. 

The driving force for this workshop is, of course, the goals stated in the 

Five-Year Research Plan of the Department of Energy, which succinctly 

states that the five-year goal of flat-plate collector research is to 

establish technologies by 1988 that industry can apply to the production 

of 15~efficient crystalline silicon modules. Among other things, this 

goal is coupled with $90/m2 silicon sheet. 

1 
SESSION I 

OVERVI~'W 

K. Prince, Chairman 
l. •• " 

SESSION I 

OVERVIEW 

H.B. Prince 

U.S. Department of Energy 

PRINCE: I want to thank the organizers for inviting me to attend this meeting. 

It has given me an opportunity to get back and read some of the literature 

again. which I haven't done as thoroughly. perhaps. as I should have done 

during the last few years. In fact. I have here a whole stack of reports 

that indicate that high efficiency is extremely interesting to many of us 

here -- and I see that many of the authors of these reports are here 

today. There are a few who are not here. but I am sure that if we need 

them we can call upon them for some help. 

Before getting into our program. I thought I should make a couple of comments to you about the 1985 budget. which many of you are concerned about. 

Two weeks ago. Congress finally got together and compromised on the 

recommendations from the Appropriations Committee. They compromised by 

going to the lower of the two numbers between the House and the Senate. 

So this puts us in a bind this coming year. The Administration asked for 

'47.5 million. and the House agreed to the '47.5 million with a provision 

that '2 million of that be spent on the Residential Experiment Stations. 

The Senate. on the other hand. took what we presented and upped it by '4 

million. which would include '2 million on the Residential Experiment 

Stations. So the net result is that we have a Program operating budget 

of '46.5 million. a capital-equipment budget of '1 million. and a construction budget of '9.5 million for the SHOD project. So we are going 

to end up with about '2 million less than we had expected from the 

President's budget. and this is putting a squeeze on all three of the 

main laboratories. that is. SERI. Sandia. and JPL. We are working this 

out now trying to find out how we meet our budget. how we perhaps extend 

contracts into the next fiscal year so we don't have to reduce as much we 

might have to. You will hear more about that from the various laboratories over the next six months as we keep revising the budget and we 

will finally end up by the first of October or the first of November with 

a final budget. 

This session will run until 11:55. We have three speakers. and this will 

give us plenty of time for discussions. questions. answers. and other 

comments that anyone wants to make. 

I was originally going to start off the session with a historical review 

of the efficiency problem. where it started and where it is going. but on 

reading the abstracts. I see there are a couple of other papers on the 

subject. so I am just going to let those speakers cover it. Joe Lindmayer 

has a little bit in his and Hartin Wolf has some in his abstract. So I 

thought what I would do today is give some general background so that 

those people who are not: familiar with solar cells specifically. and there 

are several in the audience. would have a reference point as to what the 

terminology is that we use. Perhaps we can establish some terminology 

3 
that will allow us to talk consistently during the next three days. 

On the first slide I show a general schematic of how the solar cell is 

composed; we have the material to start with, the diffused emitter or a 

p-n junction, and for this particular diagram I assumed n-on-p material. 

You put contacts on the back. We usually have some sort of an oxide 01\ 

the top surface and an antireflective coating. We usually have some ~ort 

of a grid metal contact. I used the dimenslon w as the depth of the diffused or emitter region, and d is the thickness of the device. 

Coatin~~~======~~~==~~;=~==========~~~====~ "Oxidc· 

n-typc Si 

p-typc Si Basc 

CONTINUITY EQUA T/ONS 

on n D a2n a -;;- = - - + n ~x - Itn "x {(n +Dp> E]+ 0' (x) ut Tn dy'" u 

4 

o 

w 

d 
d2p 

dz2 

d2n 

dx2 

Lp = 

BOUNDARY CONDITIONS 

p (W) =0 

n (W) =0 

g(x) = a Ne -ax 

CONTINUITY EQUATIONS 

1 p + aN e -ax 

- Lp2 Dp 

1 ~e -ax - Ln2 n + 

Dn 

= 0 

=0 

[ 

. q(V + IRs> ] 

I = 10 e AkT • 1 + 

V+IRs 

-- - IL Rsb 

R -co sb 

lac = -IL 

Voc = ~T 1n (;~ + 1 ) = ~T 1n 1:-

10 = q PnDp 

+ Lp 

5 

q npDn _ 

Ln -
FACTORS AFFECTING EFFICIENCY 

MECHANICAL FACTORS 

Depth of Junction (w) 

Thickness of Wafer (d) 

Seriel Resistance (contact geometry) 

Front Surface Rouohnell Qight trappinO) 

Contact ShadowinQ 

Operatino Temperature 

PHYSICAL FACTORS 

Base Resistivity 

(Tn' On'l'n' Ln , np) 

EmiHer Impurity Distribution 

(Tpeff: I'PeU.' Pneff• ) 

Back Surface Impurity Distribution 

Recombination and Scatterino Centers 

in Base and Emitter 

DEVICE FACTORS 

Surface Recombination Velocity (front, 

baclc, under contacts) . 

Reflectino Back Surface 

AR Coatino 

Hioh Eg Window (oxide, etc.) 

Series Resistance 

Shunt Resistance 

Reverse Saturation Current 

(Io) 

I hope this will give you some idea of the complexity of the problem. I 

can see that there are so many variations possible, and many of us have 

worked on a whole bunch of these, but to my knowledge very few of us have 

looked at the overall picture. In review of the abstracts, there are a 

couple of papers there that do cover a huge number of these parameters. 

That gives you some background and I would like to get started with the 

three talks today that we have in this session. We have only one limitation, and that is that we want to break around 11:55 because we have a 

very narrow window for lunch. In this period we will be very flexible in 

the time that we use for presentations~ and for questions and answers, 

and I hope we will have quite a few questions and answers from the floor. 

We have asked Joe Lindmayer to give us the first paper this morning, 

because Joe made a major contribution in the space program back in the 

late 60's and he developed a purple cell that gave us a step-function 

increase in the efficiency we can get with space-type cells. He is going 

to talk to us on a historical perspective of barriers to achieving highefficiency silicon solar cells. Joe founded and is still with the Solarex 

Corp. in Rockville, Maryland. 

6 
J. Lindmayer's abstract is presented here. His paper and visual material were 

not present~d for publication. 

HISTORICAL PERSPECTIVE OF BARRIERS TO ACHIEVI~G HIGH-EFFICIENCY SILICON SOLAR CELLS -

J. Lindmayer 

N8S-S1611 Solarex Corp. 

Rockville, Maryland 

Early silicon solar cells were made of metallurgical~grade silicon with very 

low efficiency; this was accomplished before the p-n junction theory was 

understood. The single-crystal silicon introduced in the mid-50's abruptly 

increased the efficiency to the 5~ to 10~ region. Throughout the 1960s 

significant research money was spent to establish the technology of the 

2 x 2 cm or 2 x 4 cm space solar cell with 10~ efficiency. At this point- a 

certain plateau has developed. 

In the early 1970s work related to the violet cell upset the status quo and 

space solar cells and cells in general became significantly more efficient. 

The rest of the decade became characterized by establishing a terrestrial 

photovoltaic technology to support the development of a new industry. Costs 

per watt became the dominant consideration and frequently the efficiency was 

compromised. This mentality is present even today as the terrestrial 

photovoltaic industry continues to develop. Attempts to introduce new 

materials and other forms of silicon dropped the efficiency and it is now a 

state of mind that accomplishing 10~ efficiency with some alternative 

combination is regarded as success. 

Silicon solar cells are clearly capable of delivering efficiencies much 

greater than 1~. As the photovoltaic industry will show signs of 

stabilization, the attention will once again focus on achieving the 

manufacturable higher efficiency solar cells. 

7 
DISCUSSION 

PRINCE: As everyone here knows. you have been very forthright in pursuing 

semicrystalline silicon, and I am just wondering what your feelings are 

as to the ultimate potential efficiency that one can obtain from such 

materials? Have you given much thought to this? 

LINDMAYER: I think that very frequently the efficiency is somewhat lower than 

~ I. ~o~l!~ing~~~~lfal Czochralski material. In getting into this kind of ~ . d;l I.U1'a~ft:1anybody who works with it will know that it creates a 

whole set of new unanswered questions. But I think the efficiency is just 

a little bit, maybe just 5~ or l~, lower than normal single-crystal at 

this time. 

LESK: Joo, in Kris Koliwad's introductory remarks, he indicated that the 

objective was 15~ efficiency in a module -- it wasn't on the slide -- but 

then he said the price has got to be a lot lower than it is now. His 

price projects to $90/m2 of substrate in the module, if you allow perhaps half of that fo~ the cast polysilicon subst~ate. Do you feel it 

will ever get to that price, considering that we still lack lS~ 

efficiency? 

LINDKAYER: This is a difficult question. Right now I think we are running a 

gap to start with. I think if we had much better personnel, or much 

better-educated people in the production lines and among those running 

production lines -- there is a gap of maybe 12~ to l3~ already and that 

lS~ would be possible to achieve. After all, many of us sit down in the 

lab and generate solar cells that are lS~ or better. But somehow the 

production line never does it. So I think the 15~ goal is achievable, 

definitely in the lab, anyway. But production is something else. 

PRINCE: I think we should bring up one other point before we go on. In order 

to get this lS~ module that Kris mentioned, we need to have cells that 

are about l8~ efficient because you have losses in assembling these cells 

into the module, and covering the module with some protection, and lost 

area, and so forth. So when we talk about lS~ modules, it means about an 18~ cell in production, which may mean a 20~ cell or a 2l~ cell in the 

laboratory. I do remember from an early experience that if you can do it 

in a laboratory, you can transfer to very good production people, then 

you can then produce exactly the same quality in the production line. 

LINDKAYER: Yes. This is an important point. A lS~ panel efficiency requires 

very much higher-efficiency cells. 

LOFERSKI: I am surprised that you are saying that the problem is with the 

education level of people on the production line. It seems to me that if 

you have a good production line going, it has to be do-able with all the 

kinds of people that you have presently on production lines, basically. 

If you want to hold the price down, you can't have Ph.D.'s making solar 

cells, so I think it is not in the education of the people but rathe.r in 

the industrial engineering that is involved or in manufacturing engineering, carrying things f~om the laboratory into production. We have to be 

8 

; 

) 

1 

~ 
able to make that transition. After all, when Arnie asked you about the 

price at that 15~ module efficiency, $90/m2 , it means $0.60 per peak 

watt and we can't even make the current 10!. efficient cells at $0.60 per 

peak watt, so there is a lot to be done; there is a big gap between where 

we are now and what is required by 1988. But anyway, I would like your 

comment on this business of who is on the production line now. I am 

surprised at that comment that you need better people. 

LINDMAYER: Well, I was merely referring to middle management.. True Ph.D. 's 

cannot run a production line. They have never succeeded. I am not advocating that there should be more Ph.D.s on the production line. The 

workers themselves do routine work, so it is the middle management in 

technical capacities that is really missing. But with respect to the 

other goal, getting down to $90/m2 , I think it is going to be hard. 

DYER: It is interesting that in the early 19509, when Mark Shepard was head 

of Texas Instruments' production of semiconductor devices, he wrote an 

article, "Ph.D.'s on the Production Line," and the results are evident. 

I think what you are saying, Joe, is that in the early stages, that is 

what you need. Once it beeomes a mature product, you can't afford it. 

But to get it going right, there is nothing wrong with it. 

PRINCE: Are there any other questions? Yes, Gene. 

RALPH: Joe, I think I see a conflict between what you practice and what you 

preach. Not just you but other companies as well. I think there is a 

definite feeling that making something cheaper means going to simpler and 

less sophisticated approaches, and I put the contacting systems, the use 

of the Semix type of materials, in that category. You give away efficiency in the hope of getting lower-cost processing, and of getting 

immediate gains that way. But you say now that you agree that the 15~ 

module goal is really the right thing to go to. NOW, it sounds to me as 

though your middle management or even your top management has to be educated then in the difference -- getting immediate cost gains by going to 

simple, cheap processing that gives you lower efficiency, versus very 

sophisticated processing that has to be automated or robotized or whatever 

it is to get the cost down. Are you saying that you are ready, or you 

would see management -- see that new approach to 15~ being the right way, 

or are we going to go back to the old way? 

LINDMAYER: Any technology change results in some efficiency drop but can be 

lIIIlediately observed as climbing up again in time as people begin to 

master that technology and understand its details. So sometimes it is 

very difficult to tell in advance that a technology change is automati-" 

cally compromising efficiency. I think it is just a philosophical point. 

MILSTEIN: I would like to comment that in the way our high-efficiency program 

has been conducted over the past year or two we have not, as we stated in 

the RFP that we issued in 1982, considered the matter of cost reduction. 

That is something that we feel is best left to industry. The point of 

doing that, though, is that it allows a researcher to investigate techniques that at the present time may be extremely expensive, but that 

9 
may lead to understanding or additional capability. They then may be 

re-engineered or reconfigured in some way to be done for less expense at 

the time you want to put them into production. In that sens~. the conception of artificially holding down the cost, if you apply it. to 

research, may simply prevent you from looking at techniques that you 

would otherwise be able to examine. You may miss something. 

LINDMAYER: I don't think we have any real conflict here. Dr. Koliwad 

carefully put the emphasis on the cost because, as the industry is now, 

industry has put in more private money than the government has put into 

this program. And it is going to be doing more of this. 

LANDSBERG: The discussion has prompted me to ask you a question, Hort, about 

the DOE program. You mentioned two figures, the $90/m2 and the lS~ 

efficiency. Why not just give the $90/m2? Why is the efficiency constraint given as well? I mean, you have a very cheap amorphous cell that 

does better than $90/m2 but is less than l~ efficient. What do you 

say about that? 

PRINCE: It is very straightforward, Peter. If you have a S~ cell versus a 

lS~ cell or module, you need three times the area; the land cost, the 

wiring cost, and so forth. There are many other costs that go up, and 

that is why you need the combination of both parameters. 

LINDMAYER: I also believe, if I could add to this, that maybe it is more 

appropriate for DOE to set up technology and scientific goals than R&D 

goals and economic goals at this point in time. 

WOLF: Joe, you mentioned that it is often advantageous to introduce a somewhat 

cheaper process and take a loss in efficiency, and the efficiency may come 

back as we gain experience. This in some cases may happen. On the other 

hand, the opposite can also easily be the case: you move a step to higher 

efficiency, but at a higher cost, and then you are learning as your production teaches you how to do this more and more cheaply. In fact, it 

seems to me if you go the other way, you also have to be very careful in 

evaluating whether the cheaper process does not have a limit that doesn't 

permit you to get back more efficiency. You mentioned metallization 

screen printing. You use relatively expensive metals, but you never get 

low resistivity, you always end up with a higher resistivity in the center 

of materials, it seems. So you have a penalty. It seems you cannot get 

through narrower lines with the screen printing process than you can with 

some other processes. You may have to -- toward the beginning -- say yes, 

it would give me a cheaper process, but I don't see where it can get me 

back to the higher efficiencies. I think you have to evaluate it carefully before you make a decision of this sort. 

LINDMAYER: I agree with you that there are two sides of this equation. 

PRINCE: I think we have to be careful that we don't get off into the cost 

aspects of silicon cells and modules. This meeting is about efficiency, 

so unless you have a specific question relating to efficiency and not 

cost, please hold them for a discussion during the coffee break. 

10 
SCHWUTTKE: Joe, 1 would like to pick up on that comment you made, that we need 

better education in manufacturing. 1 look at it in a different way. 1 

don't think we really need better education in manufacturing. We are 

confronted by a situation where you have relatively, and 1 say relatively, 

little or indifferent education on one side, and on the other side, the 

Ph~D. side, we have relatively too much education. You really are confronted with a problem; you are dealing with two different types of 

people, and this is the problem you have. It is a communication problem. 

the manufacturing guy does not respect the Ph.D. guy, the Ph.D. guy does 

not respect the manufacturing guy, so what you end up with is the following situation (1 have seen this over the years over and over and over 

again): you have two efforts running parallel and these two characters 

never talk to each other, the manufacturing guys want to outdo the 

Ph.D.'s, and the Ph.D,,"s want to outdo the manufacturing people. I think 

what we need is not better education; we need better communication, and 

that could save us an awful lot of money. 

LINDMAYER: Very good point. 

SIRTL: Mort, I come back to your comment about "let's not talk about economy, 

let's talk about high efficiency." I think it can be a dangerous attitude, at least in part, because an l8~ solar cell, even in space technology, is not reality today on a 10 x 10 cm2 substrate, and if we talk 

about the best we could do about making high-efficiency cells at present, 

we have to talk about float-zone material. It may be very nice to explore 

the best material available -- some mechanisms we don't understand -- but 

I think we should be careful not to emphasize too much that kind of investigation alone. After all we have learned to date, float-zone material 

would not be a good material as a basis for economical production, so we 

may be forced to switch too late to other systems that offer a much more 

economical background for making the solar cells. I just wanted to bring 

up that point because the float-zone defect situation, for instance, is 

much different from any kind of polycrystalline material or whatever else 

you may choose. 

PRINCE: You have a very good point there. In fact, I talked with Ted Ciszek 

specifically ~bout this problem: can we produce float-zone material at a 

similar cost tQ Czochralski material; he has given me some positive indication that it is possible. I don't know whether we should make comments 

about this at this time, or later. 

SCHUMACHER: I would like to know if anyone has ever built a module that would 

give you 15~ efficiency regardless of whether it was done by Ph.D.'s or 

who have you, and if not, why wouldn't that be a good objective -- just 

to assemble the best team you could and build the very best module you 

ever could -- and then you can begin as a second priority to go after 

reaching this cost objective. I happen to think that single-crystalline 

silicon would be a very nice thing to use in these solar cells. I would 

think you would try to get the very most out of it that you could, and I 

think that would be the ideal approach. 

LINDMAYER: I think that at least small panels have been made that are good, 

but not 1 m2 • This was really just done in the lab. 

11 
Abstract 

ASPECTS OF SILICON BULK LIFETIMES 

P.T. Landsberg 

University of Southampton, 

Southampton, S09 SNH, England. 

N85-316t; 

Following some general remarks abollt (a) high efficiencies and (b) 

recombination lifetimes, two specific questions are considered. First, an 

analysis is made of the best lifetimes which have been attained for bulk 

crystalline silicon as a function of doping concentrations. This is done by 

adopting a separability assumption that the dopants which set the Fermi level 

do not contribute to the recombination traffic which is due to the unknown 

defect. This defect is assumed to have two charge states: neutral and 

negative, the neutral defect concentration being frozen-in at some temperature 

Tf . It is essential for the higher doping concentrations to include the bandband Auger effect by using a generalisation of the Shockley-Read-Hall (S.R.H.) 

mechanism. We infer single-electron band trap recombination coefficients of 

order 10- 9 cm3 s- 1 and an unknown defect level near mid-gap. Some speculations 

concerning its nature are also offered. Secondly, the above-mentioned 

generalisation of the SRH mechanism is di'"SC'liSS'ed in detail by giving relevant 

formulae and quoting recent comparisons with experiment. This formulation gives 

a straightforward procedure for incorporating both band-band and band-trap Auger 

effects in the SRH procedure. There are two related questions which arise 1n 

this context: (a) It may sometimes be useful to write the steady-state 

occupation probability of the traps implied by SRH procedure in a form which 

approximates to the Fermi-Dirac distribution. It is shown how this can be done. 

(b) Some brief remarks about the effect on the SRH mechanism of spreading Nt 

levels at one energy uniformly over a range of energies will also be made. 

PRECEDING PAGE BCANK NOT FILMED 

13 
1. Introduction 

,!n thi.s talk I. want to discuss two topics of importance for the improveien~ ~fr s~l!con ~9lar·cells. The first «(4), relates to the problem of the 

resid~al defect in silicon. Working backwards from the measured lifetime -

doping relationship, we shall ask if there is some single level with ~ 

capture probabilities which can account for the best lifetimes. The answer 

turns out that there seems to be such a level, but to identify its precise 

nature requires more experiments. The second topic is the identification of 

Auger trap and/or Auger band coefficients by an analysis which closely 

resembles that familiar from the Shockley-Read-Hall (SRH) statistics. With 

the increasing importance of heavy doping in devices, this rarely used 

procedure is worth noting and it will be described in some detail. Although 

not new it has been used only once or twicejand it ought to be more widely 

known. 

As this is an "overview" talk, the work indicated above is preceded by 

general remarks on high efficiencies (f2) and lifetimes (f3). 

2. General remarks : efficiencies 

The achievement of 18%+ efficient solar cells based on terrestrial 

conditions and single crystal silicon hps recently been reported. A key 

element in the design is a thin (20-50 ~) Si02 layer to passivate those n+ 

silicon surface regions which are without a contact (1) A first question 

to be raised is if one knows that Si02 is the ideal layer. One knows that other 

layers can be used, for example in MIS structures(2) ; it would be interesting 

and important to know their effect on device performance. [There are of course 

other ways of attaining high efficiencies, for example by the use of ion 

implantation, high resistivity silicon and using surface passivation(3)]. This 

is the first problem to which I want to direct attention. 

A second potential method of obtaining high efficiencies is to employ 

several cells of different energy gaps in one unit (or even in separate units 

so that there are four or more terminals). If one envisages black-body 

radiation at 6000K and a very idealised model,a two gap tandem cell might push 

the efficiency up from a theoretical one-gap value of 31% to a two-gap value 

of 42.9%(4,5). SClll(' idea of the fall-off of efficiencies for non-optimal 

band gaps is obtained from Figure 1(5). More realistically,one can study 

tandem cells based on, for example, a combination of amorphous and crystalline 

silicon as has been done at M.I.T. Figure 2 shows the results of such a 

calculation assuming optimised gaps, silicon properties for all gaps, one 

sun and room temperature operation. A four-terminal arrangement is seen to be 

best, but in this calculation, one finds only a modest improvement of 30% 

efficiency over the ideal 27.5% for a single junction crystalline cell. This 

makes the additional complication arising from a second junction of doubtful 

benefit(6). An additional problem with tandem cells is that an optimal 

adjustment of a tandem cell for one spectrum is upset if the incident 

spectrum is changed by cloudiness. The investigation of such matters 

represents a second problem to which I want to direct attention. Note that 

these high theoretical efficiencies for tandem cells have not even been 

14 
E92 (eV).------'--....I----~---"?I 

2 

1 

Figure 1. Maximum iso-efficiency curves for a two-band gap 

cell at 1 sun assuming a black-body spectrum at a 

black-body temperature twenty times the ambient 

temperature (5). 

30=~~~~~:;=---§S~EP~t>.~R~AT~E~LY~ SINGLE - JUNCTION CONNECTED 

CRYSTALLINE ~~ 

CELL., ~~ 

20----~------~~~---

I 

I •••••••••• SERIES ••• •••••• CONNECTED 

.. t -. 10--------~~··~·---S-I-NG-L-E---JU-N-C~T-IO-N~··~··~·~ •• -•• ---

••• AMORPHOUS CELLS 

•• 

J 

0-5 1{) 1·5 2·0 2·5 

BOTTOM - CELL BAND GAP (e V) 

Figure 2. Maximum AMI, 1 sun conversion efficiencies of 

crystalline-on-amorphous silicon tandem structures 

at room temperature if separately connected 

(4-terminais) or in series (2-terminals)(S). 

15 
realised approximately in practice. Presumably surface problems and 

recombination at surfaces are among the difficulties which have impeded 

progress. 

Multi-gap structures entirely based on amorphous silicon have also 

been considered. For a three-gap structure in series (Eg = 2.0, 1.7, 1.45 eV) 

a 7% efficiency was attained, compared with a theoretical 24% (7). Our main 

interest here is, however, in crystalline silicon. 

There is an additional step which can be taken, namely to raise the 

mobility of the current carriers by confining them to a well in the conduction 

band produced by growing different materials on top of each other. In this 

kind of multi-hetero junction scheme the electrons travel in a two-dimensional 

well. They have dropped into it from a region containing the original dopants. 

These are thus left behind leaving to the electrons a region relatively free 

of ionised impurity scattering. The need to pursue these ideas, is my third 

problem. A start has been made with it at the Sandia National Laboratory(8). 

3. General remarks Lifetimes 

Properties of a silicon wafer may be specified by giving details concerning: 

Electrical properties (resistivity, conductivity type, lifetime, 

etc.) 

Mechanical properties (thickness, vacancy and interstitial densites, 

etc.) 

Chemical properties (chemical impurity concentrations, stoichiometry, 

etc.) 

Surface properties (surface scratches and roughness, etc.). 

Of all these many parameters I shall here been concerned only with the lifetime 

T against recombination. Because it is normally larger than the dielectric 

relaxation time TD one keeps up a non-equilibrium steady state between 

electrons and holes and can have lifetimes and diffusion lengths which are 

greater than zero. '[The opposite situation T «TD characterises the so-called 

relaxation semiconductor in which the Fermi levels are locally coincident.] 

In order to improve solar cells one has to increase T'further. 

Lifetimes may be improved by gettering metallic impurities like Au, 

Fe, Cu which provide deep recombination centres, using a mixture of 02 and HCl. 

Dislocations help to getter most impurities but unfortunately they provide 

recombi.nation sites themselves, particularly in the presence of vacancies. 

During processing the high temperatures induce the formation of thermal 

defects (vacancies, interstitials, etc.) some of which are quenched into the 

final material and cannot be annealed out altogether. Particularly when 

dislocation-free material is used, and dislocation gettering is therefore not 

available, these m~chanical defects tend to agglomorate and to give rise to 

aggregates of defects (some are known as "swirls") which also shorten lifetimes. This problem presents a "point defect dilemma"(9). 

16 
I 

I 

It should be remembered that a good understanding of lifetimes is desirable 

not only because one wants long lifetimes in solar cells. One additional 

reason is that lifetime monitoring is important in device processing. It is 

used for example in neutron transmutation doping in which the uniformly 

distributed isotope 30Si is converted into phosphorus dopant which is 

therefore also uniformly distributed: 

30 Si + 

31 P+ Sray. 

Lifetime measurements designed to assess the quality of the starting ingot 

is also in use(lO,ll). A second additional reason for understanding lifetimes 

is that for some device applications lifetime reduction is required, notably 

for fast-switching bipolar transistors. This reduction may be achieved 

(after fabrication) by electron beam irradiation, or (during fabrication) 

by introducing "killer centres" such as Au and Pt. 

4. The residual defect in silicon 

If one looks at measured silicon lifetimes as a function of doping, one 

finds the jumble of points shown in Figure 3. 

However, one may consider only the best lifetimes for given doping on 

the argument that these crystals have attained some ideal lifetime, limited 

only by a particular, but unknown, defect. This defect could be mechanical 

(interstitial), chemical, or an association of several of these. In this view 

the dopants help to set the Fermi level, but do not participate in the 

recombination traffic which limits the lifetime. The recombination defects, 

on the other hand, although of low concentration, are included in the Fermi 

level equation. This is a kind of "separability assumption" for Fermi level 

and lifetimes and it will be adopted here. What are the characteristics of this 

"residual" lifetime limiting defect? 

To answer this question we have added to the separability assumption, 

secondly,the hypothesis that the defect has only one recombination level 

and that if it is occupied it is negatively charged; otherwise it is neutral. 

A third assumption is that the concentration of neutral defects is that which 

is "frozen in" at a temperature Tf with an activation energy Ea, so that(13) 

= (1) 

The numerical factor is the atomic density of silicon. 

The procedure now is to regard (1) as giving the maximum solubility of 

the neutral defect as Tf. This is independent of the location in the material 

and of Fermi level. The defect has a negative charge state linked to Na by 

N~ / N! = exp [(F - Ed)/kTf ]. 

Hence an increase in n-doping, by raising the Fermi level, raises Nd and so 

raises 

= 

17 
Tp(IlS) 

10 

1 

0-1 

10-2 

1015 

Tp(IlS) 

100 

10 

1 

0-1 

Figure 3. 

• II • • • • • • • 

• , • 

• 

" •• 

• • 

•• 

• 

10 16 1017 1018 1019 1020 

NO (cm-3 ) 

• • • 

• 

• 

Some experimental minority hole lifetimes in 

n·type silicon (a) from reference 12. 

(b) from reference 13. 

18 
This leads to a lowering ofT (ND) with doping. However, increase in pdooing lowers the Fermi levelP and hence Nd. This leads to longer lifetimes 

Tn (NA) with doping until these lifetimes are pulled down again by the bandband Auger effect(l4) as shown in Figure 4. Assumption 2 concerning the 

charge on the unknown defect enables therefore the model to reproduce the 

asymm~tric behaviour observed experimentally as regards Tn compared with Tp' 

The lifetime curves for the correct concentration Nd of defects, as 

calculated at Tf' are used at the lower measurement temperature T, assuming 

a generalised Shockley-Read mechanism(15). They follow roughly (Nd)-l with 

doping, until they are both pulled down by band-band Auger effects. 

The notation for the recombinaticn constant is shown in Figure 5. We use 

BS, Bl, B2 for band-band recombination and T~, TS, Tl ...•. T4 for 

recombination involving traps(14). A superfix S2indicates a single-electron 

(non-Auger) transition, the other symbols refer to Auger effects. Following 

Fossum et al(13,15) one can neglect Tl' T2, T3, T4 and BS and adopt 

= 

-31 6 -1 

2 x 10 crn s 

S S As to Tl' T2 , one may regard them as fitting parameters, "along with Tf and 

Ea' The inferred values are then found to be 

S S -9 3 -1 

2Tl = T2 ~ 5 x 10 cm s 

Ea = 1.375 eV, Tf = 620 K. 

Position of defect leve~ 45 meV above mid-gap. 

The resulting fit is shown in Figure 4. 

We are left with two matters of controversy: (1) What is Tf in equn.(l)? 

(2) What is the nature of the defect specified in (2)? 

As to the first question, recall the early quenching experiments on 

silicon which led to a relation of the type(l7) 

1 = C exp (-E /kT ) T a q 

where the activation energy was found to be 0.6 eV, T was the minority carrier 

lifetime and Tq was the temperature from which the sample was quenched. 

Data enabling one to find C was given later for these thermally generated 

recombination centres: 

E = 0.9 eV. 

a 

[18; note that the captions of Figures 8 and 10 should be interchanged]. More 

recently a thermally generated donor density 

v = 

was found with C' ~ 8 x 

C' exp (-E /kT ) a q 

23 -3 10 cm ,Ea = 2.5 eV in "pure" p-type silicon. 

19 
T(flS) 

'103~ __ ~-4~~~~~~ 

~ t= 101 

B 

1014 1015 1016 1017 

N N (cm- 3 ) A' 0 

Figure 4. Doping dependence of the best room temperature minority carrier lifetime in silicon according to experiments (points). 

Asterisks indicate that the band Auger process is included 

along with the normal Shockley-Read process (unasterisked). 

Circles (for holes) and square (for electrons) represent 

experimental points (14). 

t t ~ 

t 

S . B 

1 B 2 

Tsl T 

1 1 

Figure 5. The notation for the recombination constants. 

20 
I ,I 

1 

The appropriate level was located 0.37 eV above the valence band edge (19). 

These results suggest that (1) is a reasonable assumption and that the 

freezing-in temperature Tf may be identified as the quenching temperature 

for infinitely rapid cooling at least for some heat treatment histories. 

This corresponds to the "perfect" quench. Departure from the perfect quench 

by slower cooling should lead to Tf < Tq • This relation between Tf and Tq 

needs further study. 

The second question is made difficult by the variety of levels found by 

different methods in the forbidden gap of silicon. In particular we cite 

nine relevant pre-1980 papers on thermally generated and/or quenched-in 

centres in silicon (20-28). Thus a donor level at Ev + 0.4 eV was found in 

p-type silicon in (19,20) and in boron-doped silicon in (21), but not in 

(22) where the boron concentration was heavier. It was again found in (24) 

as a complicated defect. The thermally gen~rated defec·ts were found to be 

hard to anneal out in (25) and in later work. 

In a series of later papers fast ("s") and slow ("r", "rl", "r"") thermal 

recombination centres were found and characterised. They have formation 

energies of 1.0 eV, 1.2 eV and 2.5 eV (26), the slower centres being less 

soluble. The high binding energy and the consequent difficulty of annealing 

out thermal centres was confirmed (27,28). The slow centres were attributed 

to vacancy-eu complexes and later to vacancy-oxygen complexes (29). The fast 

centres were attributed to native defects [(29), Figure 3]. 

As regards energy level structure, many inconsistencies remain. 

Some of the discrepancies between the various experiments have been attributed 

to electrically active defects connected with traces of iron in silicon which 

may have been present in varying amounts (30). They can be kept down to 

below 1014 cm-3 by special treatment. Iron-related deep levels have, in 

fact, been studied separately (31) as has the level at 0.45 eV above the 

valence band edge (32). 

Swirl defects (due to point defect agglomerates, presumably interstitial) 

of formation energy 1.3 eV - 1.4 eV were also noted in p-type floating zone 

grown heat-treated silicon (33)~ and their annealing characteristics differ 

from those of divacancies of a similar formation energy (1.3 eV). 

Two possible interpretations of the defect inferred here and 

characterised in (2) will now be proposed. The first suggestion is that it is 

a swirl. The A-type swirl, believed to consist of dislocation loops, loop 

clusters, etc., occurs in concentrations of typically 106 - 107 cm- 3, and is 

therefore not a serious candidate. B-type swirls are smaller and are found in 

concentrations up to lOll cm- 3 or so (34). This is of the order (1011 - 1013 

cm-3 ) of defect density implied by Figure 2 of (14). The formation activation 

energy of 1.3 - 1.4 eV (33) is also of the right order. If such swirls can 

supply an acceptor level near mid-gap (their energy level structure does not 

seem to be well known yet), the swirl B would be a serious candidate. This 

interpretation of the "residual" defect in silicon as used for semiconductor 

work, if correct, would be of importance for two reasons : In the first place 

swirl defects are known to have detrimental effects on silicon, and secondly 

the elimination of swirl defects is under active study. One can use slow or 

21 
- 0-4 v2 - 0-3 - 0-2 - V2 

"'-

0-1 

+ Ej + 

AI Au Cr Fe Mo Ti V V 2 

0-1 

vx 

0-2 2 

- -

0-3 - - - - - v~ 

0-4 2 - - - - 0-5 - Ev 

Figure 6. Some deep levels in s~licon due to 

divacancies V 2 (36) and due to meta II ic 

ions (37). 

22 
fast crystal pulling rates, inert ambients during growth, or annealing after 

growth to reduce their occurrence. 

A second candidate is the "s" (native, fast) recombination centre (29). 

The slow centres ("r, rl, r" ") have levels which lie too close to the band 

edges, whereas the "s" centre has a level near mid-gap. A recombination 

coefficient for minority carriers of ~10-7 cm3 s-l has beenssuggested (23) 

which is 100 times larger than our inferred values of T~ ~ T2 ~ 10-9 cm3 s-l. 

This could, however, be understood in terms of different thermal histories. 

It is, of course, possible that the "s"-centre and the swirl B centre are 

the same defect. Even a very recent study (35) on the relation between 

recombination mechanisms and doping density leaves these matters unresolved. 

It is hoped that the above suggestions may, however, stimulate further work. 

Deep level spectra are not well known, but some are shown in Figure 6 

and it will be seen that they do not apply to the residual defect identified 

here. 

5. Auger effects in trapping statistics 

In the above discussion the Shockley-Read-Hall trapping mechanism has 

been invoked in order to arrive at a lifetime. However, the effect of 

additional Auger processes was not incorporated in the original version of 

1952. This extension was made in 1963 (38) well before device engineers 

took an interest in heavy-doping phenomena. Because I believe this 

incorporation of Auger effects to yield an important new and useful concept, 

I have developed it and applied it from time to time(15,39,40). In the 

present context the motivation for such an extension of the Shockley-Read-Hall 

mechanism is particularly obvious: The reverse diode saturation current J 0 

should be kept small in a solar cell to reduce loss by recombination. The 

minority (electron) carrier recombination rate per unit volume' is for the 

simplest picture of a p-type layer 

n - n 

po 

T 

n 

= 

n 

~ 

T 

n 

(exp oy - 1) n 

2 

n. 

= 1 (expoy - 1) NATJ1. n 

where oy is the electron Fermi level excess over its equilibrium value 

divided Ry kT. It has also been assumed that the p-type material is nondegenerate with all acceptors ionised 

n p po po n~ = n N 

1 po A 

The bulk recombination can therefore be held down by heavy doping and this 

brings in Auger effects as their rate tends to dominate over single 

carrier transitions at high carrier densities. [The improvement of the basic 

material by identifying and, if possible, removing deep level recombination, 

also indicated by this argument"was dealt with in section 4]. 

The need for heavy doping can also be seen from the open-circuit voltage 

of solar cells which in a simple theory should increase with doping but in 

23 
fact declines after going through a maximum. An early curve of this kind was 

given by lIes and Soclof(41). 

Turning to the incorporation of the Auger effects shown in Figure 6 into 

the SRH trapping statistics scheme, the simplest way of doing the algebra 

may be as follows. 

Let NO and NI be the concentration of centres or defects without a 

trapped electron and with a trapped electron, and let Nd = HO + NI be 

the total defect concentration. Let n, p be electron and hole concentrations 

so that for non-degenerate lIaterial we have 

Electron capture rate 0:: nNO (G) 

Electron emission rate 0:: NI (Gnl) 

Hole capture rate 0: pN I (H) 

Hole emission rate 0:: NO (HPI) 

The coefficients of proportionality, which we shall identify later, are also 

shown. All one needs is the steady state condition for the centres, by equating 

the nett electron and hole capture rates per unit volume: 

(3 ) 

This gives steady-state occupation fractions 

= 

so that 

= 1 - (4) 

Substitution for NO and NI from (4) into the left-hand side of (3) gives the 

steady-state trap recombination rate per unit volume 

u st.st = 

np - nlPI 

(5) 

This has the general shape of the usual S.R.H. result, except that n1 ,PI' G, 

H need interpretation. 

The factors n1 and PI are not interesting; 

detailed balance is assumed: 

24 

they follow from (3) if 
= 

nN 

(----.!! ) Nl eq 

n - n 

N e d c c (6) 

where nand 

each ditided 

nc are the energies of trap level and conduction band edge, 

by kT. Similarly 

pNl n -n 

Pl = (T )eq = e v d 

0 

where ~ refers to the valence band edge. It follows that 

n p = 1 1 (np) 

eq 

2 

= n. II 

1. 

(7) 

However, G and H are more interesting : we must include all the six 

trapping processes of Figure 5, making the ele~tron capture rate per unit 

volume 

S 2 GnNO = T nNO + Tln NO + T2npNO' 1 

Le.G = T

S 

+ Tln + T2P. 1 (8) 

Similarly 

TS H = + T2n + T3P 2 (9) 

The picture is completed by adding the band-band recombination rate per unit 

volume 

Fnp, (10) 

Hence the total steady-state recombination rate per unit volume is (38) 

U = [F + (11) 

We now proceed to some special cases of interest. 

Consider now the minority carrier lifetimes. In p-type material one 

has p~PO (the equilibrium concentrations receive now a suffix zero) so that 

= 

U 

n--l1 

o 

n-n o 

25 
If n

l « n, 

1 

T 

P 

PI 

1 

T 

n 

1 

T. 

p 

= 

« p, 

c:! 

--

= nF + 

one has, underlining terms liable to dominate, 

(BS 

1 + BIn + B2P)p + (TS 

1 + TIn + T2P) N d (14) 

(BS 

1 + BIn + B2

P)n + c. (T'W 2 +Tn+ 

3 

T

4

P)Nd (15) 

These formulae were in reasonable agreement with earlier (1962) experiments on 

Germanium, when these results were first tested shortly after they were 

proposed(42) , However, it took a surprising eighteen years before an 

explicit test was made (43). Some of the results are shown in Figure 7 and 

Table 1. There is reasonable agreement between theory, equation (15) in this 

case, and experiment. [The classical S.R.H. results are found if one puts 

= (16) 

Table 1 

Some inferred values from a fit of equation (15) to the 

data of Figure 7 at 300K.Based on reference 43 

Au diffusion at 

850°C 

Au diffusion at 

920°C 

15 10-8 s 

-8 

1.3 HI· s 

-12 3 -1 ~19 3 

5.3xlO cm s 7.95 10 ~tn 

-19 3 

10.7 10 em 

We thus have a method, capable of being applied to experiments, which 

is the natural extension of S.R.H. statistics. As Auger effects have often 

to be taken into account, this method should rival S.R.H. statistics in 

popularity. The only complication is the need to know the additional 

recombination coefficients. But as was seen in (16) some of these may be 

put equal to zero in specific cases. 

There is a question of a more academic nature which the above results 

bring up: The steady-state occupation probability (4) of the recombination 

26 
N 

.... 

1 , (a) 10-1 

I (b) 

~300 K 

10-1J H A .... o 77 K ~ 

en 

:t 

---... 0. -2~ [] 400K 

10 ~ 300K 

0 

10-3 1 

1017 

77K 

~ 10-3 

I I I I I • 

1018 1019 1020 1017 1018 1019 1020 

N

D

(Cm-3 ) 

Figure 7. Hole lifetime in n-type Si as a function of electron concentration 

for different temperatures. The samples were diffused with 

Au : (a) at 850°C, (b) at 920°C. The curves are fits of 

equation (15) to the data with B~ = B2 = T 4 = 0 (43). 
1 

I i 

I 

I 

centres should go over into the normal Fermi-Dirac function in equilibrium: 

N 

1 (-1.) (17) 

Nd 0 exp( TJd - Y )+1 0 

where y is the equilibrium Fermi level divided by kT and the degeneracy 

factor Ras been absorbed in TJd . At first sight it is not easy to see how 

this can come about. However, one can rewrite (4) as 

1 = 

which solves the problem provided one can show that h + 1 in thermal 

equilibrium. This is so. In fact one finds 

h 1 --(y +y)] 

1 cosh[ 0: + -

2 (r, - h 

(18) 

exp[y 

o 2 e h 1 cosh[ 0: + "2 (y 

e 

- y )] 

o 

(19) 

where 

expo: = (20) 

In thermal equilibrium h + 1, as expected. The results (18) - (20) seem to be 

new. They were first found in reference 44. 

A question not investigated much (but see (40», though it could be of 

importance for lifetimes, is the following: How is the recombination lifetime 

changed if Nd levels at an energy Ed are spread out with constant density 

to extend from Ed - E to Ed + E? This doubt arises occasionally in modelling 

situations. To answer this question one can use the generalised S.R.H. 

process, assuming that defect-defect transitions are negligible. This matter 

is under investigation. Preliminary results suggest that, depending on the 

position of Ed and on the excess carrier concentration, the recombination 

rate can move in either direction. For a defect at mid gap a decrease is 

more likely, while an increase is favoured if the defect is in the upper part 

of the gap provided the excess carrier concentration is not too large. More 

details will be reported in due course. 

28 
6. Additional comment after the work was completed. 

A defect similar to the one inferred here (in section 4) appears to have 

been found in swirl-and dislocation-free float zone grown silicon by deep 

level transient spectroscopy and derivative surface photovoltage (45). This 

dominant recombination level was located at Ev + 0.56eV with a capture cross 

section for holes equal to twice the capture cross section for electrons: 

(21) 

in fair agreement with the specification (2), above, of the defect identified 

here. If one puts 

T2 S = f v 02S (v - 107 cm/s - thermal velocity) 

and inserts our value for T2Sand relation (21) the factor f (giving a 

recombination efficiency) turns out to be 

f = 0.05. 

The same ~esult ~ l·S found l·f T 1 S an d v1 n S are use. d Th ese au th ors 

that the defect may be a self-interstitial or a clustef of these 

third possibility in addition to the two noted in section 4. 

29 

suggest 

- this is a 
REFERENCES 

1. A. W. Blakers, M.A.Green, S. Jiqun, E. M. Keller, S.R. Wenham, 

R. B. Godfrey, T. Szpitalak and M.R.Willison, "18-percent efficient 

. terrestrial silicon solar cells", IEEE Electron Device Letters 

EDL 1, 12-13 (1984). 

2. P. T. Landsberg and C. Klimpke, "Theory of the Schottky barrier solar 

cell", Proc. Roy. Soc. A 354, 101-118 (1977). 

C. M. H. Klimpke and P. T. Landsberg, "An improved analysis of the 

Schottky barrier solar cell", Solid-State Electronics 24 401-406 (1981). 

3. M. B. Spitzer, C. J. Keavney, S. P. Tobin and J. B. Milstein, 

"Ion implanted silicon solar cells with 18% conversion efficiency", 

17th I.E.E.E. Photovoltaic Specialist Conference, Orlando, May 1984. 

4. A,de Vos, "Detailed balance limit of the efficiency of tandem solar 

cells", J.Phys. D 13, 839-846 (1980). An exposition of these theories 

is given in P. T. Landsberg, "Non-equilibrium concepts in solar energy 

conversion", NATO Advanced Study Institute, Erice, 1983 Ed. B.di Bartolo 

(New York: Plenum Press), to be published. 

5. A,de Vos and D. Vynr.ke. "Solar energy conversion: Photovoltaic versus 

photothermal conversion", 5th E.C. Photovoltaic Solar Energy 

Conference, Athens, October 1983. 

6. J. C. C. Fan and B. J. Palm , "Optimal design of amorphous/crystalline 

tandem cells", Solar Cells .!! 247-261 (1984). 

7. Y. Kuwano, M. Ohnishi, H. Nishiwaki, S. Tsuda, T. Fukatsu, 

K. Enomoto, Y. Nakashima and H. Tarni, "Multi-gap amorphous Si 

solar cells prepared by the consecutive, separated reaction chamber 

method", 16th I.E.E.E. Photovoltaic Specialist Conference, San Diego, 

Sept. 1982. 

8. R. J. Chaffin, G. C. Osbourn, L. R. Dawson and R. M. Biefeld, 

"Strained superlattice, quantum well, multijunction photovoltaic 

cell", 17th I.E.E.E. Photovoltaic Specialist Conference, Orlando, 

May 1984. 

9. E. Sirtl, "Facts and trends in silicon material processing", 

in Semiconductor Silicon 1977, Ed. H. R. Huff and E. Sirtl, (Princeton: 

Electrochemical Society, 1977), p.4. 

10. R. Westbrook (Ed.) Lifetime Factors in Silicon, Am. Soc. for the Testing 

of Materials, Spec. Tech. Publication No. 712 (1980). 

11. D. C. Gupta (Ed.) Silicon Processing, Am. Soc for the Testing of 

Materials, Spec. Tech. Publication No. 804 (1983). 

30 
12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

.. 

B. Ross, "Survey of literature on minority carrier lifetimes in silicon 

and related topics", in Lifetime Factors in Silicon reference as in 

10, p.14-28. 

J. G. Fossum and D. S. Lee, "A physical model for the dependence of 

carrier lifetime on doping density", Solid-State Electronics 25 

741-747 (1982). 

P. T. Landsberg and G. S. Kousik, "The connection between carrier 

lifetime and doping density in non-degenerate semiconductors", 

J. App. Phys. 55, (1984). 

P. T. Landsberg, "Semiconductor Statistics", in Vol. 1 (Ed. W. Paul) 

of the Handbook of Semiconductors (Ed. T. S. Moss) (Amsterdam: North 

Holland, 1982), pp. 405-416. 

J. G. Fossum, R. P. Mertens, D. S. Lee and J. F. Nijs, "Carrier 

recombination and lifetime in heavily doped silicon", Solid-State 

Electronics, 26 569-576 (1983). 

G. Bemski, "Quenched-in recombination centres in silicon", 

Physical Review 103 567-569 (1956). 

B. Ross and J. R. Madigan, "Thermal generation of recombination 

centres in silicon", Phys.Rev. 108 J.428-l433 (1957). 

L. Elstner and W. Kamprath, "Quenched-in levels in p-type Silicon", 

Phys. Status Solidi 22 541-547 (1967). 

G. Bemski and C. A. Dias, "Quenched-in defects in p-type silicon", 

J.App.Phys. 35 2983-2985 (1964). 

M. L. Swanson, "Defects in quenched silicon", Phys.Status Solidi 33 

721-730 (1969). 

G. Swenson, "Impurity conduction in quenched p-type Silicon", 

Phy.Status Solidi (a) ~ 803-808 (1970). 

V. D. Glinchuk, N. M. Litovchenko, L. F. Linnit and R. Merker, 

"Decay of excess carrier concentration in thermally treated silicon," 

Phys.Stat.Sol. (a) 18 749-756 (1973). 

W. Leskochek, H. Feichtinger and G. Vidrich, "Thermally induced 

defects in n-type and p-type silicon", Phys. Status Solidi 

(a) 20 601-610 (1973). 

+ L. D. Yau and C. T. Sah, "Quenched-in centres in silicon p n junctions", 

Solid-State Electronics, 1l 193-201 (1974). 

V. D. Glinchuk, N. M. Litovchenko and R. Merker, "Solubility and. 

origin of thermally induced recombination centres in n-type and p-type 

silicon", Phys. Status Solidi (a) 30 Kl09-ll3 (1975). 

31 
27. K. D. Glinchuk, N. M. Litovchenko and R. Merker, "The role of 

impurities in the formation of quenched-in recombination centres in 

thermally treated silicon", Phys. Stat. Solidi (a) 33 K87-90 (1976). 

28. K. D. Glinchuk, N. M. Litovchenko and R. Merker, "Effect of quenching 

rate and annealing on the concentration of quenched-in recombination 

centres in heat-treated silicon", Phys. Status Solidi (a) 35 

K157-l60 (1976). 

29. K. D. Glinchuk and N. M. Litovchenko, "Decay of excess carriers in 

thermally treated oxygen-doped silicon", Phys.Stat.Solidi (a) 58 

549-555 (1980). 

30. G. Borchardt, E. Weber and N. Wiehl, "High-purity thermal treatment 

of silicon", J. App. Phys. 52 1603-1604 (1981). 

31. K. Wiinstel and P. Wagner, "Ion-related deep levels in silicon", 

Solid State Comm. 40 797-799 (1980). 

32. D. W. Ioannou, "Comments on the Ev + 0.45 eV quenched-in level in 

silicon", Phys.Stat. Solidi (a) 72, K33-36 (1982). 

33. A. Usami, Y. Fujii and K. Morioka, "The effect of swirl defects on the 

minority carrier lifetime in heat-treated silicon crystals", 

J.Phys. DlO, 899-910 (1977). 

34. A. J. R. de Kock, "Crystal growth of bulk crystals: purification, 

doping and defects", in Handbook of Semiconductors (Ed. T. S. Moss), 

Vol.3, Materials, Properties and Preparation (Ed. S. P. Keller), 

(Amsterdam: North Holland, 1980), p.272. 

35. L. Passari and E. Susi, "Recombination mechanisms and doping density 

in silicon", J.App.Phys. 54, 3935-3937 (1983). 

36. M. Jaros, Deep Levels in Semiconductors (Bristol:Adam Hilger, 1982), 

p.253. 

37. A. Rohat gi and P. Rai-Choudhury, "Defects and carrier lifetime in 

silicon", in Silicon Processing (Ed. D. C. Gupta) American Society for 

the Testing of Materials, Special Technical Publication 804 (1983) 

pp 383-404. 

38. D. A. Evans and P. T. Landsberg, "Recombination statistics for Auger 

effects with applications to p-n junctions", Solid-State Electronics, 

~ 169-181 (1963). 

39. P. T. Landsberg, "Some general recombination statistics for semiconductor 

surfaces", I.E.E.E. Trans. Electron Devices ED 29, 1284-1286 (1982). . 

40. P. T. Landsberg and M. S. Abrahams, "Surface recombination statistics 

at traps", Solid-State Electronics 26 841-849 (1983). 

32 
41. P. A. lIes and S. 1. Soclof "Effect of impurity doping concentration 

on solar cell output", 11th I.E.E.E. Photovoltaic Specialist Conference, 

Arizona, 1975 pp 19-24. 

42. P. T. Landsberg, D. A. Evans and C. Rhys"'Roberts, "Auger effect involving 

recombination centres", Proc.Phys.Soc. 83 325-326 (1964). 

43. W. Schmid and J. Reiner, "Minority-carrier lifetime in gold-diffused 

silicon at high carrier concentration", J.App.Phys. 53 6250-6252 (1982). 

44. P. T. Landsberg and M. S. Abrahams, "Effects of surface states and 

of excitation on barrier heights in a simple model of a grain Soundary 

or a surface", J.App.Phys. L (1984). 

45. L. Jastrzebski and P. Zanzucci "Electronic characteristics of float zone 

grown silicon", (Electrochemical Society, Ed. H. R. Huff), pp 138-156. 

33 
DISCUSSION 

SCHUMACHER: Well, Peter, I guess I don't understand the whole story he.re, but 

after all, in the Shockley-Read-Hall treatment of lifetime, the shifting 

of the Fermi level is taken into account, and there is an occupancy factor 

that tells you how many electrons, how many majority carriers there are 

in the centers for recombination. Then, as a result of that, the lifetime in less heavily doped material is higher than the lifetime in more 

heavily doped material. Of course, if you change the total number of recombination centers, then you can change the lifetime. You are saying 

that the number of recombination centers is changing because of the position of the Fermi level, not just the occupancy number. In order for what 

you saying to be true, it would be necessary for the total number of 

recombination centers to change. 

LANDSBERG: Right. And so it does. I think I might not have made it clear. 

It is entirely my fault. Perhaps what I didn't explain quite well enough 

is that these dopants don't act as recombination; a kind of separability 

assumption that the defect acts as a recombination center. The dopant is 

merely there to set the Fermi level. Now, what happens is, as you said, 

the lifetime increases because the total number of defects has decreased. 

SCHUMACHER: Then the X is the total number of defects. 

LANDSBERG: No. The X is the total number of neutrals. So the neutral defect 

density is given by the solubility of the defect in the silicon. 

SCHUMACHER: Then ~ is not the total number of defects? 

LANDSBERG: There is an old paper by Hall and Shockley many years ago that 

discussed solubility. There were other people after this. They were 

talking largely about the solubility of the neutral species. That is 

always uniform; it is not affected by the p-n junction, and so on, 

because it doesn't react in an electric field because it is neutral. 

TAN: Peter, I have two simple comments, made in good faith, and I hope you 

will accept them in good faith too. The first one is that in one early 

slide you said that in order to specify the material, silicon, you have 

something called a mechanical property. Those of us who work in the 

material characterization field refer to that as a physicsl defect. This 

is simply a misnomer, not important. The important part is that to my 

knowledge, up to today, we do not know how to specify that property in 

the same sense as you would with your electrical property. 

LANDSBERG: I t,hink it; is a very interesting point. you are making, because it 

is just where I am rather ignorant. 

TAN: That is why I mentioned I made these comments in good faith. 

LINDHOLM: I will be very brief, but some of the people here might want to 

know where some of these things were published. Can you tell us what is 

the status of that manuscript? 

34 
LANDSBERG: We didn't pay any reprint charges because we couldn't afford to. 

LINDHOLM: That is a good comment for the sponsors to listen to. 

LANDSBERG: Therefore, it is delayed. It is in the Journal of Applied Physics. 

The proofs have been seen but as far as I know it has not appeared yet. 

LINDHOLM: As a point of clarification in sort of following up Joe Loferski's 

question: I think that your Tf on the slide stands for tempe.rature of 

formation. You have an activation energy of 1.3 eV, and roughly figuring 

that out, that must mean around 600K. Do you remember that? 

LANDSBERG: Yes. It was around 620K, something of that order. 

SCHWUTTKE: Just a comment in supporting the characterization people on the 

previous comment. Looking back to my early years as a student, there was 

one hot subject, and you will remember this as well as I do. People were 

totally concerned for what we called color centers, and they studied this 

from a to b to c. And every month, almost, they discovered a new symbol. 

Then later on, once I graduated, they discovered one particle of matter, 

another particle of matter and I don't know how many particles of matter 

they have discovered by now. And then we were very proud that we defined 

crystal perfection by zero dislocation density and so we got accustomed 

to zero dislocation density and crystal perfection -- to characterize 

crystal perfection by the number of dislocations. And then, I believe, a 

lot of nuclear physicists got into silicon, and from there on we have had 

this tremendous confusion about crystal perfection. Today crystal perfection does not mean that you have zero dislocation. You are really addressing the state, the point defect state, in the materials. Basically, 

you can only talk about crystal perfection if you know the condition of 

every atom and what else is floating around. You are faced with some 

very difficult problems if you want to calculate something, because we 

just cannot provide you with the necessary detailed information that you 

need to make the proper calculation. So it is basically our short.coming, 

not yours, and I would like apologize for that. 

35 
RECOMBINATION PHENOMENA IN HIGH EFFICIENCY SILICON SOLAR CELLS 

C. Tang Sah 

University of Illinois 

Urbana, Illinois 61801 

ABSTRACT 

The dominant recombination phenomena which limit the highest efficiency 

attainable in silicon solar cells under terrestrial sunlight are reviewed. The 

ultimate achievable efficiency is limited by tne two intrinsic recombination 

mechanisms, the interband Auger recombination and interband Radiative recombination, both of which occu~ in the entire cell body but principally in the 

base layer. It is estimated that an upper efficiency of 25.4% at AMl or AM1.5 

solar illumination can be attained if either Radiative or high-injection-level 

Auger recombination in the base is the only recombination loss mechanism in a 

cell with 50 micron thick base and at an absorbed photocurrent of 0.36 A/W. 

Thicker base will increase the efficiency slightly via higher absorbed photocurrent less higher Auger and Radiative recombinations in the larger volume. 

At 500 micron, the photocurrent is raised by 10.6% and the open-circuit voltage 

is reduced by about 60 mV due to larger recombination volume, giving a net 

efficiency gain of only about 0.6% to 26% at AM1. The low-level Auger recombination in the base gives a smaller efficiency of 24% in 50-micron base cell. 

This suggests that an optimum (26%) cell design is one with lowly doped 50-100 

micron thick base, a perfect BSF, and zero extrinsic recombination such as 

the thermal mechanism at recombination centers (the Shockley-Read-Hall process) 

in the bulk, on the surface and at the interfaces. The importance of recombination at the interfaces of a high-efficiency cell is demonstrated "by the 

ohmic contact on the back surface whose interface recombination velocity is 

infinite. To attain the Auger-recombination-limited efficiency in the base 

without a minority-carrier-blocking back-surface-field layer, the total " 

majority carrier density in the base must exceed 1017cm-2, an impractically 

large value requiring a one-centimeter thick cell at a doping concentration of 

1017cm- 3 which would increase Auger and Radiative recombination by 200 over a 

50 micron cell and reduce the limitlng efficiency by 5% to 20%. The importance 

of surface and interface recombination is further demonstrated by representing 

the Auger and Radiative recombination losses by effective recombination 

velocities which are about 0.33 and 3.1 cmls respectively at 25.4%. Thus, to 

reach the ultimate efficiency limit of 25.4%, real interfaces must have recombination velocities less than about 10-17Ns or 1 cmls at a surface impurity 

concentration of Ns·l017cm- 3 • The paper is concluded by demonstrating that 

the three highest efficiency cells (17,18,19%) may all be limited by the SRH 

recombination losses at recombination centers in the base layer. To reach the 

Auger and Radiative recombination-limited efficiency of 25.4%, the SRH recombination loss in the base must be decreased to ~ive a minority carrier lifetime greater than 2x1014/NB or 2 ms at 1017cm- base doping density. This 

corresponds to a dark current of 0.2 fA/cm2 in the ideal diode raw. 

37 

PRECEDING EAGE BLANK NOT FILMED 
I. INTRODUCTION 

Energy loss by photogenerated electrons and holes through scattering and 

recombination limits the ultimate performance of solar cells. Scattering 

reduces the mobllities of elect.rons and holes, increases the'series resistance 

and decreases tne fill factor (FF). Recombination increases the shunt 

c~9dypt~ce ~nd.th~ dark leakage current and decreases both the open-circuit 

voltcige ~(VOC)and 'the short-circuit current (JSC). Energy loss during these 

two collision processes (scattering and recombination) will reduce the 

maximum efficiency (EFF) which is given by EFF=FF*VOC*JSC/PIN at an absorbed 

areal solar power density of PIN. 

The ultimate efficiency is limited by two intrinsic recombination 

mechanisms in an ideal cell structure in which the scattering or series 

resistance loss and the extrinsic recombination losses are reduced to 

negligible levels. These two intrinsic recombination mechanisms are the 

interband (conduction-band to valence-band) radiative process and the interband Auger process. The interband Radiative recombination mechanism poses 

the ultimate limit while the interband Auger recombination mechanism may be 

reduced by proper cell design via dopant impurity density and layer thickness 

control. In a silicon p+/n/n+ or n+/p/p+ back-surface-field (BSF) cell design 

with 50 micron base layer thickness, the ultimate AMl (or AM1.5) efficiency is 

about 25% at room temperature and both the Radiative and Auger mechanisms 

. contribute about equally to the recombination loss. 

This paper presents an analysis of the effects of the intrinsic and 

extrinsic recombination mechanisms on the performance of silicon pin junction 

solar cells. Section II provides a review of the recombination mechanisms 

and locations and their effects on the performance of solar cell devices. 

Section III provides an analysis of the ultimate performance of ideal cells 

with no scattering losses. Section IV illustrates the effect of surface 

recombination and its large degrading effect on performance. Section V gives 

an analysis of the three highest-efficiency Single-crystalline silicon solar 

cells which have been reported. It delineates the material factors which may 

have reduced their measured performance below that predicted by ideal diode 

law. A short concluding summary is given in Section VI. 

II. RECOMBINATION MECHANISMS AND SITES 

The electron-hole recombination processes can be categorized according 

to their origin. They can be further divided by the energy exchange mechanisms 

which control the recombination rate. Recombination processes with the 

intrinsic origin are those which limit the ultimate performance of a solar 

cell. Recombination processes due to imperfections in the crystal lattice, 

grouped by their extrinsic origin, such as chemical impurities and phy~ical 

defects, can be reduced so that their deleterious effects on cell performance 

can be nearly eliminated. A categorization of these recombination processes 

are given below [1]. 

38 

, 

i 

I 

u 

I 

t. 

I 

~ 

R 

~, 

I t,
INTRINSIC MECHANISMS (Interband Transitions) 

1.1 Thermal Recombination 

1;2 Radiative Recombination 

1.3 Auger Recombinat~on 

ENERGY EXCHANGE PARTNER 

Phonons(Lattice Vibration) 

Photons 

Third Electron or Hole 

EXTRINSIC MECHANISMS (Band-Bound Transitions) ENERGY EXCHANGE PARTNER 

E.1 Thermal Recombination (SRH) 

E.2 Radiative Recombination 

E.3 Auger Recombination 

Phonons 

Photons 

Third Electron or Hole 

A main fundamental difference between the intrinsic and the extrinsic recombination mechanisms is that the initial and the final states of the electron 

are in different bands separated by a large energy gap for the intrinsic 

processes. The energy exchange during the transition is much larger than the 

largest phonon energy, about 60 meV in solids. While for the extrinsic 

processes, the initial or final states is a bound state localized at 

a lattice imperfection, either an impurity or defect site, while the other 

is an unlocalized band state. The energy exchange covers both the small 

energy range of the phonons as well as the large energies near the energy gap. 

Thus, the intrinsic processes cannot be eliminated completely, although the 

Auger process, 1. 3, can be reduced since it depends on the presence of a third 

electron or hole and hence will dominate only in regions of high electron or 

hole concentration. However, the extrinsic processes can be reduced to 

negligible level so that they no longer affect the solar cell performance. 

The reduction of the extrinsic recombination mechanisms requires crystal -

perfections and purities in starting silicon as well as stressless and clean 

solar cell fabrication processes which exceed the latest silicon very large 

scale integrated circuit (VLSI circuit) technology. 

Among the recombination processes, the intrinsic Auger and Radiative mechanism pose the ultimate limit while the extrinsic thermal (SRH or Shockley-ReadHall) mechanism is the current technology limit. The recombination rate of the 

SRH mechanism is proportional to the density of-the impurities and defects.-

These imperfections can be unintentionally but readily introduced during the 

cell fabrication procedures and they may also be present in the starting 

crystal, having been incorporated during crystal growth. Thus, to reduce the 

SRH recombination rate will tax the latest silicon VLSI technology and beyond. 

These recombination processes can occur preferentially at certain regions 

and locations of a solar cells which suggest device design and technology 

innovations to reduce and eliminate them. A schematic illustration is shown 

by a cro~s-sectional view of a p+/n/n+ cell in Fig.1. The recombination 

processes can occur in the quasi-neutral emitter p+/, base /n/, and backsurface-field /n+ layers. They can also occur in the junction space charge 

layer of the p+/n junction, as well as at the oxide/Si and metal/Si or 

metal/oxide/silicon interfaces on the front and the back surfaces of the cell. 

However, they are not all important in all of these regions. For example, 

in the highly-doped p+/ emitter layer, only t.he interband Auger and the SRH 

recombination mechanisms may be important. The interband Auger recombination 

can be important if the majority carrier density in the quasi-neutral emitter 

exceeds about 1.0E17 hole/cm2 or a sheet resistance of about 0:6 ohm per square 

39 
since Auger recombination rate for the injected or photogenerated electrons in 

the p+/ emitter layer is proportional to the square of the hole concentration, 

p2_ For another example, the SRH recombination mechanism could also be 

ifup0Ttant in the quasi-neutral p+/ emitter if the density of the defect 

recombination centers is greatly increased due to the heavy doping of the p+/ 

layer by incorporating a high concentration of boron impurity. Heavy doping 

introduces localized band-tail states and broadens the boron impurity level 

into an impurity band, both of which give a narrowing of the energy gap for 

the minority carriers or an increase of the intrinsic carrier density, ni' or 

the minority carrier density. This would increase the minority carrier 

or electron recombination rate in the quasi-neutral emitter layer and reduce 

the solar cell performance. There has been no concrete evidence showing the 

importance of the localized or band-bound Auger recombination process (E.3) in 

the heavily doped emitter, although it is anticipated due to both the large 

majority carrier density and high density of defect and dopant impurities. 

In the quasi-neutral base layer, the interbdnd Radiative, interband 

Auger, and the SRH processes may all be important. The Radiative process in 

the base layer is the ultimate performance limiting loss mechanism. It is not 

as important in the emitter since the emitter layer is rather thin 'and hence 

has a rather small recombination volume compared with the thicker quasineutral base layer. The interband Auger process in the base layer can be 

reduced by not-so-heavily doping the base. Lightly doped base would enhance 

the influence of recombination in the back-surface-field layer se. base doping 

must be optimized or not so low, resulting in significant loss from the 

interband Auger recombination process. 

Similar to the emitter, the dominant recombination processeS in the 

heavily-doped quasi-neutral back-surface-field layer are the interband Auger 

and the SRH recombination processes, but their influences are not as large as 

they are in the emitter since the emitter is close to the solar source and 

the minority carrier collecting p+/n junction than the BSF layer. 

Surface recombination can also seriously limit the efficiency of very-highefficiency solar cells. Recombination of electrons and holes at exposed 

surfaces and interfaces can occur via the various mechanisms just described. 

However, the interfaces, such as the oxide/silicon, metal/silicon and 

metal/thin-oxide/silicon interfaces which can be present in a cell, are layers 

of high density of defects and impurities. The defects, commonly known as 

dangling bonds, and the impurities can form electron and hole bound states and 

serve as sites for electron-hole recombination. Generally, the SRH mechanism 

at these interface bound states is thought to be the most dominant. However, 

for heavily doped emitter and BSF layers, the surface concentration of the 

~ajority carrier is so high that one could also expect the Auger mechanisms to 

be important, especially the interband type although the bound-band type has 

not been eliminated as a candidate. In silicon solar cells of greater than 20% 

efficiency, the recombination loss in the cell must be so low that even a 

minute amount of recombination at the interfaces can be very detrimental to 

achieving higher efficiency. At the ultimate efficiency of about 25%, an 

effective interface recombination velocity of 1 cm/s or less must be required 

to render interface recombination unimportant. This places a severe constraint 

on the high temperature processing steps used during cell fabrication to 

obtain low recombination velocity interfaces. Each increase of ten of the 

interface recomb!nation velocity will reduce the open circuit voltage by 
2.3kT/q or 59 mV at 24C and the efficiency by 10%. Fortunately, low 

interface-recombination-velocity processing techniques are well advanced in 

silicon VLSI technology. However, areal uniformity over the extremely large 

areas required of solar cells and stability are still two key unknown factors. 

The requirement of low interface recombination velocity for reaching 

very high efficiency has motivated innovative cell designs. For example, the 

very high (nearly infinite) interface recombination velocity at the metal/Si 

contact of the front contacts of a cell has prompted one design to use all 

back surface contacts [2,3J and another design in which a thin oxide layer is 

introduced between the metal and the silicon surface to take advantage of the 

very low interface recombination velocity of the oxide/silicon interface [4,5J. 

Some of the latest high efficiency silicon solar cells, recently reported, 

seem to have the interface recombination loss reduced to a negligible level 

compared with the recombination loss in the quaSi-neutral base layer [4,5,6J. 

Some quantitative analyses on these cells are given in section V. 

Another important recombination loss originates from impurity-defect 

clusters in the bulk of the cell [7J and damaged and at the exposed perimeter 

surface of the p+/n and n/n+ high/low junctions of the cell [8J. In principle, 

these recombination sites can be eliminated by revising processing procedures 

and cell structure designs. 

III. ULTIMATE PERFORMANCE OF IDEAL CELLS 

The ideal cell is one that has only the lowest intrinsic recombination 

losses, the interband Radiative and interband Auger recombinatlon losses. 

Operating in the low injection level is also desired to further minimize any 

SRH recombination losses and in particular, to take advantage of tbe more 

box-like current voltage characteristics given by the ideal dib~e law, 

J=Jl*[exp(qV/kT)-1J compared with the high level law, J=J2*[exp(qV/2kr)-lJ 

which has a more rounded or soft shoulder. 

In the following subsections of this section, the ideal diode cell will be 

analyzed to illustrate the numerical range of the solar cell parameters~ JSC, 

VOC, FF and a diode parameter, the dark current J1, in very high efficiency 

cells. This is followed by an analysis to give pr'ojected ultimate performance 

limit'if the only losses left are the intrinsic Radiative and Auger processes. 

In the next section, section IV, the importance of surface recombination is 

illustrated by two design examples. In the last section, section V, analyses 

of the three highest efficiency cells recently reported are analyzed based on 

the ideal diode cell model given here. 

The d.c. current-v0ltage equation of a diode solar cell is given by 

J = JL - J1*[exp(qV/kT) - 1~ 

- Jm*[exp(qV/mkT) - 1J 

where JL is the photocurrent density (areal), J1 is the dark leakage current 

of the ideal Shockley pIn j,cunction diode, m and Jm are the reciprocal slope 

41 
and dark curreQt of the nonideal junction diode. m=l to 2 for recombination 

in the space charger layer of the pIn junction [9]. m=2 for recombination in 

the quasi-neutral base layer at high injection level, i.e. when N=P»Dopant 

Density. m=~ if a surface channel exists across the pIn junction perimeter 

such as·the inversion channel of a MOSFET [9]. If a shunt resistive path 

exists across the bulk or the surface of the junction, m can be greater than 

~ [9]. For the interband Auger recombination mechanism, m=l at low injection 

level but drops to m=2/3 at high in.jection level. This occurs because the 

interband Auger recombination rate is proportional to N P + P N while quasineutrality at high injection levels requires that N=P=n *exp(qV/2kT), 

resulting in a current law proportional to N3 or p3 or [exp(3qV/2kT)] • 

For high efficiency cells, all the nonideal recombination losses are eliminated except the interband Auger mechanism at high injection levels. Thus, the 

Jm term can be dropped except for the interband Auger process. The ideal diode 

solar cell equation is then given by 

J = JL - J1*[exp(qV/kT) - 1]. 

The photocurrent, JL, is a weak function of recombination loss for very-highefficiency cells. It can be taken as a constant and set to the maximum 

available photocurrent for a given cell thickness. In the numerical analyses 

to be presented in this paper, JL=36mA/cm2 will be assumed for a AM1.5 spectra 

at a photon power PIN=100mW/cm2• This closely approximates the photocurrent of 

the measured AM spectra which gives 31.~9mA/cm2 at 88.92mW/cm2 photon power 

in a cell of 50 micron thick under one pass with no front surface reflection, 

presented earlier [10] based on the spectra of Thekaekara. For other conditions and cell thicknesses, only the ratio, JL/PIN=36/100=0.36 A/W needs to 

be modified. This photoresponse increases to 0.~59~ A/W when the cell becomes 

infinitely thick or all the photons are absorbed, a 27.6% increase. To reach 

higher efficiency, the cell thickness may be increased to increase the shortcircuit current, but this will increase the recombination volume so t~at a 

optimum thickness will be reached beyond which the efficiency will drop. 

Multiple passes using back-surface optical reflector in a thin cell can·avoid 

the high recombination loss in the base of a thick cell. 

. The relationship between the short-circuit current, JSC, and the opencircuit voltage, VOC, is then given by 

JSC = JL = Jl*[exp(qVOC/kT) - 1]. 

The maximum power point can be computed, without any approximation by setting 

d(J*V)/dV=O. The efficiency, EFF, at the maximum power point is then given by 

EFF = PMAX/PIN = JMAX*VMAX/PIN 

which is also used to define the fill factor, FF, given by 

FF = JMAX*VMAX/JSC*VOC. 

Thus, the maximum efficiency is given by 

EFF = FF*JSC*VOC/PIN = (JSC/PIN)*FF*VOC .. O.36*FF*VOC. 

42 
This is a familiar result which has been used to analyze high efficiency 

cell designs. To illustrate the numepical range of the parameters in the' 

very-high efficiency cells, a set of values are computed and tabulated in 

Table I. It shows that the dark current, J1, must be less than 2E-13 A/cmf or 

0.2 pA/cm2 for a 20% cell. It decreases one decade for each efficiency rise 

of 2%, reducing to 0.2 fA/cm2 at 26%, which is about the ultimate limit for a 

50 micron thick cell. The table also shows that for each 2% rise of 

efficiency, the open-circuit voltage is increased by 60 mV, consistent with 

the simple estimate we made earlier, 58.96 mV. 

TABLE I 

PERFORMANCE PARAMETERS OF VERY-HIGH-EFFICIENCY 

IDEAL DIODE SILICON SOLAR CELLS 

(AM1 or AM1.5, 24.0C) 

SOURCE J I J

se Voe FF EFF 

(A) (mA) (mV) (%) 

Theory 2.0xlO-16 36.0 840 0.8664 26.0 

Theory 2.0~10-15 36.0 780 0.8588 24.0 

Theory 2.0xlO-14 36.0 720 0.8501 22.0 

Theory 2.0xlO-13 36.0 660 0.8402 20.0 

3.2 ULTIMATE PERFORMANCE 

The ultimate performance is limited by the interband Radiative and Auger 

recombination mechanisms. The ultimate efficiency is reached when all the 

extrinsic recombination l<>~Cles are eliminated. The numerical results are 

obtained by assuming also:.;aat al1 the emitter recombination losses are 

negligible, especially the low-level interband Auger recombination loss in the 

highly doped quasi-neutral emitter layer. This is achievable by proper design 

of the emitter concentration profile so that the total majority carrier 

density in the emitter is not much higher than about 1E14 and there is a good 

p++/p+ front surface field layer to maintain the high sheet conductance and 

low series resistance. Thus, in this limit where only base recombination 

dominates, the dark current, J1 can be readily obtained by multiplying the 

position independent base recombination rate to the base thickness. The 

results for both the two intrinsic loss mechanisms and the SRH extrinsic 

mechanisms are listed next. 

43 
Radiative Recombination (Interband) 

Jl = qCo*XB*n~ 1. 

Auger Recombination (Interband) 

qCa*XB*n~ (High Level) 1. 

qCa*XB*n~*NB (Low Level) 1. 

Thermal Recombination (Bound-Band) SRH 

J2 (High Level) 

Numerical calculations are performed for silicon cells with base layer thickness of XB=50 microns at 24.0C where ni=1.0El0 cm- 3 • The Radiative recombination rate of COnI=0.62E6 is employed while the interband Auger rates are: 

CO=2.8E-31 and Cp=0.99E31 cm6 /s. To illustrate the condition at which the SRH 

recombination loss will reduce the ultimate efficiency, a base lifetime of 

100 us and diffusivity of 20 cm2 /s are assumed. 

The results are tabulated in Table II. This table also shows the results 

of two ohmic-contact cells to illustrate the effect of surface and interface 

recombination. They are discussed in the next section. 

Table II shows that the ultimate efficiency limited by Radiative recombination alone is about 25%. The Auger limits are computed for the extremes of the 

injection levels and both are close to the 25% Radiative limit. The high 

injection limit of the Auger case is reached if the majority carrier or doping 

impurity concentration in the base layer is less than about 5E16cm- 3 for the 

50 urn base thickness which gives a total carrier density in the base of 

2.5E14 cm- 3 • DeSigning and operating the cell in the high level Auger 

range by reducing the base doping may help in maintaining the high SRH 

recombination lifetime which is necessary to achieve the high efficiency, but 

the sensitivity to surface recombination becomes more severe at this high level 

as indicated in the table and discussed in the next section. 

Table II also gives the results of SRH recombination loss at both low and 

high injection levels. Two design ideas may be drawn. (i) High level 

injection should be avoided. This was arrived at previously by a simple 

observation that the high level recombination current law, exp(qV/2kT), gives 

a softer illuminated I-V curve and hence lower fill factor and efficiency. 

(ii) Table II also shows the condition at which SRH recombination loss will 

become important to lower the ultimate efficiency. The example assumes a SRH 

recombination lifetime of 100 us to give a 23% efficiency. To reach 25%, the 

SRH base lifetime must be greater than about 1000 us or 1 ms which is at the 

limit of the state-of-the-art for VLSI grade silicon crystals. 

44 
SOURCE 

Radiat~ 

Recomb. 

Auger H 

Auger L 

SRH L 

Ohmic L 

SRH H 

Ohmic H 

TABLE II 

ULTIMATE PERFORMANCE OF SILICON SOLAR CELLS 

(Including the Effect of Surface Recombination) 

J l J SC VOC FF EFF 

m J/q 

(A) (rnA) (mV) (%) 

5.0xlO-16 36.0 817 0.8637 25.1+ 1 o 2 C xBni 

3.0xlO-22 36.0 786 0.8968 25.4 2/3 a 3 C xBni 

2.3x10-15 36.0 776 0.8582 24.0 1 a 2 C xBniNB 

8.0xlO-15 36.0 746 0.8540 23.0 1 -l,c 2N-l TB Bni B 

6.4xlO-13 36.0 634 0.8354 19.1 1 Dx-1n2N 1 BiB 

8.0xlO -8 36.0 666 0.7415 17.8 2 ,-1. 

TB xBni 

6.4xlO -6 36.0 442 0.6645 10.6 2 -1 DXB n

i 

SEFF 

(em/s) 

3.1 

0.33 

14 

50 

4000 

50 

4000 

10 -3 2 17 -3 2 T=24°C; ni

=10 em Area=! em ; xB=50 llm; NB=10 em ; D=20 em Is; 

'rB=100 llS; lJ:N = 100 mW(AMl. 5); L=Low Level; H=High Level; 

o 2 6 a n -31 6/ a n p -31 6/ C ni

=O.62x10 ; CL=C =2.8x10 em S; CH=C +C =3.8x10 em s. 

IV. EFFECTS OF SURFACE AND INTERFACE RECOMBINATION 

The influence of surface and interface recombination on the efficiency 

of high efficiency cells is quite large, which has been both demonstrated 

in the laboratory [4,5,6J and recognized from simple device modeling. The 

latter will be presented in this section. 

To provide a quantitative idea of the importance of recombination at the 

surfaces and interfaces of a solar cell, the bulk recombination losses may be 

written in terms of an effective recombination velocity so that its magnitude 

can be compared with the surface and interface recombination velocity at the 

real surfaces and interfaces of a solar cell. This effective recombination 

velocity can be defined both at the low and high injection levels. In the 

following two subsections, 4.1 and 4.2, the effect of surface recombination 

will be considered for two cases. 

45 
4.1 THE EQUIVALENT RECOMBINATION VELOCITY OF A BULK RECOMBINATION PROCESS 

The equivalent recombination velocity of a bulk recombination process 

which occurs in a volume element, such as the base region, can be defined as 

that velocity at the minority carrier entrance surface which would produce the 

same recombination current. These are illustrated in Fig.2 for several 

recombination locations, some of which are the true interface recombination 

velocities and others are the equivalent recombination velocities. For example, 

SE and SB are the equivalent recombination velocities of the quasi-neutral 

emitter and base layers at the minority carrier entrance or injection 

interfaces. The true interface recombination velocity illustrated in Fig.2 

is SFI, the recombination velocity at the front oxide/silicon interface. 

Another equivalent recombination velocity in Fig.2 is SBI which is the 

effective recombination velocity of minority carriers flowing into the n+ 

BSF layer at the n/n+ entrance surface. 

These equivalent recombination velocities may be explicitly defined to 

give accurate numerical estimates on the importance of true interface 

recombination loss. They are defined through the dark current density, 

J1 = q*PB*SB + q*NE*SE 

which, when combined with the dark current expression listed in Table II and 

section 3.2, gives 

SB (XB/TB) + SBI + SBA + SBO 

and 

SE = (XE/TB) + SFI + SEA + SEO 

Here, XB and XE are the base and emitter layer thickness; SBI and SFI are the 

effective and real recombination velocity at the back and front interfaces; 

SBA and SEA are the effective recombination velocities from volume 

interband Auger recombination in the quasi-neutral base and emitter layers; 

and SBO and SEO are those from volume interband Radiative recombinations. 

These especially simple expressions are applicable for base and emitter layers 

which are thin compared with the minority carrier diffusion length, a 

condition that holds well in a high efficiency cell. They are given by 

SBT XB/TB 

SBA Ca*XB*NB2 

SBA Ca*XB*n?exp(qV/kT) 

SBO = CO*XB*NS 

(All Level SRH) 

(Low Level Auger) 

(High Level Auger) 

(All Level Radiative) 

for the base layer, and a similar set for the emitter layer. 

The numerical values are computed and listed in Table II. It is evident 

that the effective recombination velocities of the limiting loss mechanisms 

are extremely low at the ultimate 25% efficiency. The value of 3.1 cm/s 

for the Radiative recombination loss to give the 25.4% efficiency illustrates 

the importance to have low surface recombination interfaces. Unless the interface recombination velocity is reduced substantially below 3.1 cm/s, recombinaion losses at the interfaces will seriously reduce the efficiency. 

46 
The rather small value of 0.33 cm/s for the high-level Auger limit shown 

in Table 2 illustrates the large carrier density and the very high .G.uger 

recombination rate in the base. This makes the dependence on the surface 

recombination even more sensitive. 

4.2 EFFECT OF OHMIC CONTACT AND THE BACK-SURFACE-FIELD 

Table II gives another example which illustrates the importance of having 

a back surface field layer to reduce the effect of back surface recombination 

loss. This examp:"c arises from the question: Can the back surface field layer 

be replaced by a thick base and still have a very high efficiency? This is 

a practical question since the BSF layer requires extra cell fabrication 

processing at high temperatures which usually reduces the bulk lifetime in the 

quasi-neutral base. 

Since a thick base means more Auger and Radiative recombination loss, an 

ideal device model can be set up to answer the above question. In this mode, 

the only recombination in the base is the minute Auger and Radiative 

recombination and there is no BSF so that the injected minority carriers face 

the full recombination at the Si/metalcontact on the back surface. The 

interface recombination velocity at the back Si/Metal interface is assumed to 

be infinite or a perfect ohmic. Then, the dark current due to this component 

is given by 

J1 

and 

J1 

q*OB*XB- 1 *(n~ INB) ; ~ 

q*DB*XB- 1 *(~); 

SB=DB/XB (Low Level) 

SB=DB/XB (High Level) 

To determine the thickness required to reduce the efect of interface 

recombination at the back surface below that of Auger recombination in the 

[uasi-neutral emitter, we set the two recombination velocities or J1 equal. 

Consider the low level case, we have 

XB*ca*NB*nf = DB*nt/(NB*XB) 

or 

NB*XB = SQRT(DB/ca) = SQRT(20/2.8E-31) 1.0E16cm-2 

Thus, for a base doping of NB=1.0E17, we need to have a base thickness of 

XB=1000um=1mm, an impractical result. This shows the importance of having a 

good high-low potential barrier on the back surface to reduce, the back sUr'face 

recombination loss. 

IV. EVALUATION OF THREE RECENT HIGH-EFFICIENCY CELLS 

Silicon solar cells with efficiency approaching 20% (AM1) have been 

fabricated in the laboratory. Innovative cell designs have been developed to 

reduce interface and emitter recombination losses. In this section, 

the experimental data of the best cells of three industrial laborator'ies are 

compared with that predicted by the ideal diode cell theory which was used to 

produce Table I. From a comparison of the theory and experiments, it appears 

that bulk recombination in the quaSi-neutral base via the SRH mechanism is the 

limiting loss on all three cells. 

47 

' •. "., ,'r 
The experimental and computed cell performance parameters are tabulated 

in Table III. The first three rows are for the highest performance cell from 

Green [ted and listed in the first row. The computed results are 

all higher than the measured values, suggesting effects from several sources. 

TABLE III 

PERFORMANCE OF THREE HIGHEST EFFICIENCY SILICON SOLAR CELLS AND 

COMPARISON WITH IDEAL DIODE CELL THEORY 

I SOURCE J l J SC VOC FF EFF 

(A) (rnA) (mV) (%) 

Theory 3.2xlO-13 35.6 660 0.8402 19.7 

Theory 6.6xlO-13 35.6 641 0.8350 19.0 

GREEN 3.2xlO-13 35.6 641 0.822 18.7 

Theory 1. 2xlO-12 35.9 627 0.8340 18.8 

SPITZER --- 35.9 627 0.800 18.0 

Theory 2.0xlO-12 36.2 605 0.8296 18.2 

Theory 2~4xlO-12 36.2 600 0.8286 18.0 

ROHATGJ 2.0xlO-12 36.2 600 0.793 17.2 

The second two rows are for the best cell from Spitzer [5J. The theory 

is computed using the measured JSC=35.9 and VOC=627mV. The larger computed 

fill factor, 0.8340 compared with measured 0.800 suggests possible series 

resistance loss in the actual cell which is not accounted for in the ideal 

diode cell model. 

The third three rows are for the best cell from Rohatgi [6J which is a 

higher resistivity cell (4 ohm-cm versus the 0.1 to 0.3 ohm-cm of Green and 

Spitzer). The first theory row is based on the measured J1=2E-12 and JSC=36.2 

which gives VOC=605mV, FF=0.8296 and EFF=18.2%. The measured voe and the 

theory are quite close, only 5 mV different; and the lower observed efficiency 

is mainly due to the lower experimental fill factor which again suggests 

possible series resistance losses in the real cell. 

In all three cases, the computed and the measured cell performance data 

are quite close, indicating that low level recombination in the quasi-neutral 

base layer via t.he thermal or Shockley-Read-Hall mechanism at defect and 

impurity recombination sites is the dominant loss mechanism. Further 

48 
improvement to achieve efficiency greater than 20% must depend first on 

identifying the base recombination center species and then reducing their 

density further. Although emitter bulk and surface recombination are 

substantially r'educed in these three cells 50 that they elre not important at 

less than 20%, these losses may be important again and must be further 

reduced at higher efficiencies. 

VI. CONCLUSION 

Interband Auger and Radiative recombination losses in the 'base layer limit 

the AM1 efficiency to about 25% in silicon solar cells with a base thickness 

of about 50 microns. Increasing the thickness will increase t.he efficiency 

only slightly., via higher short-cireui t current. In order to eliminate the 

influence of recombination losses in the base due to the SRH thermal 

recombination mechanism at impurity and defect centers, the base lifetime must 

be greater than about 1 ms or an equivalent recombination trap density of 

less than 1E11cm-2 • In addition, all interface and surface recombination 

losses must also be reduced to give a effective recombination velocity of less 

than about 1 cm/s. These very stringent requirements indicate that the'latest 

state-of-the-art silicon VLSI technology is needed to provide the nearly perfect 

silicon crystal and the very clean and low-stress fabrication techniques which 

are necessary to produce very-high-efficiency solar cells that will approach 

the ultimate theoretical limiting efficiency. 

REFERENCES 

1. C. T. Sah, "Equivalent circuit models in semiconductor transport for thermal 

optical, Auger-impact, and tunneling recombination-generation-trapping 

processes," physica status solidi (a)7, 541-559, 16 October 19'{1. 

2. Michael D. Lammert and Richard J. Schwartz, "The interdigitated back contact 

solar. cell: A silicon solar cell for use in concentrated sunlight," IEEE 

Transaction on Electron Devices, ED-24(4),337-342, April 1977. 

3. Richard M. Swanson, S.K.Beckwith, R.A.Crane, W.D.Eades, Y.H.Kwark, D.A.Sinton 

and S.E.Swirhun, "Point-contact silicon solar cells," IEEE Trans. ED-3t(5), 

661-664, May 1984. 

4. Martin A. Green, A.W.Blakers, J.Shi, E.M.Keller and S.R.Wenham, "Highefficiency silicon'solar cells," IEEE Trans. ED-31(5), 679-683, May 1984. 

5. Mark B. Spitzer, S.P.Tobin, C.J.Keavney, "High-efficiency' ion-implanted' 

silicon solar cells," IEEE Trans. ED-31(5}, 546-550, May 1984. 

6. Ajeet Rohatgi and P. Rai-Choudhury, "Design, fabrication and analysis of 

17-18 percent efficient surfac-passivated silicon solar cells," IEEE Trans. 

ED-31(5), 596-601, May 1984. 

7. C. T. Sah, K.A.Yamakawa and-R.Lutwack, "Reduction of solar cell efficiency 

by bulk defects across the back-surface-field junction," Journal of Applied 

Physics, 53(4), 3278-3290. April 1982. 

8. C. T. Sah, K.A.Yamakawa and R.Lutwack; "Reduction of solar cell efficiency 

by edge defects across the back-surface-field junction:- a developed 

perimeter model," Solid-State Electronics, 25(9}. 851-858, Sept. 1982. 

9. C. T. Sah, "Effects of surface recombination and channel on p-n'junction 

and transistor characteristics," IRE Trans. ED-9(1), 94-108, Jan. 1962. 

10.C. T. Sah, P.C.Chan, C-K Wang, R.L-Y Sah, K.A.Yamakawa and R.Lutwack, 

"Effect of zinc impurity on silicon solar-cell efficiency!" IEEE Trans. 

ED-28(3), 304-313, March 1981. 

49 
E'15 OftlGiNA\. PAG . 

OF. POOR QUAU'T'l 

AUGER gUASI-NEUTRAl EMITTER SRH 

SPACE CHARGE lAYER 

RADIATIVE N QUASI-NEUTRAL BASE AUGER 

SRH 

AUGER N+ QUASI-NEUTRAL 

SRH BACK SURFACE FiELD lAYER 

Figure 1 A cross-section view of solar cell showing the 

dominant recombination processes and locations. 

RADIATIVE and AUGER are the interband radiative 

and Auger recombination mechanisms. SRH is the 

Shockley-Read-Hall thermal recombination at 

defect and impurity recombination centers. Recombination occurs both in the bulk layers and at the 

interfaces between oxide, silicon and metal(dark). 

--~-----SFl------~ -..,- - - -'SE 

N Sa 

Figure 2 A cross-section view of solar cell showing the recombination velocity' represent a t ion .of the recombination 

rates. BE' Sa and SSI are the effective recomhiantion 

velocities of volum~ recombination processes. SFI' 

SFM' SSl and SSM are the real interface recomb,lnation 

velocities at the front oxide/silicon, front metal/ 

silicon, back oxide/silicon and back metal/silicon 

interfaces. 

50 
DISCUSSION 

PRINCE: While we have this slide on here. if you remove the very heavy doping 

on the surface. how would that affect the efficiency? 

SAH: We can do a quick calculation. ~et me just illustrate this with a viewgraph so you can see how to go about doing that. 

TAN: Can I make a comment? I have done a similar calculation by taking the 

tail off and I see a Voc goes up by about 20 millivolts. If you start 

with 1019 and come all the way down. your Voc goes up by 20 

millivolts. 

SAH: My model here is based on all of these being from the emitter; then I 

can get a good agreement. If the base is not a limiting factor -- suppose 

it is not at all. it is just an emitter ~,.- then it is going to make quite 

a substa~tial difference. 

QUESTION: Where did the profile come from? Is that an experimental profile? 

Did that come from spreading resistance? 

SAH: No. That is from SIMS. 

LANDSBERG: I have a quick question about the possibility of radiative-limited 

lifetime. If that was ever achieved. or if that ever occurred. one would 

obviously have practically 100~ radiative converter and although. in one 

way of looking at it. it is bad to have some limit on the efficiency by 

this recombination mechanism; I could perhaps take advantage of it. Do 

you think there is any example where the efficiency is really radiativelimited? It would be quite interesting. it is just a hypothesis. 

SAH: I don't know of any example. The highest one that is recorded so far is 

still only 19~. 

SCHRODER: If you drop the surface concentration more and more. what do you 

think happens to the contact resistance? Have you looked at that? 

SAH: No. I have not taken any contact resistance. 

LOFERSKI: Just what is the difference between the high and the low level 

Auger recombination? 

SAH: The low-level Auger follows the ideal Shockley diode because the minority 

carrier density increases very little compared with base doping. 

51 
SESSION II 

HIGH-EFFICIENCY CONCEPTS 

H. Wolf, Chairman 

• 
SILICON SOLAR CELL EFFICIENCY IMPROVEMENT: STATUS AND OUTLOOK 

M. Wolf 

Dept. of Electrical Engineering~ University of Pennsylvania 

Philadelphia, PA 19104 

INTRODUCTION 

The struggle to improve the efficiency of silicon solar cells has been going 

on as long as these devices have been a commercial product. The reason is simply that efficiency, as well as operating life, is an economic attribute in their 

application as part of a system. Fig. 1 illustrates the efficiency improvements made during the thirty year existence of the silicon solar cells, from about 6% 

efficiency at the beginning to 19% in the most recent experimental cells. 

Clearly the progress has not been a steady one. In the more stationary periods, the effort was more oriented towards improving radiation resistance and yields 

on the production lines, while, in other periods, the emphasis was more directed 

to reaching new levels of efficiency through better cell design and improved 

material processing. The last few years were again in sur.h an "efficiency push" 

period, and encouraging first results have been forthcoming from the recent 

efforts. Nevertheless, considerably more efficiency advancement in silicon solar 

cells is expected, and anticipated attainment of efficiencies significantly above 

20% (AM 1.5) is being more and more discussed. Whether this goal will be 

achieved is an open question, as major advances in material processing and in 

the resulting material perfection will be required. 

The achievements along the road to efficiency improvement are best gauged by an analysis of the contributions of the individual principal loss mechanisms 

to the overall performance of a given device. Such analyses are presented in 

Table I, which lists the individual perfonnance attributes of the milestone solar 

cells of the last fifteen years. Between 1959 and 1978, all solar cell development represented in the table was oriented towards application in space. Therefore~ the available performance data are all based onAMO solar radiation, 

while the data for the more recent cells are based on AM 1.5 sunlight. To permit comparison in Table I, the space cell data were converted to AM 1.5 sunlight, using the spectral responses of the cells. 

Table I indicates that the improvements achieved in the 1970s on the space cells included primarily an advancement of the collection efficiency, and a 

reduction of the "secondary" loss factors, such as residual reflectance, or 

series resistance losses. In the more recent efforts,directed at efficiency 

improvement for terrestrial applications, further advances have been made in the 

reduction of the impact of these secondary losses, but the main emphasis has been 

placed on the improvement of the voltages. 

A study of the data in Tabl ell eads to an eva 1 ua ti on of the s ta tus of 

silicon solar cell technology: the technology is available to decrease all the 

secondary loss mechanisms to the level where efforts for their further reduction 

will be fairly unproductive; the basic collection efficiency has been improved 

53 
to the point where the beginning of its "saturationll with further reductions of 

minority carrier recombination has been reached; and further improvements are 

primarily to be achieved in the area of voltage increases through reduced 

minority carrier recombination . 

... MINORITY CARRIER RECO~1BINATION AND SOLAR CELL EFFICIENCY .,<~ ~ .. 

\" i:A Jtudy of the loss mechanisms and of their impacts, as displayed in 

Table I, reveals that recombination of minority carriers is the major basic 

effect which presently limits the efficiency of solar cells. Thus, a maximum 

efficiency value is associated with each level of the recombination rate in the 

device. The ultimate efficiency is reached when the only effective recombination mechanisms are radiative and direct band...;lo-band recombination. 

An investigation of the relationship between recombination rates and 

maximum achievable efficiency is most transparent when it is carried out on 

the "basic" solar cell (Fig. 2). This device contains only those parts which 

are absolutely necessary for its functioning as a solar cell. These parts are: 

a volume for the absorption of photons and generation of free charge carriers; 

a potential barrier for the device to perform as a generator; and contacts for 

the extraction of a current. The basic analysis even considers the contacts 

as ideal, and omits a direct consideration of their functioning. The idealized 

analysis also chooses those impurity concentrations \'/hich, in consideration of 

mi nori ty carri er recomb"i nati on, provi de the hi ghes t effi ci ency. I t then uses 

the same impurity density on both sides of the junction. 

Recombination takes place both in the volume and at the surfaces of the 

device. It is practical to start the investigation with the assumption that all 

surface recombination velocities can be made equal to zero~ and that the volume 

minority carrier lifetimes are equal in all parts of the device. This 

eliminates most influences of the device structure. Also, other device performance influencing effects are, at first, assumed to contribute zero losses. 

These considerations lead to curve 1 of Fig. 3, which represents efficiency as . function of the minority carrier lifetime in such an idealized device, essentially as an upper limit for the achievable conversion efficiencies. The curve 

is basically composed of two straight lines in this semilogarithmic plot. Below 

about 1 ms lifetime, where the curve is represented by the straight line with 

the greater slope, the recombination is strictly determined by a varying density of recombination centers as described by the Shockley-Read-Hall theory. The 

resulting variation of the lifetime at constant resistivity is indicated by the 

vertical part of the dashed line in Fig. 4. Above the value of approximately 1 ms, the lifetime is dominated by Auger recombination, that is direct band-toband recombination rather than recombination via centers. From this point on, 

to achieve a higher minority carrier lifetime, the impurity concentration has 

to be reduced. As maximum solar cell performance is obtained when the contributions of Shockley-Read-Hall type recombination and Auger recombination are 

equal, the dashed line in Fig. 4 approximately represents this condition above 

the 1 ms lifetime value. In this case, Shockley-Read-Hall recombination is 

assumed to be dominated by deep trap levels, which result in the independence of the lifetime from the impurity concentration (saturation lifetime) up to the 

transition to Auger recombination. Thus, for the 10 and 100 msllifetimes, the 

impuri ty concentration has to be reduced to 1.5xl016 and 5 x 10 5 cm- 3, 

54 
respectively. Also, because of the difference in Auger coefficients, a small 

difference in the minority carrier lifetime values for the n and the p region is obtained in these cases. 

As Fig. 4 shows, the lifetime values in recently obtained FZ ingots fall 

well below the Auger line, and are thus dominated by recombination via centers. 

For the efficiency improvements expected in the future, it will become necessary 

to reduce the recombination center density so far that Auger recombination will, 

in effect, become the lifetime limiter. 

The data discussed so far are those typically obtained by use of fully 

analytical modeling. Such modeling is restricted to low level injection. 

Estimation of the excess minority carrier densities injected across the junction 

at open circuit voltage shows that the low level injection condition (e.g., 

np «Pp 0) starts to be violated between the 1 ms and 10 ms bulk lifetime 

values. ' This would not be of much consequence were it not for the fact that the 

minority carrier lifetime values have been chosen to be at the edge of domination by Auger recombination. In consequence, the impurity densities had to 

decrease for increasing lifetime values, while the excess minority carrier 

concentrations increase. Thus, the effective lifetimes are determined by the 

excess carrier concentrations, because of Auger recombination, rather than by the recombination center density. This leads to an efficiency saturation which 

is indicated in Fig. 3 by the wavy lines. Such an efficiency limitation has 

recently also been discussed by Green [1] and by Tiedje et £11 [2], who both 

found this limitation to be less severe for very thin cells, where it ar.tual1y 

can approach the radiative recombination limit near 30%. 

It has been seen t'epeatedly that the influence of the surface recombination 

velocity on the efficiency has the shape of an S-curve (Fig. 5), with practi- cally no performance impact below a certain value of surface recombination 

velocity. Above this value, the solar cell performance falls off rather 

rapidly, until it reaches a lower saturation level. It is thus of interest 

to determine this threshold value for the surface recombination velocity. Using q a range of surface recombination velocity values for each value of minority 

carrier lifetime, surface recombination threshold values have been determined, 

defined as that value at which the power output of the device has been reduced 

by 2.5%, from its s = 0 value. This process has been carried out first for 

the back surface, and then for the front surface, 1 eadi ng to a total reducti on 

in power output of 5%. Surface recombination on the generally narrow edges of 

the device has been neglected in this process. The result is curve 2 in Fig. 3. 

The surface recombination velocity threshold values themselves are given in 

Fig. 6. Two curves are presented, as the threshold values differ for the front 

and the base surface recombination velocities for the given device structure, 

which has a nominal junction depth of 211m. It is noteworthy that the surface 

recombination velocity thresholds lie above 100 cmls, and in the 30-60 cmls 

range for bulk lifetimes of 100 11s and 1 ms, respectively. Such velocity values 

are attainable with current technology. However, to achieve the highest efficiency values, the surface recombination velocities have to be reduced below 

the 1 cmls level. 

In the device geometry chosen, the minority carrier lifetime in the front 

region can be less than assumed for Fig. 3. A sensitivity analysis similar to 

that carried out for the surface recombination velocities, provides the 

55 
"threshold" value for the front region minority carrier lifetime. It is defined 

as that value at which the power output is degraded by 1%. The resulting lifetime is shown in Fig. 7 for the various efficiency levels. As Fig. 7 shows, 

the threshold front region minority carrier lifetimes are approximately two 

orders of magni tude lower than those requi red for the base regi on. These lower 

front region values are more readily achievable in device fabrication than the 

original higher ones. 

Finally, there is an optimum device thickness connected with every minority 

carrier lifetime value. This thickness constitutes the peak value of a rather 

flat maximum. Figure 8 presents the optimum base thickness as function of the 

minority carrier lifetime for the efficiency values of Fig. 3. It is seen in 

Fi g. 8 that a 500 11m thick devi ce is bes t for 1 i fetime values above 1 ms, with 

the optimum thickness dropping off rapidly for lower lifetime values. The 

application of texturing was found to permit the use of a reduced thickness, 

as would be expected from it as well as from other light trapping measures. But 

it is also seen that the texturing provides only a small efficiency improvement 

at the highest efficiency values,as indicated by the cross in Fig. 3. 

To obtain a conception of realistically achievable efficiencies, the values 

of curve 2 in Fig. 3 have been reduced by another 10%, in order to account for 

the effects of the secondary losses. It is known that these losses, in combination, are reduceable to this level by application of the best current technologies. This 10% reduction leads to curve 3 in Fig. 3. It shows that with a 

base minority carrier lifetime of 100 11S, an efficiency of 19.8% should be 

achievable, which is a value not much above the one achieved so far in the best 

devices with somewhat lower lifetimes. It also shows that a lifetime value near 

a millisecond will be needed to achieve 22% efficiency. While millisecond lifetimes should be achievable by a combination of today's best technologies in 

semiconductor material processing, the achievement of efficiencies above 22% 

will require a considerable advancement of the material science of silicon. 

CONCEPTS FOR HIGH EFFICIENCY SOLAR CELL DESIGN 

Evaluating the current status of silicon solar cell technology (summarized 

in Table II) makes it evident that the technology is available to reduce all 

the contributions from secondary loss mechanisms to the level of maximally 2 to 3% each. This will be close to the practically achievable limits. 

Secondary loss mechanisms are those which are determined by technology factors, 

and which have a fundamental limit of zero, with the exception of the collection 

efficiency. These secondary losses include the reflectance, shading due to 

front surface metal coverage, Joule losses due to series resistance, excess 

junction current, etc. 

The evaluation also shows that the (internal) collection efficiency is, 

in all modern cells, significantly above 90%. It has also been found that the 

collection efficiency increases only slowly with further reductions of minority 

carrier recombination, giving the effect of an apparent "saturation." 

In contrast to the collection efficiency, the open circuit voltage continues to increase significantly with continued reduction of minority carrier 

recombination. This is the performance attribute which has the largest margin 

56 
for improvement at the current status of solar cell technolo-gy. The curve 

factor, finally, increases together with the open circuit voltage, although its 

increase proceeds at a smaller rate. 

A review of the progression towards the current high, level of silicon solar 

cell performance indicates that this level has been accomplished only by taking 

a global view of the device. The expression "global view" means simultaneously 

considering the influence of all loss mechanisms, and reducing each of them to 

the lowest possible level (Table III). In fact, where there are several 

performance determi ni ng mechani sms, wh-j ch act on the same attri bute and whi ch 

cannot be reduced to zel'O, then the opti mum performance is generally obtai ned 

when the different contributions are brought to equal, low levels. This rule, 

for instance, applies to the contributions to the saturation current from the 

base and from the front region. A device where the saturation current is 

clearly dominated by one or the other region is not optimized until the higher 

contribution is brought down to the level of that from the other region. 

The efforts towards efficiency improvement have so far led to a number of 

"add-ons" to the basic cell. They include: (1) a grid metallization structure 

to reduce the front layer sheet resistance; (2) a single or dual layer antireflection coating; (3) texturing of the front surface to enhance the antireflection effect and to increase the effective internal optical path length; (4) an- optical reflector at the back surface to increase the optical path length ("light trapping"); (5) passivating layers at the front and back surfaces 

to lower the effective surface recombination velocities; (6) potential steps or 

drift field regions; (7) isolating layers; and (8)- reduced area metallization 

(dot contacts)--the last three also primarily for the reduction of the effective 

surface recombination velocity. This could lead to a complicated device 

structure (Fig. 9). At least part of the purpose of applying the measures (3) 

to (8) is to reduce the recombination rates of minority tarriers, and their 

effects and limitations will be considered in the following. 

The discussions up to this point have shown that the reduction of minority 

carrier recombination is the key element in achieving significant further 

improvements in silicon solar cell performance. Contemplation of the subject reveals that there are essentially three principal paths available to the 

reduction of recombination (Table IV). The first ;s the normally considered 

avenue of decreas i ng the dens ity of recomb; nat; on centers. Thi s has to be 

accomplished in the volume of the device and on its surfaces. The second avenue 

is the reduction of the volume of the material, or of its surface area, both of 

which contain the recombination centers. For the volume, the concept is to 

utilize "thin layers" which means that their thickness is smaller than the 

diffusion length, while, for sU'riaces, it is principally to reduce the total 

surface area which contains recombination centers. For solar cells this would 

be possible only by using optical concentration. A secondary approach is to 

reduce areas of unavoidably high surface recombinat-ion velocity in favor of 

surfaces with a lower surface recombination velocity. The typical example of 

this appro~ch is the reduction of the ohmic contact area ("dot contacts"). The 

third avenue, finally, is that of reducing the density of the excess minori ty carriers, as the recombination currents both for the volume and for the surfaces 

are proportional to the excess minority carrier concentration. The density of 

the excess mi nority carri ers can be reduced, e. g., if thei r flow towards the 

outside of the volume in which recombination occurs, can be accelerated. This 

57 
particular approach is available for minority .carriers generated by the absorption of light, which means for the improvement of the collection efficiency. A 

second method is to "shield" the areas with higher excess minority carrier density from the areas with higher re·combination rates by steps of the electrostatic 

potential in the appropriate direction. This leads to a lower density of the 

excess minority carriers within the region of higher recombination rates. The 

third approach is to isolate regions or surfaces with high recombination rates, 

such as the meta 1 /semi conductor boundari es at the conta,cts, from the regi ons 

with higher minority carrier density by an intervening IIthick .layer." The 

effect of this Jlisolating layer" is that the region with the higher excess 

minority carrier density "sees" the bulk recombination rate of the intervening layer rather than the higher surface recombination rate at the other boundary 

of the thick layer. The final approach utilizes an increased dopant concentration. This is particularly effective in the case of injection of minority carriers across a forward biased potential barrier. 

Havi ng recogni zed the pri nci pa 1 concept for the .reducti on of mi nori ty 

carrier recombination, the question turns to the implementation of these concepts. A number of device structures and of design concepts are available, each 

of which addresses one or two of the principal paths to recombination reduction. 

Reducing the volume of the semiconductor in which excess minority carriers 

are present, as a means for reducing recombination, is elucidated by considering 

the relationship for the diode current (Table V). This current is proportional 

to the transport velocity which, for infinitely thick layers, equals the ratio 

of diffusion length to minority carrier lifetime. For layers which are thin 

compared to the diffusion length, however, the transport velocity approaches the 

ratio of the layer thickness to the minority carrier lifetime. Thus, continued 

reduction of the thickness further reduces the recombination current. In a 

solar cell in the open circuit condition, where the diode current has to equal the light generated current, the injected excess minority carrier density is 

proportional to the inverse transport velocity, that is proportional to the 

minority carrier lifetime and inversely proportional to the layer thickness. 

When the. lifetimes become very large or the layer thicknesses very small, the 

injected excess minority carrier density can exceed the magnitudes required for 

the low-level injection condition to hold, as discussed before, and a transition 

to Auger dominated recombination can occur. Thus, a reduction of volume recombination may not be achieved beyond the point of transition to Auger recombination. 

For the principle of the reduction of the recombination volume, only a 

reduction of the layer thickness has been discussed. An area reduction appears 

to be potentially effective only if the device cross section for the light generated current coul d be made different from that fot' the di ode current. 

A second i tern for the reducti on of recombi na ti on is the reducti on of s urface area which contains a substantial number of recombination centers 

Table VI). While in principle devices can be made smaller, the reduction of the 

"openll surfaces is difficult for solar cells, as the area is needed for the 

absorption of photons from the incident solar radiation flux. Optical concentration a"lso may not be a remedy to this situation, as it leads to an increased 

light generated current density, whi.ch again can more easily drive the device 

into the Auger recombination regime. 

sa' 
Surface area reduction can be very effective, however, where the contact 

areas are concerned, as these represent surfaces of high recombination rates. 

While means seem to be available to reduce the surface recombination velocities 

at the open surfaces, particularly if they do not have to effectively pass incident photons, the contact recombination velocities do not seem to be 

substantially reducible in practical devices. Thus the approach is being 

pursued to reduce the weighted average surface recombination velocity, by 

reducing the area of high s and replacing it with an increased area of low s. 

Limi ts to the method are approached when the spaci ng between the areas of hi gh surface recombination velocity reaches the magnitude of the diffusion length. Also, when the individual contact areas become very small, their spreading 

resistance becomes substantial, so that they start to make a significant contribution to the series resistance. 

The next possibility for decreasing recombination rates involves a reduction of the number of excess minority carriers available in regions of higher recombination center density. The first approach to this is IIshieldingll these 

areas by interspersing a suitable step in the electrostatic potential, often 

called a IIhigh/low junction,1I or a drift field (Table VII). The effect of 

reduced recombination expresses itself in the transport velocity for minority carriers across a real or imagined boundary within a given region of the device. 

The reduction of the transport velocity by the addition of a potential step is 

equal to the negative exponential of the height of the potential step or, 

expressed differently, to the ratio of the majority carrier concentrations at 

the two sides of the potential step. 

Such potential steps can be incorporated in a semiconductor device in many different forms. They may be layers containing a drift field resulting from a 

doping gradient. When such layers are relatively thin, they are ofte~ called 

high/low junctions. Such potential steps may be lIaccumulation layersll near 

the surface of a device, and are present particularly in the cases where an 

insulator covers the surface of the semiconductor, particularly when it is 

interposed between a metal and the semiconductor. Depletion layers increase 

the transport velocity and should, therefore, be avoided. Going beyond depletion leads to inversion' layers which act more like floating pn junctions which also have been proposed for shielding purposes in solar cells. The 

fl oati ng juncti ons seem to be mos t effecti ve when they act a.s true II emitters, II 

which means injection only from the emitter, no recombination current into the 

emitter. This may be the only beneficial application of an lIemitterll in a solar 

cell. The final form of a potential step is achieved in the transition to a 

material with a different bandgap, i.e., a wider bandgap. The transition to 

the wider bandgap layer is generally arranged so that it results in a high/low 

junction of the proper direction. These wide bandgap layers, when applied to 

the open part of the front surface, are generally designed so as not to collect 

a significant amount of current, but to transmit the photons to the active semiconductor volume. They are then ca 11 ed IIwi ndow 1 ayers. II 

The use of potential steps has several limitations. Firstly, the use of 

moderately high doping at the low side of high/low junctions, in order to 

achieve a high open circuit voltage (Voc ), reduces the available step height. This condition is further accentuated by the need to avoid the heavy doping effects on the hi gh side, whi ch can seri ous ly i nfl uence the devi ce performance. Similar considerations apply to accumulation layers, where it is in some cases 

59 
also difficult to provide enough charge to adequately "accumulate" in a more 

heavily doped semiconductor. An item to also watch is the capability for 

avoiding "absorption without collection" in window layers. In addition, at the 

transition between the active semiconductor and the window layer, a high concentration of interface states can substantially increase recombination. 

A third approach is to isolate the active volume of the device from a 

region with a high recombination center density by interspersing an "isolating layer." If such an interspersed layer is thicker than the difussion length 

within it, then the transport velocity at the interface between the active 

volume and the isolating layer is determined only by the ratio of diffusion 

length to minority carrier lifetime, and is practically independent of the 

transport velocity at the other boundary of the isolating layer, which, e.g., 

may be the high effective surface recombination velocity of a metal/semiconductor interface (Table VIII). The limit to the effectiveness of such an 

isolating layer is that the L/T ratio has to be adequately high, certainly 

higher than the transport velocity at the outside boundary of the. isolating layer. Also, if such an isolating layer is placed in the optical path, it can 

severely degrade the collection efficiency. 

More and more use is being made of such isolating layers. They appeared first in connection with the high/low junctions applied in the base of solar 

cells, which frequently go under the mime "BSF structures. 1I The use of such 

isolating layers has also been proposed for the front region of the device, 

where they are limited to the area shaded by the ohmic contacts (Fig. 10), while 

another recent high efficiency design uses an isolating layer in the base without application of the high/low junction (Fig. 11). 

A commonly used approach to reduci ng the dens ity of injected excess 

minority carriers, e.g., np. and to consequently achieving higher open circuit 

vo ltages, is to decrease the thermal equil i bri urn mi nority carri er concentrati on 

np 0 (Table IX). n 0 is inver.se1y proportional tothe majority carrier 

concentration and c8nsequent1y the dopant concentration. This reduces the 

saturation current, and yields a higher Voc. At the open circuit condition, 

however, the excess minority carrier concentration is returned to the same 

value as present in the ~ase of lower dopant concentration. The limits of 

achieving improvements through higher dopant concentrations are reached by the 

onset of Auger recombination, and deleterious effects are experienced through bandgap narrowing. 

After all these avenues available through device structuring possibilities 

are exhausted, then the only recourse left for the reduction of recombination 

becomes the decrease of the recombination center density itself (Table X). 

For those of these centers which are located in the volume of the material 

(bulk centers), the interest focuses on the original material processing (crystal gl'owth), and on the further role of these previously introduced centers 

during device processing. In the original material processing, attention needs 

to be directed to the reduced incorporation of impurities which cause recombinati on cen ters; to the a voi dance of crys ta 1 defect i ntroducti on, 

particularly through control of the thermal environment during crystal growth; 

to the roles of oxygen and carbon which are present in the silicon in relatively high concentrations; and to the formation of defect complexes, and particularly 

to their roles in forming or neutralizing recombination centers. 

60 
The second area, device processing, is equally important for the reduction 

of the recombination center density in the final device. The first and most 

obvious point of attention is the prevention of the introduction of new lifetime 

killing impurities. A second approach is to remove existing defects in the 

material at various stages during the device process, using treatments which 

a re genera lly connec ted wi th the name II getteri ng. .. One of the maj or problems 

in device processing, particularly during the application of high temperature pt'ocesses, is the transformation of existing inactive defects into recombination 

centers. On the other hand, it is desirable to foster the transformation of 

recombination centers to electrically inactive defects. These transformations 

may involve changes in existing complexes, or the formation of new ones. The 

transformations are often connected with the name "passivation," and one of 

the major open questions in this area is the role which hydrogen can play. 

Somewhat related to the question of reducing the bulk recombination center 

density is that of dealing with the surface recombination centers. What is meant 

here is the actual reduction of the density of recombination centers at the 

surface, rather than the effect of a reduced surface recombination velocity which often is connected with the introduction of a potential step just below 

the surface (Table XI). The usual recombination center density of untreated 

silicon surfaces is in the 1015 cm- 2 range. This number happens to be near 

the density of dangling bonds which would be expected to exist at a perfect silicon surface. If these dangling bonds should actually be responsible for 

the recombination centers, then the question arises of how these dangling bonds 

interact with other chemical species, and particularly which of these interactions result in a substantial decrease in the recombination center concentration. In addition, there is the question of which other defects form surface 

traps which act as recombination centers. Definitive answers to these questions 

may lead to the methods for effectively avoiding the introduction of these 

defects, or for their elimination, once they are in existence. 

The whole question complex on the reduction of the recombination center 

density leads to the conclusion that considerable progress in the silicon 

material science is needed, as well as in the technology of crystal preparation and of device processing. 

The preceding discussions lead to the conclusion that a high efficiency 

solar cell design will by necessity combine at least several of the methods 

known for the reduction of recombination (Table XII). It will further have 

to strike the right compromise between the conflicting design requirements, as 

a particular method may improve certain attributes of the device, but have a 

negative impact on others. And finally, all the second order effects need to 

be included in the design considerations, and the best available technologies for their reduction be applied in order to achieve the highest efficiency extractable from the silicon solar cell. The general high efficiency design 

concept, thus, wi 11 pursue the two-pronged approach of decreasing the recombination loss of minority carriers, and particularly that of the carriers injected under forward bias, and of simultaneously reducing all the secondary effects 

to near negligible values. Several cell design approaches seem to exist for 

each of these performance attributes, and the designer will have to select those 

which will yield the highest overall device performance, when applied in 

combination. And, of course, this device will have to be fabricated at a 

competi ti ve pri ce. 

61 
CONCLUSION 

It has been seen that the achievement of higher efficiencies in silicon 

solar cells depends on the reduction of all secondary losses to negligible 

values, which ;s about possible with current technology, and then on the reduction of minority carrier recombination (summarized in Table XIII). For the 

latter, four principal approaches are available, three of which are essentially remedial, handled through device design, and one is fundamental, namely the 

reduction of the recombination center density. 

All the reduction of recombination via recombination centers will only lead 

to the domi nance of Auger recombLlati on, whi ch appears to impose the ultimate 

practical limitation on solar cell efficiency. As there exist still some doubts 

on the magnitude of the Auger coefficients, this ultimately achievable efficiency can also not be certain at this time. Some rather fundamental research 

will be needed to gain the complete understanding of the band-to-band recombination effects which carry Auger's name. 

Several of the "remedial" methods for reduction of recombination involve 

high majority carrier concentrations. The onset of Auger recombination tends to 

force the efficiency versus carrier concentration curves towards zero slope, 

and the onset of bandgap narrowing then to a negative slope. Again, the bandgap narrowing effect does not seem fully explained, with the result that the various 

bandgap models in existence now lead not only to different solar cell performance expectations, but also to different cell designs for optimum performance. Again, fundamental research is needed. 

Outside of these fundamental research needs, substantial silicon material 

research, both bulk and surface, will be needed to reach substantially higher 

efficiency levels. And then we should not forget the inventiveness which could 

bring forward new, more effective remedial design concepts. 

REFERENCES 

1] Green, M. A., IILimits on the Open-Circuit Voltage and Efficiency of Silicon 

Solar Cells Imposed by Intrinsic Auger Processes," IEEE Trans. El. Devices, 

ED-31, pp. 671-678, May 1984. 

2] Tiedje, T., Yablonovitch, E., Cody, G. D., and Brook, B. G., "Limiting Efficiency of Silicon Solar Cells," ibid., pp. 711-716. 

62 

I 

I' 

~ 

! 

I 

I 
0\ 

W 

,I' 

PRIMARY CAUSES OF LOSSES ISYMBOL ,DESIGN 1970 COM'Lj'VIOLET 

PAR AM CELL CELL" 

"BLACK I 1978 I 1984 EXPER'L CELLS GOALS 

CELL" 

SPACE 

CELL SPIRE ~STINGH M.A.GREE~ 20",. 22.6 .,. 

BASE' 

,WIDTH ? 

1

3o

!,m Tn,p 3p.. Tn,p. 

300 p.m 1300pm1A1380 p.m 375 p.m 280 p.m 200p.m 200p.m 

? ? -40p.m -23p.m -25 p.m 9!ip.. 950p.. 

? (0.1 p.') 10.1 p.11 0.26p.. 2.6p.. 

FRONT, .,,'" r' "" [T" Tp,n ? 

S ? 

TREATM.· SID TOaD .. 

GLASS 

- 0.2p.m ~-0.2p.m ~0.2p.m j_0.3p.m -0.3p.m 2 p.m 2 p.m ? 'I In, -15p.' 0.1 p.. 10 p.. 

? ? .104 cmi -t04 cm.-' 10Iem.-' 10' ems-I'OIt em.-

EXT'D Ho,p TEX "IH TEXT'D + nOa"SIOI Z n 51 DUAL AR DUAL AR 

+ GLASS TozO, iOz+TlOi MO Fit 

I. LIGHT GENERATED CURRENT' . 

mg!!f:l!.TA~I&!!~!,U~..!~....!.L.:!! ___ ---I-__ -r-___ • ____ _ 44mA em-It -'-_ 

A. OPTICAL SURFACE PROPEImES (REFLECTION) II-R) 0.905 0.90 0.97 0.96 0.975 0.966 0.954 0.97 

B. CONTACT COVERAGE S 0.96 0.95 0.95 0.96 0.965 0.971A) 0.948 0.966 

C. INCOMPLETE ABSORPTION (THICkNESS)} 1: 0.951'09 0.96 0.961A 0.956 0.955 0.973 }0.95 

D. RECOMBINATION OUTSIDE DEPLETION REGI 'CaLL 0.72 O~ 0.94 0.94 0.91 0.915 0.93 

!8ULK AND SURFACE,INCLUDING CONTACTS) E. I DEAD LAYERS") II-A) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 

----------------- ---- - ----- OVERALL COLLECTION EFFICIENCY' Y 0 •• 3 0.77 0.84 0.84 0.82 0.82 0.82 0.86 0.89 

LIGHT GENERATED CU"RENT(AMtI JL- r-JL,,,lMAelll-41 28.' 34.0 37.1 37.0 36.2 36.0 36.0 37.9 39.2 

2. OPEN CIRCUIT VOLTAGE' 

FUNDAMENTAL LlMIT'~(vFlfund'0.76 ! 0.836V (jo·4.2,'0·IIAcm-lt------________________ -- -- --.---""'T"'- ) __ roo- _ 

A. RECOMBINATION OUTSIDE DEPLETION REGION (VFI • 

B. BANDGAP 

(BULK AND 

NA"ROWING SURFA.CE,INCLUOING CONTACTS I }VF~.chn.(VFI.und 0.522 ~.52810.533 JO.55l0.565JO.57 ~0.5~ 0.60 ~0.65 C. ·CURRENT LEAKAGE" (Rlhl 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 

OPEHCiRCiiiTvciLiAGE7""---- VoMYFi·E. Tvl 0.574 o.iil 0.586 0.610 0.622 0.627 0.653 0:661 0.7,5 

3. Fill FACTOR' 

fiI!.P.a..M~NTA.l.....LIM!!:... 1E!"ulI!.. __ 

A.} } (CFI' B.· SAME AS OPEN CIRCUIT VOLTAGE ICFlirchn1CFI'und 

C. (R.h) 

D. RECOMBINATION IN DEPLETION REGION (CFlodd'l 

E. SERIES RESI~~_______ ~~ __ _ 

FILL FACTOR (FF) 

RESULTING CONVERSION EFFICIENCY "1 

I-----r ---,-----'-,- ~~6.!.._ ... --,--,. ---r---

0.82 ~ 0.823 

1.0 (AI 1.0 

0.91 0.97 

0.96 0.985 

-- --- 0.716 0.78 

11.6 15.4 

0.823 0.82~ 0.83~ 0.83J 0.83~ 0.84 

1.0 1.0 1.0 1.0 1.0 1.0 

0.97 0.97 0.985 0.98 0.982 0.97 

0.98~_ ~.98 (A) ~.98 ~.98 ~.984 ~.98_ 

0.78 0.78 0.801 0.800 0.811 0.80 

0.85 

1.0 

0.97 

0.98 

0.81 

17.0 17.6 '8.1 18.1 19.1 0.200 I 0.226 

(A)' ASSUMED 

Table I 

00 

..... i! 

C!i 

0> 

::a~ 

'8~ 

?! ~, 

~ai; 
25 

.,, 

The Historical Deve lopmen. 

of Silicon Solar Cell Efficiency. 

Do not believe 

in exponential 

extrapolatlonsl 

f:"'" 15 

r 

5 

o Experimental 

x Commercial 

O~~~~ww~~wp~~~~----------~ 

1954 19641974198420042054 

--~ .. Year 

The Basic Solar Cell' 

Photon 

Flux 

--- ./V~;;:;,,~ for • Photon 

Absorption 

Contact. to 

• Extract 

Current 

Potential Barrier for 

• Collection of LIQht-Gen'd Car,I •• 

• Generation of Voltage 

Everything Else 

CAR coatings, HllLo JUnctions, extra Layers, etc) 

to overcome • Secondary Effects 

cau.ed by material, proce •• , or 

de.'gn limitations 

64 

Figure 2 

Fi gure 1 
ORIGfNAL PAGE" is 

OF. fOOR QUALITY 

STATUS OF SI SOLAR CELL TECHNOLOGY 

• T E C H N 0 LOG Y IS A V A I LAB L E TO REDUCE THE CONTRIBUTION OF EACH 

SEC 0 N DAR Y LOS S ME C If A N I S !1(REFLECTlON, CONTACT SHADING, SERIES 

RESISTANCE, ETC.) TO THE MAXIMALLY 2-3% LEVEL. 

• INTERNAL CO LL E C T ION E F F I C lEN C Y IS GENERALLY >90%; "SATURATES" WITH 

FURTHER REDUCED RECOMBINATION. 

• 0 PEN C I R CUI T VOL TAG E CONTINUES TO SUBSTANTIALLY INC REA S E WITH 

DEC REA SIN G MINORITY CARRIER R E COM BIN A T I 0 tL UP TO BASIC RECOMBINATION 

LIMIT (RADIATIVE AND AUGER). 

• CUR V E FA C TOR (FUNDAMENTAL PART OF FILL FACTOR) CAN INC REA S E (WITH Voe) 

BY A FEW PER C E NT. 

Table II 

II II 2 n on p Xj =fLm 

28 uniform doping each region . , ~.~ 

24 

22 

20 

Tp,n=Tn,p (Auger recombn. (I) . .".."... 

causes difference at ........ '1'f>.:v .... ~ 

3 higher values) /'~ *'"~.:..r .. r .. l' •. tV ..r..r.., / /<1 .. / ~,/" 

o /:. .... 'V . . /."'~ +~~~f/ ~ ~i /','/ ~,,~~ ~,e~/ ~,\C; ~~,~, .... e t'o~ ~ rJ.'~ ./ -'~ _ti·'~ No-Na -5E 16 / ,,' ,,~.... " . '" ,'" 

10-4 10-3 

lJ-Tn,p (5) 

65 

Figure 3 
10-1 \ ., "--"AUGER 1 

\ RECOMBINATION 

\ 

1 0

-2 DEEP LEVEL \ 

Sft+t RECOMB. 

Figure 4 

-

~ 

- 22 ~ 

r 20 

18 I· 10-55 

16 

l . 10-1 I 10

' 

~ 

~ 5 

iii 

a: 

~ 0 z 

8 

...J ., 

~ (I) 

z 45 ~ 

~ 40 ~ 

a:N "1 :::)1 

35 u~ ect 

!;iE 30 a: 

tiJ 

z 

25 ~ 

tX 

20 C> 

::::i 

0.71 > 

0.70 g 

0.69 > 

0.68 ~ 

0.67 j:! 

0.66 5 

> 0.65 t- 0.64 :; 

u 0.63 ~ 

0.62 u 

t 

10 102 103 10· 105 106 t 

0.61 ~ 

0.60 &. 

0.59 t 

0.58 

SURFACE RECOMBINATION VELOCITY 

102 

5 (em 5-1) 

Figure 5 

Surface Recombination 

Velocity Va lues 

for Curve (2) of 

7J VS. Tn p plot. 

103 

s (em 5-1) 

Figure 6 

66 
'0' 

~ 24 

22 

20 

16 

Front Region Lifetimes 

T p,n for 0.99"7 of curve (2) 

10-6 10-5 

~Tp,n (5) 

Figure 7 

xIO-2~--------------------------------~ Base Region Thickness Wp 

6 

-5 E 

o -4 

c.. 

3: 3 

f 2 

for maximum efficiency 

Text'd I 

o~----~----~------~----~----~ 

10-6 10-5 10-4 ' 10-3 10-2 10-1 

.. T n,p (5) Fi gure 8 

67 
H I G H E F F I C lEN C Y REQUI RES 

A G LOB A L V lEW OF THE D E V ICE, SO THAT 

ALL TECHNOLOGY-DETERMINED LOSSES 

WILL BECOME LOW • 

. 1 F 0 N E LOS S MECHAN I SM D 0 MIN ATE S -> NOT 0 P TIM I ZED 

-> RED U C E IT 

I OLD 0 P TIM I Z A T ION R IJ L E : I 

CON T RIB UTI 0 N S FROM DI FFERENT COMPONENTS 

ARE E QUA L AT M A X I MUM OR MIN I MUM. 

Table III 

Photon FI ux + + + + + + + + + 

• 

The Basic 

Solar Cell 

* 

~--Contact Grid Structure 

....---Isolating Layer 

Textured Surface 

AR Coating 

1Vt.~.+---Passivating Layer ~"T-:"-r----=-""""-"t' Po te n ti a 1St ep 

4fC--I--Main Potentia I Barrier 

Potential Step 

Optical Reflector 

~---Passlvat!ng Layer 

~~ ___ -Isolatlng Layer 

Reduced Contact 

Area 

Schematic View of the Solar Ce II -Thf'-' Has Everything" 

Figure 9 

68 
PRINCIELf: 

1..Utll: 

THE THREE PRINCIPAL PATHS TO REDUCED RECOMBINATION 

DECREASE 

1. DENSITY OF RECOMBINATION CENTERS 

• IN BULK 

• AT SURFACES I

,' [em-2] 's,t ---e> LOWER s 

2, VOL U M E OR ARE A CONTAINING RECOMBINATION CENTERS: 

• "THIN" LAYERS 

• "DOT CONTACTS" 

3, DENSITY OF EXCESS MINORITY CARRIERS 

• FAST REMOVAL TO OUTSIDE (FOR "cOll) 

• "SHIELDING" WITH POTENTIAL STEPS 

• "ISOLATING" FROM HIGHER RECOMBINATION RATE 

• HIGH DOPANT CONCENTRATION 

REDUCE VOLUME: 

(I,E" THICKNESS OF LAYERS) 

. L I Jd = qnp T d»L 

("THICK" LAYER) ("THIN" LAYER) 

Id = IL for V: VARIABLE 

oe • 

np = jqL ·W" pp,o 

NO LONGER LOW LEVEL INJECTION 

1 

(Ajd = AjL) 

(AREA REDUCTION COULD BE EFFECTIVE ONLY, IF ~d/jL RATIO COULD BE CHANGED, WITH Id/IL CONSTANT,) 

69 

} FOR "=11 

Table V 

} FOR Voe 

Table IV 
RED U C E SUR E ACE ARE A: 

OPEN SURFACES: 

LI MIT: • NEEDED FOR PHOTON ABSORPTI ON 

(CONCENTRATION: INCREASED jL: 

CONTACT AREAS: "DOT" CONTACTS 

UTILIZE AVERAGE EFFECTIVE a: 

LIMITS: • LESS EFFECTIVE WHEN SPACING < L 

• SPREADING RESISTANCE INCREASES Rs Table VI 

Table VII 

SHIELDING WITH POTENTIAL STEPS: 

GENERALLY REDUCES TRANSPORT VELOCITIES (FOR RECOMBINATION CURRENTS) 

BY: 

E 

f 

I 

I 

I 

I 

~ilJ" 5 

jr(Xl ) = qnp(xl)ul(xl ) 

p (Xl) 

= qnp(xl ) ~ u 2 (x2) 

p 2 

FORMS OF POTENTI AL "STEPS": 

• DRIFT FIELD REGIONS 

• HIGH/LOW JUNCTIONS 

• ACCUMULATION LAYERS (USUALLY UNDER INSULATORS, INCLUDING "TUNNEL CONTACTS"). 

• "FLOATING" pn JUNCTIONS (OR INVERSION LAYERS). 

• BANDGAP CHANGES (USUALLY llEG WITH HIGHILOW JUNCTION, "WINDOW LAYER"). 

UJil.IS.: 

• INCREASED DOPING AT "LOW" SIDE REDUCES AVAILABLE STEP HEIGHT. 

• "HEAVY DOPING" EFFECTS ON "HIGH SIDE" LIMIT USEFUL STEP HEIGHT. 

• ABSORPTION W/O COLLECTION IN "WINDOW LAYERS." 

• INTERFACE STATES AT TRANSITION TO ~'WINDOW LAYER," 

70 
PRINCIPLE: 

ISOLATING WITH "THICK LAYERS" 

ACTI VEL> u = !! 

VOLUME I T 

I 

'-~IS-O-LA-T"""'ING LAYER 

d l: L 

• ADEQUATELY HIGH LiT • 

• AFFECTS COLLECTION EFFICIENCY, 

IF IN IPTICAL PATH. 

Table X 

Table VII I HIGH DOPANT CONCENTRATION 

PRINCIPlE: !lY 

!! = q n ekT L T p,c T ; 2 n. v = HIGH IF n = SMALL: p,c n = _l._ 

p,c pp,c 

LlMllS.: 

• HEAVY DOPING EFFECTS. 

Table IX 

REDUCE VOLUME RECOMBINATION CENTER DENSITY: 

• ORIGINAL MATERIAL PROCESSING: 

- FEWER IMPURITIES 

- ROLES OF OXYGEN, CARBON? 

- FEWER CRYSTAL DEFECTS (THERMAL ENVIRONMENT IN X-TAL GROWTH?) 

- ROLES OF DEFECT COMPLEXES 

• DEVICE PROCESSING: 

- NO NEW IMPURITY iNTRODUCTION· 

- REMOVE EXISTING DEFECTS (GETTERING) 

- AVOID TRANSFORMATION OF Il'EFECTS TO RECOMBINATION CENTERS 

(EFFECTS OF THERNAL PROCESSES?) 

- FOSTER TRANSFORMATION OF RECOMBINATION CENTERS TO HARMLESS 

DEFECTS (PASSIVATION: CHANGES OF COMPLEXES?: ROLE OF HYDROGEN?) 

71 
N 

ORIGINAL PAGE~ 16 

OF POOR QUALITY, 

p-"'-~...J 

More #leav;ly 1JDfI~ti Fr6,,1; Layer 

U'i,MLDW Jundion 

Narrtlw Frlmi: 

------------------ Lay~r 

p Narrow 1JflU 

Layer _________________ 

- --------------- Hlglt"-" 7.un~J.;.1I 't..C1WJI .. I' 

p+ Hare He4vi{y 

Defied JJas~ lAy,,.. 

CDHiad Melal 

Figure 10 

~ ~ l ~~~:inaled 

_____ .......I~ ~ Passivotlng 

p 

j' 

n contoct~b==-~~"'~"'~ .. ~'··2··E··~ .. ~···~'f .... ~·'~'·5"'~·., 

~)L~ 

Isolating 

Loyer 

Oxide 

Sipos 

Contact 

THE EXXON HIGH EFFICIENCY DESIGN 

Figure 11 

72 
REDUCE SURFACE RECOMBINATION CENTER DENSITY: 

• PASSIVATION OF DANGLING BONDS. 

(WHICH LAYERS ARE MORE EFFECTIVE IN REDUCING SO' WHICH 

IN SUPPORTING ACCUMULATION LAYERS?) 

• WHAT OTHER DEFECTS FORM SURFACE TRAPS 

(HOW CAN THEY BE AVOIDED OR ELIMINATED?) 

A HIGH EFFICIENCY CELL DESIGN 

Table XI 

• COMBINES SEVERAL OF THE METHODS FOR REDUCTION OF RECOMBINATION. 

• STRIKES THE RIGHT COMPROMISE BETWEEN CONFLICT!NG DESIGN REQUIREMENTS. 

• REDUCES ALL SECOND ORDER EFFECTS. 

Table XII 

73 
...... 

.j::-

-,_.- -.-'--~---:-..;r 

THE GENERAL HIGH EfFICIENCY DESIGN CONCEPT 

J J 

AVAILABLE MEASURES 

EFJ=ECT· __lOCAI10N_-.ERl.NCIPLE ~Qn 

• ~EDUCE RECOMBINATION LOSS OF MINORITY CARRIERS, PARTICULARLY Ir~JECTED CARRIERS 

(HIGH Voe) : 

BULK I BASE } RECO~£INATION FRONT 

SURFACE I OPEN 

RECOMBINATION SURFACE 

CONTACT 

• SECONDARY EFFECTS 

REFLECTION FRONT 

CONTACT FRONT 

FRONT 

RS BACK 

EXCESS JUNCTION 

tuRRENI ___ - -- --- -~-

________ -.-e-·. 

REDUCE Nt PROCESSING 

REDUCE VOLUME ---- APPLY LIGHT TRAPPING 

REDUCE Nt,S} - PASSIVATION LAYER 

SHIELDING - DRIFT FIELD 

ISOLATION 

REDUCE AREA 

SHIELDING 

} ---- WINDOW LAYER 

"DOT CONTACT" 

~ TUNNEL CONTACT WITH ACCU~lULATION LAYER 

__ HIGHILOW ,JUNCTION, BSF 

~ _ HIGHILOW ,JUNCTION, WITH THICK p+ OR n+ J LAYER, OR WIDE BANDGAP LAYER 

ISOLATION THICK LAYER ALONE 

-

AR -- MULTI-LAYER AR 

TEXTURE -- TEXTURE + SINGLE AR 

REDUCE METAL _____ WRAP-AROUND DESIGN 

COVERAGE J - FINE LINE GRID 

{DEGENERATE SURFACE 

KEEP LOW - LOW METAL SHEET-RES I STANCE 

GOOD INTERCONNECT DESIGN 

KEEP LOW ----- GOOD PROCESSING 

Table XIII 
DISCUSSION 

(WOLF) 

SPITZER: Given all the tradeoffs on grid design, passivation, and the other 

things that are necessary to make a 2~ efficient cell, the question is, 

can screen-printed contacts be used for the 15~ module, or will they not 

offer enough for high-efficiency features? 

WOLF: I have been talking against screen printers at a number of meetings. 

The biggest problem I see in them is that in screen printing and sintering you don't get better resistivity·or better conductivity. Even with 

silver it seems you get conductivity only about one-third, in general, of 

what you get if you electroplate or deposit silver. You are limited by 

how thick you can make the layer in one pass. The sheet resistAnce 

becomes limited by the bulk conductivity you can get. The second problem 

is, you cannot make them very narrow. It seems that 5 mils might be 

achievable with today's technology. These are the two things I see 

against screen-printed contacts. 

SPITZER: Then. probably no. 

WOLF: I would think if you go for high efficiency. at least consider a 

secondary later. I always find the first thing is to show we can really 

make high efficiency. so letts use the best technology we know we can 

apply to get to high efficiency. then later letts think of how can we 

make them cheaper. 

Now I want to introduce the next speaker. Here is a little contradiction. 

I have been saying that all the secondary problems are minor. our current 

technology is solved; just worry about recombination. Arnie Lesk from 

Solavolt is going to tell us about all the problems that still exist in 

trying to make low-resistance contacts. So. basically. I guess it is not 

easy, and there are still a lot of problems connected with it. 

75 
SOME PRACTICAL CONSIDERATIONS FOR ECONOMICAL BACK CONTACT 

FORMATION ON HIGH EFFICIENCY SOLAR CELLS 

1. A. Lesk 

Solavolt International 

Phoenix, Arizona 

Abstract 

The back contact can detract from solar cell performance by a number of 

means: high recombination, barrier, pllotovoltage, minority carrier collection, 

resistance. These effects may act in a non-uniform fashion over the cell area, 

and complicate the analysis of photovoltaic performance aimed at a better 

understanding of the effects of device geometry and material and/or processing 

parameters. 

The back contact can be tested by reproducing it on both sides of a substrate. The dark. current-voltage characteristic should obey Ohm's law calculated 

using the resistivity of the substrate. Sintered aluminum on p-type silicon 

substrates of moderate and low resistivity behaves in this way, and so may be 

used as a reference against which other back contact technologies are measured. 

The objective is to find a back contact which performs well as a back 

contact, can be applied cheaply to large area solar cells, fits well into a 

practical process sequence, does not introduce structural damage or undesirable 

impurities into the silicon substrate, is compatible with an effective front 

contact technology, permits low temperature solder contacting, adheres well to 

silicon, and is reliable. 

1. HIGH RECOMBINATION 

2. MINORITY CARRIER COLLECTION 

3. RESISTANCE 

LINEAR 

NON-LINEAR 

4. BARRIER 

5. PHOTOVOL'I'AGE 

BACK CONTACT PROBLEMS 

p 

TABLE 1 FIGURE 1. Simple solar cell section. 

PRECEDING PAGE BLANK NOT FILI\fED 

77 
.",.,:. "-

Introduction 

Reduction of the cost of solar cell metallization is necessary if the 

project.ed loW prices for modules are to be realizid2 3Towards this goal, 

v~riou&'new technologies are under investigation. " Ba§k contact problems 

have be~n seen with some material systems, as - fabricated or after stress 

ageing. Back contact problems that can occur are listed in Table 1. 

A Model for Back Contact Studies 

Figure 1 shows a simple solar cell cross section. The back contact can 

degrade performance of the structure in two ways: 

1. by removing carriers (through recombination or collection) which 

would otherwise contribute to photo current at the P-N junction, 

or by generating carriers that increase the diffusion component 

of dark current, and 

2. by introducing resistances or barriers that reduce terminal 

voltage. 

Barrier effects on overall solar cell performance may be modified by photovoltage generation due to light reaching the back contact region. 

If we ascribe back-surface minority carrier effects on the P-N junction 

to photo current losses in the photogenerator and dark diffusion current 

increases in the n=1 diode,the rest of the back surface problems (3,4 and 5 

in Table 1) may be removed into a separate 2-port network section, as shown 

in Figure 2. The top 2-port section is the active one, with J h reduced by 

minority carrier recombination and collection at the back cont~ct, and the n=1 

diode having its dark current influenced by minority carrier generation or 

injection at the back contact. The n diode contains all the n>1 components. 

The shunt conductance Zsh may be non-linear. 

In the 2-port section at the bottom ~f Figure 2, barriers of either 

polarity, with photocurrents J h_ and J h are indicated as possible parasitics. P-13 p B 

The V-I characteristics of these barriers are generally much more conductive 

than those of a p-njunction because they are often low grade Schottky 

barriers and, particularly for large area devices, shunted in a non-uniform 

fashion. The shunt impedance ZSB may be nonlinear if the ohmic solar cell 

current traverses grain regions; this can be particularly prominent if the 

back contact region is segmented so lateral ohmic curren't in the base is 

appreciable. 

Experimental observations of the parasitic dark characteristics of the 

back contact are instructive in determining their cause and helping with their 

eliminati(J'tl. Figure 3(a) shows a section of a solar cell. Leaving off the 

p-n junction and making ohmic contact to top and bottom, Figure 3(b) , would 

place two of the lower (parasitic) 2-ports in series. If the top-to-bottom 

V-I characteristic of the structure in Figure 3(b) obeys Ohm's Law for the 

substrate material, there are no prominent back contact parasitics. Othe~ise, 

it will be necessary to use a known ohmic structure. Figure 3(c), with p 

contacts, can be entirely ohmic, e.g. foZ a 0.25 n - cm substrate 252 VM thick, 

top-to-bottom conductance is 160 mhos/cm (resistance = 6.25 mn - cm). At 36 

78 
ma/cm2

, the parasitic bulk drop is less than ~ mV. For+a 100 cm

2 cell, conductance = 16000 mhos (series resistance = .06 mQ). This p contact then becomes a 

standard against which other technologies are measured. The structure in 

Figure 3(d) can be used to measure the ohmic character of the experimental 

contact formed on the top side. 

Solar cells are sometimes made with segmented back contacts, Figure 4. 

In this type of geometry, there is a considerable amount of lateral current flow. 

By omitting the P-N junction, back contact parasitics can be tested for photogeneration. However, the bulk series resistance will be larger, and more 

susceptible to grain boundary effects. Quantitatively, consider a solar cell 

250~ thick with 5 equispaced contact lines/cm top and bottom, and a substrate 

resistivity of 0.25 Q-cm. Conductance between top and bottom contact sets 

will be approximately 20 mhos, assuming the average photocurrent induced 

majority carrier path length is 0.05cm.~ half the contact spacing, and no 

grain boundary impedance. For a 100 cm cell, g=2000 mhos, or series resistance is 0.5 mQ. This resistance is about an order of magnitude larger than 

that of a similar cell with full back-surface metallization, but still small 

enough to serve as an effective shunt for a.n othe~ise severe back surface 

barrier (e.g. an npn structure with a network of p back contacts penetrating 

to the p-type substrate). 

Some Examples 

Examples of how parasitic back-surface elements can degradG the V-I 

characteristic of an otherwise good cell are constructed by adding voltages 

of the 2-port sections at common currents. The upper 2-port V-I characteristic 

for a theoretical resistance-free base-dominatr9 th~ck diode is shown in 2 

Figure 5. ~IOameterz chosen are n=l, p=1.5xlO /cm, L =100W'1, '\l =6 24 cm IV 

sec (J _10 rnA/ cm ). Under 1-sun illumination, assuMing 36 rnA~cm , the V-I 

charac~eristic is shifted downward as shown in Figure 6., 

Figure 7 shows the effect on a 1 cm

2 cell of a series resistance of 1 Q; 

this would be obtained on a structure as given in the example illustrated in 

Figure 4 if the base resistivity were 5 Q-cm. 

Figure 8 shows the effect of a diode with a polarity opposing the P-N 

junction. The diode V-I characteristic is sketched on the left side of the 

current axis; when added to the theoretical diode curve the resultant form is 

S-shaped. This diode is on the left side of the2bottom 2-port in Figure 2. 

If this diode has a photocurrent Jp~ of 2 ma/cm , the resultant solar cell 

V-I characteristic is as sketched in Figure 9. 

If the back-surface barrier is directed in the same sense as the P-N 

junction, the main photocurrent will drive it in the reverse-bias direction. 

Figure 10 indicates the effect of 2

a very leaky "reverse" barrier; and Figure 11 

shows that. for a Jp~ of 10 rnA/cm , Voc is increa.sed although the peak power 

region is degraded. For this polarity of barrier to provide a net increase in 

cell power, its photocurrent must be very nearly as large as that of the main 

P·-N junction; a thin cell made on high resistivity, high lifetime material 

79 
(i.e. a BSF cell) would be of this type. 

Total Back Contact Requirements 

The back contact must be relatively free from the problems listed in 

Table 1, i.e., it must be capable of good optoelectronic performance. In 

addition, it must have the rest. of the characteristics listed in Table 2 if 

it is to contribute to meeting the DOE long range cost/performance goals. 

References 

1. MOD Silver Metallization for Photovoltaics, G. M. Vest and R. W. Vest, 

Quarterly Technical Report, December 1, 1983-February 29, 1984, DOE 

Contract No. NAS~7-100-956679. 

2. Development of Metallization Process, Alexander Garcia III? Quarterly 

Technical Progress Report, December 31, 1983, JPL Contract 956205. 

3. Development of an All-Metal Thick Film Cost Effective Metallization 

System for Solar Cells, Bernd Ross and Joseph Parker, Final Report, 

December 1983, DOE Contract No. NAS-7-100-955688. 

4. Accelerated Degradation of Silicon Metallization Systems, Jay W. Lathrop, 

Proceedings of the Flat~Plate Solar Array Project Research Forum on 

Photovoltaic Metallization Systems, DOE/JPL-1012--92, November 15, 1983. 

CAPABLE OF GOOD OPTOELECTRONIC 

PERFORMANCE 

ECONOMICALLY APPLICABLE TO LARGE 

AREA CELLS 

CONSISTENT WITH A PRACTICAL PROCESS 

SEQUENCE 

NON-DETERIORATING OF BULK SILICON 

PROPERTIES 

STRUCTURAL 

IMPURITIES 

COMPATIBLE WITH EFFECTIVE FRONT 

CONTACT TECHNOLOGY 

ADHERENT 

RELIABLE 

SOLDERABLE 

BACK CONTACT REQUIRE}ffiNTS 

TABLE 2 

R~ 

r----r----r--.---J1VV\J'v--o -

~--~----~----~----~----~+ 

FIGURE 2. Active (top) and ~assive 

(bottom). 2-port network sections. 

80 . 
:-----:--------, N 

p 

FI 3(a). Simp1 01 

c 11 section. 

p 

p+ 

FIGURE 3(c) . Ohm c cootac 

produc d 00 both ides 0 a 

ub trate . 

• 

UALITY 

p 

FIGURE 3(b) . Bo 0 contac 

s ruc ure produced on both 

des of a substrate. 

p 

FIGURE 3(d) . Geom ry fo 

ur ' og ohmic characteri t·cs 

p r·menta1 contac (top) . 

FIGURE 4. Segmented back contact structure. 

81 
N 

E 

~ 

« 

E 

I-j 

V mV 

zoo 400 GOO 

'30 

I~-

f,o~ UJ « 

E 

~ 

2.0 

10 

30 

L,~, zoo ~, 400 ~1 600 ,------/ V mV 

FIGURE 5. Dark V-I characteristic 

calculated for selected diode. 

FIGURE 6. Illuminated V-I 

characteristic calc~lated 

with J = 36 rnAlcm • 

se 

-200 

V mV 

1.00 400 600 

20 

L. __ 

'FIGURE 7. Ser~es resistance 

~ 1 n for 1 em • 

82 
-200 

-200 

V mV 

2.00 400 

2.0 

30 

FIGURE 8. Series "forward" 

diode. 

V mV 

2.00 400 

600 

600 

FIGURE 10. 

barrier. 

Effect of a "reverse" 

ORIGiNAL PAG~"S' 

OF POOR QUALITY 

V mV 

-200 

-200 

) 

83 

2.00 400 

2.0 

30 

FIGURE 9. Series "forward" 

diode with photocurrent. 

V mV 

2.00 400 

2.0 

30 

600 

600 

FIGURE 11. Effect of2ii "reverse" 

barrier with 10 rnA/cm photocurrent. 
I 

I 

I 

I 

j 

i I 

DISCUSSION 

CAMPBELL: Your discussion of the gridded back contacts: as I understand it, 

the requirement for a gridded back-contact system is more stringent than 

for the front contact in terms of coverage and so forth? 

LESK: I didn't mean to imply that it was tighter coverage problem. If you 

want to measure a system that looks good, you can put full coverage metal 

in the front or the back, the same metal or the same contact system, and 

it looks ohmic and you've got no resistance problems. You could still be 

doing some other things wrong; you could be putting impurities in the 

silicon, changing t,he structure, and so on, so you want to look also any 

photoeffects you might have in the back contact. 

CAMPBELL: I have a specific reference. You mentioned 10 lines per centimeter 

as being optimum for the back grid. 

LESK: 

ILES: 

LESK: 

No, I didn't say optimum. I did the calculation for that; in fact, 

that was five of each, five on the front and five on the back, and if you 

do that, and if you have a quarter of a centimeter of material, by going 

to that geometry where your current is flowing laterally over most of its 

path, its resistance is still very small. 

Here is a quick one. Do you have any views about the doubling the 

efficiency by using bifacial cells, talking about back contacts? 

Bifacial cells? Well, there is a lot written on that. I really don't 

know. If you want to make n-p-n-like structure and pick up the base contact in the middle and pick up two junctions --- is that what you are 

talking about? 

ILES: It seems a pity to spend a lot of time on the back contact and then not 

use it for generating additional current, in a sense, but it may be rather 

complicated, perhaps. 

LESK: All the schemes I've seen are much more complex because you've got to 

get the current out somehow, so you are faced perhaps with a double grid 

structure and a back, one ohmic and one p-n junction, and you've got to 

match your currents coming out of the top and the bottom, and that isn't 

the simplest. I have seen some results printed that are pretty good, but 

to my knowledge nobody has this in production. 

BICKLER: Arnie, I want to ask a question about this back surface you described, which would have a diode in the same direction as the main 

junction. I guess it relates to what Peter just said: where do you get 

the second cathode? 

LESK: Like an n-p-n structure? 

BICKLER: Well, if you have the end top cathode and bulk is the anode p what 

do you do beneath that? You could put another p as a p+ but what do 

you do for a cathode for that back layer? 

84 
I 

f 

LESK: Well, no, that's it, if you had -- let's say -- high resistivity and 

put a metal on there, you could form a Schottky barrier between the metal 

and the bulk. That would be the barrier on the back surface facing in 

the same direction as the p-n junction. The back-surface field junction 

tends to be in that direction. 

QUESTION: Could you tell us a little more about that good cell you've shown, 

having voc of 690 volts? 

LESK: A very good cell that's calculated from a lot of the numbers I've seen 

in the literature; n = 1. It wasn't made; it's calculated, just to show 

if you had that in terms of the front, how you can ruin it by what you do 

in the back. These numbers are not far from the numbers you were talking 

about as state-of-the-art. 

85 
BiSh-Efficiency Cell Concepts on Low-Cost Silicon Sheets 

INTRODUCfION 

R.O. Bell and K.V. Ravi 

Mobil Solar Enersy Corporation 

Waltham •• assach~setts 02254 N85-31621 

The stronsest leverase for reducins the cost of power senerated from 

solar enersy is the efficiency of the solar cell. It is easy to see that siven 

a tarset cost for electrical energy there is a minimum solar efficiency that 

must be exceeded even if the module cost becomes neglisible. This arises 

because of the balance of systems cost (land. support structures. power 

conditioning. wiring. etc.). For exampleD for competition with an intermediate 

load coal-fired plant. a module efficiency of above 101 must be maintained [1]. 

As this minimum efficiency is exceeded. the power costs fall rapidly. 

Thus. the drive to. produce high efficiency solar cells is very strong. 

If the technology does not have the potential for realizing this minimum value. 

then it will be non-competitive for the particular scenario projected. 

In this paper we will discuss the limitations on sheet growth material 

(primarily with reference to EFG) in terms of the defect structure and minority 

carrier lifetime. Using simple models for material parameters and behavior of 

solar cells. we will estimate what effect these various defects will have on 

performance. Given these limitations we can then propose designs for a sheet 

growth cell that will make the best of the material characteristics. 

When discussing solar cells. the material is often characterized in 

terms of a diffusion length. LD• whose square is directly proportional to the 

lifetime. ~. i.e •• Ln2 = D~. where the constant D is the diffusion coefficient. 

For a hoaogeneous ma¥erial the diffusion length is also a measure of the 

distance over which minority carriers are collected. For inhomogeneous 

material where the scale of the lifetime variations may be less than the local 

diffusion lensth. the meaning of the diffusion length as a collection distance 

breaks down. 

When techniques such as SPV or spectral response measurements are applied 

to measure diffusion lengths in inhomogeneous material. it must be kept in mind 

that the derived quantity. while often referred to as a diffusion length. is 

really a charse collection distance. It is a complex average dependins on how 

the minority carrier lifetime varies with position. Generally it is clear from 

the context if we are usinS diffusion length as a measure of local lifetime or 

. as a charse collection distance. 

PRECEDING PAGE BLANK NOT FILMED 

87 
I. DEFECTS 

The primary defects in silicon that show electrical activity, i.e., 

contribute to the majority carrier concentration or act as recombination 

ce:l]..!ers. are dislocat.i,.pns. grain boundaries, twins, inclusions including SiC 

anchsiliiates, point' defects of either a substitutional or interstitial 

chaDacter and impurities such as transition metals and oxygen and carbon [2]. 

There are other closely related defects such as swirls, stacking faults. 

partial dislocations, etc., but in this paper we will concentrate our remarks 

on the more gen~ral types listed above. 

F. Wald has recently presented a comprehensive review of defects in EFG 

silicon with a discussion of the type and number of defects [2]. Rather than 

including figures illustrating the defects, we will simply reference his paper. 

A. Dislocations 

The classic edge dislocation, which can be visualized as being formed 

by removing an atomic half plane. should exhibit a single line of silicon atoms 

whose bonding requirements are Jlot satisfied. In a simple minded picture, a 

dislocation would exhibit a series of dangling bonds. one of which is 

associated with each plane. If each of these atoms behaved as a recombination 

center. then for a dislocation density of 105 cm-z with a typical cross-section 

of 10-15 cm-a , the lif~time would be of the order of 30 ~sec which corresponds 

to a 300 ~ diffusion length in p-type material. 

In actual fact most of the broken bonds will be reconstructed [2] so the 

number of "dangling bonds" will be substantially less, thus giving a much lower 

potential for recombination. 

Another possibility might be that recombination occurs not at dangling 

bonds but rather at an impurity cloud attracted to the dislocations. If more 

than one electrically active atom were associated with each atomic plane. then 

the potential diffusion length could be reduced. We should note, though. that 

as will be discussed in Section lIB, having the electrically active 

recombination centers concentrated around the dislocations may actually result 

in a higher efficiency cell than if the same total number of impurities were 

uniformly distributed throughout the solid. 

B. Grain Boundaries 

When two grains with different orientations intersect. they form a 

grain boundary. First order and higher order twins can be considered a 

sub-class of grain boundaries. In the general case, grain boundaries can be 

constructed from a series of edge and screw dislocations. In twins a specific 

ori~'1.\tation between the grains exists, but for general grain boundaries this is 

nc t l~'!;;ce ssary. 

A convenient way to observe the electrical/recombination activity of 

dislocations and grain boundaries is by the use of EBIC. By making line scans 

perpendicular to the grain boundaries their recombination properties can be 

chara~terized typically in terms of a recombination velocity, v • and diffusion 

length, Ln [3,4]. Optical techniques. LBIC, have also been use! in a similar 

88 
~l '\ 

fashion to obtain the same material characteristics [4]. Velocities up to lOs 

em/sec have been observed with typical velocities for "strong boundaries" being 

the order of 10. em/sec. For such a velocity, the effective grain boundary 

width (L = 100 ~, a = 1000 cm- 1 ) is about 5~. The concept of an effective 

grain bo~dary width is due to Zook, and is defined as the equivalent width of 

a region from which no charge is collected. If we have a high density of 

strong boundaries (10~/cm), the loss in short circuit current can become 

significant ("). By no means do all grain boundaries have high recombination, 

and in fact many are electrically very weak or invisible. 

Also of importance is the contribu.Uon that grain boundary recombination 

can make to the reverse saturation current. A reduction of 5~ in the current 

collected corresponds to a decrease in the diffusion length by 351 for a 

homogeneous distribution of recombination centers. This would reduce the 

reverse saturation current also by 3,. and produce a decrease in open circuit 

voltage of about 10 mY. 

Grain boundary recombination can be important if the density of 

electrically active boundaries is high. Only in the case of small grain size 

such as produced by CVD or in silicon with a very high intragranular diffusion 

length will they dominate performance. " 

C. Inclusions 

The principal effect of inclusions is either to physically block the 

light or to shunt the junction. Typically, inclusions are found to be SiC or 

silicates. The contribution an ideal shunting particle mates to reverse 

leakage depends on its diameter and the sheet resistivity of the surface layer 

to which the shunting occurs. It is easy to show that for a circular shunt of 

radius, a, and sheet resistivity, Pc' the voltage drop, AV, for a distance, d, 

away from the particle is 

Pc Isc 

AV = 2 [d3 (ln(d/a) + 1/2) - a 3 /2] (1) 

For a typical I of 30 mA/cmz, AVof 0.25V, Pc of 50 O/c, the current 

not collected (which f~ equal to ndzI ) is about 5 iA/particle. In most cases 

the finite resistivity of the SiC limffs the current to less than that 

predicted by Eq. (1). The SiC density is genernlly less than one per cmz, and 

experimentally it is observed that such shunting is rarely a problem. 

In the unfortunate case, though, that the metallization covers the 

inclusion, the cell will be almost completely shunted since in this case Pc is 

very small (the order of S mO/C). Since only about 5~ of the solar cell is 

metallized, this is a rare occurrence. 

The fractional volume of a silicate particle is so small and the 

resistivity is so high that any contribution to losses by light blockage or 

shunting can probably be safely ignored. 

Measurements of the junction characteristics of EFG solar cells often 

show a contribution to the reverse saturation current that has a temperature 

89 
dependence characteristic of tunneling rather than space charge rec9mbination 

[5]. It has been suggested that this phenomenon could be due to very small 

precipitates that introduce charge centers into the space charge region. The 

loss in efficiency shows up as a soft knee and is easily measured using the 

dark I-V characteristic. 

D. Point Defects and Impurities 

So far the discussion has dealt with defects that are visible. at 

least under moderate magnification with an optical microscope or in an SEM. 

Point defects and impurities in sheet silicon are those that occupy either a 

single or a few lattice sites and cannot generally be directly imaged. The 

defects may be native. such as self interstitials or vacancies. metallic, such 

as Fe. Ti. MD. etc., or non-metallic. such as carbon and oxygen. Dopants such 

as Band P are in a sense substitutional defects. 

In order for a point defect or impurity to significantly affect the 

minority carrier lifetime (for the sake of definiteness we will talk about 

electrons in p-type material). its energy level must be located above the 

quasi-Fermi level for electrons, but not so near the conduction band edge that 

any trapped carriers can easily'be excited [6]. Shockley-Read-Hall (SRH) 

theory predicts that the most efficient recombination centers are located at 

the center of the energy gap. 

A large number of elements have been found to produce centers in the band 

gap of silicon. Their characteristics have been the subject of a number of 

publications. including those by Weber [7], Sze [8] and Schibli and Milnes [9]. 

The density of the centers must be high enough such that the probability of 

trapping a charge is significant. For a 1 ~sec lifetime with a reasonable 

cross-section (10-15 cm- 3 ), the trapping center density should be 1014 cm- 3 , 

which is a very small number in terms of chemical concentration. 

Thus, it is natural to expect that inadvertent contamination can 

drastically reduce the lifetime in silicon. In fact, it is surprising how 

tolerant EFG is to the level of metalli,: impurities. Typically impurity levels 

range from one to 10 ppm and have little correlation with cell performance. 

There is apparently a major difference between the total impurity content and 

those that contribute to recombination. Experiments [2,10] show that the 

introduction of Fe and Mo at concentrations up to 5 X 101 • cm-' can be 

tolerated. 

Besides the metallic impurities, other species such as carbon and oxygen 

are present in large quantities. The carbon comes from the crucible (if 

graphite) and die material, and the oxygen from the crucible '(i! fused quartz) 

and gaseous ambient. Individual carbon atoms in a silicon lattice are not 

electrically active but probably express their activity because of interactions 

with other defects. Oxygen when interstitial is not electrically active, but 

under various heat treatments forms complexes that act as donors or 

recombination centers. 

Oxygen has been shown to play an important role in producing EFG silicon 

with the longest diffusion length [11]. The oxygen can be introduced either 

from the ambient or from the crucible. The diffusion length for oxygenated EFG 

90 
J 

I . ! 

I 

I 

1 J 

silicon is not only higher than in EFG without additional oxygen at l~w light 

levels, but also it shows a stronger dependence on illumination level. 

In non-degenerate silicon, including CZ, float zone, EFG, etc., the 

lifetime is dominated by an SRH recombination process. This lifetime is 

generally found to decrease rapidly with doping density. Fuller [12] and 

Fossum et ale [13,14] have mo&eled the defect de~sity as if it were a chemical 

reaction driven by the doping density. The lifetime, ~, can be approximated to 

depend on the doping level, ND, as 

~ = ~ 1(1 + ND/N ) o 0 (2) 

where ~ is a constant that is a function of material quality. This is the 

e%pressYon used by Rohatgi and Rai-Choudhury [IS] when modeling high efficiency 

solar cells. Fer N they use 7 % 101 • em-I. 

o 

In one EFG experiment in which the boron concentration was varied to give 

resistivities between 0.2 and 10 O·cm, the data can be approximately fit with 

~ having a value of 0.7 ~sec [2,16]. By contrast the Auger recombination, 

e~en in high quality material, does not dominate until the resistivity is below 

0.1 O·cm. Other EFG material has been grown with a diffusion length of over 

ISO ~ at 4 O·cm which would imply a value of ~o of 10 ~sec. 

II • SOLAR CELL PERFORMANCE 

A good deal of work has been devoted to modeling the behavior of solar 

cells but mostly on homogeneous material (both with respect to depth and areal 

distribution). With ribbon material this is not necessarily a good assumption 

and at times the effect of inhomogeneous distributions of minority recombination 

centers, crystalline defects and majority carrier doping cannot be neglected. 

In this section we model the behavior of an EFG solar cell to determine 

how to get the most out of it. An outline of the technique is given in the 

Appendi%. It is similar to the approach suggested by Wolf [17] and can include 

surface recombination, doping dependent lifetimes including Auger .nd SRH, and 

band gap narrowing. Calculations based on the solution of the diffusion 

equation, including electric fields produced by doping gradients, give similar 

results when applied to the same cases modeled here. 

In the first part of this section we calculate the charge generation and 

collection distributions produced by the solar spectrum. Ne~t we discuss some 

aspects of inhomogeneous distributions of lifetime and effect on solar cells. 

Finally, the effect of resistivity and surface palsivation is considered. 

Of course, as whan attempting to extract the highest possible efficiency 

from any cell, it is important that the metal coverage be as little as possible 

consistent with a low series resistance and that any anti-reflection coating be 

optimized whether one or two layers. Because sheet growth materials, except for 

web, generally do not have a predetermined orientation, surface etching to 

produce faceting is not an option, although growth using a corrugated die to 

produce an equivalent effect may be possible. 

91 
A. Charge Generation Rate 

Figure 1 shows a plot of the charge generation rate for an AMI.S [18] 

spectrum in silicon [19]. By far the highest generation rate is close to the 

surface. If we integrate this curve and normalize it relative to the total 

possible hole eleQtron pairs produced (Fig. 2), we see that Sa. of the possible 

charge is generated within 5 ~ of the surface and 9a. within 150 ~. 

There is quite a long tail on the optical absorption so even though most 

charge is generated relatively near the surface, if we want to collect almost 

all minority carriers (95 to 9~) a very long diffusion length (the order of 

1000 ~) would be required. 

B. Areal Inhomogeneities 

Calculations have been made of the effect of areal lifetime 

inhomogeneities on solar cells. In general the regions with a low lifetime 

dominate the performance, both by the effect on short circuit current and open 

circuit voltage [20]. Although this result might, at first reading, seem to 

indicate that a homogeneous mahrial is best, it can be shown through simple 

arguments that when the total number of recomb.ination centers is held fixed, an 

inhomogeneous distribution can produce a cell with a higher efficiency than one 

in which the centers are uniformly distributed [21]. Thus, what at first glance 

might be considered a disadvantage of sheet grown silicon can really be an 

advantage. Assuming that the'behavior of recombination centers is independent 

of concentration, if,the recombination centers are concentrated in a few small 

regions, then the performance may be improved. 

Figure 3 shows a plot of the relative efficiency as a function of the 

amount of poor area. Depending upon the ratio of the number of recombination 

centers in the poor area to the good area. the maximum efficiency occurs when 

the poor area occupies between 10 and 3a. of the total cell area. Obviously it 

is better if the total number of impurities or recombination centers can be 

minimized, but if they are present it is desirable that they be segregated 

rather than uniformly distributed. 

C. Optimum Resistivity 

High efficiency solar ~ells have been made using either moderate 

resistivity silicon with a long lifetime or low resistivity with a moderate 

lifetime material. Recently, Green [22] has analyzed the effect of Auger 

recombination on the open circuit voltage and efficiency and concludes that for 

heavily and lightly doped material, Auger recombination place.s the most 

stringent limitation on solar cell performance. He estimates a maximum open 

circuit voltage of about 720 mV for "thick" cells. As we have seen in Section 

lID, the observed practical lifetime limit of the base is not Auger but is 

probably related to a defect/dopant interaction. 

Figure 4 shows a plot of the calculated efficiency assuming that the + 

lifetime is given by Eq. (2) with ~ of 1 and 10 ~sec. The parameters of the n 

region have been adjusted so that tRey do not contribute to losses of the solar 

cell. Clearly a 1" efficient solar cell can be made for the larger value of ~o 

but not.for the lower value. 

92 
j 

1 

! 

I 

~ 

D. Surface Passivation 

In the analysis made above, it was assumed that the the surface was 

well passivated, i.e., recombinatipn was nellisible. Much re~ent work 

demonstrates th~ importan~e of the correct treatment of the n rei ion if the 

maximum is to be obtained from solar cells [15,23,24]. With a base lifetime of 

10 psec, the effective recombination velocity. v = D/L, must be less than about 

2 x 10· em/sec. To be base limited requires that the contribution from the 

emitter. includinl surface and material recombination, must be less than this. 

Techniques have been developed for passivatinl both float ~one and CZ 

[15.24]. There is no r.eason to bel ieve that they ca~ot be applied to sheet 

Irown materials. At the doping levels used in the n layer, Auger limitations 

on the lifetime should be dominant even in relatively low quality material. 

Auger recombination varias like the square of the doping density. whereas 

defect/doping recombination varies direQtly with dopinl density. This means 

that at high enough doping the ultimate limitation will be Auser. The inherent 

built-in electric fields produced during any diffusion process. especially for 

shallow junctions. will minimize emitter recombination. 

II I. SUJDlARY 

The opUmum EFG cell will have the hilhest dopinl consistent with the 

defect/dopins limit on lifetime. It probably will be below 1 O.cm. The 

junction depth will be shallow with a nheet resistivity of at least 100 0/0. 

Green et al. [23] have shown that the sheet resistivity needs to be above 100 

0/0 if the recombinttion is to be dominated by the surface rather than the bulk 

properties of the n res ion. 

The thickness of the base will probably be determined by the ability to 

handle thin sheets rather than the requirement for any back surface field. With 

modest diffuiion lensths, the sain in efficiency with back surface fields is not 

important until the substrates are so thin that practical·handlins problems rule 

out their use. For example, the peak efficiency for a 100 pm diffusion length 

BSF cell. peaks at a sample thickness of about 60 pm, but it is only about 81 

better than a thick <) 300 pm) solar cell. 

Another critical aspect is to oontrol the lifetime of the finished cell. 

Post fabricadon techniques have been developed. suoh AI hydro.en passivation, 

to improve material quality after fabrication [25]. This works well even thou,h 

only a relatively thin re,ion is affeoted because the open cirouit volta.e and 

fill factor are controlled to a lar,e extent by the material properties very 

close to the surface. . 

IV. OONCLUSION 

The achievement of hilh cell efficienciel in Iheet lilioon. ,rown at hi,h 

rates and prone to oontain lilnificant den.~tiel of imperfections and 

impurities, requires developments in both crYltal ,rowth teohnoio,y and oell 

prooesalnl approaohes. Variations 'in orystal ,rowth of importanoe include 

control over defect Itruoture and impurity oontent. Key developments include 

the followin,: 

93 
~l 

'-J 

I 

<a) 

(b) 

Control over impurity content in crystal growth from the 

~elt is needed to decrease the number of lifetime reducing 

impurities. In the case of EFG, this includes appropriate 

purification of elements of the crystal growth machine. 

Control over defect structure and density is needed to 

minimize defect-impurity interactions. Areas .of interest 

here include reduction in plastic deformation as a 

consequence of post-growth heat treatment and the 

minimization of residual stress. In this context, it is 

preferable to increase the area rate of production by the 

growth of wide crystals grown at moderate linear growth 

rates than by increasing linear growth rates, since defect 

generation by plastic deformation in response to 

thermo-elastic and thermo-plastic stresses appears to be a 

stronger function of linear growth rates than of the 

crystal width. 

(c) The influence and role of carbon in silicon continues to be 

an unknown quantity. A better understanding of the 

influence of carbon (and oxygen) on electrical phenomena in 

silicon is needed. 

Device processing impli~ations are many. The key ones have been touched 

upon in this paper. The fundamental issue is one of achieving the optimum 

synergy between base-material quality and device processing variables. At the 

current stage of development of low-cost silicon sheet technologies, a strong 

coupling between material quality, and thus the variables during crystal growth, 

and device processing variables exists. The challenges are twofold: (1) the 

optimization of this coupling for maximwn performance at minimal cost, and (2) a 

decoupling of m-aterials from processing by continual improvement in base 

material quality to make it less sensitive to processing variables. 

94 
Appendix - Solar Cell Efficienoy Calcplatiop 

A number of different sohemes to model sol~r cells have been developed 

over the years sinoe Prince [26] showed how oell effioienoy varied with band 

gap. Probably the most accurate and mathematically rilorous is that by Hauser 

and oo-workers [27,28]. They solve the funda.ental device equations but the 

procedure is complicated and requires large amounts of computer time. Other 

first order models such as the use of a shifted diode ourve, a typical example 

being Wysocki and Rappaport [29], do not generally allow for inclusion of 

effects such as electric fields, heavy, doping and baok surface fields. 

Recently though, Wolf [17,30] has suggested a technique which relies on 

the simplicity of the diode model but allows inclusion of heavy dopinl effects 

by the concept of a so-called transport velocity. This id'ea was introduced by 

Gunn [31] for the study of carrier accumulation associated with semiconductor 

junctions. Bowler and Wolf [17] have used the technique to make estimates of 

the ultimate efficiency of solar cells and how they depend on various 

geometrical and material parameters. 

We have adapted their procedure to examine what might be expected for EFG 

material. The transport velocity concept was combined with models of charge 

generation and collection to look at the solar cell output paxameters. 

Theory 

As shown by Gunn [31], for p-type material the diode current at any 

position, j(x), can be expressed by 

j(x) = qn(x}u(x) (A1) 

where n(x) is the minority carrier density, u(%) is the transport velocity, and 

q is the electronic charge. 

If the diffusion coefficient. D, and minority carrier diffusion length, L, 

are constant over a region 'between x and x', u(x) transforms such that 

u(x) 

D [ u (~ , ) L + tanh x ~ x' ,] 

= L 1 + u(x')L x - x' 

D tanh L 

(41) 

Thus, if we know the value of u at some position x', then with Eq. (A~) we can 

calculate it at x. If the various parameters are not constant, then the region 

can be divided up into steps such that the variation is small over any liven 

region and repeated applications of Eq. (41) can be use. Note that as (x - x') 

becomes large compared to L, '11(X) goes to D/L. 

The transformation for a+high/lo¥ junction (a chanle in carrier 

concentration such as at a pip or nln + junction) is 

95, 
(Al) 

At the junction, n(x.) is determined by the barrier height, V, such that 

J 

n.a 

n(x.) =-1:._ [exp(qV/kT) -1] J p 

where n. is the intrinsic carrier concentration. 

1 

(A4) 

Combining Eqs. (AI) and (A4) at t~e junction and using the light generated 

current, jsc' to offset the diode equation, we obtain 

j = jo [exp(qV/kT) 1] + jsc (ASa) 

n.a 

1 

jo = q - u(x.) P J (ASb) 

A similar treatment will give the contribution from the n region. Also, 

to account for recombination in the space charge region, a term of the form 

j '[exp(qV/2kT) - 1], where j" = qn.W/~ is added to Eq. (ASa). W is the width 

o~ the space charge region ana ~ = L!/D is the lifetime. 

Thus, to model a solar cell, we divide it up into regions where the 

properties are uniform. Starting with a value for the surface recombination 

velocity, S, where u(x) = S, we apply either Eq. (Al) or (Al) repeatedly until 

we have arrived at the J·unction with a value of u(x.). We next calculate J. J sc with an expression of the fo~m 

"'min 

j = qJ (1 - R(A» f/J (A) Q(A) dA 

sc (A6) 

o 

where f/J(A) is the flux for the desired spectrum (here we have used AM1.S [11] 

normalized to 100 mW/cma), Q(A) is the charge collection discussed below and 

R(A) is the reflectivity at the+front surface. The contributions from the space 

charge region and the surfaee n layer also are added to j . se 

The solar cell is now characterhed by Eq. (AS) whe:n J , j , and j . 0 0 sc depend on materlal and geometrical parameters. Because of surface coverage by 

the metal g~id and optical losses in the AR coating, R(A) is not zero. For 

simplicity, in the calculation R(A) = 0.15 was used for all wavelengths. The 

peak power, Pm' is given by d(jV)dV = 0 and the open circuit volt.ge by 

j(Voc ) = 0, both of which expressions,were evaluated numerically. The fill 

factQr, W. h 

FF = P IV J. 

m oc sc (A7) 

96 
A couple of other itoas aust also be included. At hilh carrier 

concentrations. Auger and defect/dopinl recoabination becoaes important and 

their effect on lifetime is included. D allo depends on carrier concentration. 

Through band lap narrowing. ni varies at high dopinl levels. Appropriate models 

for thele dependencie& were uled. 

Calculation of Q(A) 

The basic equations goyerning the flow of minority carriers in a 

semiconductor are the current equation and charle continuity equation [19], 

which in one dimension are 

J

' = nE+ D!J! n q J1 q ax 

U is the net recombination rate and normally is set equal to n"':. At 

equilibrium where an/at = 0 and with no electric field. i.e •• E = O. by 

substituting Eq. (A8) into (A9) we obtain the diffusion equation 

(AS) 

(A9) 

(AlO) 

G is the optical generation term. For the geometry shown in Fig. Al. 

where light can reflect off the back surface, G will be 

G = a[exp.(-ax) + R exp(a(x - 2d»] (All) 

where R is the reflectivity of the back surface. 

We use the general boundary conditions that the carrier concentration is 

zero at the front junction and that the current, including surface 

recombination, is continuous at x = d 

n = 0 at x = 0 

q D dn = Snq - 1 dx 0 

x = d 

10 is the current produced in the region outside d. 

de temined by 

1 = q D ~ P dx at x = 0 

97 

The current, 1 • is 

p. 

(Al2a) 

(Al2b) 

(AU) 
The solution requires some algebrnic manipulation and is as follows. 

1 = gaL [K_ + K+R e-2ad] p 1 - (aLP 

+ 10/[cosh(t/L) + ~L sinh(t/L)] 

where K+ = [(D/L ± aLS) + (S ± aD)ctnh(t/L) 

- exp(~t) (S ± aD)/sinh(t/L)] 

I[D/L ctnh(t/L) + S] 

For the n+ layer, a similar expression, 1 , is obtained. It is 

essentially Eqs. (*14) and (A1S) with t replace! by -t' where t' is the 

thickness of the n region. 

(A14) 

(A1S) 

After multiplying by a factor that accounts for the optical absorption in 

the n+ layer, the charge collection, Q(A) used in Eq. (A6) is just 

Q(1) = (1 + 1 )/q p n (A16) 

Typical results are shown in Fig A2 where the efficiency is plotted as a 

function of thickness of the base thickness for various resistivities. diffusion 

lengths and back surface conditions. 

98 
REFERENCES 

1. Five Year Research Plan, 1984-1988, Photovoltaics: Electricity from 

Sunlight, DOE/CE-0072, U.S. Department of Energy, ~~y 1983. 

2. F. Wald, Presented at the European Materials Research Society and to be 

published in 1. Phys. Applique. 

3. I.D. Zook, Appl. Phys. Letters, 37, 223 (1980). 

4. C. Donolato, 1. Appl. Phys., 54.1314 (1983). 

5. G.F.l. Garlick and A.H. Kachare, Appl. Phys. Letters, 36, 911 (1980). 

6. 1.1. Hanoka, R.O. Bell and B.R. Bathey. Proc. of Sym. on Electronic and 

Optical Properties of Polycrystalline or Impure Semiconductors and Novel 

Growth Methods, (Ed. by K.V. Ravi and B. O'Mara) p. 76, (The Electrochem. 

Soc. Pennington, N.l., 1980). 

7. E.R. Weber, Appl. r~ys. AlO, 1 (1983). 

8. S.M. Sze, "Physics of Semiconductor Devices", (Wiley-Interscience, New 

York, 1969), p. 30. 

9. E. Schibli and A.G. Milnes. Mater. Science Engr., !, 173 (1967). 

10. Private communication. M.C. Cretella and B. Bathey. 

11. B. Mackintosh, I.P. Kalejs, C.T. Ho and F. V. Wald, Proceedings of the 

Third CEC Photovoltaic Solar Energy Conf., Ed. W. Palz (Dordrecht, D. 

Reidel, 1980). 

12. C.S. Fuller, "Defect Interactions in Semiconductors", Semiconductors, 

(Edited by N.B. Hannay), Academic Press, New York (1975). 

13. I.G. Fossum and D.S. Lee, Solid State Electron., 25, 741 (1982). 

14. I.G. Fossum, R.P. Mertens, D.S. Lee and I.F. Nijs, Solid State Elect~on. 

26, 569 (1983). 

15. A. Rhohatgi and P. Rai-Choudhury, IEEE Trans. Electron Dev., ED-31, 596 

(1984) • 

16. Private communication M.C. Cretella. 

17. D.L. Bowler and M. Wolf, IEEE Trans. Components, Hybrids and Manufacturing 

Tech., CHMT-3, 464 (1980). 

18. ASTM Standard E-891, "Terrestrial Direct Normal Solar Spectral Irradiance 

for Air Mass 1.5". 

99 
19. D.E. Aspnes and A.A. Stunda, Phys. Rev. B, 27, 985 (1983). 

20. F.A. Lindholm, ~.A. Mazer, ~.R. Dacis and ~.I. Arreola, Solid State 

Electron., 23,967 (1980). 

21. R.O. Bell, Solid State Electron., ~~, 175 (1982). 

22. M.A. Green, IEEE Trans Electron. Dev., ED-31, 671 (1984). 

23. M.A. Green, A.W. Blakers,~. Shi, E.M. Keller and S.R. Wenham, IEEE Trans. 

Electron. Dev., ED-31, 679 (1984). 

24. M.B. Spitzer, S.P. Tobin and C.J. Keavney, IEEE Trans. Electron. Dev., 

ED-31, 546 (1984) 

25. ~.I. Hanoka, C.H. Seager, D.J. Sharp and J.K.G. Panitz, Appl. Phys. 

Letters, ~, 618 (1983). 

26. M. Prince, ~. Appl. Phys., 26,534 (1955). 

27. P.M. Dunbar and J.R. Hauser, A Theoretical Analysis of the Current-Voltage 

Characteristic of Solar Cells, Semioonductor Device Laboratory, North 

Carolina State University, Raleigh, NC, NASA Grant NGR 34-002-195, August 

1975 and August 1976. 

28. R.C. Y. Fang and J.R. Hauser, ibid., September 1977 and January 1979. 

29. J.J. Wysocki and P. Rappaport, J. Appl. Phys.j 31, 571 (1960). 

30. M. Wolf, IEEE Trans. Electron Devices, ED-27, 751 (1980). 

31. J.B. Gunn, ~. Electron.-Contr., !, 17 (1958). 

100 
,... 

o 

,... 

-u • { 

u 

a: 

: 

III 

~ ex: 

z 

o 

j: 

;I 

III 

Z 

III 

c:I 

I~~' --------~--------~--------~ 

loZl 

AM 1.5 SPECTRUM 

IOOmW/cmZ 

SURFACE 

10", IOO~~~~ 10 I 

DEPTH BELOW SURFACE (~m' 

0.1 

Fig. 1. Charge generation rate as a function 

of depth below the surface of the 

standard AMl.5 spectrum. -

IOO,r--------.--------.--------.---------

C 

III 

~ 

C 

a: 

III 

z 

III 

c:I 

III S c:I 

ex: 

c 

% 

0 

~ • 

0.1 1.0 -10 

THICKNESS (~m) 

(lSC'm •• = 43.6 mA/c~ 

100 ""/C~ 

All 1.5 

100 1000 

Fig. 2. Relative number of hole-electron pairs generated 

between the surface and depth t. The curve is 

normalized with respect to the number of photons being absorbed in a thick piece of silicon. 
tVNz=IO 

o os 

AlIA 

L.= 10 fJ- m,AMI.5 

1.0 

Fig. 3. Normalized solar cell efficiency as a function of poor 

area for different relative numbers of recombination 

centers. 

20~-----------r------------r------------r-----------' 

't.= 15 f'-S 

't.=I,...S 

0.01 0.1 10 100 

~ (a.·em) 

Fig. 4. Efficiency of a solar cell as a function of resistivity whose minority carrier lifetime varies as given by Eq. (2) in the text. 

102 
n=O 

(a) 

(b) ~ 

-

F" 

10 

d ____ .... 

t--_ 

R 

OZJLm 

Fig. Al. Geometry used to calculate 

solar cell performance. The 

photons are incident on the 

left-hand side. 

5 = 103 cm/S --........ '1--"------..... - ... 

t 

L=200 ,...ml 

411'cm I L=200 ,...m 

2A'em 

1000 

Fig. A2. (a) Physical dimensions and electrical parameters used in calculating solar cell perfonmance. (b) Calculated efficiency of 

solar cell as a function of total sample thickness for various 

diffusion lengths and resistivities. The curve labeled No BSF 

is the result with no back surface field being present. 

103 
-I 

-~ 

" 

\ 

DISCUSSION 

DYER: Is there still a preferred orientation of the grain structure in these 

sheet structures, and is that [110], the surface of it? 

BELL: The surface tends to be OK, the orientation is a {211}. Correction: 

it tends to be. 

DYER: What about the surface? 

BELL: I believe it is close to [110], we call it an equilibrium structure. As 

you grow, no matter what orientation you start with, you are growing to a 

certain distance. It essentially tends to become {211}. 

DYER: How close is that to <110>? Is it plus or minus 10 degrees, five 

degrees---? 

BELL: Ten or 20 degrees is the type of thing that one sees. 

QUESTION: You mentioned the possibility of silicon carbide particles shunting 

the junction. Have you run into a situation where a grid line hits a 

particle? 

BELL: Yes, I should mention that in the unfortunate event that a grid line 

hits a particle, the cell is shorted. Luckily, if you only have 5~ good 

coverage and something less than 1 per cube per cm2, the probability is 

fairly low. 

QUESTION: As you go to larger cells the probability of that will increase. 

BELL: That's right, but even_when we are talking about 50 cm2 cells it is 

well under O.l~, I really don't know what the statistics are but it is 

quite low. 

LESK: Ast has written several reports in which he uses a 12000C anneal on 

EFG materials, passivates the grain boundaries at this location. The results in his reports are quite striking. You haven't mentioned that 

bydrogen passivation. I wonder if you might comment on which one works 

best. 

BELL: We find, certainly, that the heat treatments that one gives to the 

material c~n have fairly dramatic effects on its behavior. We have found 

that if one goes to a high temperature, like to 12000 , for a fairly 

short period of time -- 10 minutes to a half an hour, something like that 

-- often one finds an improved performance. The problem is, we are 

dealingwith a fairly complicated situation; material grown from e quartz 

crucible and material grown from a carbon crucible often have somewhat 

different behavior. Although people from Mobil and others have had a lot 

of theories and ideas on what is going on, in my mind there is no clear 

picture. Th~re is a lot of interaction going on. 

QUESTION: I would like to ask a question about hydrogen passivation. Are 

104 
these passivating the grain boundaries, mainly, or also impurities and 

defects? How do you apply it in the high-temperature form, atomic form 

or cosmic form? 

BELL: I really wish I had another slide to show the grain. Jack Hanoka is 

going to discuss the work that we have done with hydrogen passivation; 

I'll just say that it does passivate the grain boundaries and other 

parameters, but we will let Jack talk about the details. 

. 105 
HIGH LIFETIME SOLAR CELL PROCESSING AND DESIGN 

R. M. Swanson 

Stanfol"d University 

Stanford, California 

Introduction 

In order to maximize erriciency a solar cell must, a) absorb as much light as possible in electron-hole 

production, b) transport as large a fraction as possible of the electrons to the n-type terminal and holes to 

the p-type terminal without their first recombining, and c) produce as high as possible terminal voltage. 

Step a) is largely fixed by the spectrum of sunlight and the rundamental absorption characteristics of 

silicon, although some improvements are possible through texturizing induced light trapping and backsurface reflectors. Steps b) and c) are, however, dependent on the recombination mechanisms or the cell. 

The recombination, on the contrary, is strongly influenced by cell processing and design. This paper 

presents some of the lessons learned during the development of the EPRI point-contact-cell (1). 

Cell Dependence on Recombination 

A useful way to visualize solar cell operation is through the following pair of equations: 

I=Ih-1 p ree 

. V = (kT/q)ln(pn/n.2) - V 1 res 

(1) 

(2J 

The first equation is easily derived by integrating the continuity equation (1, p. A-I) and says that the 

terminal current, I, equals the photo-current of electron-hole pairs, I

ph' minus the recombination current, 

I . In this case the recombination current must be defined as follows ree 

I =1 +1 +1 +1 ree bulk surface p,n cont n,p cont (3) 

The nature of each term in (3) will be described briefly here and then in more detail in the next section. 

Ibulk is the bulk recombination throughout the entire volume of silicon. In otherwords, ir the steadystate electron-hole volume recombination rate is R, then Ibulk is the volume integral of R throughout the 

entire device. 

I rf is the recombination occuring at the surface in regions with no metal contact. su ace 

I t is the current of holes flowing into the n-type metal contact (ie., the minority carrier 

p, neon 

recombination current) and I t that of electrons flowing into the p-type metal contact. 

n, peon 

To a first approximation the terminal voltage is simply related to the pn product through equation (2) 

which, in effect, assumes constant quasi-Fermi levels throughout the device. Even though the actual pn 

product varies with position in a real device, this equation reveals the essential element in device design 

because, along with voltage, all the recombination mechanisms increase with pn product. Thus the 

maximum power point occurs at that pn product which balances recombination loss with voltage gain. 

Improving efficiency comes down to reducing recombination as much as possible. 

The last term in equation (2) is the resistive loss in the cell. In devices which rely on conductivity 

modulation to obtain low base region resisitive loss it is additionally important to maintain a high pn 

107 

PRECEDING .PAGE BLANK NOT FILMED 
1 

"' 

product to provide as mu~h conductivit.y modulation as possible. Thus these devices are particularly 

sensitve to recombinataion. 

Reducing Recombination 

TY{ltcally bulk recombination is a combination of devect related recombination (which is usually 

modeled by a Shockley-Read-Hall (SRH) type formula., without any real experimental justification), Auger 

recombination, and radiative recombination. In this case one has 

where 

R = vt"NT [ I 

.~ n + n;exp( ~,;:E; )1 + .~ [p + n;exp( - Ez",;:E; )1 

pn-n? 

+ B(pn - nj

2

) + Cn(n2

p - no

2po) + 

C (p2n _ p 2n ) 

p 0 0 

B = 2 X 10-15 cm3/sec 

C = 3 X 10-31 cm6/sec n . 

C = 1 X 10-31 cm6/sec 

p 

(radiative recombination) 

(eeh Auger coefficient) 

(ehh Auger coeCCicient) 

(4) 

The radiative term is usually negligible, except when discussing fundamental limits where the remaining 

recombination terms have arbitrarily been set. to zero. The magnitudes of C and C are somewhat in n p 

dispute but are undoubtedly within an orger of magnitUde of those shown in equation (4) which are from 

(2). The designer can control Auger recombination only by varying the doping density as a function of 

position in the device. 

The deCect related (SRH) term is strongly dependent on the nature and concemtration oC process induced 

defects and contaminants. Typically a matel'ial will have both donor and acceptor type deep level deCects. 

Undcr low level injection acceptors will usually dominate the recombination process in n-type material and 

vise-versa in p-type material. This is because hole capture in n-type material would be the rate limiting 

process and hole capture is an attractive process Cor acceptors. Under high level injection the SRH 

recombination lifetime becomes T = l/Ntvth{l/an + l/a

p)' Since one oC the capture processes (electron 

or hole) must be attractive and the other neutral one would expect that under high level injetion the 

IiCetime would be considerably greater as the neutral capture becomes rate limiting Cor both acceptors and 

donors. We have Cound that high level bulk liCetimes over 1000 JlS can be obtained in completed devices 

when high resil!itivity float-zone silicon is used as the starting material. The low-level liCetime is typically 

a Cactor of 3 to 10 less. Careful processing is required to routinely obtain high lifetime. We have Cound 

the following procedures suCficient (but not necessarily necessary) to this end. 

a) Never use metal tweezers to handle wafers. 

b) Always perform a RCA (3) clean prior to high temperature steps. 

108 
c) Process in a class 100 clean area. 

d) Perodically clean furnace tubes with Hel. 

surface recombination 

Surface recombination appears to be more a function of the preparation procedure for rorming the 

passivating oxide layer, rather than being highly sensitive to contamination as is bulk recombination. 

Those procedures that have been found to produce high quality Si-Si02 interraces for MOS transistors 

appear to minimize the surface recombination velocity. 

Dry thermal oxidation followed by a low temperature hydrogenation produces surfaces with a mid-gap 

interface state density of around 1 X 1010 /cm2

eV. Figures 1 and 2 show the measured interrace state 

density for such an oxide in the upper and lower portions of the bandgap, respectively. These 

measurements, done using DLTS, show no evidence or the so called U shaped continuum but rather a 

monotonic decrease from conduction to valence band. 

By performing an inert atmosphere anneal after oxidation the density of interface states can be reduced 

to about 1 X 109 /cm2eV. Such a surface has a measured high level interface recombination velocity of 2 

to 5 em/sec. This rather low value can be understood by referring to figures 3 and 4 which show the 

measured electron and hole capture cross-sections (4). One finds that the electron capture cross section is 

generally orders of magnitude larger than that for holes. Under high level conditions most of the 

recombination will occur for those states where (J and (J are approximately equal. This occurs at about n p 

0.2 e V below mid-gap where they are in the mid 10-16/ cm2e V range. At higher energies (J becomes 

p 

smaller and limits the recombination rate, and similarly for (J. Using the data of figures 1 through 4 to n 

calculate the recombination velocity using SRH theory yields 2 cm/sec, in agreement with mesurements. 

(This calculation assumes that the interface charge is small enough to produce negligible band bending.) 

The data of figures 3 and 4 indicate the surprising result that p-type surfaces should have a much larger 

recombination velocity than n-type because of the large differences in cwss sections. We are currently 

investigating whether this is proves to be the case. 

Furt-her work is needed to develop methods which produce MOS quality interfaces on very thin oxides 

suitable for use under anti-reflection layers. 

contact recombination 

Keeping carriers fr,?m the contact m'~tal proves to be a most challanging problem of the cell design. The 

traditional approach is to create potential barriers by doping which are sufficiently wide to support a 

significant diffusion potential (ie., the gradient in pn product across the barrier does not cause too much 

minority carrier current). 

Because of tbe well known confluence of heavy doping effects such as reduced bandgap and lifetime such 

barriers are not as effective as one might want. Never-the-Iess, it can be shown (1, p. AS) the 

recombination current in the barrier and contact ca.n always be writen, so long as the doped barrier is not 

high level injected, 

I = Io(pn/n.2 - 1) rec . I (5) 

109 
where the pn product is evaluated in the space charge region at the edge or the barrier. 10 will he called 

the barrier saturation current in analogy with the terminology or ideal diode theory. Indeed, ir the 

separation or quasi Fermi levels at the space charge region equals the applied terminal voltage then 

equation (5) gives the typical 

I

ree = lo(exp(qV /kT) - 1) (6) 

Calculated saturation currents appear in figures 5 and 6 ror Gaussian n-type doping profiles (6). Notice 

that in regions which have a high recombination velocity such as under metal contacts, deep dirrusions 

with surrace concentration around 1020 cm_3 produce the best results. If such dirrusions are used to keep 

carriers away rrom surraces Our experwith low recombination velocity, then shallow dirrusions with 

surrace concentration around 101U cm-3 give the best results. Our experience, however, is that ~n this case 

no difrusion at all is the best choice, provided the surface is well passivated. or course, in a conventional 

cell the surrace diffusion has the additional role or transporting majority carriers to the contacts and 

cannot be simply eliminated. In cells with high lifetime and hence long dirrusion length, it is possible to 

rely on diffusion of carriers to the contact regions and dispense with the surrace dirfusion except under the 

contacts. This is the approach of the point-con tact-cell (1). 

It is interesting to compare the relative magnitudes or the various sources or recombination. Assuming 

that, a). we have a 100 /Lm thick undoped base with a high level liretime or 1000 /LS, b) the surrace 

recombina.tion velocity is 2 cm/sec, and c) the nand p barrier saturation currents are both 3 X 10-13 

A/cm2 the methods or the preceeding sections can be used to calculate the recombination currents. 

When the pn product is (1017 cm3)2, as might occur in a concentrator cell, one calculates the rollowing: 

bulk, SRH 

bulk, radiative 

bulk, Auger 

surface 

dirfused regions 

J A/cm2 

ree 

0.160 

0.032 

0.160 

0.064 

28.5 

These results show the overwhelming influence or contact recombination on the operation or the cell 

when the other sources or recombination are reduced by carerul processing. At a pn prod~ct or (3 X 1015 

cm-3) 2, as might occur at one sun, these results become 

bulk, SRH 

bulk radiative 

bulk, Auger 

surrace 

dirrused regions 

I mA/cm2 

ree 

4.8 

2.9 X 10-2 

4.3 X 10-3 

1.9 

25.7 

At one sun the contact recombination dominates the other sources or recombination , though not so 

completely as in the concentrator case; 

110 
references 

1. R. M. Swanson, ·Point Contact Silicon Solar Cells,· EPRI report AP-2859, May 1983. 

2. J. Dziewiour and W.Schmid, Appl. Phys. Lett. 31, p. 346 (1977). 

3. W. Kerm and D. A. Poutinen, RCA Review, June 1970, pp. 187-207. 

4. R. M. Swanson and W. D. Eades, being prepared ror publication. 

111 
, 

, 

~ 

l 

1011 

-- .... I 

" 

> 

QI ~ 

I N 

I 

E 

u 

-

>-

l- i- -

1 

(/) 

z , 

1 W 

o 10 I 10 I- -! 

I a.. .... i <{ 

a:: ~ 

IW ~ 

U 

<{ 

L!-

a:: ~ 

w 

IZ 

9 

1~0.4 

QS-HF 

C-V 

I 

-0.2 

x· ... _-_ .... --- ... --- --~. x-.......... 

_x-x-x-xe=--- -.- .-- ...---_ .... --- ... 

, 

MID 

GAP 

TRAP ENERGY (eV) 

• • x DLTS 

x 

I 

0.2 

Figure 1. Density or interrace states in the upper portion or the bandgap. 

112 

0.4 
--• > 

ClI 

N 

• E 

u 

-

>-

l-

(/) 

Z 

j.U 

-0 

a. 

« 

ct 

IW 

U 

« 

u.. 

ct 

W 

IZ 

1011r----------------------------------------

-

109~ ______ ~~ ______ ~ ________ _L ________ ~ 

MID 

GAP 

-0.4 -0.2 0.2 0.4 

TRAP ENERGY (eV) 

Figure 2. Density or interface states in the lower portion or the bandgap. 

113 
10-

12 __ ---------------------------------, 

u 

-

z 

o 

-..... 

u -13 

UJ 10 - (/) ~ 

(/) 

(/) 

o 

n:: 

·U 

-

--at::. 

cP .... ~ 0 ~ f ~\ A OJ UJ 

a:: 

:::> 

..... 

Q. « -14 

U 10 fz Io ln:: 

/ \ 

f \ ..... 

U 

W 

...J 

UJ 

I- 0 5.0 ms 

c 2.5 ms 

A 0.5 ms 

9 = 1 

c 

\ 

10-15~ ___ ~1 ______ ~1~---~~1---~1~---~~1---~1~~~ -0.1 MID 0.1 0.2 0.3 0.4 0.5 

GAP 

TRAP ENERGY (eV) 

Figure 3. Electron capture cross section or Si-Si02 interrace states. 

114 
10-14 __ ------------------~----------__, 

C'I -

E 

u 

-

Z 

~'0-15 

U 

UJ 

(/) 

(/) 

(/) 

o· 

a:: 

u 

UJ 

a:: 

::J 

:J: 10-16 

« 

u 

UJ 

-I 

o 

::t 

o 

.5: 

o 5.0 ms 

o 2.5 ms 

AO.5 ms. 

9 = 1 

-17L-__ -L ____ ~ __ ~~--~--~~--~~~ 10 -0.5 -0.4 -0.3 -0.2 -0.1 0.2 

TRAP ENERGY (eV) 

Figure 4. Hole capture cross section of Si-Si02 interface states. 

ll5 
1 

I 

I 

1 

s= CD em/sec 

- 1020 M 

I 

E 

0 

-

Z 

0 

..... 

« 

n:: 

..... 

z 

UJ 

U 

Z 

0 

U 

UJ 1019 

u 

« 

Un:: 

::J 

(J) 

100 70 50 30 20 15 10 7 5 

EMITTER SATURATION CURRENT (10-13A Icm 2 ) 

1 10 

EMITTER 'THICKNESS (f-Lm) 

Figure 5. Calculated saturat,ion current density ror Gaussian profile emitters with infinite surface· 

recombination velocity. 

116 
5 4 

- 10 C") 20 I 

E 

u 

---

Z 

0 

t( 

0:: 

.... 

Z 

UJ 

U 

Z 

0 

U 

UJ 

1019 u 

« 

u. 

0:: 

::J 

(/) 

0.8 0.9 1.5 2 3 

EMITTER SATURATION CURRENT (10- 13 A/cm2 ) 

1 10 

EMITTER THICKNESS (p.m) 

Figure 6. Calculated saturation current density ror Gaussian emitters with s = 103 em/sec. 

117 
, .' . 

I 

"4 

DISCUSSION 

LINDHOLM: Dick, I have a couple of questions. The first is in connection 

with your last remark. Do you think you need a two-dimensional code or a 

three-dimensional code? 

SWANSON: For the point contact cell I think you need a three-dimensional code. 

If you made the lines as st~ipes, a two-dimensional code would be 

adequate. 

LINDHOLM: Would you comment on your preference for the open voltage over the 

conductivity method for determining high injection lifetime? Why you use 

it at the end. and also say a little more on the photoconductive decay 

method for in-process lifetime? 

SWANSON: The open-circuit voltage decay: I like it because it is very easlrto 

do, and once you understand what it is doing it is easy to extract data 

from i.t. In the type of cell we are talking abouf~f where the diffusion 

length is much greater than the thickness of the deviee~ after interrupting the current, a very short period of time later the carriers are 

more or less uniformly· distributed from the front to the back of the 

device, and this makes the analysis of the transient very simple. 

Basically you have one recombination term that is going as n2, that is 

the diffused areas, and that gives you a steeper slope in the beginning. 

It allows you to extract the Jots and then it goes into a linear region 

where the recombination going is n, and there is a straight line on the 

decay, and you pick the lifetime off that. 

LINDHOLM: Have you written s~mething on that? Published? 

SWANSON: No. There is, but I am just using things from the literature on it. 

LINDHOLM: How about the photoconductivity decay in process lifetime monitoring? 

SWANSON: That is essentially a similar circuit to the one in High Lifetime 

Factors in Silicon Processing, which is a book from ASGF. Our· particular 

implementation of it is simply a three-turn coil with 10 megahertz of RF 

flowing through it that is laid near the sample, and then we use a General 

Radio strobe attached to it to excite the carriers. We look at, essentially, the back EMF across the coil as a function of time, which -- in 

effect the silicon looks like a single-turn secondary, coupled to this, 

whose resistance is a function of time, and that gets reflected into the 

impedance looking into the coil~ so that the real part of the impedance 

of the coil is a function of the conductivity, etc. I will send you a 

writeup we have on that. I wrote it up because the people from 

Westinghouse wanted to see it, so I made a bunch of copies. We had no 

intention of publishing because it really is the same --

SPITZER: I am interested in hearing some more about your tips for highlifetime processing. That is something we are working hard on. The 

first question is: did you find it necessary to use double-wall furnaces, 

118 
or do you use those? 

SWANSON: Well, Mark, you will have to understand: being in the University 

environment, I have no secrets at all. However, we have tried silicon 

tubes, silicon carbide tubes, double-wall quartz tubes, double-wall quartz 

tubes inside of silicon carbide tubes, and plain silicon tubes with and 

without alumina liners. 

SPITZER: We can't afford that in industry. 

SWANSON: We couldn't afford that either. They were all given to us by interested parties. What I can say in retrospect is, though, that the system 

we are using now, which has given us the best results, is a plain quartz 

tube inside an alumina liner. 

SPITZER: What about processing gases? Did you spend a lot of time judging 

various suppliers and things like that? 

SWANSON: We did. We just used boil-off nitrogen and oxygen but we have had 

about five major lifetime crashes in the history of the program. At one 

time we thought it was gas. We hooked up a residual gas analyzer to our 

gas system and saw sulphur dioxide in the nitrogen and thought it was 

sulphur but then it turned out that was an artifact of the residual gas 

analyzer, and it turned out not, in that particular case, to be from the 

gas but to be from bacteria in the water. So we have never seen any 

evidence in boil-off that there was any need for more purity than we are 

obtaining' routinely in the boil-off. 

S~ITZER: Do you use boil-off hydrogen? 

SWANSON: We don't use hydrogen. 

SPITZER: No hydrogen. 

SCHRODER: How do you measure S of 2 cm/second? 

SWANSON: We meesured that by the photoconductivity decay method. 

SCHRODER: These are surface recombinations velocities, right? 

SWANSON: These are high-level surface recombinations velocities, which were 

measured by taking samples of different thicknesses, ranging from around 

20 micrometers to 300 micrometers, and their h.igh-resistivity float-zone 

material, oxidizing both sides and measuring the recombination lifetime, 

with our standard, as a function of thickness. 

WOLF: Do these lifetimes then include the effect of the accumulation layer? 

SWANSON: We measure effective recombination lifetime. However, the oxides we 

have produced, which are standard MOS-type oxides, have fixed charge densities under 109 , I think, and when they are injected at 1017 , any 

kind of potential band due to that is very, very small. One of the 

challenges that faces one in this, one we have not fully resolved, is how 

119 
to get similar performance on very thin oxides suitable for putting under 

an antireflection ~oating. These are all state-of-the-art MOS-type 

oxides, high-temperature dry oxidation followed by nitrogen atmosphere anne~l and low-temperature hydrogenation. 

WOLF: Now, what you mentioned about the DI water and the bacteria sounds 

extremely interesting and it seems to me that you said if you have really 

pure water then there are no bacteria. So the bacteria comes with the 

indication whether your water is basically purified well or not. Is that 

right? 

SWANSON: No. The problem is that most people monitor -- at least, in our 

laboratory until we discovered this -- we routinelynlonitor resistivity 

but not bacteria count. The resistivity can be in real good shape and 

have a very high bacteria count. 

WOLF: DI water generally does not contain ions, and still bacferia can thrive 

on that? 

SWANSON: I really don't know how they live in there but they do. They metabolize the plastic pipe, or that is what I have been told. They are 

anaerobic and whatever. 

TAN: Allow me to make a conwent on your last. Except for the first item, 

which is the float-zone silicon, the rest is standard practice of the 

integrated circuit industry. Off the record, I can also support him 

about the bacteria business. It is all true. 

SWANSON: I don't know how you can go about getting these kinds of lifetimes 

in Czochralski or other materials. We were misled because, being a poor 

university, we were in one of those periods where silicon was hard to 

get. Wacker gave us silicon in boxes that said it was Czochra1ski 

material. But it turned out that it was mislabeled. It was actually 

float-zone material. We worked on that for a year, and we then ordered 

new material from them thinking they have got the hot stuff. It came 

back that we were getting 20 to 50 microseconds, and that is when we had 

the material analyzed and found that it was indeed float-zone material. 

Then we worked with the Czochralski material for over a year and were 

unable to get the lifetime. 

SCHWARTZ: How did you measure the capture cross sections in surface states? 

To me it is a very surprising result. 

SWANSON: It was to us too, and these data are being prepared for publication. 

It was done using DLTS in a capture mode. Just like you would use DLTS 

for bulk levels by shortening and filling the pulse width. We used 

essentially small-signal DLTS, where we wiggled the interface a little 

bit, so we filled emptying traps in a dE about a known point, and then 

varied the filling pulse time and watched the decay signals. 

SCHWARTZ: It appears to me t·hat your fall-off in capture cross section is so 

rapid that one would not see it., so that experiment doesn't seem to fit. 

120 
SWANSON: Right now we are making measurements of recombination velocity 

versus doping levels to see if we get the results predicted by 

integrating the SRH equation over those. 

121 
I 

1 

I 

I 

I 

SILICON MINP SOLAR CELLS 

N85-31623 

Larry C. Olsen, F.W.·Addis and W.A. Miller 

Joint Center for Graduate Study 

Richland, Washington 99352 

ABSTRACT 

The MINP solar cell concept reffi!rf?\ to' a cell structure designed to be a 

base region dominated device. Thus , 'it' i,i;;'desirable that recombination losses 

are reduced to the point that they occu~ only in the base region. The most 

unique feature of the MINP cell design is that a tunneling contact is utilized 

for the metallic contact on the front surface. The areas under the collector 

grid .!lnd bus bar are passivated by a thin oxide of tunneling thickness. 

Efforts must also be taken to minimize re.combination at the surface between 

grid lines, at the junction periphery and within the emitter. This paper 

includes results of both theoretical and experimental studies of silicon 

MINP cells. Performance calculations are described which give expected 

efficiencies as a function of base resistivity and junction depth. Fabrication 

and Characterization of cells are discussed which are based on 0.2 ohm-cm 

substrates, diffused emitters on the orde~ of 0.15 to 0.20 ~m deep, and with 

Mg MIS collector grids. A total area, ~ efficiency of 16.8% has been achieved. 

Detailed analyses of photocurrent and cufrent loss mechanisms are presented 

and utilized to discuss future directions of research. Finally, results 

reported by other workers are discussed. 

1. INTRODUCTION 

This paper concerns approaches to high efficiency silicon solar cells 

based on the MINP concept. This term is used to denote shallow junction 

~/p cells which utilize a MIS contact for the front collector grid. The 

MINP structure was first discussed by Green, et al. 1 Recently Green and 

coworkers have fabricated cells exhibiting efficiencies on the order of 19%. 

As a result, the MINP concept has become' 'one of the mos t promising approaches 

to fabricating high efficiency silicon cells. 

Key features of MINP cells are described in Figure 1. A shallow emitter 

is used in an effort to minimize current losses in the emitter region. The 

front surface is passivated to reduce'surface recombination. If the base 

region losses can be reduced as a result of a back-surface-field, then a 

p+ region is established at the back surface. In order that the emitter 

current losses are further reduced, anMI.S· contact is used for the front 

collector grid. A metal must be chosen which will accumulate the ~ surface. 

Thus, the area under the iront contact is also passivated. Ti and Mg have 

work functions below 4.0 eVe As a result, these two metals are appropriate 

for the front tunneling contact. In summary the MINP cell has features similar 

to other shallow emitter, high efficiency Silicon cells. Clearly, the most 

unique feature is the MIS (tunneling)c:9nt,a.et us.ed for the coHee tor grid. ~,,>:' .:.t··: ,',. . , 

In the next section the theoretical performance of MINP cells will be 

discussed. Detailed disc.ussions are then given regarding cell fabrication, 

photocurrent, current loss mechanisms, the Mg/nSi tunnelling contact, and 

solar cell efficiency. 

123 P.RECEDING PAGE BLANK NOT FILMED 
I 

! 

i 

I 

j 

I 

I 

I 

! 

I ! 

2. LIMITING THEORETICAL PERFORMANCE 

:~ . Mpdelingcalculations have been conducted to appraise the potential of 

;the:MINP concept 'and to provide guidance for device design. These studies 

are based on two sources of minority carrier li~etime data, namely, the LSA 

advisory board2 , and that of Fischer and Pschunder3 • 

In ortier to determine an upper limit to cell performance, it was assumed 

that the device properties were completely determined by the base region. 

Thus, the junction depth was considered to be vanishingly small and the front 

surface recombination velocity was set equal to zero. Modeling calculations 

discussed in this paper are based on an assumed cell thickness of 380 ~m (15 

mils), since experimental studies have primarily been based on cells with that 

thickness. 

Calculated values of the maximum, active area photocurrent are plotted 

versus base region resistivity in Figure 2. The modeling calculations were 

carried out for the two sets of lifetime data and for two condltions at the 

back contact. An AMI irradiance spectrum appropriate for Phoenix, Arizona 

was used in calculating photocurrent. 

Theoretical values of the reverse saturation current (JBO) are plotted 

versus base resistivity and NA in Figure 3. Auger recombination and bandgap 

narrowing are taken into account as done in Reference 1. Calculated values 

of VOC are also given assuming J SC = 36 mAl cm2 • With LSA lifetimes, the V C 

for a base region dominated cell can approach 690 mV. Due to Auger recomb~na­ tion, there is no reason to use base resistivities below 0.1 ohm-em. 

Calculated active area AMI efficiencies are described by Figure 4. If 

one assumes that lifetimes are given by LSA values, then a base resistivity 

in the range of 0.1 to 0.2 ohm-cm is optimum for cells with ohmic contacts, 

while the resistivity can be any value greater than 0.1 ohm-em for cells with 

a BSF. If FP values are assumed, then it is best to use base region resistivities 

between 0.1 and 1.0 ohm-em. 

3. CELL FABRICATION 

The basic approaches to cell fabrication involve steps listed in Table 1. 

To date emitter diffusions have been obtained from ASEC and Spectrolab. 

The junction depths are on the order of 0.15 to 0.20 1Jm. Phosphorus concentration profiles obtained by SIMS and spreading resistance analysis (SPA) are 

shown in Figure 5. The error limits are estimated to be + 50% for both profiles. Thus, the error limits overlap. Although very limited data has been 

acquired, it appears that the surface donor concentration is on the order of 

0.5 to 1.Oxl020 cm-3 • 

In the case of approach A (Table 1), the wafers are scribed and cleaned, 

an Al layer is deposited onto the back surface. Heat treatment at SOOoC 

establishes an ohmic contact on. the back and a 15 to 20 A, tunnelable oxide 

forms on the front surface. Thi~ oxide layer provides some passivation on 

the front surface. Of course, it also serves as a~ interfacial layer for 

the MIS, collector grid or 'tunneling' contacts on the front surface. 

The MIS collector grid is, formed with a. low work function metal. Mg has 

been used il\ this work. Using Approach A, the cell is completed by depositing an AR coating(s}. 

The key difference with Approach B is that a 100 to 150 A layer of Si02 

is grown onto the front surface to achieve a lower surface state nens1ty. 

12,4 
4. PHOTO CURRENT 

In order to maximize the photocurrent, and to interpret experimental 

results, detailed analyses of photon and carrier economy have been carried out. 

In particular, optimum AR structures have been determined for both polished 

and textured cells. Essential information for such analysis is the internal 

photoresponse for the cell. 

Figure 6 shows a typical result for the internal photoresponse of a 

polished cell structure. Calculated curves are based on cell parameters as 

indicated. nle wave length region between 750 nm and 1050 nm is the most 

important one for determining the minority carrier diffusion length. A value 

of L = 150 m appears to fit the data fairly well. 

Figure 7 describes the approach taken in determining the optimum AR layer 

structure for polished and textured cells. Optical cconstants must be known 

for each layer in the multilayer stack. Photon transmittance into silicor. 

is calculated with a computer code, and used in an integration over the chosen 

irradiance spectrum. The optimum AR layer structure is determined by maximizing 

JpH· 

Figure 8 summarizes calculation of JpH for polished and textured cells. 

Most of the plots are for L = 150 ~m. The active area JpH is plotted versus 

NI, the index of the antireflecting layer adjacent to silicon. For a single 

AR case (lL-AR), Nl is of course the index of the single AR coating. For 

each value of Nl in single AR structures, there is an optimum value of the 

layer thickness. In the case of a two layer structure, there are, of course, 

optimum value of thickness at which the plotted value of JpH occurs. 

Calculations show that it is desirable to use a textured surface. A single 

AR coating on top of a textured cell leads to a possible 38.3 mA/cm2 compared 

to the possible 37 mA/cm2 achievable with a double AR on a polished surface. 

Furthermore, with a double AR OIl a textured surface, a value of nearly 39 

mA/cm2 becomes possible. Thus results are based on assuming L = 150 m. 

If one assumes a Fischer-Pschunder value for L (500 ~), a value of 42.5 

mA/cm2 becomes a possibility. 

Table 2 indicates some of the best active area values of JpH measured by 

SERI. Those values are fairly compatible with results given in Figure 8. 

It would appear that the diffusion length of the material used by Green and 

coworkers is slightly larger than 150 .~. The JCGS result of 37.8 mA/cm2 

for a textured/lJ.-AR case is slightly less than the possible 38.2 mAl cm2 , 

probably due to absorption. The Spire reesult may be due to a smaller 

diffusion length or absorption in the AR coating. 

5. CURRENT LOSS MECHANISMS 

Current-voltage characteristics are being studied in detail in order 

that limiting current mechanisms can be identified and understood. Figure 9 

summarizes the theory for the current loss mechanisms under consideration. 

Temperature dependent current-voltage characteristics are particularly useful 

for determining I-V mechanisms. The activation energy coupled with the 

n-value and magnitude of J o can often suggest the operative current loss mechanism. Table 3 lists the range of values for key I-V parameters. 

125 

F ...... .." .r 
The emitter. recomblnation current is likely to be a dominant loss mechanism 

in low resistivity devices. Calculated values of JOE are plotted vs the surface 

donor concentration (Ns) in Figure 10. The work of Fossum and Shibib4 was used 

to calculate JOE. The effects of bandgap narrowing and of the low lifetime in 

the emitter are taken into account. Values of JOB are indicated assuming LSA 

and FP lifetimes, as well as ohmic and BSF conditions for the back contact. 

In addition, values of VOC calculated assuming J SC = 36 mA/cm2 are given. 

The estimated value of JO for the 19% cell of Green, et al is based on the 

assumption that n = 1. 

I-V data are taken with a computer based data acquisition system over a 

range of temperatures and under both dark and illuminated conditions. The 

approach to data analysis is summarized in Figure 11. The approach used for 

analyzing illuminated data is similar. In general, we observe two current 

mechanisms, one dominant at low voltages and one dominant at higher voltages. 

These current mechanisms are referred to as the lower and upper mechanisms, 

respectively. 

Transformed I-V characteristics for an MINP cell are shown in Figure 12. 

The two mechanisms are clearly evident. Values for the JO and n of the upper 

mechanism, and JO and B of the lower mechanism were determined for each temperature. Results are typically obtained for ten temperatures. The value of 

the upper mechanism is plotted versus lOOD/T in Figure 12. From this plot, 

one obtains a value for 4> = 1.08 eV. In analyzing the temperature dependent 

data, JOO(T) is assumed to vary with temperature as r4(T-TO), with To = 100oK. 

Some results of I-V analyses carried out for MINP cells are given in 

Table 4. In particular, the results for the upper mechanism are given. 

The lower mechanism is discussed below. Results for analysis of both illuminated and dark data are given. Only results of I-V analyses were included, for 

which temperature studies were made, except for cells 84-21 and 84-22. These 

devices were made just recently. Consider cell 83-25. Since n = 1, and 4> = 1.08 

eV, it appears that the current-voltage characteristics are limited by the 

emitter current with bandgap narrowing of ~E = 0.12 eVa In all of the other 

cases, n is in the range of 1.04 to 1.09, and 4> lies in the range of 0.7 to 

0.8 eV, except for cell 84-5. These parameters suggest either depletion 

region recombination or field emission. Further study is required to allow 

one to choose between these possibilities, and to relate the results to processing. It is not clear at this time what is the proper model for 84-5. 

The upper mechansim is usually described by n ~ 1.0 to 1.07 and JO ~ 

2 x 10-12 Alcm2 • At this point it would appear that recombination in the 

depletion region or field emission by holes near the metallurgical junction 

explain the upper mechanism. A possible reduction of the magnitude of this 

mechanism may be accomplished by reducing NS. 

The lower mechanism is not presently limiting cell performance. It 

could do so in the future, as the upper mechanism is improved. Thus, we 

must eventually understand the lower mechanism. 

126 
6. THE Mg/n-Si TUNNELING.CONTACT 

The MIS collector grid is a key feature of the MINP cell. The term 

'tunneling contact' is often applied to this contact and will be used in 

this paper. Figure l3A illustrates the expected electron band diagram at the 

Mg-nSi interface. Since the work function of Mg is less than 4.0 eV, the 

silicon surface is accumulated as shown. Majority carriers can readily tunnel 

through the 20 A interfacial layer, thus providing a good ohmic contact. 

The primary purpose for using a tunneling contact is to minimize the 

recombination under the contact. Thus, it is of interest to estimate the surface recombination velocity for this interface. We will examine this question 

in two ways. First, it is informative to investigate MIS diodes on p-type 

silicon. Figure lOB indicates possible comman current loss mechanisms. 

Mg/pSi MIS cells have been fabricated and found to have excellent properties. 

Figure 14 shows I-V characteristics for two devices. Device 82 MgSi-14 shows 

a rather weak lower voltage mechanism, while the mo~e recently fabricated 

device 84 MgSi-l exhibits essentially no lower mechanism. More significantly, 

the upper mechanism for 84 MgSi-l corresponds to an ideal diode. The I-V 

parameters are n = 1.00 and JO = 4.8 x 10-13 A/cm2 • This value of JO~ can be 

interpreted in terms of a barrier height of ~BP = Eg and A = 32 a/cm • 

Thus, one can conclude that in the case of an Mg/pSi contact, there is no 

significant surface recombination (c), or tunneling/recombination (d). 

The I-V analyses of MINP cells can provide information about surface 

recombination under the Mg contact on ~/p structures more directly. The Mg 

contact area is not the same for the cells listed in Table 4. Referring to 

cells 84-21 and 84-22, the Mg contact area differs by a factor of 20. Yet 

the JO is very similar for the two devices. In fact, JO for 84-21 is larger 

than for 84-22. If recombination under the Mg contact were the dominant loss 

mechanism for 84-22, the JO should be slnaller for a device with the contact 

covering less area. 

More effort will be devoted to characterize recombination under the MIS 

contact. However, recombination losses appear to be low enough to allow JO 

to decrease below 10-12 Alcm2• 

7. CELL EFFICIENCIES 

Two types of cell structure are being pursued, namely~ an MINP configuration with a polished front surface; and MINP cells with textured front 

surfaces. These structures will be referred to as 'polished' and 'textured'. 

The best result obtained with a polished cell is described by Figure 11. 

The current-voltage characteristics were measured by SERI. As noted, the 

efficiency was 15.6%, and VOC = 636 mV. This cell utilized a single AR layer 

of SiO. The SiO is deposited rapidly so that the index of refraction is near 

1.9. Analysis indicates that a silicon homojunction with a single AR layer 

can provide an active area AM! photocurrent of 35.5 mAl cm2 • The total area 

current in such a case for our cells would be 33.4 mAlcm2 (6% shadowing). 

The best total area value of JSC obtained for a cell with a single SiO layer 

is 31.8 mAlcm2 • Thus, it appears that approximately 1.6 mAlcm2 are lost 

due to photon absorption in the SiO film. Future efforts will concentrate on 

the use of a double AR coating on a polished cell structure. 

127 
SERI measured current-voltage characteristics for the best textured cell 

are given in Figure 16. Although J S has been increased to 35.5 mA/cm2 , 

FF and VOC are slightly lower than t~at achieved with a polished cell. Part 

of this decrease is due to the fact that the junction area of the textured cell 

is larger than the standard cell by a factor of 1.7, but most of the effect 

is primarily because the j unction has not been optimized for the textured cells. 

8. CONCLUSIONS 

The MINP cell structure is a shallow emmitter cell structure. The unique 

feature of the MINP cell is the tunneling contact used for the collector grid. 

Like any shallow emitter cell, the front surface must be well passivated and 

emitter losses minimized before base limited performance can be achieved. 

Efficienci'es of 25% should eventually be possible. Figure 17 indicates the 

kind of property improvements needed to achieve 20%, and then 25%. 

ACKNOWLEDGEMENTS 

The authors wish to acknowledge the financial support of the Solar Energy Research Institute(Contract XBB-2-02090-5). 

128 
REFERENCES 

1. M. A. Green, et aI, "The MINP Solar Cell - A New High Voltage, 

High Efficiency Silicon· Solar Cell," Conf. Record, 15th IEEE 

Photovoltaics Specialists Conf., Orlando, p. 1405, 1981. 

2. M. Wolf, "High Efficiency Silicon Solar Cells," Conf. Rec., 14th 

I'EEEPhotovoltaics Specialists Conf., Sari Diego, p. 674, 1980. 

3. H. Fischer and W. Pschunder, "Impact of Material and Junction 

properties on Silicon Solar Cell Efficiency," Conf. Rec., 11 th 

IEEE Photovoltaics Specia1ist~; Conf., Scottsdale, p. 15, 1975. 

4. Jerry G. Fossum and M. Ayman Shibib, IEEE TRANS ON ELEC. DEV 

ED-28, 1018(1981). 

TABLE 1 

MINP CELL FABRICATION 

A. WITH THIN PASSIVATING OXIDE 

1. Diffuse Emitter into Wafer. 

2. Scribe into 2 cm x 2 cm Substrates. 

3. Clean Substrate (Basically RCA Process). 

4. Deposit Aluminum Back Contact. 

5. Sinter Back Contact at 500 C and Grow 15 

to 20 A Tunnelable Oxide on Front Surface 

6. Deposit Collector Grid Based on a Tunneling 

Contact. 

7. Deposit an AR layer(s). 

B. WITH THICK PASSIVATING OXIDE 

1,2 and 3 Same as Above. 

4. Grow 100 to 150 A Si02 Layer for Passivation of 

Front Surface. 

5. Define Contact Openings and Remove Oxide on Back Surface. 

6. Complete cell by Using Steps 4 Through 7 Given Above. 

129 
TABLE 2 

EXPERIMENTAL RESULTS FOR AMl PHOTOCURRENT 

0.2 Ohm-em P-TYPE BASE 

CELL THICKNESS = 15 mils 

TOTAL ACTIVE 

. AR GRID AREAAM1 AREA 

CELL STRUCTURE SHADOWING JPH AM1 JPH 

GREEN. ET AL 2l-AR 4.2% 36.0 37.6 

ZnS/MgFz 

SPIRE TEXTURED 3-4% 36.1 37.2-37.6 

1 L-AR(TazOe) 

JCGS TEXTURED 6% 35.5 37.8 

84-6 1L-AR(SiO.) 

TABLE 3 

KEY PARAMETERS FOR CURRENT MECHANISMS 

J-V RELATIONSHIP FOR ACTIVATION ENERGY 

CURRENT MECHANISM V»kT .1 (eV) 

EMITTER RECOMBINATION JOE axp(V/nkT) 1.2 - (AE) EMITTER 

n=1 BGN 

BASE REGION Joaexp (V/nkT) 1.2 - (!lE) BASE 

RECOMBINATION n=1 BGN 

DEPLETION LAYER JOR 8xp(V/nkT) Ec-Et OR Et-Ev 

RECOMBINATION n~1T02 

FIELD EMISSION JOF exp(CV) O.B TO 1.0 

C=_1- + B 

nkT 

TUNNELING JOT8Xp(BV) TYPICALLY 0.1 TO 0.2 

ASSUMEO FORM OF Joi: 

Joi = Joo (T) exp( - +/kT) 

130 
TABLE 4 

I-V PARAMETERS FOR HIGH-VOLTAGE CURRENT-LOSS MECHANISM 

UPPER MECHANISM 

FRONT Mg AVERAGE 

CONTACT DARK ERROR ACTIVATION 

AREA OR FOR UPPER ENERGY, . J

o CELL (%) ILLUM RANGE (%) 4> (eV) n (A/cm2) 

83-22 6 ILLUM 0.19 0.73 1.04 2.1 E-12 

83-23 6 DARK 0.19 0.71 1.09 1.5E-11 

83-25 6 DARK 0.63 1.08 1.00 2.2 E-12 

83-26 6 DARK 0.28 0.81 1.04 4.4 E-12 

84-5 0.6 DARK 0.19 1.15 1.04 2.4 E-12 

84-6 6 DARK 0.33 0.80 1.07 2.4 E-11 

84-21 0.3 ILLUM 0.40 - 1.09 5.3 E-12 

84-22 6 ILLUM 0.40 - 1.05 2.6 E-12 

TABLE 5 

EXPERIMENTAL RESULTS FOR MINP CELL AMI EFFICIENCIES 

METAL 

USED FOR 

MIS 

CELL CONTACT 

GREEN. Et 81 Ti 

JCGS Mg 

84-4 

JCGS Mg 

84-6 

0.2 Ohm-em P-TYPE BASE 

CELL THICKNESS = 15 mils 

AR GRID Jse 

STRUCTURE SHADOWING (rnA/em') 

2L-AR 4% 36.0 

ZnS/MgF. 

2L-AR 6% 31.1 

SiN/SiO. 

TEXTURED 6% 35.5 

1 L-AR(SiO.) 

AM1 

Voe EFFICIENCY 

(mV) FF (%) 

650 0.812 19.0 

636 0.787 15.6 

617 0.768 16.84 

Results for Green, et aI, were reported at the IEEE 16 th 

Photovoltaic Specialists Conference. 

131 
MIS CONTACT 

USING Mg OR 

PASSIVATED 

SURFACE 

N-TVPE EMITTER 

1000 A TO 2500 A 

. P-TVPE 

BASE 

(0.1 TO 2 

P+ REGION 

TO PROVIDE 

BACK SURFACE 

FIELD 

10-12 

i 

~ 

i 

.... 

10-13 

ARLAVER 

BACK CONTACT 

Fi gure 1. MINP Sol ar Cell Concept. 

10 5 2 

e(Q·eml 

CELL THICKNESS = 15 mMs Jse = 36.0 mA/em' 

FOR Voe CALCULATION 

UFETIME DATA 

---FISCHER 

___ LSA & PSCHUNDER 

0.60 

0.65 

~ 0 

2: 

g 

> 

0.70 

Figure 2. Base Region Contribution to JO vs Acceptor Concentration for 15 mil 

Cell Thickness. 

132 
1 • BASE REGION CElL • IDEAL AR AND NO SHADOWING 

• PHOENIX AM1 SPECTRUM • 80% BSR • cal THICKNESS = 15 mil 

44 

42 

~ 40 

~ 

c( 

Sf .., 38 

i 

c( 

POUSHED 

IID8LAR 

36 

UFETIME DATA: 

----FISCHER II PSCHUNDER 34 ---lSA 

32L---L-~L-~~--~--L-~-L--~--~~~0 .01 0.1 1.0 1 • 

BASE RESISTIVITY (OHM-cm) 

Figure 3. Calculated AMI JPH vs Base Resistivity for 15 mil Cell Thickness, 

Assuming 100% Photon Transmittance And No Grid Shadowing. 

Figure 4. 

~ > " z 

w 

i3 

Ii: 

... 

w 

i 

c( 

• 8ASE REGION DOMINATED CELL • IDEAL AR AND NO SHADOWING 

• PHOENIX AM1 SPECTRUM .80% BSR 

• CELL THICKNESS = 15 mils 

30~--r--.~~~L-~--'--r"---'--~-,-,, 

25 

20 

15 UFETIME DATA: 

---- FISCHER II PSCHUNDER 

--- LSA 

10L---L---L-~-L __ -L __ ~~_Lj __ ~ __ ~ __ ~~ 

.01 0.1 1.0 

BASE RESISTIVITY (OHM - em) 

Calculated ANI Cell Efficiency For 15 mil Cell Thickness, Assuming 100% Photon Transmittance And No Gri d Shadowi ng • . 

133 
1021 

II 

0 SPREADING 

RESISTANCE 

'0 II - SIMS 

0 

...... 

Ul 

E 

0 0 .... 

.!!! 0 II 

Z 0 0 

H 0 le( 0 a: 

IZ 

W 

Col 

Z 

0 

tJ 

II 

p 

1011lL-____ -L ______ ~--~~~~~~----~ o 0.10 0.20 0.30 0 .... 0 0.50 

DEPTH (microns) 

Figl.~re 5~· Phosphorus Concentration vs Depth For MINP Cell • ..... 

80. 

~ W 

In 

2 

l( 60. In 

w 

a: 

~ 0 

iE 

MSlNP2 IS A .2 OHM-CM BARE 51 ..I 40 • c( 

2 CELL. WITH NO aRID IN lHE BEAM. a: 

w CI\l..CULATEO CURVES HAVE OHMIC ... 

~ BACK CONTACTS.S(F)-1.2E •• XJ".28 

2 0 • 0(11-3.33. W::.091. ANO AN AL 

BACK SURFACE REFLECTOR. 

300· 450 800 750 900 1050 1200 

WAVELENGTH (nml 

Fi gure 6. Internal Photoresponse For ~lINP Cell. 

134 
Figure 7. 

Figure 8. 

POLISHED CELL TEXTURED CELL 

• DETERMINE T" VS • .t 

FOR GIVEN AR STRUCTURE 

• USE REPRESENTATIVE SI 

BASED ON alii VS • .A AND 

CELL STRUCTURE 

00 

• DETERMINE JPH =8) FATASAd.t 

9, =12°,9.=4° @A=600nm 

REGARDLESS OF AR STRUCTURE 

• ACCOUNT FOR TWO 

PHOTON PATHS AND 

REFLECTION OFF BACK 

• SA = SAt + SAl 

• DETERMINE N" N., AND THICKNESSES 

WHICH YIEI.D MAXIMUM J PH 

Description of Approach to Optimum AR Layer Analysis. 

46 

15 mil CELL THICKNESS 

PHOENIX SPECTRUM 

L=150, Ohmic BACK CONTACT 

44 - - - L=500, BSF 

N.=1.3 1.4 1.5 

- - -~ -... -... 

42 - TEXTURED (2L-ARI .. 

E. 

ci 

S 40 

if: N.=1.3 1.4 1.5 ., 

... TEXTURED 2L-AR , " " :IE 

< - 38 

t 

> 

w 

< 

iL-AR 

N.=1.3 tt. 

1.4 

1.5 

~ 1.6 

36 

TEXTURED (NO ARI 

34 

32 

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 

N"INDEX OF LAYER ADJACENT TO SILICON 

Calculated JpU vs Nl, The Index Of The AR Layer Adjacent To Silicon, For Polished And Textured Cells. 

135 
1 

J 

I 

~ 

I 

~ 

I 

~ 

I 

.i 

! 

1. EMITTER RECOMBINATION CURRENT 

V 

J = JOE [exP(nkTl - 1] 

n = 1 

FOR RM TEMPANALVSIS: 

en·2 

JOE=~}·GF 

GF IS A FCT OF WHo SP. DPO &. Tp 

FOR INTERPRETATION OF TEMPERATURE 

DEPENDENT DATA: 

A JOE = Joo (TI exp ( kT I 

+ = 1.20 - (AEI EMITTER 

BGN 

•• 

000 

2. BASE REGION RECOMBINATION CURRENT 3. DEPLETION LAVER RECOMBINATION CURRENT 

V 

J = JOB [exP(nkT) - 1] 

n = 1 

J - e.I!i2 Ln . G 

OB - NA Tn F 

-=:t = JOO IT) exp( kT I 

+ = 1.20 - (AEI BASE 

BGN 

4. TUNNELING/RECOMBINATION 

J = JOT exp(BVI V » kT 

B TEMPERATURE INDEPENDENT 

-+ JOT = JOO exp( kT I 

+ TVPICALL V 0 TO O.S eV 

S. FIELD EMISSION 

J 

C 

= JOF exp(CVI 

= i. + B nkT 

JOF = JOO exp( -+ /kTI 

+ = fVbi f=n- 1 

V 

J = JOR exp (nkT' V » kT 

·JOR = ,~o exp ( ;1 I 

+ = (Et-Evl OR (Ee-Ed n = 1 TO 2 

FOR n~2. +~Eg/2 FOR n~1 t +~0.8 eV 

o 0 0 0 0 

Figure 9. Summary Of Theory For Current Loss Mechanisms. 

136 
~1 ~, 

j 

j 

.1' 

_ V 

1 

I J 

'I 

:~ ., 

., 

E 

~ 

!$ 

... 

0 .., 

10-11 

10-12 

10-13 

10-14 

I-----~ 

600 

620 

640 

660 V~(mV) 

AS UMING 

J SC =36 mA/cm2 

AND n=1.0 

BASE REGION J O FOR 

Q=0.2 Q-cm 

THICI(NESS = 15 mils 

10-15~ ____ ~ __ ~~~~~~ ______ ~ __ ~~~~~ .. ______ ~ 

1018 

Figure 10. 

1019 1020 

JOE vs Surface Donor Concentration (NS) For Range Of 

Values of Surface RecQmbination Velocity. 

I-V. RELATIONSHIP (Vj » kT) 

IHEAS = I

j + V/nki 

Vj = VMEAS -RS IKEAS 

Ij = 101 exp(BVj ) + 102 exp(V/nkT) 

FITTING PROCEOU~E 

1. SELECT RS AND RSH 

2. GENERATE (Ij • Vj ) 

3. CONSIDER (Ij • Vj ) FOR REGION 1 

Ij " 101 exp(BVj ) 

L0ge(ljl = L0ge (lo1 )+BVj 

LEAST SQUARES FI T =- 1

01' B 

'MEAS (f----::.n------, 

Figure 11. Appreach To Dark 

I-V Analysis. 

4. CONSIDER (Ij • Vjl FOR REGION 2 

Ij2 • Ij - 101 exp(BVj ) 

• 102 exp(V /nkT) 

LEAST SQUARES FIT - '02' B 

5. ITERATE BETWEEN REGIONS 1 AND 2 UNTIL 

ACH I EVE CONVERGENCE. 

6. CARRY OUT STEPS 1 THROUGH 5 FOR 

ARRAY OF R AND R VALUES. SELECT 

VALUES OF ~ARAHET~"S WHICH PROVIDE 

BE'. T FIT TO DATA. 

137 

REGION 1 
$ 

Iz 

w 

a:: 

a:: 

~ 

u 

z 

0 

~ 

U 

z 

~ ..., 

(A) 

.-3BoC 10- , I- • 18°C 

413°C . 713°C 

10 -2 ~ 

r10 -3 I 

0 .1 

I I 

.2 .3 .4 

I 1.( 

: :f . 

• x 

:.; 

• . x " . , 

. . " , 

.5 .6 

I 

. • 

• 

. - • • 

.7 

JUNCTION VOLTAGE 

TRANSFORMED 

I-V DATA 

10-9~ ____ ~-'I __ -------O __ --____ ' 

.. .. DIV-83SINP2S 

7/5/84 

PHI 1.138 EV - ~ JB13 = 2.1X1B A 6 

. M = 4 

·.TB = 1BBoK -

•.. - •.. - .. 10-'4L-________ ~1 ________ ~ _____ • __ ~ 

2.5 3.0 3.5 4.0 

1000/T(OKI 

ACTIVATION 

ENERGY 

ANALYSIS 

Figure 12. Current-Voltage Characteristics Of An MINP Cell Based On 

A Polished Substrate. 

(B) 

INJECTION @ O""'vr-__ INJECTION 

PHOTOCURRENT .------

@ - .............. -

---0 

TUNNELING CONTACT 

FOR N + IP CELL 

0000 

Mg/pSi DIODE 

Figure 13. Electron Band Diagrams For Tunneling Contact On N+ Surface, 

And MIS Device On A P-type Substrate. 

138 
, I 

• I .\ 

I 

J 

I 

I 

· i 

· I 

· F. 

I 

. , 

. 

! 

10-2 

10-5 

• 82 MgSi 14 

o 84 MgSi 1 

10-6IL ____ ~I----~----~----~ __ ~ ____ ~ ____ ~~ .0 .1 .2 .3 .4 .5 .6 .7 

JUNCTION VOLTAGE (VOLTS) 

Figure 14 •. Current-Voltage Characteristics Of Mg/pSi MIS Devices Based 

On 0.2 n-cm Silicon. 

0.14 

0.12 

0.10 

III 

a O.OB 

E 

ID O.OB 

.... 0.04 

Z 

UJ 

a: 0.02 

a: 

:J 0 U 

-0.02 

-0.04 

" 

-O.OB 

SAMPLE: 84 SiNP4 

TEMP. = 28.0 DC 

AREA = 3.97 em' 

Voc = 0.6363 VOLTS 

Jsc = 31.10 mA/em' 

FILL FACTOR = 78.72% 

EFFICIENCY 

000 

(I) (II <r1 

= 15.58% 

o 0 0 0 000 <r1 (II (I) "If 10 CD " 

000 000 0 0 000 

I I I 

VOLTAGE (volts) 

Figure 15. Illuminated Current-Voltage Characteristics Measured By SERI For 

MINP Cell With Polished Surface And SiO AR Layer. 

139 

"---- • 
0 . 18 

O. <I 

0 . 12 

O. :1 0 

a. 

10 

0.08 

.... 0.08 

tZ 0.04 

W 

a: 0.02 

:J 

U 0 

-0.02 

-0 . 04 

-0.08 

SAM P 

TEMP. - 2 8.0 oC 

AR .. 3.94 em" 

V = 0.617 VO T 

J - 35.53 m ma 

Fill FACTOR .. 76.83% 

EFFICIENCY .. 16.84% 

0 0000 0 0 0 0 0 ~ N ~ ~ N ~ ~ ~ w 

o 0 0 0 0 0 0 0 0 0 0 

I I I 

VOLTAGE (vol s ) 

Figur 16 Illumin d Current-Voltage Characteristics Measur ed By SERI For 

MINP CELL 1 . t h Textured Surface. 

• NEED 

I L 

TO ACHI 

• MU T UCE 

Sp TO 10 ' 

• WITH V U 

O L D J o WILL BE DE~REASED TO " 3 )( 10- '" Alem" 

ENT 

• MUST USE DOUBLE AR 

WITH TEXTURED SURFACE 

OR WITH COMPLETE 

OPTICAL CONFINEMENT 

PROJECTED PERFORMANCE 

30 

t 

Z 25 !!! 

u 

it 

Iti 

... 

:I 

c( 20 

16 

Jsc(mA/cm") 36.0 36.0 

Voc(mV) 630 650 

FF .794 '.812 

Jo(A!cm") 1 )( 10-12 4 .5 )( 10 - 13 

n·VALUe 1.0 1.0 

Ns(cm - ') 6 )( 10" 4 )( 10" 

. SURF Rec veL 10' 10' 

DIFF LENGTH 150 150 

GRID SHADOW 4% 4% 

CELL THICKNESS 15 mi. 15mh 

BACK SURF Ohmic Ohmic 

25% 

36.7 40.9 

670 720 

.820 .850 

2 )( 10 - '" 3 )( 10- '" 

1.0 1.0 

2 x 10'· 2 )( 10 " 

10' 10' 

200 500 (F&P) 

3% 2% 

15 mil 10mla 

BSF BSF 

Fig re 17. Estimated Property Improvements For High Efficiency MINP 

Cells. 

140 
DISCUSSION 

SWANSON: How did you grow the thin oxides? 

OLSEN: After we deposit aluminum to establish the back contact, a heat treatment at 5000C is carried out, and that process will grow a 20A oxide. 

SWANSON: Just from residual water, from the air? 

OLSEN: Bill (Addis), why don't you comment on that? 

ADDIS: The oxidation is carried out in a tube furnace. 

SWANSON: Dry oxygen? 

OLSEN: Yes. 

SWANSON: Have you investigated different ways of forming the oxide and found 

whether any are better than others? 

OLSEN: Not yet. We would like to try nitriding, and I have some thoughts on 

pursuing that further, but right now we have been going with the standard 

20A oxide. 

SWANSON: Have you measured the contact resistance? 

OLSEN: I think so. On the O.3~ area coverage, on a 2 x 2 solar cell, RS is 

still below 0.1 ohm. 

SWANSON: Doesn't seem good for concentrators .. 

OLSEN: Something seems to happen. It's strange; when the area goes down you 

get higher current density. The contact resistance goes down. 

SWANSON: Did I read you correctly that you got a better JO without the n 

layer under there than you did with the n layer? You said 3 x 10-13 

(A/cm2). 

OLSEN: No. That was for an MIS structure. Magnesium on p-type. 

SWANSON: That is what I meant. 

OLSEN: I think that is pertinent, mainly because it tells you something of 

the quality of the magnesium deposition and what it does to the p-type 

material. But it is a different situation, it appears, when you deposit 

onto an n-·type surface. For a Mg/p-Si MIS diode, the value of 

3 x 10-13 is approximately the theoretical value for JO' 

SWANSON: One would think you would want to take the n-layer out then, if it 

is--

141 
OLSEN: Well, the problem with an MIS structure is the magnitude of photocurrent, which is too low. You just can't get adequate optical coupling, 

that is, transmission of the photons through the metal. Maybe something 

worth considering along the same lines is an inversion-layer cell. That 

is one without any doping done at all. That is something we have worked 

on in the past. 

SWANSON: I sort of had the feeling that the phosphorus diffusion is not giving 

you the p~rformance it could. 

OLSEN: That's true. I think it is really hard to pin all this down. But I 

think it is clear that Green and his group have tailored their emitter to 

some degree and they have reduced the emitter recombination. 

KEAVNEY: When you said you had 20 A of oxide underneath the metal, I assume 

you measured that by ellipsometry. 

OLSEN: That is right. 

KEAVNEY: Do you have any ideas as to whether that is really 20 A of oxide 

or whether there is an organic contamination throwing off the measurement? 

OLSEN: The ellipsometry gives you 15 to 20 A and it is not really clear what 

that means. You really have to couple that information with other information such as MIS current-voltage characterization. The MIS devices we 

have looked at are really high-quality ones. So that tells us that the 

interfacial layer is of high quality. Then, also, surface recombination 

effects in the solar cells themselves seem to be reasonable. 

WOLF: It seems to me that Marty Green told us at the Photovoltaic Specialists 

Conference that his 19~ cell was not an MINP structure but a dot contact 

structure. He had a new acronym for it too, PEST or something like that. 

OLSEN: A dot contact cell, that is just what we made too. That simply means 

that you put slots in the thermal oxide on the surface, and the collector 

grid o.nly contacts a small area. But the question is: what is the natu,re 

of his contact at the interface? 

WOLF: That is right. That is what I thinking. 

OLSEN: He didn't think it was HIS anymore? 

WOLF: That was my impression. 

OLSEN: I wouldn't argue about it. They do sinter, like the standard procedure. I think, in theory, titanium can be used as an MIS contact. It 

just may be vel'y difficult to keep the oxygen out of it and get a decent 

contact. Maybe that is why you have to sinter. We have stuck with magnesium because it is not limiting us at this point and we haven't been 

motivated to change. But we are considering changing, because the use of 

magnesium impacts other processes. So we will move to try titanium as 

well, eventual~y. 

142 
" 

> \ 

\ ·'f ~ >-

I, 

I 

i 

I 

I 

WOLF: Another thing. I was a little surprised that you took the band gap as 

1.2 eV. That is the zero Kelvin numbe~. Really it is, at room temperature, more like 1.1. 

OLSEN: I know that. But if you look at the band gap expression versus temperature, it is 1.2~ minus some constant, times temperature. The constant 

times temperature divided by kT gives you an e-constant so that goes 

out into the pre-exponential number. 

WOLF: So that is where you put it? 

OLSEN: Yes. I hope that was clear to others. The band gap, I agree is 1.12, 

but it is the temperature dependence that I wanted to account for. An 

activation analysis gets 1.2 minus the bandgap narrowing. 

QUESTION: (Inaudible; concerning the use of magnesium.) 

OLSEN: No. We can't heat treat it. We haven't used titanium, but Green, for 

example, does heat treat at something like 4500C. 

WOLF: I thought we might have some questions with respect to all the papers 

together, and overall comments on the afternoon session -- even the 

morning session -- before we break up. One comment I would like to make: 

I feel that what we really all sat and listened to this afternoon was 

perhaps more how do we model, what do we learn out of the modeling, and 

how does whet we are doing actually relate to what we calculate? Rather 

than, really, concepts on how to get higher eff~ciency. So it seems to 

me it was more really modeling results and what did we learn from the 

modeling. I don't know whether that is challenging enough for more discussion or not. We certainly, some of us, use low-level modeling and get 

up to some point with that, and then comes high-level modeling beyond 

that. We will hear more about modeling tomorrow in any case. 

LESK: I am still confused. In the back contact you had only BSF. Specifically, what is the difference between ohmic and a BSF back-surface contact? 

OLSEN: Well, BSF refers to back-surface field. An adequate BSF yields a surface recombination velocity of zero. 

LESK: 

S 

'I am not sure I got that right. 

= 0 -- that means BSF? 

OLSEN: That's right. 

In BSF -- in your equation you put 

LESK: For ohmic, S is infinity but if you are maintaining the equilibrium in 

order to carry concentration to the back contact, that means ohmic. Is 

that the way it is used? 

OLSEN: Yes. The point is with low-cost silicon sheet material, the use of a 

BSF makes little difference to current. But, if you increase the life--

time, then a BSF can have a significant impact on photocurrent. 

143 
1 

j 

J 

1 

j 

WOLF: Are these things we are looking at here really all the approaches we 

can pursue to get to a higher efficiency? Are there things we should be 

looking at in addition? Does what we have been talking about really 

exhaust the methods available at this time? 

SPITZER: I wanted to mention a few things. On the idea of how to improve 

efficiency, I think some people referred to this. We are neglecting lots 

of current. The theoretical limit is 44 and if you tune up the base diffusion length, that current could easily be raised from 36, which most 

people are achieving, to about 38 with a back-surface reflector and diffusion length of 300 micrometers, which doesn't seem that hard to do. 

And, say, with 38 milliamps/m2 and a voltage of 660, with a fill factor 

of 0.8, that would be 20~. So I think some attention should be addressed 

to improving J sc . 

WOLF: It seems essentially that everybody who is working on high-efficiency 

cells sees how he can make the next step to get 20~. It seems that this 

is just about imminent. I think the big question after that becomes, how 

do we get to 22 or 23, and do we really have to get the trap densities 

down, or are there other remedial steps we can be doing to get the efficiencies up? Have we really exhausted all the cell-design approaches to 

a large enough degree for this next step? 

SWANSON: I think the goal of l5~ modules is rather modest in view of the 19~ 

cells that are already being made. 

WOLF: No. 

SWANSON: We are talking efficiency, not getting cost down. But I think if 

you want to go to the l5~ range, you should very seriously consider the 

Yablonovich design, which in my opinion has the potential of 25~. 

WOLF: He combines again a number of the things we have been discussing, and 

also Dick Swanson. How to get high lifetime is one of his key aspects. 

How to get the lifetime up, how to get the surface recombination velocity 

down, use a wider band-gap material on one side, etc. 

DYER: I have been out of this field for a number of years, but what are the 

difficulties with that overlap approach that someone mentioned earlier? 

WOLF: It is called the shingling of cells. 

DYER: What is the difficulty with that? You mentioned it, but 1 don't see 

any --

WOLF: Well, I don't think I mentioned that by saying there was a difficulty 

with it. It has been used for a long time in making submodules for space 

arrays. I guess it has given a certain amount of inflexibility within 

the array. One other approach was to make flexible interconnects, but 

still overlapping as far as individual soldering together is concerned. 

DYER: Does it come out so it is not worth it, is what I am after. 

144 
WOLF: Ro. 

DYER: Is it such that it is very successful and you can say, Well. we can 

gain back all that we devote to metallization, or is it not. worth it? 

WOLF: Well, you have no contact shading at all on the front, so you have all 

active surface that way. I see a little bit of a problem if the whole 

cell length is only 2 millimeters and then you overlap. You get quite a 

bit out of the horizontal with the whole thing, but I don't think that is 

too much of a problem area. You can somehow adjust for it again. No. I 

don't see a major problem with it. I guess from a manufacturing viewpoint it might be t.ough to make so many vet'y small li tUe devices and 

then assemble them into a bigger thing. It might give extra cost. But 

that's not fundamental. Somehow you can imagine some nice assembly 

machine that handles all these tiny little parts and makes a bigger thing 

out of it. 

145 
DINNER PRESENTATION 

HIGH-EFFICIENCY 

SOLAR-CELL RESEARCH FOR 

SPACE APPLICATIONS 

D. Flood, NASA Lewis 

Research Center 
HIGH EFFICIENCY SOLAR CELL RESEARCH FOR SPACE APPLICATIONS 

Dennis J. Flood 

NASA Lewis Research Center 

Cleveland, Ohio 

ABSTRACT 

NASA involvement in photovoltaic energy conversion research, development, and applications spans over two decades of continuous progress. Led by the 

Lewis Research Center's Photovoltaic Branch, Agency programs in solar cell 

research and development have produced a sound technology base for a broad 

range of space applications. Although space power requirements are mission 

dependent, there are fundamental objectives which guide the NASA photovoltaic 

program. They are to improve efficiency, increase life, reduce mass, and 

reduce the cost of photovoltaic energy converters and arrays. Consequently, 

the programs in place at Lewis Research Center range from fundamental 

research on advanced concepts to technology a~vances for improving the 

space-worthiness of solar arrays. This paper will describe several key activities in the Lewis program. 

INTRODUCTION 

The cell research activities at Lewis divide roughly into the following 

categories: advanced devices, gallium arsenide and other III-V compound 

solar cells, and high efficiency silicon cells. Work in all of these 

categories will be described. Particular attention will be given to a new 

strategy for efficient solar energy conversion which seeks to overcome the 

fundamental limitations inherent with all semiconductor photovoltaic 

converters. The approach exploits a well-known mechanism for absorption of 

light in thin metallic films of common metals, such as aluminum or silver: 

the coupling of light to surface plasmons. Surface plasmons can have 

suitable ranges for energy transport, (up to centimeters in the IR), and can 

absorb from the ultraviolet to the infrared. Energy conversion then occurs 

by transfering the surface plasmon energy to an array of inelastic tunnel 

diodes, where a current of tunneling electrons can be created. Key technical 

barriers have been identified and will be discussed, along with recent 

results aimed at eliminating them. 

The magnitude of NASAls photovoltaic space power activities can be seen 

in Figure 1. With the exception of the Skylab launch in 1973, most NASA 

missions have been at the 2 or 3 kilowatt level or below. Future NASA 

missions may be an entirely different story, however. The desire for more 

sophisticated, longer-lived missions will push power requirements up an order 

of magnitude and more. A low-earth orbiting manned space station, for 

example, might require up to 125 kilowatts of power in the station itself. 

This would, 'in turn, require a solar array output capacity in excess of 300 

kilowatts, and would represent over two and one-half times the power 

generating capacity that NASA has launched in the past 20 years. Such an 

147 
array will be the dominant physical feature of the Space Station, and will 

place a premium onvr~ducing the area, weight, and cost of large space arrays. . ~ .... ~~ ~ ~ Ji -~ :fulure power~feqiJirements for geosynchronous applications are also 

expected to rise in the coming decades, although few such missions will be 

soley NASAls. The primary uses of GEO spacecraft will be for commercial and 

military communications networks. In these applications in particular, a 

premium is placed on higher efficiency, lighter weight, and longer life. 

Cost is important, but is not as important a driver as it is for large LEO 

arrays. A key figure of merit for GEO arrays is the ratio of power out to 

total array mass in W/kg. NASAls most recent GEO satellite, TDRSS, had an 

approximate beginning-of-life specific power of 35 W/kg, with a BOL power of 

about 3 kilowatts. Future communications satellite power requirements are 

expected to be from 3 to 5 times that level. Moreover, volume and weight constraints of current and proposed GEO launch vehicles make it desirable to 

increase both efficiency and specific power significantly beyond present levels. End-of-life specific powers approaching 250 W/kg may well be 

required to meet such constraints. The payoff will be measured directly in 

terms of increases in the active payload of the satellite. 

The foregoing discussion is by no means exhaustive of all future space photovoltaic applications. It is intended only to put into context the 

rationale behind the current major thrusts of NASAls solar cell research and 

development program. 

HIGH EFFICIENCY SILICON SOLAR CELL RESEARCH 

Figure 2 summarizes the situation with regard to space solar cells since 

approximately 1960. Essentially, all space cells flown at that time were 

made from 10 ohm-cm starting material, and had AMO efficiencies on the order 

of 10 percent. Work in the ear"1y 1970 's resulted in the COMSAT violet cell 

(Reference 1) with an efficiency approaching 15 percent, but it quickly became clear that higher efficiencies could not be aChieved without improving the open-circuit voltage, and that could not be done without lowering the 

resistivity of the starting material. Current densities in the high efficiency 10 ohm-cm cells approached 50 ma/cm2, and could not reasonably be expected to go much higher in that material. In the mid 1970 's, 

therefore, Lewis Research Center initiated a concerted effort to develop an 

18 percent AMO cell, which had been estimated by Brandhorst (Reference 2) to 

be the maximum practical efficiency for silicon. The effort concentrated on 

raising the open-circuit voltage to the 700 millivolt range. The initial 

work resulted in open circuit voltages of nearly 650mV, but efficiencies 

were lower than desired because of the lower current-generating capabilities 

of the low resistivity cells. 

Several techniques have been advanced for raising the voltage in low 

resistivity cells. Among them is the multi-step diffusion process developed 

at Lewis Research Center, which produced a Voc approaching 650 mV (Reference 

3). The process was later used by COMSAT to produce a 14.5 per'cent AMO cell 

(Reference 4). This achievement was quickly followed by the development of 

cell designs at the University of New South Wales, under a NASA grant, which 

achieved 16 percent AMO, and Vocls approaching 680 mV. These cells, 

developed by Martin Green and co-workers (References 5, 6), have been 

148 
subjected to an intensive analysis at Lewis Research Center in an attempt to 

elucidate the mechanism(s) responsible for their improved performance. That 

work, reported by Weizer (Reference 7) at the last Photovoltaic Specialists Conference, has produced some surprising results. In brief, it was shown 

that: 

1. It is not the perfection of the emitter, but a previously unrecognized improvement in the base that is responsible for the high Voc's obtained in the MINMIS cell. 

2. The high voltage in the MINP cell is the result of the same 

improvement in the base as in the ft'IINMIS cell, coupled with a 

reduction in the emitter 10. 

3. The enhanced base characteristics of both cell designs are the result 

of a reduced minority carrier mobility in the starting silicon 

material used for these cells. 

Based on these results, it now appears that voltages approaching 800 mV 

are achievable in 0.1 ohm-cm silicon cells with full utilization of the MINP 

surface passivation techniques. AMO efficiencies approaching 20 percent may 

yet be possible in silicon. Work toward that goal will be continued in the 

Lewis Research Center program. 

III-V CELL RESEARCH 

Emphasis in the NASA solar cell research program has shifted from silicon 

during the past few years to the wide variety of semiconducting compounds 

formed from elements in columns three and five in the periodic table. The 

program ranges from basic materials science to pre-pilot cell design 

optimization studies. The activities fall roughly into three categories: (1) GaAs concentrator cells; (2) thin film cells; and (3) multi-junction cells. Resistance to the damage caused by charged particle radiation in the 

natural space environment is a major consideration in the III-V cell area, 

and along with efficiency, forms an important part of the justification for 

it. 

NASAls interest in III-V concentrator cells arises in part because of 

their potential for lowering the cost of very large solar arrays, such as are 

anticipated for a future Space Station. Figure 3 summarizes the results of a 

study of multi-hundred kilowatt array designs (Reference 8). The plot of 

combined cell and component costs versus concentration ratio shows the 

existance of a broad minimum between approximately 20x and 200x. Figure 4 

illustrates a concentrator design currently under development at TRW, under 

contract to Marshall Space Flight Center. Specifications for this miniature 

cassegrainian system call for a 4 mm diameter cell capable of 20 percent at 

125x and 85°C. Lewis Research Center has two contracts in place, one with 

Varian and one with Hughes Research, to design and produce such cells. With 

19 percent already demonstrated, there appear to be no apparent technical 

"show-stoppers" which will prevent realization of the program goal of 22 

percent at operating conditions. This application dramatically illustrates 

the higher efficiency and higher temperature capabilities of GaAs compared to 

silicon. GaAs concentrator cells will have' over twice the efficiency of 

149 
silicon at the operating temperatures projected for this array design. The 

physical dimensions of the cell are illustrated in Figure 5. The diameter of 

the illuminated area is 4 mm, while the length of one edge is 5 mm. The 

approximately 60 to 1 reduction in processed semiconductor area compared to a 

planar of equal output is the primary reason for the projected lower cost of 

this array design. An additional assumption, of course, is that the cost per unit area of the concentrator optics will be significantly lower than the 

equivalent area of r.1"'~::::es'~~d semiconductor materi ale The anticipated cell 

output at operati; (l':">~'itions is approximately 0.4 watts. Based on informal 

estimates, the projected cost of such cells could be on the order of 30 to 50 

1>/watt. 

Cost is not the only reason for interest in concentrator arrays for space 

application. A second very important reason, again depending on mission 

requirements, is the inherent shielding provided by the concentrator element 

against the natural radiation environment encountered in many orbits. 

Although not important for LEO applications, the design may make possible the 

use of photovoltaic power generators in some of the mid-altitude orbits that 

have previously been dismissed because of their high density radiation 

environment. Beyond that, if high efficiency can be coupled with lightweight 

concentrator optics, such arrays could eventually be flown in GEO. 

Research on thin film solar cells is directed toward improving their 

performance, not only in terms of their efficiency, but also in terms of 

their radiation resistance. An important thrust for the NASA space power 

program is the development of technology for the next generation of GEO 

communications spacecraft. At present, about 23 percent of the satellite 

mass launched to orbit must be dedicated to the power system, which is 

approximately the same fraction that is available for the payload itself. 

The benefits derivable from reducing the power system mass are directly translatable into revenue for commercial satellites, and into increased 

capability for non-commercial satellites. One approach under investigation 

at the present time for producing ultralightweight solar cells is the CLEFT 

process developed at the Linco1n Laboratory by John Fan and co-workers 

(References 9, 10, 11, 12). Progress in this area is well-known, and a 

detailed discussion need not be included here. The NASA goal is to 

demonstrate a 4 micron thick GaAs cell with at least 20 percent AMO 

efficiency, which suffers no more than a 10 percent loss of power 'after 10 

years of exposure to the GEO radiation environment. The goal is ambitious, 

but achieving it could result in significant reductions in the mass of the 

solar array for GEO systems. The cell development work at Lincoln Laboratory is supported at Lewis Research Center by in-house cell evaluation 

measurements and radiation damage studies. The best cell specific power demonstrated to-date is 5400 watts/kg, achieved with a 5.5 micron thick cell 

with gridded back contacts with an AMO efficiency slightly greater than 14 

percent. A cross-section of the cell is shown in Figure 6. The illuminated 

area is 0.51 cm2. There are many technological challenges to overcome 

before the CLEFT cell can be considered a viable candidate for use in space. Chief among them are the following: development of a UV-resistant adhesive to 

use in the film transfer process; improving the open-circuit voltage and ' 

fill-factor; establishing the radiation tolerance of the cell; and perhaps the most formidible among them, developing a suitable interconnect technology 

for joining 5 micron thick cells together in an array! 

150 
As is well-known, the efficiency of a typical single junction solar cell 

is limited fundamentally by the location of its bandgap within the solar 

spectrum, in this case the air mass zero (AMO) spectrum. Early calculations 

of multi-bandgap cell efficiencies at AMO (Reference 13) indicated that a 

total conversion efficiency of approximately 30 percent could be achieved in 

a three-cell stack under 100x illumination. The cell structure initially selected by NASA is shown in the first column of the table below, and was 

driven by the assumed requirement that the structure had to be 

lattice-matched throughout. The second column shows the current distribution 

of bandgaps for the structure, and is a result of the successful 

demonstration of composition grading between the various active layers of the 

cell. The latter technique allows for greater flexibility in the choice of 

bandgaps to achieve short-circuit current matching from each constituent cell 

in the stack. The lower bandgaps should produce a slightly higher efficiency than those of column one, and should make fabrication of the tunnel junction between the bottom and middle cells somewhat easier. (The high doping 

densities required for a tunnel junction interconnect are easier to achieve 

in a lower bandgap ~aterial.) The interconnect between the middle and top 

cells can be some sort of metal interconnect, such as the Varian-developed MIC (Reference 14). 

TABLE 1 

Multi-Junction Cell Bandgaps 

Cell 

Lower 

Middle 

Upper 

L-M 

1.15 

1.55 

2.05 

C-G 

1.15 

1.43 

1.95 

An int~resting simplification of the above structure is to use just two 

junctions, and to mechanically stack them. As has been pointed out by Fan 

(Reference 15), such a structure can be either a two, three, or four terminal 

device, without introducing much complexity into its fabrication. The 

monolithic stack, on the other hand) is most easily made into a two terminal 

device. There is some loss of efficiency in the AMO spectrum fora two 

junction cell, but there may also be a trade-off in the radiation hardness of 

the two structures which favors a two-junction, four terminal device. If the 

end-of-life performance of a series-connected multi-junction cell is to be 

maintained at reasonable levels, it becomes necessary to develop constituent 

cells which degrade by in a matched fashion in a radiation environment. 

Although possible in principle, it presents a formidable challenge to realize 

in practice. A four terminal device avoids the requirement for 

current-matching altogethers and does not, therefore, suffer any additional 

degradation beyond that of each of the constituent cells. 

ADVANCED CONCEPT SOLAR CELLS 

The calculated efficiency of an ideal cascade solar cell reaches a 

maximum when more than six bandgaps have been included in ·the stack, and can 

approach 60 percent in the AMO spectrum (Reference 16). Taking the real 

system losses into account, however, shows that the maximum has been passed 

151 
after three bandgaps have been included (Reference 17). As mentioned above, the practical maximum AMO efficiency of a three cell stack is expected to be 

30 percent, even under 100x illumination. The question that naturally arises 

is whether that efficiency limit, which appears to be inherent with 

semiconductor p-n junctions, can be transcended by some means. The problem is that the ordinary p-n junction solar cell in effect converts the incoming broadband solar radiation into a flow of monoenergetic electrons (and holes), 

the energy of which is determined by the semiconductor bandgap. While the 

coupling mechanism, i.e. the creation of electron-hole pairs, is broadband in 

nature, the excess kinetic energy imparted to the electron-hole pairs by 

photons with energies greater than the bandgap is essentially not 

transportable. It is lost in collisions with lattice phonons in a matter of 

picoseconds, resulting in very short ranges for the excited carriers. An 

initial requirement, then, for any major increase in efficiency, is to 

identify a mechanism for broadband absorption of the solar spectrum which 

creates a corresponding spectrum of electronic excitations in the absorber 

with ranges long enough that energy can be extracted from them. Thin films 

of common metals su~h as silver, aluminum, and gold can support a quantized, oscillatory excitation of their two-dimensional quasi-free electron gas known 

as a surface plasmon. The surface plasmons are produced by exterior electric 

fields incident on the boundary between the metal film and a dielectric 

medium. For large wave vectors the plasma waves behave like real surface 

waves: their electromagnetic field is concentrated around the boundary within 

a distance of approximately 10 angstroms. For small wave vectors the fields 

extend far into space, and resemble more and more those of a photon propagating along the boundary. The surface plasma wave behaves very much 

like a guided electromagnetic wave in a dielectric ~aveguide, except that the 

waveguide in this case is a metal film, and therefore very lossy. The 

latter fact limits the range of the surface plasmons at the high energy end 

of the spectrum to distances on the order of 70 to 100 microns. Propagation 

lengths for surface plasmons in the infrared, however, can approach several 

centimeters (Reference 18). A large body of literature exists which 

describes the properties of surface plasmons, and discusses several 

experiments in which they can either be observed or utilized. (See e.g., the 

monograph by Raether, Reference 19). The coupling between surface plasmons 

and photons can be very strong under the proper conditions, and is well 

understood theoretically. It can be shown that only the p-polarized 

component of the incident radiation can be coupled to a smooth film for 

example, and in such a way that the width of the acceptance angle is very small. In addition, the acceptance angle itself varies with wavelength. Such properties have all been verified experimentally. 

Conceptually, the direct conversion of solar energy to electricity requires the follov~ng processes: photon absorption, which either creates 

"free" charges (electron-hole pairs, photoelectrons, etc.) or imparts kinetic 

energy to a charge carrier (the surface plasmon, e.g.); and charge separation. The latter occurs by creating a potential barrier for some of 

the charge carriel~s while others are allowed to pass \ the p-n junction for 

electron-hole pairs, e.g., and a tunnel diode for energetic electrons). If 

photon absorption does not occur in the region where the charges are 

separated, then energy transport must occur from the absorption region to the 

barrier region. Charge collection and flow in an external circuit complete the picture. Since the surface plasmon is a quantized, collective 

oscillation of a two dimensional electron gas, the momentum imparted to the 

152 
surface plasmon by the incoming photon must be transferred to a mobile, free 

electron below the surface before any charge separation can occur. The 

latter requires, therefore, some sort of interaction mechanism between the 

surface plasmon and a free electron. 

It is clear from the preceeding discussions that any attempt to create a 

solar energy conversion device based on surface plasmon absorption of the 

solar spectrum must address for key technical barriers: (1) broadband 

coupling of sunlight to surface plasmons at a single acceptance angle; (2) 

low-loss energy transfer from the absorption to the barrier region; (3) 

coupling between the surface plasmons and mobile charge carriers in the 

region of the potential barrier; and (4) efficient charge transfer from the 

low to the high energy side of the potential barrier. A possible approach for dealing with the fourth problem involves inelastic electron tunneling 

-through a thin film metal-insulator-metal structure. If the film thicknesses 

have been properly chosen, such a structure supports a coupled mode between 

surface plasmons in both metal films. This coupled mode, or junction plasmon, is able to propagate along the length of the structure, and by 

virtue of the strong electric field it creates in the oxide, can provide an 

inelastic tunneling channel for an electron impinging on the barrier at that 

instant. Preliminary calculations conducted at Lewis Research Center 

indicate such a mechanism, while possible in principle, is beset with 

difficulties. Not the least among them are the need to limit the reverse 

tunneling current to acceptably low levels, and the very limited range of the 

junction plasmon in general (typically a few tenths of a micron). A suitably 

chosen semiconductor thin film can be incorporated on the low energy side of 

the junction in such a way that its bandgap eliminates the final states for 

the reverse tunneling process, but the impact of doing so on the ability of 

the structure to support a junction plasmon is unknown at present. In order 

for the process to go at all, it is first necessary to transfer energy from 

the surface to the junction plasmons. Here the problem is that the junction 

plasmon has a much lower velocity than a surface plasmon of the same 

frequency, so some sort of momentum-matching transfer mechanism is required. Figure 7 shows schematically one possibility. Calculations show that a 

grating can promote energy transfer between monoenergetic surface and 

junction plasmons with better than 90 percent efficiency (Reference 20). The 

feasibility of doing the same with a broad spectrum of plasmons has yet to be 

firmly established. The proposed approach in effect uses a junction plasmon 

as an intermediary between the surface plasmons and tunneling electrons. 

What is still required, however, is experimental verification of the 

approaches that oil.ve been out 1 i ned here. 

Mechanisms which affect surface plasmon coupling and range (barriers 1 

and 2) are relatively well-known and understood. Recent results for the 

latter obtained in the NASA program are summarized in Figure 8 (Reference 

21), which contains a plot of surface plasmon range as a function of 

wavelength with film thickness as a parameter. The structure for which the 

propagation distances have been calculated is shown in the inset. An 

important result is that the calculated damping matches experimental re.sults 

on dirty films, and seems to indicate that ohmic losses have been 

overestimated in previous calculations. A series of experiments aimed at 

exploring surface plasmon propagation in such structures has been started. 

The initial work will investigate the so-called end-fire coupling technique 

for injecting surface plasmons into the structure shown in Figure 8. The 

153 
technique is well-known in integrated optics. Instead of matching the 

incident field to a surface plasmon wave vector along the direction of 

propagation, the field distributions are matched across the end face of the 

sample. That is, the incident field is focussed onto the end face of the 

structure with a field distribution which matches as closely as possible that 

of a surface plasmon. In addition to investigating the generation of 

long-range surface plasmons, the same experiments will investigate the 

coupling efficiency of the technique. The results of a first order 

perturbation theory calculation are shown in Figure 9 (Reference 22). The 

salient point is that an optimized incident field distribution yields a 

greater than 80 percent coupling efficiency for a silver film for wavelengths 

from 0.4 microns to more than 1.2 microns, and as the figure shows, the 

efficiency is relatively independent of the incident spot size. This 

approach has several important features. For example, all of the modes 

originate at the same point, and therefore the propagation distance can be 

used to discriminate wavelength regions for absorption. In addition, the 

beam shaping and focussing can be done by external, miniature optics. Both 

of these have impact not only on the experimental efforts just described, but 

also on the actual configuration of such a device should it become a 

reality. Is is conceivable, for example, that such a device could be used in 

the miniature cassegrainian concentrator system described earlier in this 

paper. 

A second approach for investigating the coupling of sunlight to surface 

plasmons is shown schematically in Figure 10. In this approach, the film on 

which surface plasmon generation is desired is evaporated onto a glass prism, and is covered with a dielectric layer onto which a metal-island film is then 

evaporated. The effect of the island film is to broaden the acceptance angle from a few tenths of a degree to as much a five degrees at half-maximum in 

the absorption (Reference 23). The measurements also show that as much as 90 

percent of the p-polarized component of the top quarter of the solar spectrum 

can be absorbed by a silver island-film, with similar results for the 

mid-quarter with a gold island film. The results can be explained in terms 

of an incident radiation field interacting with dipole located near a 

conducting thin film, with suitable modifications which take the macroscopic size of the metal-island into account. By combining measurements of the 

surface plasmon dispersion curve for a silver film and measurements of the 

dipole frequency shifts (isolated dipole vs. a dipole near a conducting film) 

with theory, the coupling efficiency between the radiation field and surface 

plasmons can be estimated. (The dipole absorbs energy from the 

normally-incident, unpolarized light beam and loses it by one of three 

processes: reradiation; surface plasmon generation in the thin film; and 

ohmic heating.) The earlier reflectivity data indicated that as much as 97 

percent of the indicent radiation was absorbed by a silver island film. 

However, the detailed calculations indicate that a maximum of about 40 

percent of the total incoming energy is transfered to surface plasmons in the 

underlying silver film (Reference 24). Moreover, the maximum is a function 

of both the wavelength of the incident light, and of the spacer-layer thickness. An important feature of this approach, however, is that both the 

sand p polarizations can couple to the structure. Additional work is 

required to assess the importance of the shape of the metal-islands on the 

absorption, and to determine the optimum structure for maximum efficiency. 

154 
As the preceeding discussion demonstrates, there are several key barriers 

that must be addressed just to determine the feasibility of a surface plasmon 

solar converter. Although we have made strides in our basic understanding of 

many of them, the final outcome is far from clear. Work will continue on the 

key questions that have thus far been identified. If and when any technical 

"show-stoppers" are identified, the progran will be brought to an end. Until 

such time, however, the effort presumes success. 

CONCLUSION 

The NASA space photovoltaic research and technology program has its roots in 

the days of the first real solar cell. In the three decades since then 

(1954-1984), the Agency's program has not only developed technology for the 

current generation of photovoltaic power systems in space, it continues to 

lay foundations for the future. A key element in the success of the NASA 

program is its overriding philosophy that the most important driver is high efficiency. Without exception, program objectives are to achieve high cell 

efficiency first, and to address balance-of-system considerations second. 

The success of this approach is attested to by the many applications of space 

photovoltaics, from NASA to military to commercial missions. Once the path 

to high efficiency has been demonstrated, additional developments follow 

which reduce it to practice in a cost-effective manner. In many instances 

those developments are encouraged with government funding. In many other 

instances such developments have occurred at the initiative of the commercial 

sector. The net result has been steady progress for nearly three decades. 

References 

1. J. Lindmayer and J.F. Allison, Ninth IEEE Photovoltaic 

Specialists Conference, 1973 

2. Henry W. Brandhorst, Jr., "Silicon Solar Cell Efficiency 

- Prac.:tice and Promise," Ninth IEEE Photovoltaic 

Specialists Conference, 1973 

3. M.P. Godlewski, T.M. Klucher, G.A. Mazaris, and V.G. 

Weizer, "Open Circuit Voltage Improvements in Low 

Resistivity Solar Cells," Fourteenth IEEE Photovoltaic 

Specialists Conf., 1980 

4. R.A.Arndt, A Meulenberg, J.F. Allison, and V.G. Weizer, 

"Advances in High Output Voltage Silicon Solar Cells," 

Fifteenth Photovoltaic Specialists Conf., 1981 

5. R.B. Godfrey and M.A. Green, "High Efficiency Silicon 

MinMis Solar Cell Design and Experimental Results," IEEE 

Trans. Electron Devices, vol. ED-27, pp. 737-745, ApriJ, 

1980 

155 
6. A.W. Bakers and M.A. Green, "678-mv Open-Circuit Voltage 

Si licon Solar Cells," App. Phys. Lett., vol. 39, pp. 

483-485, 15 Sept., 1981 

7. V.G. Weizer, C.K. Swartz, R.E. Hart, and M.P. Godlewski, 

"Voltage Controlling Mechanisms in Low Resistivity Silicon 

Solar Cells - A Unified Approach," Seventeenth Photovoltaic 

Specialists Conf., 1984 

8. "Study of Multi-Hundred f<ilowatt Solar Arrays for 

Earth-Orbital Applications," NASA Contract #NAS8-32986, 

Final Report 

9. John C.C. Fan, C.O. Bozler, and R.L. Chapman, Appl. 

Phys. Lett. ~g, 390, 1978 

10. John C.C. Fan, "GaAs Shallow Homojunction Solar Cells" 

NASA CR-165167, 1980 

11. R.W. McClelland, C.O. Bozler, and J.C.C. Fan, Appl. 

Phys. Lett. ~Z,560, 1980 

12. J.C.C. Fan "High Efficiency, Low Cost Thin GaAs Solar 

Cells," NASA CR-168265, 1982 

13. T.J~ Maloney, Solar Energy Mater. ~, 359, 1981 

14. P.G. Borden, et ai, "Progress Toward Cascade Cells Made 

by OM-VPE," Proceedings of a Conference on Space 

Photovoltaic Research and Technology, Lewis Research 

Center, Cleveland, Ohio, 1982 

15. J.C.C. Fan, "Optimal Design of High Efficiency 

Single-Junction and Tandem Concentrator Space Cells at 80C 

and 100 Suns," Proceedings of a Conference on Space 

Photovoltaic Research and Technology, Lewis Research 

Center, Cleveland Ohio, 1983 

16. N.A. Gokcen and J.J. Loferski, "Efficiency of Tandem 

Solar Cell Systems as a Function of Temperature and 

Concentration Ratio," Proceedings of a Conference on Solar 

Cell High Efficiency and Radiation Damage, Lewis Research 

Center, Cleveland, Ohio, 1979 

17. A. Bennett a,i,d L.C. Olsen, "AnalYSis of Multiple Cell 

Concentrator Photovoltaic Systems," Thirteenth IEEE 

Photovoltaic Specialists Conference, 868, 1978 

18. A.S. Barker, Jr., Phys. Rev. ~~, 5418, 1973 

19. H. Raether, "Surface Polaritons," edited by V.M. 

Agranovich and D.L. Mills, North Holland Press,New York, 

1982 

156 
20. Lynn Anderson, private communication 

21. G. Stegeman, NASA Grant NAG3-250, private communication 

22. 6. Stegeman, NASA Grant NAG3-250, private communication 

23. W.R. Holland and D.G. Hall, Phys Rev. Lett.§g *12, 

1041, 1984 

24. D.G. Hall, private communication 

157 
200 

150 

POWER (kW) 

100 

50 

°60 

CUMULATIVE 

65 70 75 

YEAR 

80 85 

Figure 1. Total Space Power Launched for NASA Missions. 

20 

~ 

,: 

0 

z 

w 

0 

it 

u. 15 w 

z 

0 

iii 

a: 

w 

> 

z 

0 

0 

10 

FLIGHT QUALITY SOLAR CELLS 

Laboratory ~--~~ r-1 ~ Concentrator 

Demo. l:': 

1960 

"'-- GALLIUM ARSENIDE 

~~[].-

/" [I[IJrextured Surface 

rim Low Reallllvity 

~Back Surface Field 

[[OA/R Coaling 

Shallow Juncllon 

Super Blue cen Standard 

1970 1980 1990 

Figure 2. Space Quality Solar Cell Technology. 

158 
EaTIMATED 

coan • 

". 

~1L-~~~~~~~~ 1 Z ••• ~ • __ _ L-~ _ __ ~~~ 

CONCENTRATION RATIO 

Figure 3 . Array Component Cosls Versus Concenlralion Ralio. 

INCIDENT LIGHT 

-0 i ~ r 

I 

LIGHT I 

CATCH ER CONE I 

I 

PRIMARY ~ REF LECTOR C::::::::::~~_I ~===::;-\=:::J 

SOLAR 

CEl 

MOLYBDENUM 

BASE 

ALUMINUM 

RADIATOR 

SECONDARY 

REF LECTOR 

Figure 4. Minialure Cas.egrainian Concenlralor Concepl. 

159 
20 

18 

16 

EFFICIENCY 

14 

12 

1.0 10.0 

CONCENTRATION RATIO 

---- T= 25°C 

T= SOoC 

100.0 

Figure 5. Miniature Concentrator Cell Efficiency vs. 

Concentration Ratio (AMO). 

UGHT 

1 

FAONT 

CONTACT 

FINGEA 

Figure 6. CLEFT Cell Cross Section. 

160 
PRISM COUPLE 

LJGHT TO PLASMON 

~ 

OF 

Figure 7. Surface to Junction Plasmon Grating Coupler 

Concept. 

-E 

E 

-

w 

U 

Z 

< 

~ 

(J) 

C 

Z 

o 

i= 

< 

(!) 

< 

10 00 

100 

10 

0. '0.1 ~ /, "

,= 2 .0.0-' t /;'/ JI 

o METAL(SllVER) h ~ 

0. '.? ; "," 2.07,,; ~ 

0 .01 

o. 001 '---"""'"---'----""'----''---"'''---~ 

o 4 8 12 

WAVELENGTH 'X (MICRONS) 

Figure 8. Surf.ce Plasmon Range. 

161 
COUPLING 

EFF I.C I ENCY 

0.4 0.6 1.0 

20% 

2.0 4.0 

Figure 9. Endfire Coupling Efficiency as a Function of the 

Ratio R of the Beam Width Plasmon Field Penetration Depth. 

-11--- substrate 

o 

Ag 500 A o 

LiF 50- 600 A 

o Ag island film 30 A 

Figure 10. Light Coupling 

by Metal-Island Films. 

Sample Cross-section at Top. 

Measurement Schematic at Side. 

162 

prism 
SESSION III 

SURFACE-INTERFACE EFFECTS 

L. Kazmerski, Chairman 
NEW ADATOK KODEL FOR Si(lll) 7X7 AND 

Si(lll)Ge 5X5 RECONSTRUCTED SURFACES 

N85-31625 

(Ini~ially published in Phys. Review B, Vol. 30, No.8, 15 October 1984) 

D.J. Chadi 

Palo Alto Research Center 

Xerox Corp. 

Palo Alto, California 94304 

A new adatom structure with significantly less angular strain than the 

simple adatom geometry is proposed. The model involves a rebonding of 

~1/8 of surface atoms to the substrate in a manner similar to that 

occurring in the ff-bonded-chain structure for the Si(lll) 2X1 ~urface. The interference between adatom and substrate reconstructions 

forces the smallest threefold-symmetric unit cells to be 5X5 and 7X7 

in size. The proposed reconstructed-adatom model gives rise to 

structural features in good agreement with experiment. In particular, 

the inhomogeneous corrugation of the two halves of the 7X7 unit cell 

seen in vacuum-tunneling microscopy and the apparent need for stacking 

fault sequences in ion-channeling experiments are accounted for. The 

results of surface energy and structure calculations on 2X2, 3K3, 5X5, 

and 7X7 adatom models are presented. 

I. INTRODUCTION 

The first real-space imaging of the 7X7 reconstructed Si(ll11 surface by 

Binnig et aLl has generated new interest in the precise nature of the 

atomic bonding at this surface. Vacuum-tunneling microscopy1 reveals 12 

maxima in the unit cell and deep holes at the corners and sides of the unit 

cell with a corrugation as large as 2.8~. Except for a corner site, the 

lateral positions of the maxima coincide with the adatoms of Harrison's 

mode12 and the vacancies of the Lander model. 3 Binnig et al. l suggested 

that the deep and i~homogeneotis co~rugations of the surface should be 

explainable by a simple relaxation or modification of the Harrison adatom 

model. The nature of the modifications to be made has remained unclear, 

however, because tunneling microscopy does not provide direct information on 

the surface bonding geometry even though it yields valuable information on the 

surface corrugation. 

Despite the fact that the adatom model gives the best agreement of any 

simple structure with the vacuum-tunneling results, it has not received 

universal acceptance as the correct structure for the 7X7 surface. This is 

primarily because it is presently unclear whether this model is consistent 

with other experimental data or with theoretical considerations. J:r'Ot' example, 

complementary information on the surface atomic structure from a r~cent 

analysis4 Qf Rutherford backscattering experiments5,6 indicates that the . . . ABCABC . . • stacking sequence, characteristic of face-centered-cubic 

crystals, may be broken at the surface. Additional evidence for stacking 

faults or surface dislocations has been deduced from low-energy-electron 

diffraction (LEED) data,4 and from transmission electron microscopy.7 

163 
~ Ii;. ~1 : . ': ~ 

~ several'models8- lO which incorporate stacking fault sequences in the unit 

cell and have structural features consistent with the observations of Binnig 

et al. l have been proposed recently and will be examined in this paper. 

The acceptance of the ada tom model for the 7X7 surface appears difficult 

also from theoretical considerations. The surface energy of the thermodynamically stable 7X7 surface should be lower than that of the metastable cleaved 

2Xl surface. In particular, the 7X7 surface should have a lower surface 

energy than the ff-bonded-chain structure. 11 ,12 In going from a chain to 

an adatom structure, the favorable energy lowering from ~ bonding is presumably lost and, in addition, a significantly larger lattice strain is 

introduced. The recent calculations of Northrup and Cohen13 for a 2X2 

adatom model indicate, however, that the lowering of the dangling-bond density 

by a factor of 2 is sufficient to compensate for most of this energy loss. 

The 2X2 adatom model is found to be 0.12 eV (per IX! unit area) higher in 

energy than the ff-bonded structure. This energy, although comparable in 

size to the magnitude of typical surface reconstruction energies, is 

sufficiently small that it makes further investigations of the adatom model 

necessary. 13 

In addition to constraints from vacuum-tunneling microscopy,1 ionchanneling4 and surface-energy considerations the model for the annealed 

(111) surfaces of si and Ge has to account for a large body of other experimental data. These include nucleation of the 7X7 structure at steps;14 the 

appearance of stable 5X5 and 7X7 periodicities15 for Sn on Ge(111) and16 

for Ge on Si(111) surfaces; the similarities and differences in the 

photoemission17- l9 and optical-absorption20 ,21 spectra of 2X1 and 7X7 

surfaces; evidence for unique surface and subsurface hydrogen chemisorption 

sites on the 7X7 surface;22 the possibility of magnetic ordering at low 

temperatures;23 and a unique physisorption site geometry24 for Xe and Kr. 

In this paper the structural and energetic aspects of the 7X7 and 5X5 

reconstructions are examined via total-energy calculations on a·variety of 

models and on unit cells ranging from 2X2 to 7X7 in size. Large unit cells 

were used to eliminate uncertainties regarding the influence of unit-cell 

dimensions on the magnitude of the relaxation energy fo~ any particular model, 

and because flor the adatom geometry proposed in this paper, the minimum unit 

cell size is 5X5. 

The paper is organized as follows. The results of energy-minimization 

calculations for the conventional type of adatom model are discussed in 

Sec. II. For the particular case of a 2X2 rectangular lattice, the results 

are compared with those from ab initio self-consistent pseudopotential 

calculations of Northrup and Cohen. 13 The surface energy for this structure 

is taken as a reference for comparing the differences between various 

structures discussed in this and subsequent sections. 

The possibility of substrate reconstruction involving a rebonding of 

atoms (as opposed to simple atomic relaxation) is discussed in Sec. III. The 

motivation for this is the reduction of the large angular strains present in 

the conventional adatom model. The smallest structure for which this is 

possible is a rectangular 2X2 lattice. For this lattice, the results are 

found to be only marginally better than the old rectangularadatommodel. 

164 
Surprisingly, as shown in this section, it is found that as a result of the 

interference between the adatom and substrate reconstructions, hexagonal 2X2» 

4X4, and 6X6 periodic structures are not possible for the new geometry. If 

the structure is required to have threefold symmetry, then the smallest 

hexagonal AXA unit cells are SXS and 7X7. A 3X3 structure l~cking the 

threefold symmetry is calculated to have a much higher surface energy than the 

conventional adatom model. The reduced surface energy of larger unit cells is 

not primarily a result of the rotational symmetry but arises from a removal of 

constraints inherent in smaller lattices. 

The results of calculations on the new SXS adatom geometry and a discussion of experimental results on the SXS and 7X7 structures are presented in 

Sec. IV where it is shown that the model gives the following. 

(i) A surface corrugation consistent with that observed in vacuumtunneling experiments. l It provides an explanation for the inhomogeneous 

corrugation of the surface by having different relaxations and reconstructions 

in the two halves of the unit cell. 

(ii) Structural elements resembling those arIsIng from stacking faults 

at the surface. 4 These come about directly as a consequence of the rebonding occurring in the substrate layer and are in good agreement with 

structural features deduced from ion channeling. 

(iii) A lowering of the surface energy making the new structure energetically competitive with the ff-bonded-chain modelll,l2 for the 2Xl surface. 

(iv) An explanation for the striking similarity in polarization and 

angular dependence ot normal photoemission spectra for the surface states at 

~O.8 eV below the Fermi energy Er in both the 2Xl and 7X7 surfaces. l7 ,l8 

Measured relative to the valence-band maximuml9 instead of EF. this state 

is ~O.3 eV more bound in the 2Xl surface than in the 7X7 surface. The new 

adatom model provides a simple explanation for this energy difference. 

(v) Specific surface sites where hydrogen chemisorption is most likely 

to occur. It is proposed that hydrogen chemisorption at these sites leads to 

a large decrease of the surface energy. 

(vi) A greatly enhanced interaction among distant dangling bondE as 

compared to the simple adatom model. This suggests that a magnetic oraering 

of spins should make a small but non-negligible contribution to the stability 

of SXS and 7XS structures. 

The results of calculations for Himpsel's trimer model8 are discussed 

in Sec. V. The tight-binding-based method of caicuialion2S is reviewed 

briefly in Sec. VI. 

II. SIMPLE ADATOM MODELS 

A. Angular strains 

"!l'wo adatom models wHh rectangular and hexagonal 2X2 unit cells are shown 

in Fig. 1. In the "ideal" configuration where all bond lengths are equal to 

165 
those in the bulk, the adatom is one interlayer spacing (~O. 78 .1' in Si) 

above the substrate. the large angular strains in this simple adatom 

configuration caQ be appreciated by considering the distributions of angles 

e at the fourfold-coordinated surface atoms capped by the adatom. At each 

one of these second-,layer atoms, there are three angles with the values of 

(1) 

which deviate sharply from the ideal tetrahedral angle of 109.470 • 

the adatom models shown in Fig. 1 are for the situation where the adatom 

is on a "hollow" site. If the adatom is placed on a site above a second-layer 

atom, then larger angular strains in addition to large bond-length strains 

develop. 

(a) ___ --___ --~ 

@ Adatom 

o Surface atom 

• Second..Javer atom· 

Fig. 1. top views of simple adatom models with rectangular and 

hexagonal 2X2 periodicities are shown in (a) and (b). In the 

unrelaxed geometry, the adatom falls on the intersection of the three 

straight lines joining surface atoms to second-layer atoms. the 

resulting 1800 angles go to 1600 -1650 after relaxation. 

the surface energy of the top-site geometry is sufficiently higher than the 

hollow-siteconfiguration13 that it will not be considered in. this paper. 

the top-site geometry is also inconsistent with the results of 

vacuum-tunneling microscopy.1 

166 ,~.- , / ... ~ 
It may be argued that relaxation of surface atoms will result in a large 

decrease of the angular strain energy. However, the present calcu19tions for 

lattices from 2X2 to 7X7 in size show that the angles in Eq. (1) relax at best 

to values of 1600 and 810 , respectively. The angular relaxation is 

achieved at the cost of increasing the adatom-substrate bond length by =4.5~ 

over the bulk bond length. For a 2X2 hexagonal lattice, the reduction in 

total energy resulting from relaxatiQn is about 1.4 eV per adatom. 

Considerations based on the angull1.'· strain energy of the adatom model 

suggest that this energy can be decrel>:.}ed appreciably if the equilibrium 

adatom-substrate bond length is larger than the underlying bulk bond length. 

A larger bond length prevents the adatom from falling on a straight line with 

surface and second-layer atoms, thus decreasing al from 1800 . For the 

Ge(lll)-Sn and Si(lll)-Ge systems where the Ge-Sn and Si-Ge bond lengths are 

both larger than substrate bond lengths, otber possibilities for the 

optimization of the angular distributions exist if an intermixing of the 

different atomic species takes place. The Ge(lll.)-Sn adatom model is 

discussed below in Sec. C. The role of misfit strain energies in the 

reconstruction of annealed surfaces has been discussed by Phillips.26 

B. Surface energy of the rectangular 2X2 adatom 

model from tight-binding and pseudopotential calculations 

Northrup and Cohenl3 have recently calculated the total-energy and 

atomic structure of a rectangular 2X2 adatom model [see F"ig. 1(a)] using the 

self-consistent pseudopotential method. They find that the relaxed adatom 

~eometry has a surface energy lower by 0.17 eV/(lX1 unit cell) relative to the 

unrelaxed ideal 2X? surface and higher by 0.19 eV/(lX2 unit cell) as compared 

to Pandey's tr-bonded-chain geometry.ll,12 The removal of the lateral 

strains and frustrations inherent in the rectangular 2X2 lattice, which can be 

achieved, for example, by going to a hexagonal lattice, was proposed to lead 

to an even more stable adatom geometry. The present calculations, as 

described in more detail below, confirm this picture and show that a reduction 

of 0.05 eV/(lX1 unit cell) occurs in going from the rectangular to the 

hexagonal adatom geometry. 

The atomic and electronic structure of the ada tom geometry obtained from 

the two calculations are in generally very good agreement. However, the 

tight-binding calculations presented here for various adatom geomet~ies 

predict the relative surface-energy differences between various adatom 

geometries more accurately than the differences between dissimilar geometries 

such as the ideal l:'lurface and the adatom geometry. This is because the 

limited !23 basis set used in the calculations is too small to adequately 

account for the large angular strains present in adatom models. Compared to 

pseudopotential calculations,13 the energy of the optimized rectangular 

adatom model is calculated to be 0.03 eV/(lxl cell) higher than that of the 

unrelaxed ideal surface instead of 0.17 eV/(lXl cell) lower. Despite this 

problem of the tight-binding method in underestimating the binding energy of 

an adatom, it is expected to be more useful and accurate in comparing the 

relative energy differences between similar types of adatom structures 

considered in this paper. Defining y as 

y = surface energy (in eV/lXl unit cell) (2) 

167 
and taking the rectangular 2X2 lattice as reference, in the following sections 

the changes ~y in surface energy relative to the value for this lattice are 

given. On the basis of Northrup and Cohen's caleulation,13 a decrease in 

y of greater than 0.19 eV/(lX1 cell) should make the adatom geometry more 

favorable than the ff-bonded-chain model. 

C. Results of calculations on Si(111) adatom models 

1. Rectangular 2X2 cell 

The adatom and three substrate layers were allowed to relax. The optimum 

atomic geometry was calculated from a minimization of Hellmann-Feynman 

forces. 25 In the unrelaxed geometry the adatom is approximately 0.78 A 

above the surface layer. After relaxation, the adatom moves flway from the 

surface by an extra 0.39 A. This is in good agreement with the 0.33 A 

calculated by Northrup and Cohen. 13 The present tight-binding calculations 

give a bond-length stretching of 4.9~ at the surface as compared to 3.4~ 

obtained previously.13 Some angular distributions, with the pseudopotential 

values given in parentheses, are 

(3) 

about the ada tom, and 

(4) 

around the surface atoms capped by the ada tom. Much smaller maximal angular 

deviations of +120 and -50 from the ideal tetrahedral value occur about 

atoms on the second and third layers at the surface, respectively. The 

rectangular lattices lead to lateral strains and frustrations which are 

expected to be less severe in the hexagonal 2X2 cell discussed below. 

2. Hexagonal 2X2 cell 

The use of a hexagonal instead of a rectangular cell is calculated to 

lead to an energy lowering of 0.2 eV/adatom or equivalently to a change in 

surface energy of 

~'Y = -0.05 eV/(1X1 unit cell). 

Thi~ can be attributed to a slight decrease of the angular and bond-length 

strains on this surface. The adatom-surface bond length is stretched by 

~4.4~ (as compared to =:4.9~ before) and the angular distributions are 

about the ada tom, and 

around the surface atoms capped by the adatom. Smaller deviations of +100 

and _40 from the ideal tetrahedral value are also found in the second and 

third layers below the surface. 

168 

(5) 

(6) 

(7) 
.j 

The 0.05-eV drop per lXl unit cell in tbe energy of the 2X2 hexagonal 

cell relative to the rectangular geometry brings the energy of this structure 

to within 0.14 eV/atom of the ~-bonded-chain structure. The question, 

therefore, arises as to whether the use of larger unit cells will lead to a 

further reduction of this energy. 

3. Ge(111)-Sn: 2X2 adatom model 

The addition of a fraction of a monolayer of Sn to the Ge(111) surface is 

known27 to result in a metastable 2X2 structure before the formation of 

stable 5X5 and 7X7 patterns. 15 ,27 The larger covalent rad,ius of Sn compared 

to Ge reduces the angular strains. For the optimum hexagonal 2X2 geometry, 

the Sn adatoms are calculated to be 1.6 A above the Ge surface. The 

optimization of structure leads to a Sn-Ge bond length of 2.73 A which is 4~ 

larger than the sum of the respective covalent radii. The angular 

distributions are 

e = 88.60 (8) 

on the adatoms, and 

e - 157.30 , 83.2° (9) 

on the substrate atoms capped by Sn. As shown in Sec. IV, a reconstruction of 

the subsurface leads to a lowering of the enet'gy and results in a larger unit 

cell. This is consistent with the observed 27 metastability of the 2X2 

reconstructed Ge(111)-Sn structure. 

4. 5X5 and 7X7 adatom models 

Simple adatom models with 5X5 and 7X7 unit cells, with, respectively, 6 

and 12 adatoms per cell, were examined to test whether the greater degrees of 

freedom for atomic relaxation would lead to a lower surface~nergy. No 

restrictions on the atomic displacements were imposed. Each surface atom was 

moved in the direction of the Hellmann-Feynman forces 25 acting on it by an 

amount proportional to the force. New forces were then calculated and the 

process was repeated. The most extensive tests were made on 5X5 lattices. 

The adatoms as well as the first three atomic layers at the surface (i.e., a 

total of 81 atoms per cell) were allowed to relax. After many iteration~, the 

surface energy of the 5X5 adatom structure was calculated to be 

~0.04 eV/atom lower than that of the hexagonal 2X2 structure. About 10 

iterations were also made for the 7X7 structure. Because of the large size of 

the unit cell, only the 12 adatoms and the first surface layer were allowed to 

relax. From the magnitude of the Hellmann-Feynman forces acting on the atoms, 

it can be estimated that the structure and surface energy of the 7X7 lattice 

will be nearly the same as that of the 5X5 lattice. It appears that an 

increase in unit-cell size will not result in a sufficiently large decrease in 

the surface energy of the ada tom model to explain the occurrence of such 

superstructures on annealed surfaces. For the simple adatom model, a 4X4 unit 

cell should be nearly as likely to occur as a 5XS, 6X6, or a 7X7 cell. 

169 
III. NEW ADATOK KODEL 

A. Rectangular 2X2 cell 

The simple adatom model leads to three highly strained 1800 angles per 

adatom in the ideal structure where all bond lengths are equal to the bulk 

value. As shown in Sec. II, atomic relaxations lead to somewhat reduced 

angular strains and to values of around 1600 for these angles. A 

reconstruction mechanism that leads to a further reduction in the strain 

energy resulting in angles of ~135° is demonstrated in Fig. 2 for the case 

of a rectangular 2X2 lattice. The ~econstruction involves a rebonding of the 

"rest" atom (Le., the surface atom not capped by the adatom) to the substrate 

in a manner similar to that occurring for the u-bonded-chain model. 11,12 

The reconstruction results in a reversal of the coordinations of the rest atom 

and a second-layer atom: The rest atoms become fourfold coordinated by 

becoming, in essence, a second-layer atom bonded to a third-layer atom, and 

the second-layer atoms becomes like a threefold-coordinated first-layer atom. 

The top views of the ideal and reconstructed surface are depicted 

schematically in Figs. 2(a) and 2(b); the corresponding side views are shown 

in Figs. 2(c) and 2(d). It can be seen that the reconstruction improves the 

values of two out of three ~1800 angles at the surface. There does not 

appear to be any simple way' of reducing all the strains via reconstruction. 

The reconstruction shown in Fig. 2(b) improves the bonding of the adatom to 

the substrate by forcing two of the dangling bonds to become better aligned 

with the adatom. An opti.mization of the structure also shows reduced 

bond-length strains. The adatom substrate bond length is calculated to be 

~3.5~ longer than the bulk value (instead of ~4.9~ before the 

reconstruction). The model has mirror reflection symmetry through a plane 

passing through the ada'tom. 

The constraints on atomic relaxations inherent in a rectangular 2X2 

rectangular lattice are found to limit the energy reduction from rebonding to 

~0.06 eV/adatom. The energy of the new structure is, therefore, still • ~0.14 eV/adatom higher than that of t,he simple hexagonal 2X2 adatom 

structure discussed in Sec. II. One reason for the relatively high energy of 

the new structure is that the release of the strains at the surface creates 

additional stress at subsurface layers. The 2X2 lattice does not allow a 

satisfactory relaxation of these layers that will lead to a significant 

reduction of the surface energy. The new adatom geometry leads to an enhanced 

interaction between the dangling bonds on adatoms and rest atoms. For the 

particular case of the rectangular 2X2 geometry, this does not lead to a 

lowering of the electronic energy because the term involving this interaction 

has a zero sum over the two-dimensional Brillouin zone. The predicted higher 

surface energy of rectangular versus relaxed or reconstructed hexagonal 2X2 

cells is consistent with the experimental observation 27 of only the latter 

periodicity for the Ge(lll)-Sn 2X2 system. 

B. Hexagonal 2X2, 4X4, and 6X6 cells 

The new reconstructed type of adatom model, surprisingly, rules out 

hexagonal 2X2, 4X4, or even 6X6 unit cells. This results from the requirement 

that the adatom should always be kept threefold coordinated. As shown in 

Fig. 3 for the hexagonal 2X2 case, this condition is incompatible with the 

170 
1 

I 

i 

1 

I I 

f 

H i 

I 

~ 

I 

i 

I 

i 

I 

i 

(a) __ -~ __ -~. 

(c) 

1 

(b) 

1 

@ Adatom 

o Surface atom 

• Second-layer atom 

FIG. 2. Arrows in (a) show the top view of the directions of surface 

atomic displacements leading to a reconstruction of the simple 2X2 

rectangular adatom model. The resulting structure is shown in (b). 

The rebonding is si.milar t.o that occurring in the 11'-bonded-chain 

reconstruction of the Si(lll) 2Xl surface. It transforms 2/3 of the 

~l65° angles to ~135°. The corresponding side views of the 

ideal and reconstructed surfaces are shown in (c) and (d). 

periodicity of the unit cell. The rebonding of the rest atom (i.e., atom 3 in 

Fig. 3) to the substrate does not lead to relaxation of any of the ~l800 

angles created by the adatom. To reduce these angles, it is necessary to 

rebond type-l atom to the substrate. This, however, would result in the 

adatom becoming twofold coordinated,raising the surface energy considerably. 

It is simply not possible to keep the adatom threefold coordinated and, 

simultaneously, relax the angular strains in a hexagonal 2X2 lattice. Exactly 

the same type of problem persists for the larger 4X4, 6X6, and possibly other 

2nX2n hexagonal cells. This aspect of the new adatom model is in sharp 

contract to the conventional adatom geometry where 2.n.X2n. periodicities can be 

easily achieved. 

171 
r

-'''~,   ! 

@ Adatom 

o Surface atom 

• Second-layer atom 

FIG. 3. This top-view figure illustrates that a rebonding of atoms, 

of the type shown in Fig. 2 for the rectangular 2X2 cell, is not 

possible for the hexagonal 2X2 cell. In order to get a reduction in 

the angular strain energy, it would be necessary to move atom 1 in 

the direction shown and make it a second-layer atom while making atom 

2 a first-layer atom. This would result in the adatom becom-lng 

twofold coordinated, leading to an increase in the surface energy. 

It can be seen that the rebonding of "rest·· atom 3 does not lead to 

any lowering of the strain energy. 

C. Hexagonal 3X3 lattice 

The smallest hexagonal nXn lattice for the reconstructed adatom model is 

3X3 in size, as shown in Fig. 4. The directions of surface atomic 

displacements leading to the reconstruction of the substrate are indicated by 

arrows in Fig. 4(a) and the resulting structure is shown in Fig. 4(b). The 

optimized structure is calculated to have a surface energy 0.5 eV/(3X3 unit 

cell) higher than for the relaxed but unreconstructed adatom geometry. One 

reason for this is the extremely large bond-length strains (~6.4~ and S.7~) 

at the surface resulting from reconstruction. These are the largest strains 

for any of the adatom models examined. Another reason for the high surface 

energy is that reconstructions transforms only 2/9 of the 1600 -1800 angles 

to ~135° as opposed to 2/3 of such angles in the rectangular 2X2 case. In 

addition, the reconstructed 3X3 adatom model cannot be made to have the 

threefold symmetry of the underlying substrate. 

IV. SXS AND 7X7 RECONSTRUCTED (111) SURFACES 

A. Reconstructed adatom model 

The smallest unit cells for Which the reconstruction of the adstom model 

can be made to have threefold rotational symmetry are SXS and 7X7. in size. 

The presence of this symmetry is accompanied by the removal of frustrations 

encountered in smaller unit cells. The directions of motion of surface-layer 

172 
FIG. 4. Top views of the Si(lll) 3X3 surface are shown. The 

reconstructed 3X3 adatom model has a mirror plane going through the 

long diagonal but it lacks threefold rotational symmetry. The 

directions of atomic motions leading to a reconstruction of the 

substrate is shown in (a) and the resulting structure is shown in 

(b). Only one ~165° angle is transformed to a ~135° angle 

for each rebonding, as opposed to twice as many in 5X5 and 7X7 

lattices. The atomic designations are the same as in Figs. 1-3. 

atoms (i.e., rest atoms) which bond to the substrate to form the modified 

adatom model are shown by arrows in Figs. 5(a) and 6(a). The fraction of 

surface atoms participating in the reconstruction of the adatom model is 

nearly 1/8 in both the 5X5 and 7X7 structures. The rebonding of each atom 

transforms two 1600 -1800 angles into ~134° angles. The lateral 

positions of the adatoms on the left triangular region of the 5X5 structure 

are calculated to be modified by ~0.05 A relative to their ideal values as 

a result of this rebonding. No such change occurs on the right triangular 

section. 

The requirement that every adatom should be close to a boundary of the 

unit cell (such that a reconstruction of the underlying surface similar to 

those for the 5X5 and 7X7 surfaces can occur) rules out adatom models with 

marginally larger (e.g., 9X9) unit cells. For the 5X5 and 7X7 structures, the 

short diagonal of the unit cell is equivalent to a boundary line of the cell 

asa result of threefold rotational symmetry. All the adatoms .within "hese 

173 
structures are. therefore. adjacent to a boundary. For larger cells, a number 

of adatoms would be forced to the interior of the unit cell and away from the 

boundaries. This would raise the surface energy since comparable 

reconstruction of the substrate could not occur for these atoms. 

The release of strain energy associated with the reconstruction of the 

substrate is calculated to be large locally. Each rebonding is calculated to 

release ~0.7 eV in energy. This value is obtained by comparing the total 

energy for the optimized conventional 5X5 adatom model with that obtained for 

the new 5X5 structure. The latter has a surface energy which is lower than 

the reference rectangular 2X2 lattice (sea Sec. II) by 

~y~ -0.14 eV/(lX1 unit cell). (10) 

The simple reconstruction of just the left half of the 5X5 lattice goes a long 

way towards the ~-0.19 eV/atom needed to make the adatom model competitive 

with the chain model for the 2X1 cleaved surface. Because of the depth of the 

reconstruction. it is not presently feasible to do any meaningful calculations 

on the new 7X7 structure. It is assumed here that the results of the 

calculations on the 5X5 surface are applicable for the most part to the 7X7 

surface. 

FIG. 5~ A top view of the ideal 5X5 adatom model is shown in (a). 

The directions of atomic motions leading to a reconstruction of the 

substrate are indicated by arrows. The .resu1ting reconstructed 

structure is shown in (b). and the point of large stress in the right 

triangular region is indicated by an arrow. The atomic designati~.,.s 

are tile same as in Figs. 1-3. 

174 
, , , 

, , 

1 " ~'I 

:~ 

I 

I 

I 

FIG. 6. Ideal and reconstructed adatom models for the 7X7 surface 

are shown in (a) and (b), respectively. The arrows in (a) give the 

directions of atomic displacements leading to the rebonding. The 

points of high stress in the left and right triangular regions are 

indicated by arrows in (b). As discussed in the text, hydrogen 

chemisorption at these sites would enhance the stability of the 

structure. The atomic designations are the same as in Figs. 1-3. 

The 5X5 and 7X7 structures shown in Figs. 5(b) and 6(b) have a 

reconstructed adatom geometry on the left half of the cell and a conventional 

type of adatom structure on the right half. The presenc,e of an adatom at the 

corner of the unit cell is energetically unfavorable since it leads to a 

locally ~3X~3 structure. Adatom structures with this periodicity have a 

higher surface energy than those with a 2X2 lattice. From Figs. 5(b) and 6(b) 

it can be seen that the relation of equivalent sets of adatoms in the 5X5 and 

7X7 lattices [e.g., the adatoms in the left half of the unit cells in 

Figs. 5(b) and 6(b)] with respect to the centers of their respective 

triangular regions is reversed in the two cell structures. 

Several possibilities for the reconstruction of the right triangular 

section of the unit cell, as well as for the corner, were considered. Three 

of the reconstructions for the corner are shown in Fig. 7. The last two 

reconstructions preserve the threefold symmetry of the unit cell, whereas the 

first one breaks this symmetry. For the 5X5 lattice, none of these 

recons-l:.ructions is found to lower the ,energy; in fact, they all result in an 

increase of the total energy. Other types of atomic rearrangements at the 

corner cannot be ruled out. A comparison of the calculated structural and 

electronic properties of the 5X5 structure with the available experimental 

data is given in the following sections. 

175 
I 

1 

l 

4 

il 

ff 

~ 

I ! 

(al (hI (e) 

(d) Ie) (f) 

FIG. 7. Three possible modes of atomic displacements at the corner 

of a 5X5 or 7X7 unit cell are shown in (a), (b), and (c). The 

corresponding structures resulting from reconstruction are shown in 

(d), (e), and (f), respectively. structures (b) and (c) preserve the 

threefold symmetry of the unit cell whereas (a) breaks this symmetry 

but maintains mirror reflection symmetry. All three types of 

reconstruction are found to result in an increase in energy. The 

atomic designations are the same as in.Figs. 1-3. 

B. Vacuum-tunneling microscopy 

The presence of two different ada tom structures on each triangular half 

of the eell is consistent with results from vacuum-tunneling measurements1 ,28 

on the Si(111)-7X7 surface. The present calculations on a 5X5 surface show 

that the adatoms on the two halves of the unit cell differ in their heights 

relative to a reference (111) plane by ~z~0.19±0.03 A, with the 

adatoms on the left half being higher. This is reversed for the conventional 

adatom model, where the difference is calculated to be -0.03 A for the 5X5 

surface and -0.02 A for the 7X7 surface. Recent tunneling measurements 28 

indicate a difference of ~0.3 A. The sign of the difference is in 

176 
agreement with that calculated for the new adatom geometry. The atomic 

rebonding occurring along the boundaries of the unit cell leads to depressions 

along the edges and the short diagonal of the unit cell which are consistent 

with those observed in tunneling microscopy. 

The maximum difference between the height of an ada tom to a second-layer 

atom at the corner is calculated to be ~1.9±O.3 A. The experimental! 

value of the corrugation is ~2.8±O.3 A. The rest atoms at the corner 

would have to relax more deeply towards the bulk for the measured corrugation 

to be this large. For the particular case of the rectangular 2X2 lattice, the 

tight-binding method (as compared to the pseudopotential method13 ) may 

underestimate this inward relaxation. Applying the results of the 

calculations for the SXS lattice to the 7X7 structure, the height difference 

between adatoms on the left (right) and the central atom of the left (right) 

triangular region is l.SS±O.2 A (O.94±O.2 A) as compared to the 

values of 1.2±0.3 A (O.7±0.2 A) from vacuum tunneling. 1 with the 

possible exception of the corner where further atomic relaxations may occur, 

the modified adatom provides a satisfactory overall description of the 

experimental results on the 7X7 surface corrugation. 

c. Rutherford backscattering 

The proposed SXS and 7X7 structures have structural features, arising 

from reconstructi·on, resembling those from stacking faults at the surface. On 

the ideal (111) surface, the projection of the three bonds made by a surface 

atom with its three nearest-neighbor second-layer atoms onto a (111) plane 

forms either a Y pattern or an "invertedtt Y pattern which is rotated by 1800 

from it. If stacking fault sequences occur at the surfac.e, 4 then both 

patterns are simultaneously present. The modified adatom model demonstrates 

that such a feature can also arise as a result of reconstruction even in the 

absence of stacking faults. The rebonding of a surface atom to the substrate 

causes a reversal of the Y pattern next to it. An examination of the 

calculated atomic structure and lattice spacings of the modified adatom model 

shows it to be in good agreement with the structural features deduced by 

Bennett et al. 4 from recent Rutherford backscattering experiments. S,6 The 

new adatom model is expected to be consistent with the results of 

impact-collision ion spectroscopy of Aono et a1. 29 which give evid.ence for 

an adatom geometry but, at the same time, rule out the conventional, 

unreconstructed adatom model. 

D. Magnetic ordering 

The reconstruction of the simple ada tom model greatly enhances the 

interactions between neighboring dangling bonds by bringing them much closer 

together. The interaction between the dangling bonds on the SXS surface is 

estimated to make a small [~O.5 eV!(lXl unit cell)] but non-negligible 

contribution to the lowering of the total energy. This is in contrast to the 

situation for the 2Xl ff-bonded chain structure where second-nearest-neighbor 

interactions make no contribution to the stabilization of the structure 

because the phase constraint on the wave function resulting from the Bloch 

condition leads to a cos(ka) term in the electronic energy with a zero 

integral over the Brillouin zone. For the proposed SXS and 7X7 structures 

spin-polarization effects similar to those considered previously30-32 for 

c - 3 177 
smaller lattices are also expected to make a further (=0.04 eV/interacting 

dangling bond) contribution to the stability of the structure. Possible 

evidence for a magnetic ordering on the 7X7 surface resulting in a very small 

gap in the electronic excitation spectrum has been obtained recently from 

low-temperature measurements. 23 

E. Photoemission 

strong indirect e~idence for the adatom reconstruction proposed in this 

paper is provided by normal photoemission spectra17- 19 on.Si(111) 2X1 and 

7X7 reconstructed surfaces. These measurements show a surface state at 0.8 eV 

below the Fermi energy EF on both surfaces with nearly identical 

polarization and angular dependence of photoemission intensity at normal 

emission. 17 ,18 Measured relative to the bulk valence-band maximum instead 

of EF' the two states lie at -0.7 eV and -0.4 eV for the 2Xl and 7X7 

surfaces, respective1y.19 The present calculations of the electronic 

structure for the SXS stru'cture shown in Fig. S(b) and for the 2Xl 

reconstructed ff-bonded-chain mode111 ,l2 predict a binding-energy 

difference of 0.24 eV and show the conwon origin of the two states. The 

sharply localized and multiply degenerate state at -0.4 eV for the SXS surface 

is calculated to arise primarily from the dangling bonds of the 

threefold-coordinated surface atoms that were initially second-layer atoms 

before the (2X2)-like reconstruction. The lower binding energy of this state 

relative to the one on the 2Xl surface is a consequence of the absence of 

nearest-neighbor ff bonding on the 7X7 surface. The r~duced emission 

intensity for the 7X7 surface is consistent with the smaller density of these 

type of atoms on this surface. The similarity between the 2Xl and 7X7 

surfaces is expected to hold only near normal emission where the phase of the 

wave function is invariant over all equivalent dangling bonds on the 2Xl 

surface. 

F. LEED 

Additional strong evidence in favor of some 2Xl-type reconstruction on 

the 7X7 surface is provided by LEED. Defining the effective "ll2-order" 

spectra of the 7X7 surface to be the average of the 3/7 and 4/7 

fractional-order spectra, Yang and Jona33 have found remarkable similarities 

in the 1/2 spectra of the 2Xl and 7X7 surfaces. They have also shown that the 

7X7 surface possesses at least one mirror plane along the doubling direction 

of the 2Xl surface. These results of LEED are in agreement with the modified 

adatom model proposed in this paper. The question of whether the 7X7 surface 

possesses only one mirror plane or three such planes leading to threefold 

rotational symmetry was also raised by the LEED measurements. Surface 

reconstruction leading to a reduced symmetry can lead, in principle, to a 

reduction in the total energy. The present calculations show that the removal 

of threefold symmetry on the SXS surface, by additional 2Xl-like 

reconstructions at the corner atoms, Figs. 7(a) and 7(b), which still maintain 

mirror symmetry along the [2it] direction, results in an increase in the 

surface energy. The present calculations indicate that the threefold symmetry 

of the 7X7 LEED Pattern is intrinsic and not the result of an averaging over 

three single domain patterns. 

178 
• I 

j 

! 

I 

G. Hydrogen chemisorption 

The 5XS and 7X7 unit cell contain points of high stress at the positions 

of second-layer atoms marked by arrows in Figs. S(b) and 6(b). The stress is 

caused by the passage of three =1800 angles through these sites. The 

surface minimizes its energy by exerting a large outward force on these 

second-layer atoms which moves them up by =0.35 A. reducing the 1800 

angles to =1630. The large stress at these points increases the 

probability of bond rupture upon exposure to hydrogen. The breaking of the 

second- to third-layer bonds at these points. together with the chemisorption 

of one hydrogen atom at each of the resulting dangling bonds. should lead to a 

very large decrease in energy. The recent high-resolution infrared 

spectroscopy of Chabal et al. 22 on Si(ll1) 7X7 surfaces covered by a few 

percent of a monolayer of hydrogen has provided evidence for unique 

chemisorption sites at the surface and the subsurface. For the 7X7 model 

proposed here [Fib. 6(b)] this would suggest a greater probability for 

hydrogen chemisorption on the left half of the unit cell (at the position of 

the arrow) than on the right triangular region. 

Evidence for the formation of SiH2 and SiH3 complexes in the early 

stages of hydrogen chemisorption on the Si(111) 7X7 surface has been obtained 

by Wagner et a!.34 from electron-energy-loss studies. The most probable 

atomic sites to form such complexes are the adatoms where the strained 

adatom-surface bonds are most likely to break upon exposure to atomic 

hydrogen. Hydrogen ch,emisorption leads to a lowering of the surface energies 

of SX5 and 7X7 adatom structures. Experimentally, it is known3S that 

hydrogen chemisorption does not remove the seventh-order periodicity of the 

Si(111) surface. 

H. Optical absorption 

In the energy range of =0.4-1.0 eV, the strength of optical absorp]tion 

between surface states on the S1(111) 7X7 surface is at least an order of 

magnitude smaller than on the 2X1 surface. For the latter case, two recent 

optical studies36 ,37 have provided strong evidence for the u-bonded-chain 

model. 11 For this structure. the magnitude of the optical transition matrix 

element can be shown to be proportional to the nearest-neighbor u-bonding 

interaction between dangling bonds. The weakness of the optical-absorption 

intensity on the 7X7 surface is related to the more distant and much weaker 

hopping matrix element between dangling bonds. The calculations for the 5XS 

structure show narrow empty .!.2z-symmetry surface-state bands at 0.13-0.28 eV 

and a't 0.39-0.45 eV at above the valence"':band maximum (VB!!) which are strongly 

localized on the adatoms. The highest filled surface states are calculated to 

be =0.4 eV below the VB!!. These states are also .!.2z in character and are 

localized on the fourfold atoms which become threefold coordinated as a result 

of reconstruction. Transitions between these states are expected to be very 

weak as a result of the small hybridization between the orbitals. At higher 

excitation energies (1-3 eV), differential external reflectivity 

measurements38 show a surface-state transition at 1.76 eV. 

I. Nucleation at steps 

A study of the phase transition between the Si(111) 7X7 and 1X1 

179 
structures at Tc~8300C via reflection electron microscopy14 reveals 

that the 7X7 structure nucleates preferentially at steps. From the 

observation that the shapes of the steps change spontaneously and continuously 

above Tc. it was concluded that the 7X7 reconstruction involved an ordering 

of either adatoms or vacancies. 14 In the context of the new adatom model 

for the 7X7 surface. the role of steps in the nucleation process is to force 

initially a linear ordering of adatoms along the step. If the binding energy 

of adatoms near the step is larger than that of adatoms on the terrace so that 

they remain effectively pinned at the step while the other adatoms can move, 

then a two-dimensional ordering of atoms should eventually result. A greater 

binding energy near a step is reasonable because of the greater freedom for 

atomic relaxation at such a site. The 7X7 to lXl order-disorder 

transition39 probably results when all adatoms become mobile. At lower 

temperatures (T5~2S0C). where surface atomic mobilities are smaller, steps 

tend to increase the 2Xl to 7X7 transition temperature. 40 

J. Adsorption of closed-shell atoms 

Recent studies24 ,41 of Ar, Kr, and Xe adsorption on the Si(111) 7X7 

surface have provided useful information on the atomic structure of this 

surface. The measurements provide evidence for a unique chemisorption site at 

the surface which is most probably associated with the deep hole at the corner 

of the unit cell seen in tunneling microscopy. By measuring the amount of 

adsorbed Kr and Xe as a function of temperature at fixed pressure, Conrad and 

Webb24 were able to demonstrate inadequacies in nearly all the structural 

models that have been proposed for this surface. More recently Demuth and 

Schell-Sorokin4l have reported ultraviolet photoemission mea~urements of the 

coverage-dependent electron binding energies of adsorbed Ar and Xe on Si(lll) 

surfaces. Their results favor the Harrison-Binnigl ,2 type of adatom model 

for the 7X7 surface to the exclusion of most other structural models. The 

three types of adsorption sites inferred from the measurements are indicative, 

however, of a structure more complex than the simple adatom geometry. This is 

consistent with vacuum-tunneling results 1 and with the reconstructed adatom 

model presented in this paper. 

V. TRIMER MODEL 

In addition to adatom models, Himpselts trimer mode18 for the 7X7 

reconstruction was examined in detail. The model is similar to the 

ff-bonded-chain model for the Si(lll) 2Xl surface except that only one-half 

as much rebonding of atoms is required to create it. Furthermore, in common 

with the models proposed by McRae9 and Bennett,10 stacking-fault sequences 

are explicitly included in the structure. This leads to bonding between 

second-layer atoms along the boundaries of the unit cell leading to a ~16~ 

reduction in dangling-bond density from the lXl surface. It was suggested8 

that the reduction in the number of broken bonds together with ff bonding 

would stabilize the timer model against the 2Xl chain model. 

Using a SXS lattice, the atomic structure of the trimer model was fully 

optimized. The calculations show that the model has a higher surface energy 

than either the ideal lXl surface or the simple adatom model. The surface 

energy is calculated to be ~0.3 eV/lXl unit cell higher than the 

reconstructed adatom model. The ff bonding in the trimer model is found to 

180 
be not as effective as in the 2X1 chain model. Calculations for an optimized 

2X2 trimer model (which replaces the large strains associated with the 

stacking-fault sequences of the 5X5 structure with other unavoidable strains) 

give an identical surface energy when corrections for a 16~ lower 

dangling-bond density are made. For 5X5 and 7X7 lattices, the results of the 

calculations indicate that the bonding between second-layer atoms which is 

required in stacking-fault models of the surface reconstruction leads to large 

strains which are energetically unfavorable. 

VI. METHOD OF CALCULATION 

The use of the empirical tight-binding method in force and 

energy-minimization calculations is discussed in detail in Ref. 25. In this 

section~ the approach employed in calculating the surface energies for the 

large unit cells discussed above is examined. 

As in previous calculations, a slab geomet~y infinitely periodic in two 

dimensions was used. The criterion for choosing the thickness of the slab is 

that the relaxations or reconstructions on the two ends of the slab should 

remain independent of each other. To reduce the need for a large number of 

layers in the present calculations, the dangling bonds on one end of the slab 

were eliminated by the addition of hydrogen for all the surfaces studies. To 

account for the effects of hydrogenation on the total energy, an additional 

calculation in which hydrogen was added to both ends of an ideal slab had to 

be made. One-half of the total energy of the latter geometry was subtracted 

from the energy of the struct.ure with hydrogen on only one side of it, to 

determine the total energy §tot of the remaining N atoms. The surface 

energy y was then calculated by dividing the energy 

6§ = §tot (N) - NEO (11) 

by the area of the surface unit cell. In Eq. (11), §O is the binding energy 

per atom in the crystalline, diamond-structure environment. 

The calculations on 5X5 adatom geometries were done with a 131-atom unit 

cell consisting of six adatoms, four complete (111) layers (100 atoms), and 25 

hydrogen atoms. The hydrogen layer and the si layer adjacent to it were held 

fixed in nearly all the calculations. The remaining 81 atoms were allowed to 

relax. The relaxed atomic geometries were determined by moving each atom 

along the direction of the Hellmann-Feynman force acting on it. The 

calculation of this force within the tight-binding method is straightforward 

and has been previously discussed. 25 The modified adatom model proposed in 

this paper leads to a relaxation extending deeper into the bulk than is the 

case for the simple adatom model. For this reason, it was not possible to 

test the new adatom model for the 7X7 surface. For the conventional adatom 

model, however, a calculation of the atomic structure was made. In these 

calculations, a 159-atom unit cell consisting of 12 adatoms, two full (111) 

layers (98 atoms), and 49 hydrogen atoms was used. 

VII. CONCLUSIONS 

A ne-.,: a.ciatom model differing from the conventional model by a 

reconstruction of the substrate is proposed. The new adatom structure 

181 
p~ovides an explanation for the 7X7 and 5X5 size of the unit cells seen on 

annealed Si(111) and Si(lll)-Ge surfaces, respectively. The model is 

consistent with structural information from vacuum-tunneling microscopy. It 

also provides simple explanations for stacking-fault-type features expected 

f~om Rutherford backscattering experiments and for similarities in the LEED 

and photoemission spect~a of 2Xl and 7X7 surfaces. 

ACKNOWLEDGMENTS 

I am grateful to Dr. John North~up for many stimulat~ng discussions. 

This work is supported in part by the U.S. Office of Naval Research through 

Contract No. N00014-82-C-0244. 

1 

2 

3 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

REFERENCES 

G. Binnig. H. Rohrer, Ch. Gerbe~, and E. Weibel, Phys. Rev. Lett. 50, 120 

(1983). 

W.A. Harrison, Surf. Sci. 55, 1 (1976). 

J.J. Lander, G.W. Gobeli, and J. Mor~ison, J. Appl. Phys. 34, 2298 

(1963); J.J. Lander, in Progress in Solid state Chemistry, edited by H. 

Reiss (Pergamon, Oxford, 1965), Vol. II, p. 26. 

P.A. Bennett, L.C. Feldman, Y. Kuk, E.G. McRae, and J.E. Rowe, Phys. Rev. 

B 28, 3656 (1983). 

R.J. Culbertson, L.C. Feldman, and P.J. Silverman, Phys. Rev. Lett. 45, 

2043 (1980). 

R.M. Tromp, E.J. van Loenen, M. Iwami, and F.W. Saris, Solid State 

Commun. 44, 971 (1982). 

P.M. Petroff and R.J. Wilson, Phys. Rev. Lett. 51, 199 (1983). 

F.J. Himpsel, Phys. Rev. B 27, 7782 (1933). 

E.G. McRae, Phys. Rev. B 28, 2305 (1983). 

P.A. Bennett (unpublished). This model involves adatoms, stacking-fault 

sequences, and dimers at the surface. 

K.C. Pandey, Phys. Rev. Lett. 47, 1913 (1981); 49, 223 (1982). 

J.E. Northrup and M.L. Cohen, Phys. Rev. Lett. 49, 1349 (1982); J. Vae. 

Sci. Technol. 21,333 (1982). 

J.E. Northrup and M.L. Cohen, Phys. Rev. B 29, 1966 (1984). 

N. Osakabe, Y. Tanishiro, K. Yagi, and G. Honjo, Surf. Sci. 109, 353 

(1981); N. Osakabe, K. Yagi, and G. Honjo, Jpn. J. ApI. Phys. 19, L309 

(1980). 

182 
15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

T. Ichikawa and S. Ino, Solid State C01llllun. 27, 483 (1978). 

H.J. Gossmann, J.C. Bean, L.C. Feldman, and W.K. Gibson, Surf. Sci. 138, 

L175 (1984). 

D.J. Chadi, R.S. Bauer, R.H. Williams, G.V. Hansson, R.Z. Bachrach, J.C. 

Kiddelsen, F. Houzay, G.K. Guichar, R. Pinchaux, and Y. Petroff, Phys. 

Rev. Lett. 44, 799 (1980). 

F. Houzay, G.K. Guichar, R. Pinchaux, and Y. Petroff, J. Vac. Sci. 

Technol. 18, 860 (1981). 

F.J. Himpsel, P. Heimann, and D.E. Eastman, Phys. Rev. B 24, 2003 (1981); 

F.J. Himpsel, D.E. Eastman, P. Heimann, and B. Reihl, Phys. Rev. B 24, 

1120 (1981). 

G. Chiarotti, P. Chiaradia, and S. Nannarone, Surf. Sci. 49, 315 (1975). 

G. Chiarotti, S. Nannarone, R. Pastore, and P. Chiaradia, Phys. Rev. B 4, 

3398 (1971). 

Y.J. Chabal, G.S. Higashi, and S.B. Christman, Phys. Rev. B 28, 4472 

(1983); Y.J. Chabal, Phys. Rev. Lett. SO, 1850 (1983). 

J.E. Demuth, B.N.J. Persson, and A.J. Schell-Sorokin, Phys. Rev. Lett. 

51, 2214 (1983). 

E. Conrad and K.B. Webb, Surf. Sci. 129, 37 (1980). 

D.J. Chadi, Phys. Rev. B 29, 785 (1984). 

J.C. Phillips, Phys. Rev. Lett. 45, 90S (1980). 

S.B. DiCenzo, P.A. Bennett, D. Tribula, P. Thiry, G.K. Wertheim, and J.E. 

Rowe (unpublished). 

G. Binnig and H. Rohrer, J. Vac. Sci. Technol. (to be published). 

K. Aono, R. Souda, C. Oshima, and Y. Ishizawa, Phys. Rev. Lett. 51, 801 

(1983) . 

R. Del Sole and D.J. Chadi, Phys. Rev. B 24, 7431 (1981); D.J. Chadi and 

R. Del Sole, J. Vac. Sci. technol. 21,319 (1982). 

J.E. Northrup and K.L. Cohen, Phys. Rev. Lett. 47, 1910 (1981). 

K. Lannoo and G. Allan, Surf. Sci. 115, L138 (1982); G. Allan and K. 

Lannoo, ibid .• 73, 11 (1977). 

W.S. Yang and F. Jona, Solid State C01llllun. 48, 377 (1983). 

H. Wagner, R. Butz, U. Backes, and D. Bruchmann, Solid State Commun. 38, 

1155 (1981). 

183 
35 

36 

37 

38 

39 

40 

41 

T. Sakurai and H.D. Hagstrum. Phys. Rev. B 12 5349 (1975). 

P. Chiaradia. A. Cricenti. S. Selci, and G. Chiarotti. Phys. Rev. Lett. 

52. 1145 (1984). 

H.A. Olmstead and N.H. Amer. Phys. Rev. Lett. 52. 1148 (1984). 

P.E. Wierenga. A. Van Si1fhout. and H.J. Sparnaay. Surf. Sci. 87. 43 

(1979) . 

H.B. Webb and P.A. Bennett. Surf. Sci. 31. 104 (1981); J. Vac. Sci. 

Technol. 18. 847 (1981). 

P.O. Auer and W. Honch. Jpn. J. Appl. Phys. Suppl. 2. Pt. 2. p. 397 

(1974). 

J.E. Demuth and A.J. Schell-Sorokin. J. Vac. Sci. Technol. A 2. 808 

(1984) . 

184 
DISCUSSION 

RAO: I believe you said as part of your talk that these bonds have residual 

ionic charges. What is the effect of ionic charges? Can you get compensation in these charges by other atoms moving in? What is the physical manifestation of this? 

KAZKERSKI: The physical manifestation i.s an increase in the work function at 

the surface. You can actually predict that there shpuld be about 0.5 eV 

increase in the work function. Measured, the work function increases 

about 0.35 eVe You can get rid of most of these things by hydrogen ion. 

You get an increase in the work function because of the way the atoms are 

oriented. You can tell which end is negative and which one is positive, 

and then calculate the work function increase. 

DYER: This work has very far-reaching, important considerations for many uses 

of silicon, and I compliment you and your workers on this. I-have a 

question that arises in my mind right away. Supposing you wer~ dissolving away silicon or melting away silicon, do you visualize that these 

structures would occur instantaneously or would they take some time to 

come up? 

CHADI:The reason is,for the activation barrier to go to the annealed silicon 7 x 7 structure you can measure the activation energy by going to the 

following experiment: You take the [100] surface, which is 2 x 1, and you 

keep it at, let's say, 2000C. When this has been done, then you wait, 

and measure the time that you have to wait to get the 7 x 7, and you do 

that at 3000C, 4000C, and so on. From the time that is required to 

transform the 2 x 1 to the 7 x 7 surface, you get an activation energy of 

about one-half eV per atom, to go from the 2 x 1 to the 7 x 7 structure. 

But if the temperature is high, if you are close to 8000C, then the 

structure appears spontaneously. The atomic mobilities are very large at 

8000C. The Japanese have shown by beautiful microscopy measurements 

that the 7 x 7 structure nucleates at steps. I believe the reason it 

nucleates at steps is that you get a one-dimensional ordering of the 

atoms along the steps, which eventually lead to a three-dimensional 

-ordering over the entire surface. 

SAH: I would like to ask you if you could give us the implication of the 

results you find on oxidized silicon? How does that affect the interface 

states recombination velocity? On oxidized silicon at high temperature? 

CHADI: I have done some work on silicon oxide interfaces that I did not mentiD~ here. This work has been done mostly on clean surfaces with no 

oxide. I have done some work on hydrogenated silicon [111] and [100] 

surfaces. If you add hydrogen to these surfaces, then all the recon-:-

struction goes away. You end up with a much lower surface energy if you 

have essentially an ideal surface with every dangling bond saturated by . hydrogen. The 7 x 7 surface, however, is known to to be an extremely 

stable surface. A Japanese group reported that they exposed it to 

hydrogen and oxyge~ and to air for several days and they were still 

seeing 7th-order spots in their leads. It is a very stable structure. 

185 
GRUNTHANER: I have two questions. One is: are you familiar with a recent 

paper that Linus Pauling put out, looking at your asymmetric dimer situation on <100>? 

CHADI: I forgot to mention that there was some controversy with the silicon 

<100>. The chemists, particularly Goddard at Caltech. suggested that 

asymmetry was not reasonable, that it should remain symmetric. I heard 

that in a conference where Pauling was present; Pauling took issue with 

Goddard. I later wrote this paper in the Physical Review suggesting 

giving chemical arguments why silicon <100> should have asymmetric 

dimer structure. In fact, they found the structure very close to mine, 

using very simple chemical arguments. His idea was that, essentially, 

there were two configurations. covalent configuration and ionic configuration, and these two configurations had roughly similar energies -- that 

they would mix in two different configurations that gave asymmetry. 

GRUNTHANER: The thought that was quite fascinating that came out I)f that was 

these incredibly simple arguments that he has developed out of atomic 

orbital theory. He comes up with disgustingly close numbers in terms of 

what you were able to get out. 

CHADI: I had the same ideas after I did the calculations. In fact. I had the 

angles on the viewgraph. If you look at what happens when you go from 

the symmetric to the asynmetric dimer: in the symmetric dimer you still 

have all 1900 angles. Very close to tetrahedral. Whereas when you go 

to the asymmetric dimer, one of the bonds becomes sp2-bonded. essentially. The angles can relax to close to 1200 • The sp2 bond is very 

strong; much stronger than the sp3 bond. The other one becomes P-bonded 

and the P bonding is c.lose to the sp3 bond. So you gain energy that 

way. and that is essentially Pauling's argument. 

GRUNTHANER: That is what brings up the second question. When you did this 

calculation of the effective grain boundary in silicon material, I assume 

that out of the calculation you get the chemical implication of bonding 

and antibonding states, and of the energy distances between those. For 

the grain boundary in silicon. buried down in the silicon in your slab, 

you essentially get something like a bonding-antibonding splitting in 

there that I assume you can compare with what you can get for the normal 

Sp3 bonding in silicon. So the question is, was there any difference 

in gap implied in that rehybridization in the 5- and 7-membered rings? 

And then the second part of that: was there any indication of the change 

in hybridization? Namely, is the S contribution to bonding really following the kind of orbital electro-negativity ideas that are being 

develop'ed now? 

CHADl: As I am sure that you are aware, the grain boundary 1 considered was a 

continuous grain boundary. There were no dangling bond~. It was a perfect bonding at every site. 

GRUNTHANER: But the geometry is quite different around the silicon site. I am 

wondering whether there is an application for that in the sap. 

186 
CHADI: I looked at the static charge distribution at the grain boundary and I 

found, amazingly, that most of the atoms were neutral to within 200ths of 

an electron. However, there were a few atoms at the boundary that haa 

deviations from neutrality of ± 0.1 electrons. As far as the electronic 

states -- I looked at those; whenever you have five or seven full rings, 

there is a very characteristic state that is forbidden essentially for 

even numbers of rings of atoms, and' these states occur at two well-defined 

positions where you have pseudo-gaps. If you look at the four ba~ds of 

density state then there is one of these pseudo-gaps at about 0.08 eV 

below the valence band. This is a very sharp state .. There is also a 

sharp state in the conduction band, I don't know at what energy, but 

there is nothing in the band gap. The band gap is free of any defect 

state associated with the grain boundary. 

MILSTEIN: After Grunthaner's comment about Li~us Pauling discussing this, I 

am not sure that I have anything further to say. The issue I was looking 

at was the matter where you described the thermodynamic transformation, 

and the argument that crossed my mind is that in the carbon system, 

diamond is not thermodynamically stable, although we have all seen such 

objects, and they stand around for quite some time. I think the issue I 

would raise is that this should be viewed from the point of view of the 

bonding of Period 4 elements. In that sense, I think, when you go from 

carbon to silicon the transformations occur more readily, clearly, but 

when you talk about a pi-bonded system, it's a straight organic system. 

That is where it comes from. 

CHADI: That's right. However, this might be easy for you to say, but the 

chemist, I know Goddard for example, believes that the pi-bonding of 

silicon is very weak and I think it is weak, it is much, much -- by a 

factor of three -- weaker in magnitude than the pi-bonding in carbon. 

However, it does occur. Some would argue that pi-bonding should not 

exist in silicon, whereas there is strong evidence now, at least on the 

silicon surface, that pi-bonding does exist, and it is very, very weak. 

As I mentioned, absorption between surface states, with the polarization 

dependence of the absorption. The only structure that agrees with that 

measurement and also photon emission is the chain structure. So you have 

to convince the chemists. I believe, at the surface at least, there is 

pi-bonding, and it makes a contribution to the stability of the surface. 

The question is: how strong is it? The'chemists say it is very weak. 

MILSTEIN: Obviously, it has to be very weak. I don't think there is any 

argument about that. 

CHADI: It is much stronger than carbon. 

MILSTEIN: That probably also explains why diamond exists, because thermodynamically it ought not to. You have a big enough activation energy to 

get over it to change it to graphite. 

CHADI: Yes. The activation energy is very big there. 

HAHOkA: I would like to pursue this thing about the hydrogen on the surface 

again. That was for a (111] surface, is that right? 

187 
CHADI: For the [111] surface it goes to an ideal, yes, the reconstruction 

goes away and also for the [100], if you add hydrogen; it first saturates 

the dangling bonds, and it stays 2 x 1, but then if you add more hydrogen 

then it breaks the silicon-silicon dimer bond and you get a dihydride on 

the [100] surface. 

HAHOKA: That is interesting, because there is IR spectroscopic evidence of an 

SiH2 being formed at the surface. Of course, there you have much higher 

concentrations. That is what I was going to ask you about. 

CHADI: In fact, if you put water on the silicon [100] you get both silicon 

hydrogen and silicon OH modes, you ge.t the association. There is a lot 

of work in Ii with oxygen, hydrogen and water on the silicon surfaces. 

KAZMERSKI: We want to thank you very much, D.J. I will point out that this 

is an ideal case for the experimentalists, where D.J. won the Peter Mark 

Award and got $500 for his work, and I just saw that Benig and Rohr got 

the King Faisal Award at considerably more money, almost like a Nobel 

Prize. 

188 

-"---~----"'---'-- --------
COMPOSITIONAL ANALYSIS OF SILICON 

L.L. Kazmerski 

Solar Energy Research Institute 

Golden, Colorado 80401 

ABSTRACT 

N85-31626 

The use of surface analysis methods in the· detection and evaluation of 

elemental and impurity species in Si is presented. Examples are provided from 

polycrystalline Si and high-efficiency MINP cells. Auger electron spectroscopy 

and secondary ion mass spectrometry are used to complement microelectrical data 

obtained by electron-beam induced-current measurements. A new method is discussed which utilizes the volume indexing of digital SIMS signals, providing 

compositional information and impurity maps on internal materials/device interfaces. 

I. INTRODUCTION 

Impurities control the electro-optical properties of semiconductors and 

the operating lifetime and performance of solid-state devices. For such 

devices (including solar cells), it is important to know not only the levels of 

such impurities, but also their location and chemical state within the host 

lattice. A number of compositional characterization techniques are available 

to perform these analyses, mostly based on a bulk or volume scale. Surface 

analysis methods (1) - those that provide chemical and compositional information on the topmost atomic layers of a surface - have enhanced research and 

problem-solving in the semiconductor device 'area due to their complementary 

abilities to detect impurity (elemental, ionic, molecular) species, provide 

depth-compositional information (with ion-etching), determine chemical bonding 

states, map impurity localizations on surfaces or interfaces, and, evaluate 

integrity of interfaces. The common surface analysis techniques are summarized 

in Table 1. From this information, some of the strengths and limitations of 

the techniques can be deduced. For example, Auger electron spectroscopy (AES) 

can provide excellent spatial resolution due to the ability to focus the electron input probe. It lacks, however, the sensitivity to trace impurities which 

secondary ion mass spectrometry (SIMS) provides. X-ray photoelectron spectroscopy(XPS) complements these techniques in that it is the most developed and 

most reli~ble for providing chemical state information, with minimum inherent 

beam c:iama ge • 

This paper focuses on the iIiyestiga tion of impurities in silicon solar 

cells, examining both single-crystal and polycrystalline types. The applications of AES and SIMS to elemental analysis in these devices are emphasized. 

Specifically, the interrelationships among the chemistry and composition .of 

grains and grain bO\lnda ries, the electro-optical properties of the intergrain 

regions, and photovoltaic cell performance will be covered. The microelec189 

• 
Table 1. Summary 01 Selected Surface Analy.l. Technique. 

AES EELS SIMS XPS UPS 

- Probe electron electron Ion (+. -) x-ray uUravlolet 

Detected Speclel electron electron Ion (+. -) electron electron 0 0 

Spatial Relolutlon -300 A -300 A c1 .. m 102 -10~ lim -10' lim 

0 0 0 0 0 

Depth Relolutlon 5 - 50 A 5 - 50 A ~3 A 5 -50 A 5 - 50A 

Detection Senlltlvlty 0.1 at-OJo 0.1 at-OJo <0.001 at-% 0.1 at-% 0.1 at-OJo 

trical characterization of specific cell regions is accomplished by electronbeam-induced-current (EBIC) measurements, which provide information on the 

spa tial distribution of current losses. Two impurity me,chanisms are covered: 

(1) the segregation of oxygen (and other impurities) to the grain boundaries 

during hea t trea tments or high tempera ture processing of the devices. And, 

(11) the passivation of the grain boundaries by incorporation of hydrogen in 

these regions. This hydrogen localization is determined directly and correlated with the microelectrical properties of these same regions, as well as 

cell performance. Of special interest is the introduction of a new method to 

detect and spatially-resolve impurities and elemental distributions within 

solid-state devices using digitally-acquired and indexed SIMS (2). This method 

permits the determination of impurity localization or distributions on internal 

device interfaces, with fracturing or otherwise exposing such areas. The 

utilization of this method in profiling higher efficiency Si cells is exampled. 

11. OXYGEN SEGREGATION IN POLYCRYSTALLlRE SILICON 

At the grain boundary, dislocations and bonding alterations make the 

material structurally and possibly chemically different than the bulk material 

in the grains. Thus the electrochemical potential in the grain boundary is 

generally different than in the grains. This potential difference provides a 

depletion region that can be the site of minority carrier recombination. The 

disruption can also provide a region for the localization of impurities, either 

from segregation of inherent species or of purposely-placed ones. The segregation of impurities to the intergrain regions has been demonstrated in cast and 

directioPAlly-solidified Si (3). AES and SIMS has been utilized in conjunction 

with fracturing techniques to identify impurity species on the grain boundary 

planes.. The fracturing process provides a method for the side-by-side analysis 

of a region - as indicated by the AES data of Fig. 1. However,' inherent to 

this process is the loss of a large portion of the grain boundary plane. 

Because the electron probe can be scanned very effectively, impurity ~ps can 

be produced in the course of such AES (or SIMS) investigations. Such a mapping 

sequence is presented in Fig. 2. The benefit of this segregation process is 

that the grain regions themselves have significantly higher purity - with associated improvement of their electronic properties and device suitability. The 

grain boundary regions which act as sinks for such impurities are potential 

regions for enhanced minority carrier loss or impurity diffusion (shunting), 

but do not significantly degrade the cell performance unless impurity content 

is exceedingly high or the grain size is very small. 

190 
1- 2 

°u 

1200 

Mrgy (eV) 

1800 

191 

2 

Fig . 1 . AES suweys 0 mctured 

Si grain boundary: (a) grain 

region; (b) grain boundary . 

Al PA 'Itr 

UALITY 

Fig. 2. AES mapping sequence of 

impurities on fractured grain 

boundary . 
-u 

iii 

~ 

-

c:: 

...I 

<I 

O~S~lo-p-'e~(/~~-m~)~---------.----------r-------~ 

(8) 0.004__ _- Unhealed ----. "",.",.----

(b) 0.004:::::--=:::::--_ ~,... T = 500°C --------...... (c) 0.005- T = 600°C 

(d) 0.030- T = 640°C 

-0.4 T = 650°C 

(I) 0.088 T = 750°C 

-0.8 

T = 900°C 

(g) 0.094 

-1.0 

-1.2 

Silicon Grain Boundaries 

-30 -15 o 15 30 

Distance (J.im) 

Fig. 3. EBIC Zinescans 

across Si grain boundaries as a function of 

i;hermaZ processing. Heat 

treatments are for 30 min 

in argon atmosphere. 

The electrical activity of some grain boundaries in polycrystalline Si has 

been reported to be strongly affected by heat treatment (3,4). EBIC and compositional data from surface analysis measurements have been used to correlate 

the presences of oxygen at the grain boundaries with the electrical activation 

of these regions. The origin of the oxygen and resulting activity of the grain 

boundary is linked to ·the thermal history of the sample of devices (5). This 

is illustrated in the EBIC data of Fig. 3. The junction in this case is formed 

by an MIS structure fabricated on the individual grain boundary and adjacent 

grains at temperatures below lOOoC in order to minimize additional thermal 

effects. The EBIC responses for unheated, T = 500oC, and T = 6000 C cases are 

very similar, indicating that this mild thermal processing has little effect on 

the boundary region. If the temperature is increased, the E1HC responses 

increase correspondingly, indicating the electrical act~vation of these 

regions. The critical range for this activation is between 6000 C and 6-50oC. 

Heating beyond 9000 C does not seem to further affect the EHIC response, unless 

recrystallization occurs near the melting temperature. The slope of the 

Ln(IEBIC) vs.distance curves relates to the values of grain boundary recombination velocity (Sgb) and effective diffusion 1. ength (Leff) (6). The existance 

of oxygen a t the grain bounda ries of annealed Si has been demons tra ted using 

fracturing with SlMS. Figure 4 shows such data for an unanealled sample and 

one heated to 750oC. Increases in the oxide-signals (e.g., the Si044 peak) are 

apparent. However, the fracturing process is difficult, and has less-thandesired repeatability and control. 

192 
Fig. 4. SIMS survey of 

unanneaZed and anneaZed 

grain boundaries. 

Ci 

c 

CJ) 

en - c 

o 

-

-

I I I I I 

SIOH+ 

SI+ 

SIO+ .. 

Mass (amu) 

III. VOLUME INDEXING OF IMPURITIES AND ELEI£NTS 

I I 

Silicon 

Grain Boundary _ 

(clean) 

-

-

-

The ability to reliably defect, map and quantify elemental or compositional information at regions within a solid-state device has been accomplished 

by the method illustrated in Fig. 5. In this, selected ion signals corresponding to elements or molecules of interest, are measured and stored (indexed 

for intensity, spatial location) digitally for an incremental volume encompassing the region or interface under analysis. A computer can be used to 

track the region of interest (e.g., grain boundary plane) by maximizing the 

presence of impurities which are known to exist in such regions. Thus, the 

internal interface can he exposed by spatially transforming the detected 

signals - even though the sputter profiling/SIMS operation is carried out at 

some angle to this plane. This avoids the loss of information experienced in 

the fracturing technique. The da ta can be coded for ion type, spa tial origin 

(X, Y, Z) and concentration level. Additionally, the results can be color 

coded for more effective presentation. 

A s;i;:mple example, which utilizes the depth profiling capabilities of the 

technique, is presented in Fig. 6. These data show the cross-sectional distribution of impurities in a high-efficiency Si MINP solar cell. The device 

structure has a double layer (ZnS/MgF) anti-reflection coating. A thin S1-

oxide layer (- 30 A) covers the phosphorous·-diffused, boron-doped substrate. 

The relevant secondary ion species utilized in the profiling sequence designated in Fig. 6. The expanded view of the oxide-semiconductor region 

illustrate the uniformity of the oxide itself • Because only a -black/white 

193 
SI Wafer Segment 

Fig . 5. Repr e entation 0 SIMS vo Zume i ndexing scheme . 

Fig . 6. Cross- ecMon SIMS profiZe 0 Si MINP stl'Ucture . 

illu ration is p itt d in this publicat on, th r v 

not ind x don u 8 1 r ty . How v r, h ph~ phorous di 

t o p k at bout 102 fcm3 , with n mum of 101 fcm3 d t c 

interdi fusion of th ARC 1s 1 0 ob rv ble. 

concentra t ons re 

tribution is hown 

d in Fig . 6. Same 

This hod s Iso b n ffective for inv stigation h segr ga ion 0 

oxyg n in polycrys l11n Si ith h r tm n. Th d ta present d in Fig. 7 

are ob ined by tr nsla 1n ttl< volum -indexed SI MS da ta in ord r to vi 

boundary rom "b" n Fig . 5 . A ain, th b ck and white format r quir d or 

this paper ha prev n d the unambiguous coding for concentra ion level, an& 

the da ta pre. nt, d in Fig . 7 r pr sent a hr shold 0 1 x 1017 f cm2 for S104 

and 1 x lO HSfcm3 or C. Figur 7a repr s nt th gr in boundary plan 0 a 

boundary heated t o 6000 C. The s olid bla k regions are carbon , and af~ 

decora ted by oxygen--as indica ted by t intense dot pattern from the SiO 

SIMS signal. The presence of any S1-0 content for grain bounda ries processed 

194 
\\\\\\\\\\Si28 Fe~ 

Fig . 'l . SIMS apping equence 0 Si grain boundary shorving oxygen 

eg egation a a nc-tion 0 heat tr eatment . Impuri ty pecie key 

i incLuded. 

belo 5000 C is usually a egr gat d purity pecies (e .g ., C, Fe, i, 

Al) . the ann ng te p r tur is incr sed, th amount of oxygen at th 

bound ry i ob erv d 0 incr Such data are shown in Figs. 7b-f, and correlat dir c ly ith th e ctrical ctivation of t hes regions d rmin d by 

EHIC (F g . 3) . Spat ly-re olv d-mino ity carrier lifetim measur ement , and 

the d termination of the rain boundary barrier heigh have b en reported (4,5) 

and directly complement these results. Thus , the segregation of oxyg n to the 

grain undaries re ults rom high-temperature material/cell processing, and 

appear to b th origin 0 th electrical activation of thes e regions. 

IV. HYDllOQiR PASS AT 0 

Th ef ectiv ne 0 hydrogen tr nt on alt rin th electrical 

prop tie 0 polycrystall1n Si nd in improving th operational characteristic of c s has been demons ra ed. The ef ect 0 such hydrog n 

proces ing i shown in th J-V characteri ics 0 Fig . 8. Th cell undergoes a 

chang n f ciency from 5. 8% to 7. 7% (no antireflection coating) upon 

hydrogen treatm n . Although the phenomenological ef cts of th hydrogen 

proc ssing on cell improvem nt have been obs rv d littl is known abou th 

incorporation 0 thi impurl y sp cie into th grain boundary or its pos ible 

intera ct on ith the segr g t d oxyg n that might b present in that r gion . 

Dube, t a1. (7) hav shown that hydrogen does alter th EBIC r pons of 

representat ve devices. They have deduced a diffusion coefficient for H in the 

Si grain boundary by examining the boundary rom the side and along its length. 

195 
This analysis does not detect hydrogen directly, and assumes that the hydrogen 

is indeed localized there and responsible for the response. Figure 9 shows 

the effect of hydrogen trea tment on a specific grain boundary. The E1HC 

response of Fig. 9a is for a decrease significantly with hydrogen treatment 

(Fig. 9b). Reheating this same boundary to 9000 C "restores" the active 

response, but the magnitude is decreased somewhat. A second hydrogen treatment 

passiva tes the region again, with the response slightly less than after the 

initial hydrogen processing. These data are complemented by the grain boundary 

barrier height vs. light irradiation data of Fig. 10. The sequence is (a) 

unannealecl grain boundary; (b) hydrogen-treated; (c) annealed, 900PC; (d) 

second hydrogen treatment; (e) annealed, 900oC; and, (f) th:i.rd hydrogen treatment. The barrier height is ·improved, and becomes less sensitive to light 

intensity after the hydrogen passivation. In addition, the barrier height is 

observed to decrease with each successive hydrogen processing. 

The incorporation of the hydrogen in the grain boundary and the relationship between the hydrogen and oxygen concentrations in that region are illustra ted in Figs. 11-15. Figure 11 presents conventional SIMS depth-compositional profiles of gydrogen, measured by the magnitude of the SiH3 peak (with 

a threshold of 101H"/cm2 in these figures). The Si28 peak is provided for 

reference. Figure !la, band c represent data on similar grain boundaries 

hydrogen-processed for 1, 2 and 4 minutes. Figure 12 provides similar data 

taken on a grain boundary (a) before and (b) after hydrogen passivation. A 

generally constant Si044 signal is measured before the hydrogen processing. 

Since previous data have shown that the heat treatment and correlated oxygen 

segregation is primarily responsible for the activation of grain boundary electrical response, it is proposed that the hydrogen passivation is a result of 

the chemical interaction of the species at the grain boundary plane. 

-

N 

E 

u 

....... 

< 

E 

-

>-

'u; -

c 

cu 

C 

-c 

... 

~ 

::s 

U 

5 

10 

Polycrystalline Si 

pIn Solar Cells 

15L-__ --(a-)-A-s-.-Fa-b-r-ic-a-te-d------~ 

(b) H ·Passivated 

20~ ___ ~---------------------~ 

o 

Voltage (V) 

196 

Fig, 8, Light currentvoZtage characterization 

for poZycrystaZZine Si 

soZar ceZZs: (aJ as fabricated; (b) H2

-passivated, 
-u 

iii 

1&1 

--

c 

... 

<l 

Or-----------,-----------~------------r_----------, 

(a) Heated, T = 9000 e 

-0.4 

-0.8 

(e) Heated, T = 9000 e 

-1.0 

(d) H -Treated __ 

--..... , .", ~- " //. '.. .", '-"'" 

Silicon Grain Boundaries 

-30 -15 o 15 30 

Distance (pm) 

Fig. 9. EBIC linescans for Si grain boundary: (aJ annealed at 

9000(, for 30 min. in Ar: (bJ H2-passivated~ 4 min. 275°C; 

(aJ reheated~ T = 900oC~ 30 min. in Ar; and~ (dJ H2-passivated 

again. 

This interaction is illustrated in the SIMS area maps of Figs. (13-15). A 

computer-processed SIMS map sequence of the intersection of the grain boundary 

with the wafer surface is presented in Fig. 13. The sample was initially 

annealed to 900oC, and the boundary contains a high oxygen conterit. Hydrogen 

decora.tion of the region is noted after 1 min of the passivation processing. 

Figure 13c shows almost complete hydrogen decoration after 2 min of processing. 

Using the technique to examine the grain boundary composition within plane 

described earlier in this paper, the penetration of the hydrogen down the 

boundary plane as a function of processing time is evidenced in Fig. 14 for 

passivation treatments of 0.5, 1, 3, 4 and 6 minutes. The grain boundary was 

annealed initially to 900oC. The relatively high initial heat treatment pro197 
-

> CIJ 

-.., iT 

0.4 

0" 0.2 

100 

10.1 

'i 

c 

at 

0 

(I) 10'2 

:E 

en 

10.3 

10" 

0 

(b) T :- 600°C 

/"" X'-

,7 -. \ 

\ 

\ 

\(8) 

, 

, 

1.0 

Irradiance (mW/cm2) 

,J' ~, '-._, ~/' ,\.,.0., 

\ 

" 

'\ 

\ 

\SiH~' 

\ 

\ 

\ 

\ 

\ 

, 

\ 

\ \....'\ , 1\ 

Silicon Grain Boundarias" '-

4 

Depth (J.Im) 

''''''''-. 

10 

5121 

"" ", (c) 

\ 

\ 

\ 

Fig. 10. Dependence of grain 

boundary barrier potential on 

light irradiation level for 

unannealed grain boundary in 

sequence of alternate treatments similar to Fig. 9. 

\ 51M3' 

\ 

". 

\ 

\ 

\ 

.\ 

Fig. 11. SIMS depth compositional profile down grain boundary for: (aJ 1 

min; (b) 2 min.; and (cJ 4 min. H2

-passivation processed Si. 

198 
100 

10-1 

o -

10-3 

10-4 

(b) H -Treatment 

o 

Silicon Grain Boundaries 

4 

Depth (pm) 

6 

Fig. 12. SIMS depth compositional profile data for: (a) annealed~ 900oC~ 30 min. in Ar; and~ (b) H2

-passivated 

processed Si grain boundary. (b') shows oxide level as 

function of depth after H2-trea~aent. 

vides fer a high oxygen content of the boundary. The interaction of the 

hydrogen with the oxYgen present at the boundary is better illustrated in the 

grain boundary of Fig. 15. This sample had been annealed to 7500 C before the 

passivation process, and the oxygen at the boundary is sOll).ewhat less than the 

previous case. The hydrogen incorporation is observed to be enhanced in those 

regions that initially are oxidized. The exact chemistry of this process is 

not known. Methods similar to the specialized SIMS technique are currently 

being developed (e.g., digitally-resolved EELS) in order to investigate the 

chemical interaction of the species in-situ, during the treatments. 

199 
Fig . 13. SIMS mapping sequenae 0 grain boundary inter e tion wi th 

wa er ace a nation 0 pa ivation time hewing decorat ion 0 

boundary with hydrogen. 

1IIIIIIIIIsi

28 Fe 

Fig . 14. SIMS mapping sequence howing hydrogen penetration 0 

grain bounda.ry pZane a a function 0 pa sivation proce ing time . Grain boundary heated to 9000 C before pa siva ion. 

200 
Fig . 15. SIMS mapping equence ho!JJing hydrogen - oxygen inte~ation at grain boundary heated to 

7S00C be ore pa sivation. 

Y. SUMltAR.Y 

Th de c ion of impuritie in silicon using AES and SIMS has been demonnd th correIa ion of impuriti s with icroel ctrical characteristics 

xampl d . Th interrelationships among grain boundary impurity 

specie, rain boundary I ctrical prop rti sand olar cell perfor nce in 

polyc ystallin Si have b en demonstrat d . Specifically , two impurity 

mechani m ha eben valuated: (i) th segregation of oxygen t o the int rgrain 

r egions during h t tr nts; nd, (ii) th incorporation of hydrogen in 

these r gion during th p s ivation proc s. Finally, a specially developed 

SIMS impurity pping techniqu s been i troduced which, for the first time , 

all ow th inve tigati on of the composition of a grain boundary surface 

utilizing volume indexing during the SIMS profiling. 

Ackno 

Th author gratefully ackno ledges th inputs, as istanc and ork of J .R. 

Dick , .J . t on , T.P. Massopu t, P.J . ,Ire nd and A.B . S rtzlander of SERI , 

all of whom contributed greatly to the work of this paper . The author is a 0 

greatef ul to D.W. Ritchie of SERI f or his encouragement of this work. This 

work was supported by the U.S. Department of Energy under Contract Number EG77-C-01-4042. 

201 
BEFERENCZS 

1. See, for example, A.W. Czanderna, Ed., Methods of Surface Analysis 

(Elsevier Scientific, New York; 1975). 

2. L.L. Kazmerski, Proc. 17th IEEE Photovoltaic Spec. Conf., Orlando (IEEE, 

New York; 1984) (in-press). 

3. D. Redfield, Appl. Phys. Lett. 38, 174 (1981). 

4. L.L. Kazmerski and J.R. Dick, J~Vac. Sci. Technol~ A2, 1120 (1984). 

5. L.L. Kazmerski, Prec. 5th EC SolarPhotovoltaic cOnf:" (Reidel, 1984) (inpress). 

6. J.r. Hanoka, C.H. Seager, D.J. Sharp and J.K.G. Panitz, J. Appl. Phys. 42, 

618 (1983). -

7. C. Dube, J.r. Hano~~ and D.B. Sandstrom, Appl. Phys. Lett. 44, 425 (1983). 

202 

. 

.
DISCUSSION 

LOFERSK!: Toward the surf.ce part of the Green cell, it's certainly a little 

bit astonishing, isn't it, that the phosphorus concentration is decreasing aa you so toward the surface? Is that what you really meant or did 

you say it backwards? 

KAZKERSKI: I think that in most SIMS data you will see a slight decrease in 

the signal right toward the surfac~. The whole thickness of the phosphorus region we showed the~e is only about 2000 A. 

LOFERSKI: And how about the thickness of the oxide region? .1aat did you say 

it was, greater than 20 A? 

KAZMERSKI: Well it should be about 20 A but if you look there, it looks like 

the data is spread out and it looks more like SO or 60 A. 

LOFERSKI: So it is 50 or 60 A, is what you would estimate? 

KAZKERSKI: Yes, I am sure it is sbout 50 or 60 A. 

LOFERSKI: But you are saying that as you go toward the surface, even in an 

ordinary cell, if you did it with this volume indexing, you would find a 

decrease in the phosphorus concentration? 

KAZMERSKI: Yes. I think so. You are seeing about 500 A, that region that 

it decreases from 2020 down to 1018 cm-3. 

LOFERSKI: Yesterday Larry Olsen was showing some comparisons of a spreading 

resistance measurement profile and a SIMS profile, and there is a significant difference in the way they look. You mentioned being careful about 

using SIMS profiling because of the damage it does. If you compar4~ a 

spreading resistance with a SIMS profile, which you would recommend as 

the more likely one to be correct? 

KAZMERSKI: It depends on what you are looking for. Certainly one wouldn't 

want to measure resistance using SIMS, but for a pure represent~tion of 

the profile, if the SIKS is done correctly, I'd would go with the SIMI~. 

LOFERSKI: I guess that actually his profile did show a drop-off at the surface 

too, as I recall. 

MILSTEIN: The RCA SIMS profile showed it going up all the way to the surface. 

To change the subject on you, you mentioned in terms of your SIMS resolution that you could resolve mass peaks for different species which had 

the same mass-to-charge. ratio, for example, 31, phosphorus, and three 

silicon species, and quite frankly I am quite curious as to how that is 

done and whether you care to comment on it. 

KAZMERSKI: You mean how to resol.ve it? 

203 
• 

MILSTEIN: Well, if you had the same charge-to-mass ratio, and going through 

something like a quadripole mass analyzer. 

KAZMERSKI: It's not a quadrip01e. This is a magnetic sector. You would 

never be able to do it in a quadripole. You just have the mass separation. It is done with a magnetic sector and this is all done on the 

Cemaca system. So you have your mass resolution as something like 

50,000. It is not a quadripo1e. You would never be able to get that 

mass resolution with a quadripo1e. On a quadrip01e it would look just 

like one peak. In fact, on some quadrip01es that we have seen, the mass 

resolution even drops off as a function of the time to mass, and some" 

times you get an overla.pping of two masses. 

CAMPBELL: Have you looked at the hydrogen distribution as a function of depth 

in any single-crystal silicon? 

KAZMERSKI: We looked at -- not really in single-crystal -- we looked at the 

geain regions in the silicon material here too, you know in the adjacent 

grain, and did not see any penetration. As a matter of fact, what we saw 

was some interaction with the oxide that might have been present eight on 

the surface, but not a peneteation into the grains. 

CAMPBELL: There was some indication at the last PVSC that there was a bulk 

effect with hydrogen passivation. 

KAZMERSKI: Yes. I heard that too, and we tQlked to the people and I think 

the peneteation on the grains was not significant. 

KEAVNEY: I wanted to ask about the low-temperatuee-annealed samples that have 

unactivated grain boundaries. What was their thermal history before they 

were annealed? 

KAZMERSKI: I should go back. What we are doing is looking at one geain 

boundary of an unannealed sample. It doesn't mean that theee weren't 

active grain boundaries also in that sample. We selected one that was 

not active to begin with. Its thermal hi~tory was that this was a 

directionally solidified sample with a grain size of about one-half to 

three-quarters of a centimeter that had not seen any processing befoee· 

hand, fOl-ming the junction for EBle was done by a low-tempei'ature oxidation at about 1000C. So that is the highest temperatuee the device had 

seen before any e1ecteical measurements were taken. 

KEAVNEY: Do you know how quickly it was cooled feom the melt? 

KAZMERSKI: No. 

KEAVNEY: How quickly was the temperature cooled feom the samples that were 

annealed at 9000C? 

KAZMERSKI: The annealing procedure was to remove them feom the annealing furnace and they were probably cooled over one-half hour or so. 

RAI-CHOUDHURY: You mentioned hydrogen passivating defects; apparently oxygen 

204 

-~---,-
is active in it. 1 have two questions: Did you look at this defect by 

DLTS as to what kind of defect level it is? The other question is: Do 

you feel that oxygen was present in a precipitated form, rather than a 

single point defect, for it to be activated or deactivated? Can you make 

any comments on th~se? 

KAZMERSKI: The first one: We did not do any DLTS on those things so 1 have 

no idea. 1 think that the people at SERI who had been doing DLTS on this 

polycrystalline material -- it is not a very satisfying measurement. You 

really have to spend a lot of time, so when the peoPle attempted to do 

some DLTS, it looked like it was very difficult to identify any levels. 

1 am sorry, 1 missed your second question. 

RAI-CHOUDHURY: 1 have a lot of concern about oxygen, what it is doing to 

silicon, Czochralski silicon, and so forth. Does the oxygen, for it to 

be passivated by hydrogen -- it seemed like it should be present as it 

precipitated -- or can it react with hydrogen if it is present in the 

point defect without a cluster, without a precipitation? 

KAZMERSKI: 1 really can't answer that, but 1 see no reason why not, if you 

look at the hydrogen and see there are also some point defects and other 

defects in there which are decorated by oxygen. The hydrogen seems to 

passivate those too, so 1 guess that would be true. 

By the way, something in here, even though we see the hydrogen going down 

the grain boundary, there is still oxygen in the background. It is not 

like the oxygen is coming off, when the hydrogen goes the oxygen is 

leaving. There still is oxygen present. 

TAN: If 1 may make a comment. Normally oxygen in silicon is not electrically 

active. Very difficult to pick up any level by the DLTS. So 1 believe, 

really, that we simply don't know what we are passivating. Where is this 

hydrogen? And the final thing is to say some form of dangling bond ---

whether they are related to oxygen or not --- 1 don't think that question 

can be settled at this moment. 

KAZMERSKI: I think that all we can do is say, there is the existence of o~ygen and hydrogen, and there is some interaction between the two 

species. 

WOLF: You answered onl!( one part. of my question, namely, the oxygen is st.ill 

there unt.il the hydrogen comes, but as you showed, as you increase t.he 

annealing temperature, more and more oxygen appears. Now where does it 

come from? Is it just. activated so it becomes visible, or does it dif--

fuse there from the outside, from the atmosphere, lik~ the hydrogen comes 

in from the outside, or does it come out of the crystal? 

KAZMERSKI: Well, presumably, it comes from t.he crystal. The annealing has 

been done in vacuum and it has been done in argon, it has been done in 

nitrogen, in a controlled atmosphere, so it is doubtful that it is coming 

from outside, and we presume that it is coming from the inside. Once 

again, the level here is about 1017 cm-3 of oxygen. 

205 
WOLF: Which is probably an order of magnitude less than what you would expect 

to be present in Czochralski, if it is a Cz type crystal. 

KAZKERSKI: Or an order of magnitude more. 

WOLF: You expect around 1018 cm-3 usually, don't you? 

KAZKERSKI: I guess, at least in these data, the bulk data shows about 

1016 cm-3. 

WOLF: Another comment I want to make is with respect to the Green cell. It 

seems your cross section was done not under the metal contact, but in 

between the contacts, and there should be about 100 to 200 A of oxide, 

not 20 A. There is a thicker oxide between the contacts normally. The 

20 A are only under the contacts. 

KAZKERSKI: These data might be correct but the surface was thicker than 

20 A. I said more like 60 A. 

WOLF: Yes. That is what you said. 

OLSEN: I think it is between 50 and 100 A, is where he is using now. 

Between the contacts. That is what I was going to say. 

KAZKERSKI: Well, then the data might be OK. 

OLSEN: I have another question. Was that a zinc sulfide and magnesium 

fluoride? Is that the correct order? Is zinc sulfide on top? It is 

usually the other way around. 

HAHOKA: What is your sensitivity for oxygen? Isn't it around the low 

1017 cm-3? At least that is what I hear from Evans who does SIKS, 

out on the West Coast. 

KAZKERSKI: It is 1016 cm-3. 

HAHOKA: So yo~rs is better than that, then. Second question: When you do 

this volume imaging, you showed a picture of your sputtering, basically a 

perfect parallel pipe, and in fact when you sputter your volume isn't it 

a thing where your sides slope? And isn't that sputter in that shape 

also a function of material when you are sputtering? 

KAZKERSKI: What l am doing is only collecting the data from that rectangle. 

The sputtering may be more than that but the data are only being recorded 

from that rectangle. 

HAHOKA: So you are picking your rectangle within the sputter volume. 

KAZKERSKI: That is correct. 

QUESTION: I wanted to go back to Joe Loferski's question on the profile. You 

indicated that the concentration of the phosphorus fell off near the 

surface, but I didn't understand whether that was an artifact of the 

206 
measurement or whether you think that that is, in fact, what is happening 

to the profile. 

~ZKERSKI: I think that is what is happening to the profile. Right near, 

within 500 A of the surface, it drops off a little and then comes up 

and then goes down. 

no: It seems to me that when the hydrogen passivates, not all grain boundaries are passivated equally. Now, do you have a characterization of 

these grain boundaries? Which kind of grain boundaries get deactivated 

with the hydrogen and which don't? 

KAZMERSKI: We have seen that same thing. The only data I have showed you 

here is to be able to represent the volume indexing and attrition, but I 

think that is true that the grain boundaries are being affected differently. In fact, the only grain boundaries we are working with here are 

medium-angle grain boundaries, and I should point that out too. There is 

about a 28 or 30 degree mismatch between the <111> angles and the two 

grains. So that it could very well be that the st~ucture of those g~ain 

boundaries is different, if you go to low-angle g~ain boundaries or even 

to higher-angle grain boundaries which will have different elect~ical 

properties. 

no: Another question, which has to do with Martin Wolf's question. As you 

go away from the grain boundary do you find a concent~ation gradient of 

the oxygen, can we see it? 

KAZMERSKI: Yes. You can do the same sort of thing. As you go away f~om the 

boundary itself you can see the decrease in oxygen concentration. 

RAO: So can you calculate the diffusion coefficient and see if it matches up 

with the bulk diffusion coefficient of oxygen in silicon? 

KAZMERSKI: You could do that. I never thought of that but you could do that. 

GRUNTHANER: When I have looked at silicon oxide st~uctures that have seen ion 

beams, whether those ion beams be argon systems or they be cesium systems, 

there is SUbstantial generation of intermediate oxidation states from 

silicon sputtering mixing. Now, in the data you are showing here, in 

these grain boundaries in the oxygen and hydrogen passivation, they are 

quite clearly being taken on the same sample in the same general area 

where you are then exposing the system subsequently to the hydrogen. Now 

my question is, to what extent do you expect there is a degree of activation of the ion beam interactions with the oxygen going on to the subsequent decoration that you are seeing with the hydrogen, since presumably 

you are doing this in a static mode? 

KAZMERSKI: First of all, each one of those hydrogen cases is for a separate 

sample of a grain boundary that has been cut and divided so the hydrogen 

passivation was done separately on each one. So it is not the same grain 

boundary in that case. You can see if you look at it that there are different structures. As a matter of fact, when the carbon that is present 

at some of the regions are not the same grain boundary itself, it is a 

207 
1 

g 

1 

I 

I 

I 

sequence of six grain boundaries that~ are cut in sequence going across. 

They are in the same grain boundary length but the grain boundary is cut 

into six adjacent pieces. It is not the same region each time. So it is 

not passivated. And then measure, because as soon as you meaS~lre it you 

are done with that sample. 

208 
N85-31827 

Nitridation of Si02 for Surface Passivation 

I. INTRODUCTION 

Stefan K-C Lai 

Intel Corp., 3065 Bowers Ave., 

Santa Clara, CA 95051 

Thermal silicon dioxide has been one of the ~ost important insulator for 

the present microelectronic technology. Not only is it an almost perfect 

insul~tor, its interface with silicon is very close to ideal, giving the 

lowest density of electrically active interface traps. Active transistors can 

only be fabricated successfully because of the low density of electronic 

traps. Furthermore, the low density of interface traps also provides an ideal 

passivation for the silicon surface electrically. 

Silicon dioxide, however, is not perfect. The oxide network is actually a 

very porous network, allowing the diffusion of gaseous species through it, 

especially at elevated temperatures. This can change the electrical and thus 

the passivation properties of the oxide. Also, the oxide network can be very 

easily damaged by energetic particles and high energy radiation. This damage 

gives rise to an increased density of electronic states, both in the bulk of 

the oxide and at the silicon-silicon dioxide interface. The sum of the above 

effects is a long term degradation of the oxide and its interface wl.th 

silicon, especially in the space environment. 

Besides the above factors, there is a third factor that provides the 

driving force in the search for a better insulator: the defect density of 

silicon dioxide increases with decreasing oxide thicknesses. With the scaling 

of device dimensions in the quest for the highest packing density in 

integrated circuits, the vertical dimensions are also scaled. It is expected 

that 10nm oxides will be used extensively in half micron devices by the end of 

this decade. The yield and reliability of the present oxide system may not be 

able to satisfy the requirement. 

It was under these conditions that Ito et al set out to develop a better 

insulator for silicon. They first reported the direct nitridation process to 

form. a thermal nitride (1). However, such processes require very high 

temperatures and long process times. The nitrides formed were only of limited 

thicknesses (up to 5nm) and rich in oxygen (l ,2). The films obtained are 

believed to be basically oxynitride layers. Next, they reported on the 

nitridation of $ilicon dioxide, which is the subject of this paper (3,4). 

II. NITRIDATION OF SILICON DIOXIDE 

Experiments on the nitridation of silicon dioxide has been reported many 

times in the literature (5). Ito et al first reported the thermal nitridation 

of silicon dioxide in ammonia (3). They reported that nitridation retarded the 

209 
destructive breakdown of silicon dioxide films (4). They explained the effect 

by the fact that the current through the oxide was much more uniform. They had 

also reported in detail the MOS characteristics of silicon dioxide nitrided 

under different conditions (6). Since then, it has been reported that nitrided 

oxide was effective in reducing the diffusion of boron through the dielectric, 

compared to the case of pure oxide (7). Terry et al reported on the radiation 

effects in nitrided oxide (8). They observed that there was very little 

generation of interface traps after radiation damage. 

There have also been many papers published on the material characterization of the nitrided oxide (5). The common observation was that after 

nitridation, the dielectric was a very effective barrier to the diffusion of 

oxygen and water: it demonstrated very high oxidati.on resistance. This is 

consistent with the observation that it is an effective boron diffusion 

barrier. Auger:experiments showed that there was a build up of nitrogen close 

to the silicon-silicon dioxide interface, resulting in a layer that was 

difficult to etch chemically and was probably the major barrier layer (9). 

Recently, more detail XPS (X-ray Photoelectron Spectroscopy) experiments 

showed that the nitrogen layer was located at a small distance (2.5nm) away 

from the interface (10). In general, the results were not completely 

consistent, which was probably due to the fac:.t thp. process control was very 

difficult. Trace amount of oxygen or other impurities can change the reaction 

kinetics. The process history of the film may also affect the material 

characteristics. 

In the present paper, an attempt will be made to relate the electrical 

properties of the film to the process history. A model is proposed to explain 

some of the observed results. It will be shown that with our present knowledge 

of the dielectric, it shows a lot of promise for its use in surface 

passivation, both for its resistance to impurity diffusion and for its 

resistance to radiation damage effects. 

III. ELECTRON TRAPPING 

Electron trapping can be used as a sensitive probe to the impurities and 

defects in silicon dioxide or related insulators and their interfaces with 

silicon. Generally, electron traps can be divided into two categories: 

intrinsic traps and high field generated traps (11). Intrinsic traps are traps 

that are present in the oxide after processing, either as impurities such as 

arsenic (12) or water related centers (13), or due to high energy processing 

such as plasma etching (14). The plasma or other high energy radiation give 

rise to hole trapping close to the interface and neutral electron traps in the 

bulk of the oxide. The electron traps can be filled by low field electron 

trapping experiments, most conveniently the injection of electrons by RF 

avalanche processes in silicon (13). Each kind of electron traps have their 

characteristic capture cross section which can act as a signature to their 

origin (11). The trapping process also follows classical trapping kinetics: 

the traps are filled ov~r time, and the flatband voltage shift due to electron 

trapping will saturate. 

When an oxide is Subjected to high current and high electric field under 

the Fowler Nordheim tunneling condition, additional electron traps are. 

actually generated by the process (15). In this case, the Hatband voltage 

210 
does not saturate but will continue to increase with increasing electron 

fluence, until final breakdown due to the build up of a very high internal 

electric field due to the high density of trapped electron (16). The high 

field trap generation process is very similar to radiation damage. They both 

give rise to positive charge at the interface and the interface traps in both 

cases show a characteristic peak above midgap close to the conduction band 

(17). An increase in electron traps is observed in the bulk of the oxide, 

similar to the generation of neutral traps (11). 

The change in the density of low field electron traps after the 

nitridation process was studied (18). In the experiment, oxides were annealed 

in ammonia at different temperatures for different times, with the results for 

one temperature shown in Figure 1. It can be seen after the nitridation 

process, there was a large increase in electron trapping at low electron 

fluence. When the trapping curves were analyzed, it was concluded that the 

in£I,ase 2in trapping was due to an electron trap with capture cross section of 

10 cm • Nitridation at higher temperatures and longer times gave the same 

electron trap with the same capture cross section. However, the saturation 

density was slightly different, with slight increases for higher temperatures 

and longer times. This electron trap has been identified as due to OH centers 

in the oxide. This was confirmed when it was shown that from infrared 

absorption spectroscopy, an increase in density of OH bonds similar in density 

to the electron traps was observed. It was postulated that in the nitridation 

reaction, oxygen might be released from the oxide and reacted with the 

hydrogen 1n ammonia to give rise to the OH bonds. 

The trapping process under high ele'ctric field for Fowler Nordheim 

tunneling in thin dielectric was then studied. The experiment involved the 

passing of constant current through the dielectric. Any electron trapping 

would increase the voltage required for the same current. Thus, the change in 

gate voltage is a measure of electron trapping. The trapping curve for the 

oxide in Figure 2 is characteristic of high field trapping process: there was 

an initial decrease in gate voltage due to the generation of holes, which 

actually enhanced the injection of electron. After about ten seconds, the 

curve changed in d.irection and there was a continuous increase in vol tage 

shift due to the generation of additional electron traps. This is to be 

contrasted with the classical picture where the curve would saturate when all 

the traps are filled. For the nitrided oxide (NO), there was little or no hole 

trapping and the increase in electron trapping was faster compared to an 

ox1.de. The dielectric actually broke down in a short time because of the high 

internal field. The third sample called ONO (oxidized nitrided OXide) showed 

little hole trapping as well as little electron trapping. Electrically, this 

seems to be the most stable dielectric for the three studied. The lack of 

electron trapping in ONO was confirmed wh~ it was shown that there was no 

w~ndow clelsing after extended cycles in E PROMs (19). Other experiments in 

E PROM had shown that there was hardly any hole trapping for ONO. 

The properties of the dielectrics were studied further by subjecting the 

samples tel high . temperature anneal in an inert atmosphere (Nitrogen). The 

results WE!re shown in Figure 3. For the oxide, the trapping process was 

increased slightly, but with the same characteristic features. The most 

dramatic (:hange was observed in the nitrided oxide (NO). The density of 

electron traps was reduced to very low levels, similar to ONO before anneal. 

For ONO, there was actually a slight increase in trapping. 

211 
The above results is for a given nitridation condition. When the 

nitridation time is reduced by half, different results were obtained. For NO, 

the initial electron trapping was reduced. On the other hand, after the high 

temperature anneal, the electron trapping was only partially reduced. The 

results seemed to indicate that the dielectric is a mix between oxide and 

nitrided oxide. It is very important to realize that different process 

conditions affect the trapping properties significantly. The degree of 

nitridation initially and the post nitridation thermal cycle both change the 

dielectric characteristic. Furthermore, the nitridation conditions used in the 

present experiments are typically much more gentle compared to those reported 

in literature because the films were intended to be used in state of the art 

VLSI processes. Different results may be obtained for those heavily nitrided 

films. 

To understand the experiments better, quasi-static capacitance curves 

(QCV) were obtained for the samples before and after different amount of 

electron fluence. Any interface trap generation will give distortion in the 

QCV curves while bulk trapping will give horizontal shift in the curves. The 

interface trap generation process was very similar to the bulk electron 

trapping process. The results are shown in Figure 4. For an oxide, after the 

high electron fluence, there was increasing distortion in the QCV curve. There 

was also a characteristic structure in the curve which was due to an interface 

trap peak. Similar peaks were observed in oxides damaged by radiation. This 

strongly links the present high field damage process to the radiation damage 

process. For the unannealed NO, little or no distortion in the QCV curve was 

observed. Instead, an almost parallel shift in the curve was observed. It can 

then be concluded that there was no generation of interface traps, and there 

was high density of electron traps in the bulk of the dielectric. Finally, for 

ONO and also annealed2NO, there was little of no change in the CV curves after 

up to two coulombs/cm • 

IV. MODEL 

The above results can be explained by a very simple model. For an oxide, 

the electron trapping was due to high field generated traps. For the nitrided 

oxide with no anneal, there was more electron trapping which can be explained 

by the increase in OR centers shown in Figure 1. The only question is: what 

happened in the case of ONO? The effect can be explained by assuming that 

after nitridation, the density of high field generated traps were reduced to 

~ery low levels. This is supported by the results of the QCV experiment: there 

was no generation of interface traps, which are related to high field 

generated traps in the bulk of the oxide. Then, for ONO, the extra anneal 

reduces the density of OR to very low levels. This reduction after anneal has 

been reported before (20). With no OR sites and no high field generated traps, 

there is very little electron trapping. Oxygen is not required to reduce the 

density of electron traps;. When the nitrided oxide was annealed in nitrogen, 

the lowest density of electron traps were obtained. 

For a pure oxide, the high temperature anneal actually has an opposite 

effect on trap generation. Such an anneal has been shown to increase positive 

charge trapping and interface trap generation after radiation damage (21). In 

Figure 3, the high field trap generation in oxide was increased after the high 

temperature anneal. For ONO, the oxidation could have increased the oxide 

212 
» 

properties such that after anneal, the rate of electron trapping was also 

increased. 

The same model can be used to explain the observation at the 

silicon--dielectric interface. The nitridation process changes the interface 

such that it is no longer susceptible to high field damage. Recently, the 

detail of the interface damage process at the interface was studied (22). It 

was shown that the characteristic interface peak was not generated when holes 

were first trapped at the interface. Only when an electron was captured by the 

hole that the interface trap pe&.k was observed. A model based on strained 

bonds at the interface was used satisfactorily to explain the observation. It 

was also proposed that the model. can be used to explain radiation damage and 

neutral trap generation in the bulk of the oxide. From the present 

experimental results, the high field trap generation process can also be 

explained by the same model. In the simplest term, the damage process under 

high electric field and high energy radiation have similar origin. 

The present results thus show that nitridation modifies the oxide network 

in a major way. It can be postulated that the nitrogen may go in and replace 

the strained bonds selectively, forming a silicon-nitrogen structure which may 

be much more stable. Possibly, the bonds are no longer "strained" and when 

holes are captured at the sites, the bonds do not go through a relaxation 

process. On capture of electrons, the bonds will return to their original 

state and no permanent damage states are generated. 

For samples which were not nitrided for as long a time, there will be a 

lower density of OR traps. Also, the reduction of strained bonds by 

nitridation will also be limited. After the OH sites are reduced by an anneal 

process, the remaining strained bonds can give rise to significant electron 

trapping under high field conditions. 

The reduction of OH bonds through anneal is basically a diffusion 

process. The thickness of oxide and the annealed temperature thus play a very 

important part in determining the final density of OR sites in the dielectric. 

The above experiments were carried out ~n oxides in the lOnm range because the 

dielectric was intended to be used in E PROMs. In this thickness range, it was 

shown above that it is possible to reduce the OR sites to very low levels. 

However, it is also important to remember that after the nitridation process, 

the dielectric is a very effective diffusion barrier. It would not be 

surprising that for thicker nitrided oxide, it would be much more difficult to 

reduce the OH sites, giving rise to a high density of bulk electron traps. 

This may explain some of the inconsistency that may have been observed. 

v. DISCUSSION 

There are two properties of the nitrided oxide discussed above that make 

it promising as a new pielectric for surface passivation. Firstly, the 

dielectric is a very good diffusion barrier. It gives the surface much better 

protection to the possibility of degradation from impurity elements. Secondly, 

from the results presented above, it appears that the dielectric is also very 

stable electrically. Specifically, the silicon-dielectric interface may not be 

degraded in a radiation environment. The use of the dielectric thus provides 

potentially a very stable passivation for silicon. 

213 

----.. _--.-----:----
The present work has been only limited in scope, even though it shed a 

lot of light on the electrical properties as related to the chemistry of the 

system. No attempt had been made to study the detail of all the process 

conditions and correlate to radiation damage experiments. It is important to 

study the whole system in a comprehensive and detail manner in order to 

realize the full potential of the system. 

VI. ACKNOWLEDGEMENT 

The work reported in this pap.c was started while the author was with IBM 

Thomas J. Watson R~search Center and continued when he joined Intel 

Corporation. He would like to thank the many people at both places who have 

contributed to the work and that the names are too many 'to he listed here. 

VII. REFERENCES 

(1) T. Ito, S. Hijiya, T. Nozaki, H. Arakawa, M. Shinoda and Y. Fukukawa, J. 

Electrochem. Soc., 125, 448-452, (1978). 

(2) S.P. Murarka, C.C. Chang and A.C. Adams, J. Electrochem. Soc., 126, 

996-1003, (1979). 

(3) T. Ito, T. Nozaki and H. Ishikawa, J. Electrochem. Soc., 127, 2053-2057, 

(1980) • 

(4) T. Ito, H. Arakawa, T. Nozaki and H. Ishikawa, J. Electrochem. Soc., 127, 

2248-2251, (1980). 

(5) For a general review: J.A. Nemetz and R.E. Tressler, Solid State Tech., 

26(2), 79-85 and 26(9), 209-216, (1983). 

(6) T. Ito, T. Nakamura and H. Ishikawa, J. Electrochem. Soc., 129, 184-188, 

(1982) • 

(7) S.S. Wong, C.G. Sodini, T.W. Ekstedt, H.R. Grinolds, K.H. Jackson and 

S.H. Kwan, J. Electrochem. Soc., 130, 1139-1143, (1983). 

(8) F.L. Terry, Jr., R.J. Aucoin, M.L. Naiman and S.D. Senturia, IEEE Elect. 

Dev. Lett., EDL-4, 191-193, (1983). 

(9) F.H.P.M. Habraken, A.E.T. Kuiper, Y. Tamminga and J.B. Theeten, J. Appl. 

Phys., 53, 6996-7002, (1982). 

(10) R.P. Vasquez, M.H. Hecht, F.J. Grunthaner and M.L. Naiman, Appl. Phys. 

Lett., 44, 969-971, (1984). 

(11) D.J. DiMaria, The Physics of Si02 and Its Interface, Proceedings of the 

International Topical Conference, Pergamon Press, N.Y.,_160-178, (1978). 

(12) R. F. DeKeersmaecker and D. J • DiMaria, J. Appl. Phys., 51, 1085-1101, 

(1980) • 

(13) D.R. Young, R.A. Irene, D.J. DiMaria, R.F. Dekeersmaecker and H.Z. 

Massoud, J. Appl. Phys., 50, 6366-6372, (1979). 

(14) L.M. Ephrath and D.J. DiMaria, Solid State Tech., 24(4), 182-188, (1981). 

(15) C. Jenq, T. Rananath, C. Huang, S. Jones and T. Chang IEDM Tech. Digest, 

IEDH81, 388-391, (1981). 

(16) E. Harari, J. Appl. Phys., 49, 2478-2489, (1978). 

(17) T.P. Ma, G. Scoggan and R. Leone, Appl. Phys. Lett., 27, 61-63, (1975). 

(18) S.K. Lai, D.W. Dong and A. Hartstein, J. Electrochemo Soc., 129, 

2042-2044, (1982). 

(19) C.S. Jenq, T.L. Chiu, B. Joshi and J. Hu, IEDM Tech. Digest, IEDH82, 

811-812, (1982). 

(20) S.K. Lai, D.R. Young, J.A. Calise and F.J. Feigl, J. Appl. Phys., 52, 

5691-5695, (1981). 

214 
(21) E.P. EerNisse and G.F. Derbenwick, IEEE Trans. on Nucl. Sci., HS-23, 

1534-1539, (1976). 

(22) S.K. Lai, J. Appl. Phys., 54, 2540-2546, (1983) • 

.... 

La.. 

-:J:CO 

en 

.r /,,-

i 

! 

; 

I 

i 

f o : 

Z ! « . m : .... N 

« 

...J 

L&.. 

...... ....----

.. _ ...... -•...•.......... _ ..................•......•..•.•. _ ...... -.-.... _ ............•. 

Dox = 51 nm 

I = 5.78x10-5/cm2 

NO ANNEAL 

900°C 1 HOUR AMMONIA 

o ~ ___ ~ ______ ~~~~ ___ -L ______ ~ __ ~~ __ -L _____ J- ____ ~ ___ ~ ____ ~ 

o 2x1017 4x1017 6x1017 8x10'7 

INJECTED CHARGE (cm-2) 

Figure 1: Flatband voltage shift as a function ·of injected electrons for a 

51nm oxide with and without the ammonia anneal. The large increase initially 

for the anne~\ef: s~mple was due to a new electron trap with capture cross 

section of 10 /cm. 

215 
1.4 

1.2 

1.0 

.8 

.6 

"" U') 

f- .4 -oJ 

0 

> 

'-' 

t!l .2 > 

<l 

. 0 

-.2 

~.4 -

-.6 

-.8 

__ ..... ox 

- - - - NO •••• ••• OND 

··V STRESS @ 5Xl04

6 AMP 

CAP AREA = 4xl0- CM2 

•• '!} • 

r. 0NO 

. . . . •••• 

SAMPLES WITHOUT ANNEAL 

1 10 100 1000 

LOG STRESS TIME (SEC) 

10000 

Figure 2: The changes in voltages across oxide, NO and ONO capacitors under 

constant current as a function of Log time. This is a measure of electron 

trapping which results in the shifts of IV curves under Fowler Nordheim 

injection. 

216 
1.4 

1.2 

1.0 

.8 

.6 ...... 

en 

!:i 

0 .~ > 

--Cl > .2 

<3 

0 

-.2 

-.4 

-.6 

-.8 

__ ox 

---- NO 

•••. •••• ONO 

-v STRESS a Sxl0-6 AMP 

CAP AREA = 4xlO-4 CM2 

o 

ox (2HR) 

V 

ONO (2HR) 

.-:;...; 

.0 NO (2HR) o __ /

-- _ ... -- --~ 

AFTER 2HR 107SoC N2 ANNEAL 

1 10 100 1000 10000 

LOG STRESS TIME (SEC) 

Figure 3: The changes in voltages across oxide, NO and ONO capacitors under 

constant current as a function of Log time. The samples were annealed for 2 

hours at l0750C in nitrogen. 

217 
150 ,,,.. .. ":,, .. , /.'"/ ,"/ 

, /: 

120 I' /1 I ,: 

i\ hi,' i: f i" 

SO '\ ,'\( 

\: " 

u.. H~: OX !;: Q. , . 

. u6 , 

, 

" 

30 

01 I I I I , -4 -3 -2 -1 Q 2 

Vg(V) 

150 .-.-..::::-..... 

...... " 

... , 

-. \ \ ' 

120 ' \ \ ' \ \ , ' 

I \ , ' 

90 I UNAtlNEALED , u.. , /' 

Q. ' " , NO 60 ' ~, i 

0 'r I 1 

! /' , 30 v'V 

0 , 

-4 -3 -2 -1 0 1 2 

Vg (VI 

15C 

120 

90 ~ 

u.. ONO Q. 

0 60 

30 

0 

-4 -3 -2 -1 0 2 

Vg (vI 

Figure 4: Quasi-static capacitance curves for an oxide, NO and ONO. The family 

of capacitance curves in each plot was due to increasing stresses across the 

dielectrics2 under constant current. The stress was approximately 0.5 

coulombs/em per step. 

218 
DISCUSSION 

ROHATGI: I can see that nitrided oxides are very good for VLSI, but from the 

point of your solar cells, they may not work because most of the nitrided 

oxides have been fabricated at temperatures of around 11000C to 

12000C. 

LAI: Well, I can tell you that for our purposes, for our work, we look at 

nitration conditions, which is consistent with VLSI processing. The conditions that I have shown you, up until now, in detail, there is no inconsistency at all with VLSI processing. 

ROHATGI: That is what I am trying to point out, it is very good for VLSI because it takes care of radiation problems. 

LAI: By VLSI, I mean that we are going away from high-temperature processes 

altogether. I don't see the nitration condition we have used is much 

lighter, compared with everything that is reported in the literature. 

ROHATGI: I have made some nitrated oxide for passivating solar cells. Our 

solar-cell junctions have to be very thin, also, so I stayed at temperatures around 8500C. So I grew 100 A oxide nitrided in ammonia at 

850, and there was no reel difference in the passivating properties of 

the oxide I had and the nitrided oxide. Then I went to a thermal nitride 

without any oxide, trying to make an MIS contact, and that was even worse. 

So it looks like if you are going to use this nitrided approach you have 

to figure out a way of doing it at low temperatures, because you don't 

see all these beneficial effects. 

LAI: Well, I guess the important thing is, what properties you look at for 

passivation. I will have to calibrate it to the point of data I have 

here. Have you looked at interface properties, CV curves, at bonded or 

impurity diffusion, those kinds of conditions? 

ROHATGI: I think interface properties is the key here, because that is what 

determines the surface recombination velocity', and like you said, unless 

you do the nitridation at temperatures 900 or above, you don't see all 

the good effects that have been reported in literature. 

LAI: That is what I said earlier, though. I don't think my experience has 

been that it does not really improve the surface. But all I have stated 

here is more for long-term reliability, and it is a much more stable 

system, which I think is a very important thing, at least for our process. 

GRUNTHANER: I think the dielectric material that you are looking at with the 

nitrided oxide shows a lot of really exciting possibilities, particularly 

in, terms of generation ~echanisms of more excited states. But there is 

one piece of information that you mayor may not be aware of that has 

come out of the Hewlett-Packard studies, which I think may have some 

severe impact on the solar cell situation here. That is, the experiments 

looking at the lattice imaging of the silicon surface, comparing thin 

Si02 films with these nitrided oxides. The interesting thing about 

219 
those results is that the surface of the silicon itself at the very abrupt 

determination, the last three or four atomic layers of the silicon, has 

significantly relaxed. There is much less strain at that surface situation, as you can see from the lattice-imaging TEM micrographs, and I 

think there are some very serious implications for some of these recombination losses and so on in that. I don't know what they will turn out 

to be but I think --

LAI: Well, is that good or bad. though? 

GRUNTHAHER: That's right. I don't know which way it is going to go. but there 

clearly is a difference. and I think the first difference that has really 

been seen is in these dielectric films that have been grown. A variety 

of other approaches have been taken. but always very similar reconstruction strains, and so on, on the surface of the silicon. Yet only in this 

nitrided oxide are they seeing an actual relaxation of the top surface 

there for such sharp and c~herent planes. 

RAO: In those annealing experiments -- this is just a takeoff on his question -- what happens when you use, say. an inert gas like argon at the same 

temperature instead of nitrogen? Have you had any results on that? 

LAI: No. I have not done the experiment. 

220 
N85-31628 ( 

SURFACE PASSIVATION AND JUNCTION FORMATION USING LOW ENERGY HYDROGEN IMPLANTS 

I. Introduction 

S. J. Fonash 

Engineering Science Program 

The Pennsylvania State University 

University Park, PA 16802 

The use of high current, low energy ion beams in device fabrication is a 

relatively recent development. Outstanding examples of this new, emerging use 

of low energy ions are the passivation of grain boundaries in polycrystalline 

silicon with low energy, hydrogen ion implantation [1] and the solar cell performance improvement resulting from low energy hydrogen ion implantation into 

Mobil Solar ribbon [2] •. Recently we have demonstrated that there are additional, 

innovative applications for low energy hydrogen ion implants which can be very 

useful for crystalline silicon. We discuss these new applications for high 

current, low energy hydrogen ion implants in this paper. 

The paper is arranged as follows: first, the effects of low energy hydrogen 

ion beams on crystalline Si surfaces are consid~red; next, the effect of 

these beams on bulk defects in crystalline Si is addressed; and, finally, specific 

applications of H+ implants to crystalline 8i processing are discussed. In all 

of the situations reported on here, the hydrogen beams were produced using a 

high current Kaufman ion source. 

II. Hydrogen Beams: A Cause and Cure for Surface Defects 

When a low energy hydrogen ion beam impinges on a single crystal silicon 

surface, the surface is sputter etched, hydrogen is implanted, and the silicon 

lattice is damaged. That low energy hydrogen ion beams damage Si surfaces may 

seem surprising in view of the ability of such beams to passivate grain boundaries in polycrystalline Si. However, the presence of this damage is demonstrated 

in Fig. 1. The figure shows Rutherford backscattering (RBS) data for two 

silicon samples: one which was subjected to a 0.4 keV H+ beam and another which 

was subjected to a 1. 0 keV H+ beam. The two traces for these cases are RBS 

channeling data; the third trace is the random backscattering yield from a 

silicon sample. 

As may be seen from the figure the lattice damage from to 1.0 keV a+ beam 

exists deeper down into the Si than does the lattice damage from the 0.4 keV u+ 

beam. Convert ins the energy scale into a measure of the field of energy dissipation for the ~ ions gives a 200 A deep layer of lattice damage for 0.4 keV u+ 

and a 400 A deep layer for'l.O keV a+ ions. This measure of the lattice damage 

is based on the full width in energy of the RBS channeling peak at half maximum 

of the yield. By noting that the channeling peak yields for both 0.4 u+ and 

1.0 a+ beam exposures coincide with the random yield, it can be deduced that 

this layer of lattice damage, resulting from exposure to the hydrogen beams 

(dosage ~1018 cm-2 in both cases), is amorphized. 

221 
A further demonstration of the fact that low energy hydrogen ion beams 

themselves damage Si is provided by Table I. This table gives peak to peak 

heights for the electron spin resonance (ESR) signature of silicon dangling 

bonds [3]. The table shows how this ESR measure of lattice damage varies as 

the H+ ion beam energy is varied from 0.2 keV to 1.0 keV. The data indicate 

that lattice damage increases up to 'VO.S keV and then appears to saturate. 

This saturation effect may be due to sputtering which reduces the volume of 

damaged ~teria1 or to an annealing effect •. Again all the dosages were of the 

order of 'V1018 cm-2 • 

Ion Beam 

Species & Energy 

Control Sample 

0.2 keV 

0.4 keV 

0.6 keV 

O.S keV 

1.0 keV 

0.2 keV 

0.4 keV 

1.0 keV 

TABLE I 

Peak-to-Peak ESR Signal Heights 

Minimum Power 

Microwave 

<1 

<1 

<1 

<1 

'V2 

'VI. S 

<1 

<1 

'VS. S 

ESR Signal Heights 

Medium.Power Maximum Power 

Microwave Microwave 

<1 

'V1 

'V2 

'\,2 

'V4.S 

'V4 

'V2 

~3 

'V3.S 

'VS.S 

'V7 

An electrical assessment of the damage caused at crystalline Si surfaces 

by low energy hydrogen ion beams is presented in Fig. 2. Here current-voltage 

(I-V) data are given for Au dots deposited on p-Si. As expected Au contacts to 

chemically prepared p-Si (the control) show a low barrier height. However, Au 

contacts to chemically prepared p-Si, which was subsequently subjected to various ~ beam exposures, yield I-V characteristics which indicate the presence of 

positive charge. That is, positive charge is created in a layer near the Si 

surface due to the H+ beam exposure and this causes the increased barrier 

height seen in Fig. 2 [3-6]. 

Thus the RBS data of Fig. 1, the ESR data of Table I, and the I-V data of 

Fig. 2 establish that low energy ~ ion beams damage single crystal Si surfaces. 

All measures of this damage agree that it is worse at the higher energies (for 

the range used) and least at the lower energies. However, these measures do 

not all yield data that va~y with energy in exactly the same manner. For 

example, the amount of positive charge present, as judged from the I-V data, is 

not found to be simply proportional to the strength of the ESR signal. 

Other low energy ion beams also damage single crystal silicon surfaces. 

In fact, as we will see, they inflict more damage (holding dosage and beam 

energy constant) than does hydrogen. We begin this consideration of the damage 

222 
effects of other ion beams by turning to Fig. 3. This figure establishes that 

low energy Ar+ beams (again a total of ~1018 ions/cm2 impinged on these samples) 

damage the silicon lattice at and below the surface. In this case the RBS data 

indicatethatothe field over which energy is dissipated by 0.4 keV Ar+ ions 

extends ~100 A below the surface whereas the field over which energy is dissipated by 1.0 keV Ar+ ions extends ~200 1~ These RBS data point out that the 

Ar+ beams, unlike the hydrogen, have not been able to amorphise the Si surface 

layer. 

Table I also contains the ESR assessment of the damage caused by Ar+ ion 

beams. As may be noted from the table, the damage increases with beam energy 

and the damage signal is higher for Ar+, for the same dosage and energy, than 

it is for S+. Fig. 4 shows the I-V data for a Au dot on p-Si which was chemically prepared and subsequently subjected.to a 1.0 keV Ar+ beam. The positively 

charged surface layer (i.e., the surface layer containing damage-induced donors) 

is clearly present as a result of the Ar+ exposure as is apparent from the I-V 

characteristic. 

Hydrogen ion beams cause surface damage and other ion beams such as would 

be present in plasma deposition, sputtering, or dry etching (we took Ar+ as an 

example), also cause surface damage. This observation immediately causes several 

questions to present themselves: (1) how does the damage caused by ~ compare 

with that caused by Ar+, (2) how can g+ implants passivate poly Si and Mobil 

Solar ribbon Si without causing surface damage, and (3) can H+ implants passivate the damage caused by Ar+ implants. We begin addressing these questions by 

comparing ~ and Ar+ ion beam damage in single crystal Si. 

As may be seen from Fig. 1 and 3, the RBS channeling data indicate that 

the field of damage (Si atoms knocked out of their lattice positions) is more 

extensive, for a given dosage and energy, for hydrogen than it is for argon. 

Also the hydrogen amorphises the Si surface layer; the argon does not. However, 

the ESR data of Table I indicate that there are more dangling bonds in the damage layers caused by Ar+ -- even thdugh Figs. 1 and 3 show these Ar+ - caused 

layers are thinner -- than there are in the corresponding (same energy and 

dosage) layers caused by a+. This is our first indication that, although the s+ 

beam is very effective in tearing up the Si lattice, it also passivates its own 

damage as seen by the reduced ESR signal. The I-V data of Figs. 2 and 4 support 

this contention; i.e., there is less positive charge present after a 1.0 s+ ion 

beam exposure than there is after a 1. 0 Ar+ ion beam exposure (both s.ituations 

had a total of ~1018 ions/cm2 impinging on the Si). 

This brings us to the question of how can ~ implants passivate poly Si 

and Mobil Solar ribbon Si without causing surface damage. We be1:i.eve the answer 

must be that these g+ implants do cause damage .tothe surfaces of. these materials. 

The picture that emerges 1s as follows: As the·S+ is implanted, if the se1fcaused damage is not too severe, some H can escape the implant region and diffuse 

to bulk defects or grain boundaries for passivation. The implant induced surface 

damage'is partially (or completely) passivated by remaining hydrogen. This layer 

can then remain, be etched off, or be annealed out. We speculate that, if it 

remains in a completed n+/p solar cell structure, any residual positive charge 

in the layer would only perform the beneficial service of forming a front surface 

field which would aid short wave length spectral response. However, if dangling 

bonds also remain these could increase surface recombination in the emitter 1ead223 
] 

1 

I 

I 

ing to a degradation in Voc (if it is controlled by the emitter) and to a degradation in the short wavelength spectral response. Put another way, if Voc degrades 

after ~ implantation, it suggests that Voc is being controlled by the emitter 

and emitter recombination is being enhanced by exposure to the ~ beam. 

The pertinent question of whether or not g+ implants can passivate surface 

lattice damage now needs to be considered. To do that we turn to Fig. 4. Here 

we see the I-V characteristic for an Au dot evaporated onto Si that has been subjected to 1.0 keV Ar+.and then subjected to 0.4 keV rr+ beams. The Ar+ damage 

seen in Fig. 4 (1. 0 keV Ar+ I-V curve) is clearly passivated by the H+ implant. 

In fact, the damage (as judged by the presence of positive charge) is seen from 

Figs. 2 and 4 to be less after the Ar+ plus rr+ beam exposures than it is after a 

simple 0.4 keV g+ beam exposure. 

Comparing Figures 2 and 4 indicates that there iH a synergism involved in 

the 1.0 Ar+ exposure/0.4 ~ exposure. One can sp~culate that the damage caused 

by the 1.0 keV Ar+ beam retards the penetration of the subsequent 0.4 keV g+ 

beam trapping the hydrogen ina smaller volume. This allows it to be more effective in passivating the donor levels (positive charge) caused by the Ar+ ion beam 

lattice damage. However, this retardation of the hydrogen by the Ar+ damage has 

yet to be established by RBS. It also must be determined if the remaining damage 

(after 1.0 Ar+/0.4 ~) is electrically inactive but detectable by ESR measurements. 

It is clear that hydrogen implants can be the cause as well as the cure fo~ 

surface damage in crystalline silicon. The manner in which the hydrogen acts 

(i.e., whether it results in a net cure or cause of damage) depends on the previous history of the surface. It remains to be determined if implanting through 

thin oxide or nitride layers can modify this behavior and if hydrogen implants 

can improve the quality of thin oxide/Si or thin nitride/Si interfaces. 

III. Hydrogen Beams: A Cure for Bulk Defects 

From the results of Section II, from references [1] and [2], and from. the 

wealth of data from amorphous Si work, it seems clear that hydrogen implants can 

passivate dangling bonds lil silicon. Hence, if hydrogen can reach bonding defects in bulk Si, it will passivate them. Recently, it has also been suggested 

that hydrogen can passivate deep levels resulting from impurities in silicon 

[7,8]. However, this latter point remains somewhat in doubt since surface damage, 

incurred in the act of introducing the hydrogen, can getter fast diffusing impurities. Hence it remains to establish if hydrogen is passivating deep impurity 

levels or, if hydrogen-caused damage, is gettering the impurities. 

IV. Applications of ~ Implants to Crystalline Silicon 

A. Surface Property Modification 

As was discussed in Section II, if Si is exposed to a low energy hydrogen ion beam, ·there is a surface layer produced which contains lattice damage. 

This lattice damage gives rise to donor levels which cause the barrier seen in 

Fig. 2. As noted in Fig. 2, there is also an insulating Si:H or Si:H:O layer 

produced by the lower energy g+ ion beam exposures [4]. Its presence is not 

224 
.. 

detected in Fig. 2 (it would appear as a large series resistance in the I-V) 

since these samples were all given an HF etch and DI water rinse. 

The presence of this apparently wide gap, insulating Si:H or Si:H:O layer, 

produced by the lower energy ~ beam exposures, is seen in Fig. 5. This figure 

presents capacitance-voltage (C-V) data for a p-type Si sample that was subjected 

to a 0.4 keV ~ ion beam. In this case the Au front contact was deposited on the 

~ implanted surface without the HF etch to allow the insulating surface film to 

remain. These C-V data show that the wide gap Si:H or Si:H:O layer is capable of 

supporting both accumulation and inversion; i. e., the layer is, ,a good insulator. 

We note that the conducting, lattice-damaged layer, containing the donor'levels 

giving rise to the barrier seen in Fig. 2, lies below this insulating layer. T~s 

same type of insulating layer appears for the lower energy H+ implants onn-type single crystal Si samples also. 

This wide gap insulating surface layer created by the lower energy u+ implants appears attractive for surface passivation of solar cells. The u+ implants which produce this layer seem especially attractive for n+ emitter structures since the wide-gap layer could passivate the emitter surface while the 

donor layer, produced by the H+ implant, would create a front surface field. 

Such ~ implants, when done through thin oxides or nitrides, may produce optimum 

emitter structures. However, this all remains speculation at this point since 

the effect of this processing on emitter recombination has not been determined 

nor has there been any attempt at optimization, or at studying, the effects of 

the presence of thin oxide or nitride layers. 

" 

B. Low Temperature Junction Formation 

From the preceeding sections and from the literature there is extensive 

evidence pointing towards the virtues of hydrogen in the passivation of electrically active bonding defects in silicon. Hence, it seems only natural to determine if u+ implants can improve the quality of implanted, shallow n+/p and p+/n 

junctions. The objective is to obtain high quality, low leakage implanted shallow junctions without recourse to the high temperature processing currently 

employed. 

In our study, n+/p diode structures were fabricated by implanting 75-keV As+ 

ions into (100) p-type Si which had channel stops present. The dosage used was 

5 x 1015 As atoms/cm2 and the implant area was 3.7 x 10-2 cm2• Using a Kaufmantype ion source, we subsequently implanted low-energy hydrogen ions into the 

damaged silicon. The hydrogen ion beam had an accelerating voltage of 0.4 keV, 

an extractor voltage of 0.3 keV, and an accelerator current of 200 mAo These 

silicon samples were then annealed at 500 or 600°C for 1 hr. in nitrogen or argon 

ambients. Spreading resistance measurements were subsequently made to examine 

the dopant profile and the degree of dopant activation. Current-volt age-temper ature (I-V-T) measurements were made to examine the diode characteristics and 

transport mechanisms. Experj,mental details may be obtained from ref. [9]. 

We found that the low-t,emperature anneal, following the 11+ implant, is a 

very necessary part of this processing. The characteristics of our diodes, immediately after the ~ implantation but before the low-temperature anneal, are 

extremely poor. The high series resistance and very large leakage currents (of 

the order of hundreds of llA/cm2) indicate that the damage has not been fully 

passivated and that the dopant is not activated by the hydrogen implant alone. 

The inactivity of the dopant is borne out by the spreading resistance measure225 
• 

ments. (See Fig. 6). The lack of dopant activation after the W implant is not 

surpri~ing as the temperature of the silicon sample during the W implant rises 

to temperatures less than 150°C. The results of our spreading resistance measurements (Fig. 6) indicate that junction depth after a 600°C I-hr. anneal shows 

very little dopant redistribution. The dopant concentration as measured from 

spreading resistance shows that most of the implanted As has been activated by 

this 600°C anneal following the H+ implantation. 

Turning specifically to the diode I-V behavior resulting from this HILT 

processing (from hydrogen ion-assisted, low temperature anneal), it is seen in 

Fig. 7 that excellent diode characteristics result even though processing temperatures have never exceeded 600°C. Leakage currents of the order of 5 nA/cm2 at 

1.5 volt reverse bias are attained for ~5-10n-cm p-Si base material. The forward 

bias n-factors in this case are n = 1.03 over ~5 decades. We have obtained simi1are results for p+/n implanted junctions. 

In summary, we assert that this novel, genuinely low-temperature process 

offers an alternative to the nmnerous other processes being investigated to 

anneal out implantation damage and to activate dopants in implanted Si. Our preliminary studies, with very little optimization, show that this low-energy 

hydrogen-ion implantation/low-temperature anneal processing for damage passivation and dopant activation gives results comparable to the other annealing processes (we have looked at p+/n junctions also). In addition it allows for passivation of any residual defects and thereby provides an advantage not offered by 

other techniques. Although at present '" we use furnace anneals to activate the 

dopants, we are by no means limited to them and can use low-energy W implants 

in conjunction with lower-temperature RTA approaches. This will reduce the 

processing time involved. With the development of broad-beam ion sources, this 

process can very easily be adapted to the fabrication of the extremely shallow 

junctions needed for solar cells. 

At this time the mechanism by which hydrogen implants improve device characteristics is not clear. Indeed several groups (including us) have found that 

H begins to evolve from silicon at a temperature of ~350°C and is completely 

lost by 600°C. Thus the simple explanation of hydrogen bonding itself to the 

silicon "dangling bonds" does not seem to be adequate. Further work to identify 

the mechanisms of annealing and dopant activation is under way. 

C. Enhancement of Web Solar Cell Performance 

As we first pointed out at the 1983 European Photovoltaics Conference 

Meeting [10], low energy hydrogen ion implants can improve the performance of 

solar cells fabricated on Westinghouse web material. Subsequently [11] we have 

shown that these low energy implants reduce the 30 for the recombinationdiffusion current controlling Voc and,thereby, enhance Voc in these cells. Also 

the long wavelength spectral response is improved by the implants [11] implying 

the diffusion length is increased in the base. This latter fact suggests that 

J o is c'ontro1led by the base.; consequently, Voc and the spectral response improve 

due to an improved base diffusion length. From this picture one is led to the 

deduction that the s+ implant is passivating bulk defects in the web Si. 

There is an alternative explanation: the W implants may be reducing recombination in the emitter; i.e •. , J o may be controlled by the emitter. Theenhanced 

long wavelength spectral response would not be due to enhance base properties in 

226 
this picture; but, rather, it would be due to a widened band gap in the emitter 

which allows long wavelength photons to penetrate into the base. That is, before 

the u+ implant the band gap in the emitter is narrowed due to the high doping 

levels used in the Westinghouse cells. This narrow band gap causes enhanced 

long wavelength photon absorption in the emitter. After the ~ implant, the band 

gap is widened and, as noted, these photons can now penetrate into the base giving 

an apparent increase in the base diffusion length. 

Whether base material properties are actually being.improved by these W- implants into web material or whether all the changes (reduced recombination and 

widened band gap) are taking. place in the emitter remains to be determined. Given 

the fact that sample history affects the way hydrogen interacts with Si - as we 

established in Section II - it follows that the interaction of ~ implants with 

web Si can be a complicated phenomenon which needs additional study .. 

V. Conclusions 

As a result of our examination to date of the effects of hydrogen ion beam 

exposure on crystalline silicon, the following conclusions may be drawn: 

1. Hydrogen ion exposure can cause, as well as cure, surface defects. 

These defects include damage-causeq donor states and dangling bonds. 

Whether a hydrogen implant results in increased damaged or passivation depends on the energy of the implant and on the past processing 

history of the silicon surface. 

2. Very low energy hydrogen ions can produce a wide-gap insulating 

film at the surface of silicon. It may be possible to use this 

layer, perhaps by implanting through thin oxide or nitride films, 

to passivate surfaces. 

3. Hydrogen ion exposure can passivate bulk bonding defects. 

4. Hydrogen implants can be used to give high quality, shallow implanted junctions. The use of the hydrogen implant allow this to 

be accomplished with processing temperatures of only 600o e. 

5. Low energy hydrogen implants can improve solar cell performance. 

It appears that there are two possible scenarios that can explain 

this: 

One assumes that the hydrogen implants do not affect the 

emitter or, in the other extreme, damage the emitter. It 

is assumed that the implants passivate bulk defects. In 

this case, cells where Voc is controlled by the base would 

show enhancement of the Voc after the hydrogen implant and 

cells where Vo~ is controlled by the emitter would show no 

change in Voc or degradation. In both situations the long 

wavelength spectral response should improve. 

The other scenario assumes that the hydrogen implants reduce 

recombination in the emitter and also may widen the band gap 

227 
in the emitter, depending on emitter doping level. In this 

case, cells where Voc is controlled by the base would show 

no change in Voc after an implant; however, cells where Voc 

is controlled by the emitter would show improvement. In 

both situations the long wavelength spectral response may 

improve due to band gap widening. 

Acknowledgements 

We wish to thank P. Rai-Choudhury and A. Rohatgi of the Westinghouse R&D 

Center for providing the impurity doped Si as well as the web Si. We also wish 

to thank E. Poindexter and P. Caplan of the U. S. Army Electronics Technology 

and Devices Laboratory for the ESR measurements and E. Wolf of Cornell's National 

Research and Resource Facility for Submicron Structures for the broad technical 

support of tnat facility. 

Portions of this work were supported by the National Science Foundation 

under Grant #ECS-8305646. 

References 

1. C. H. Seager, D. J. Sharp, J. K. G. Panitz, and R. V. D'Aiello, J. Vac. Sci. 

and Technol., 20 (3), 430, 1982. 

2. J. Hanoka, C. Seager, D. Sharp, and J. Panitz, Appl. Phys. Lett. 42, 618 

(1983) • 

3. R. Sin.gh, S. Fonash, P. Caplan, and E. Poindexter, Appl. Phys. Lett., 43, 

502 (1983). 

4. R. Singh, S. FDnash, S. Ashok, P. Caplan, J. Shappirio, M. Hage-Ali, and 

J. Ponpon, J. Vac. Sci. Technol. Al, 334 (1983). 

5. J.-S. Wang, S. Fonash, and S. Ashok, IEEE Electron Device Lett., EDL-4 

433 (1983). 

6. A. Climent and S. J. Fonash, J. Appl. Phys., July 1984. 

7. S. Pearton and A. Tavendale, Phys. Rev. B26, 7105 (1982). 

8. S. Pearton, J. Kahn, W. Hansen, and E. Haller, J. Appl. Phys. 55, 1464 

(1984) • 

9. R. Singh, S. J. Fonash, A. Rohatgi, P. Rai-Choudhury, and J. Giganti, 

J. Appl. Phys. 55, 867 (1984). 

10. R~ Singh, S. Fonash, A. Rohatgi, and P. Rai-Choudhury, Proc. European 

Photovolta~c Conference, Athens, Greece (1983). 

11. D. J.1eier, A. Rohatgi, R. Campbell,' P. Alexander, S. Fonash, and R. Singh, 

Photovoltaic Specialists Conference, Orlando, Florida, May, 1984. 

228 
o 

-J 

LU 

;: 

1.0KeV H 

0.4 KeV H 

IAMPSI 

ENERGY 

0.2 k~V 

IF& RI 

Figure 1. Rutherford backscattering 

channeling data for 0.4 keV and 1.0 keV ~ 

beam exposures. Also shown is the random 

yield. 

O.6k(,VIRI 

/

CONT ROL O.B k<!V IRI 

IF,R) ~_0.4 kC'VIRI V ~ ~lO ,,' '" 

f H+ IMPLANTS 

p-Si (100) 1-IOn.-em 

F - FORWARD 

R - REVERSE 

Imm Au DOTS 12801{1 

/ ~ " L~EC:::5 10"6 (AI BACK CONTACT .L. __ ....-_____ ...-_____ ..-____ _ 

0.0 0.1 0.2 

V I VOLTS) 

Figure 2. Current-voltage (I-V) data for Au dots evaporated onto p-Si surfaces 

subjected to various hydrogen ion beam exposures. The Au dots were deposited 

after the ~ exposures and aft.er an HF etch and DI water rinse. This etch and 

rinse is used to remove a higa resistance Si:H or S:R:O layer that forms for the 

lower energy beams. See Figure 6. 

229 
C 

..J 

I.&J 

>-

0.4 K"V Ar 

1 lAMPS) 

ENERGY 

Figure 3. Rutherford backscattering 

channeling data for 0.4 keV and 1.0 

keV Ar+ beam exposures. Also shown is 

the random yield. 

- 1.0 keV Ar+ /0.4 kC?V 

IF'RI 

F - FORWARD 

R -REVERSE 

, 

/ ........ 1.0 keV 

Art I FI 

10"6 .&..----:"':"""-----~.......I.:...----jr_------ 0.0 0.1 0: 2 

V 'VOLTS) 

Figure 4. Current-voltage (I-V) data for Au dots evaporated onto p-Si surfaces 

subjected to 1.0 Ar+ exposure. In one case the Ar+ exposure was followed by an 

H+ exposure. In each case the Au dots were deposited after the ion exposures and 

after an HF etch and DI water rinse. 

230 
t 

-!; -

u 

OR~Gt~AL PABfi: ~S 

OF. POOR QUAliTY 

CAPACITANCE VS VSUL 

FOR p-Si SUBJECT 

TO a4 KeV H+ 

caMHI) 

/RONT CONTACT 

~_MOOIFIED I" Sf LAYER 

BACIC CONTACT7 

+2 +4 +6 

Vsub (VoUs'-

Figure 5. Capacitance-voltage data for p-Si which was implanted with 

~ (0.4 keV beam energy) but which was not given the subsequent HF 

etch and DI rinse used for the samples of Fig. 2. Accumulation and 

inversion are clearly occurring due to the presence of an insulating 

surface film. 

231 
'~--+-LSS Profile 

, 

I 

8 

70 

60 

!!O 

40 

30 

lO"'I,--_,o~_--:::'-.b-----=+'::-----:4. 0.25 0;50 0.7!! 

V (VOLTS) 

Figure 6. Spreading resistance plots for 

75 keV As+ implanted 81. Treatments 

following the As+ implants are shown on 

the figure as is the theoretical L88 

profile. 

Figure 7. Current-vo1tage-temperature 

data for As+ implanted 8i. This n+/p 

diode structure has had a 0.4 keV g+ 

implant for 1 minute followed by a 600°C 

1 hour furnace anneal in N2. The diode 

area is 3.7 x 10-2 cm-2• . 

232 

/ 
DISCUSSION 

TURNER: I would propose an experiment by which you might be able to differentiate between those two models. That is, to shine blue li&ht and red 

light -- as long as it is not infrared -- on the back of the cell, cut a 

window through the back metallization and shine light on that, and that 

will be sensitive to the diffusion length through the base of the material. The emitter won't make any difference, except for minor reflectivity. 

FONASH: That is a good suggestion. 

KAZMERSKI: Or you could try implanting through the rear. 

FONASH: We haven't tried the former suggestion, the latter suggestion is being 

tried right now. We are trying implanting through the rear. 

LESK: In your one-minute implantations, with your system, what dose are you 

getting? 

FONASH: The dosages are on the order of l018/cm2. 

LESK: And that is your general dose you are using for all this work? 

In the last work you talked about, the emitter band-gap widening, were 

your measurements taken "before the AR coat or after, and if after, did 

the temperature involved in the AR coat deposition have any effect on the 

annealing? 

FONASH: The measurements that I just showed for the web material -,- all the 

data that I showed was before AR coating. There was no temperature processing involved at all in that. Now Westinghouse has subsequently taken 

these cells and put on AR coatings to see what would happen and the performance continues to be enhanced to the degree that one would expect from 

an AR coating. They have also done -- and again, I think Ajeet (Rohatgi) 

will probably discuss this -- Westinghouse has also taken these cells that 

we have implanted and they have done some temperature stability studies on 

them, and what have you, and the answer to your general question is that 

they don't find any de9tabilization on the cells with moderate temperature 

cycling. 

SCHRODER: Have you done any DLTS measurements on the damage layers themselves? 

FONASH: Yes we have. 

SCHRODER: The data you showed was after it was removed, on the gold sample? 

FONASH: Yes it was. 

SCHRODER: On the previous samples? 

FONASH: We have done DLTS, and we see a broad damage signal around the middle 

233 
of the gap. a little bit above the middle of gap. We have also implanted 

silicon into silicon and done DLTS to compare the damage signals. and they 

compare. But that is work that we have just been into for about a month 

or so. I would not really like to comment on that too much. other than 

to say that we are doing precisely what you have suggested. 

SCHRODER: OK. Another question is, do you think your hydrogen implant conditions are similar to what I assume you referred to -- proton work, plasma, 

or even recently, I think. they use an electron technique? 

FONASH: That is right. 

SCHRODER: Are the conditions similar, you think? 

FONASH: In a plasma, as you know. the governing quantity that one needs to 

look at is the voltage across the sheet, because that is the energy that 

the ions would impact the surface with. So I really don't know; given the 

power. there is no way to convert that directly into what the energy of 

the ions-is, so I can't comment on whether the situation is the same. I 

don't know the energy of their ions when they impact the surface. They 

are also talking about a process where they do the hydrogen treatment at 

3000C. as I remember. It is done for something like two hours. To 

summarize my answer, I don't know the energy of their ions. Theirs is a 

process done at elevated temperature. and it is a process that is done 

for some two hours .. Ours is a process that is done at essentially room 

temperature, at one minute, for very carefully controlled ion energy. 

LOFERSKI: I was going to suggest perhaps a third mechanism that would account 

for the increase of diffusion length in the Westinghouse web samples. 

Perhaps, also, for what is going on in that gold-doped cell. You know, 

for one thing, the implantation certainly produces a lot of vacancies in 

the silicon, at interstitials and vacancies. You know the work by George 

Watkins -- and the ESR studies in silicon -- and of other people, that 

shows that vacancies form complexes and these complexes are what result 

in the deep levels that control lifetime. Now vacancies can also -- some 

of the complexes can be in a direction where they wipe out something that 

was a lifetime killer, and, you know, just neutralize it. so that it is 

possible that what is happening in both cases is that you have generated 

vacancies in excess of what you wOlild have had at that temperature and 

they go down into the complexes; the vacancies are very mobile. Watkins 

showed that you don't see any free vacancies. and if you produce them at 

temperatures higher than, I think something at lK. they move rapidly even 

down there at 20K, and so forth. 

FONASH: I realize that. 

LOFERSKI: So, anyway, that is another possibility. 

FONASH: I think it is a possibility. That is one of the reasons why we are 

going to the implant from the back. But there is always a possibility 

that that experiment. implant from the back, cou.J.d be clouded by the 

vacancies coming all the way up to the emitter. One could always argue 

that that is not the definitive experiment. I am aware of the high 

234 I 
mobility of vacancies, and it does indeed further cloud the issue. Getting back to the gold, I don't think"it is the explanation there, because 

I think we have pretty well established that the gold is captured in that 

damaged layer and we remove it when we etch off the damaged layer. 

LOFERSKI: I was wondering about the gold, whether anybody has studied gold and 

vacancies, complexes; whether Watkins has done that or not? 

FONASH: I don't know. 

MILSTEIN: As you may be aware -- I am sure aware -- we also looked at hydrogen implants at 300 eY in web materials and our RBS data and some other 

things differ a little bit from yours. At 400 eY for 1000 minutes of 

passivation, just to make sure we saw the damage if it was going to be 

there. We saw no amorphous material, and that is consistent with the 

fact that we saw no change in the reflectance under those implant conditions. However, when we went to 900 eY or 1500 eY, we saw several hundred 

A of amorphous material, and in fact we saw a very dramatic change in 

the absorption, which is consistent with the appearance of amorphous 

material. In that sense, I would question whether at 400 eY, which is a 

mere 100 eY above where we were, you are seeing the kinds of things you 

are seeing. 

FONASH: Well, I don't question it, because we have reproduced it several 

times, so I know it's real. And I think these other data -- there is a 

group at IBK for example, that has used Rutherford back-scattering to 

study damage incurred in reactive ion etching, and they have found that 

for comparable energies, 300 eY, 400 eY, the RBS does indeed detect a 

substantially damaged layer. So I don't doubt the data, that there is a 

damaged layer that is produced there at 400 eY. 

MILSTEIN: Well, we saw latticed damage, 1600 A of lattice damage, we did 

not see amorphous at 400 eY. 

FONASH: Oh, you mean the RBS yield was not up to the amorphous level? 

MILSTEIN: That is correct. 

FONASH: Well, I don't know the explanation for that other than to suggest that 

perhaps you did some t.herma1 treatment. It could be that your energies 

are not the same. 

MILSTEIN: No .. 

FONASH: Well, we find this reproducible. 

SAH: I would like to ask you if you have tried it on an encapsulated silicon? 

FONASH: Yes. 

SAM: What happens? 

FONASH: Well, what do you want to discuss? 

235 
SAH: For instance, you called this level a donor level. 

FONASH: That is right, it is symmetric. It lowers the barrier in n-type 

silicon. We have published that in a number of places. 

SAH: It is still donor, or is it not donor? 

FONASH: It is still donor. It lowers the barrier in n-type silicon. In other 

words, you get an n+n type of layer on n-type silicon. You see, it's 

one of the first things we did to see if the effect is symmetric between 

p and n silicon, and indeed it is. It is not a special case of a donor 

that shows up for p material and mysteriously disappears for n type 

material. 

HANOKA: The stuff we've done leaves no doubt that the first of your two explanations is the right one. The second one is not, because we have done 

a lot of diffusion-length measurements using, let's say, a liquid-junction 

technique, which does not change the sample at all. It is totally nondestructive. It doesn't heat it or anything. We take a sample with no 

junction, just measure diffusion length for an implanted sample. Diffusion length definitely goes up, and it's definitely a bulk effect. We 

etch off samples and measure it again. The sam~ sort of thing. Etch off 

some of the material and measure again. 

FONASH: What energies are you using now? 

HANOKA: These are higher energies. I think 1500 to 1700 eV. 

FONASH: I think we have to keep that in mind -- that you are talking about 

energies that are 1500 eV. 

HANOKA: But I don't see where that makes a difference here. 

FONASH: Well, just last week we did some implants for Westinghouse. We took 

a sample -- Westinghouse had measured the diffusion length by surface 

photovo1tage -- we did the implant and gave them the samples back. They 

measured the diffusion length by surface photovoltage and it didn't 

change. But we are down around 400 eV. 

HANOKA: We do find the diffusion length changes from sample to sample. It is 

a function of the kind of defects you have in the sample. 

FONASH: Well, I think an important point is, you are looking at your material, are you not? 

HANOKA: This is only on EFG now. 

FONASH: Right. And we are ~ooking at web material, and the nature of the defects is quite different, is it not? In your material don't you have a 

lot of defects that intersect the surface, and so one could think of conduits that could carry the hydrogen down into the bulk. 

HANOKA: That's right. 

236 
,,!~I 

•. ' "f t 

" ('~'~ 

\ -'~~\ 

rONASH: We have & different kind of meterial, so I think we have to watch an 

apples-and-oranses kind of comparison. 

HANOIA: Well, I still think it is apples, but I think it is McIntosh and 

Delicious. 

LorERSKI: I just wonder if the difference between your relults and his could 

relate to temperature control. 

rONASH: That's what I think. 

LorERSKI: Dose up to 1017 cm-3 in one minute at 400 eVe That is a big 

jolt of energy, and the temperature may be fluctuating. 

rONASH: Well, of course it works the other way though, doesn't it? You would 

think that we might get some regrowth if we are dumping all that hydrogen 

in in such a short time, but yet he is claiming that perhaps he's got some 

regrowth. So I think it is going in the opposite direction. 

LOFERSKI: If he has the same dose as you have for that long he is going to 

explode the surface. 

FONASH: I think he is using the same dose. 

HANOKA: A factor of three lower. 

rONASH: Oh, is it a factor of three lower? 

LorERSKI: A lot less. 

rONASH: I think temperature is the key to that difficulty. I don't think 

there is anything fundamentally significant in that. 

237 
~ N85-31629 

" 

I ,} 

-I 

j 

Frank J. Grunthaner's abstract is presented here. His paper and visual 

material were not presented for publications. 

CHEMICAL STRUCTURE OF INTERFACES 

Frank J. Grunthaner 

Jet Propulsion Laboratory 

California Institute of Technology 

Pasadena, California 

The interfacial structure of silicon/dielectric and silicon/metal systems is 

particularly amenable to analysis using a combination of surface spectroscopies together with a variety of chemical structures of Si/Si02' 

Si/Si02Si3N4' Si/Si2N20, Si/S~02/Al, and Si/Native Oxide 

interfaces using high resolution (0.350 eV FWHH) X-ray photoelectron 

spectroscopy. The general structure of these dielectric interfaces entails a 

monolayer chemical transition layer at the Si/~ielectric boundary, which 

consists of specific distributions of the intermediate oxidation states of 

silicon (Si+1 , Si,+2, and -Si+3 ), which appear to be related to local 

morphology of the silicon substrate. Amorphous Si substrates show a wide 

variety of hydrogenated Si and Si(OH)x states that are not observed in 

thermal oxidation of single crystal material. Extended Si02 layers greater 

than 8 A in thickness are shown to be stoichiometric Si02 , but to exhibit 

a wide variety of local network structures. In the nitrogen-containing 

systems, we see an approach to stoichiometric oxynitride compounds with 

interesting impurity- and electron-trapping properties. In native oxides, we 

find substantial topographical non-uniformity in oxide thickness and 

composition (e.g., a nominal 25A oxide can be shown to have 4 different 

areal distributions of Si02 ranging in thickness from 12 to 165 A). 

Analysis of metal/oxide interfacial layers is accomplished by analytical 

removal of the Si substrate by UHV XeF2 dry etching methods. The general 

question of the importance of the chemical state of the starting silicon 

surface to the final dielectric/silicon interface composition will be 

addressed in a series of experiments using covalent silicon surface 

sUbstitution. Finally, the modification of silicon surface bonding and 

hybridization in the presence of sub-monolayer levels of transition metals 

will be examined from the perspective of a modification in interfacial 

reactivity. 

PRECEDING PAGE BLANE NOT FILMED 

239 
No discussion. 

DISCUSSION 

(GRUNTHANER) 

240 
SESSION IV 

BULK EFFECTS 

E. Sirtl, Chairman 
N85-31630 

Erhard Sirtl's abstract is presented here. His paper and visual material were 

not presented for publication. 

STRUCTURAL DEFECTS IN CRYSTALLINE SILICON 

Erhard Sirtl 

Heliotronie GmbH 

Burghausen, Federal Republic of Germany 

The basic photovoltaic properties of a given crystalline silicon specimen seem 

to be governed by density and nature of two- to three-dimensional lattice 

defects. These are mainly generated by primary growth conditions as grain 

boundaries of more or less intrinsic character or second-phase precipitates 

from supersaturated solutions of carbon or oxygen. Considerably high values 

of both solubility and diffusivity in connection with their abundance in 

common refractory material systems account for the predominance of the two 

particular elements. Unsaturated dislocations of different types very often 

can be seen as a consequence of the existence of more-dimensional defects as 

described initially. 

The final performance of a solar cell, however. is dependent of the 

concentration and distribution of recombination-active centers in the 

different regions of this device. Typical representatives are fast-diffusing 

transition metals in form of either single atoms or simple complexes. 

Their avoidance, annihilation, or removal has been of great concern in 

different fields of electronic materials development for years. Presently we 

are still in a very early stage of thorough comprehension in terms of 

interaction of metal atoms with the one- to three-dimensional crystal defects 

discussed. 

241 
DISCUSSION 

RAI-CHOUDHURY: What needs to be improved in polycrystalline silicon, without 

paying a price for solar performance? 

SIRTL: (First part of answer not recorded) .wouldn't it bs better to take 

a single crystal? It was not the alternative for us in this case, because 

we didn't work on that, and we didn't even plan to work on that because 

we wanted to create something that has to be much more economical in the 

future. But we were pleased to see that grain boundaries in general must 

not mean, from the beginning, a terrible situation. If we optimize that 

over the years, in a certain way, we may well end up with something that 

will just p'lease us to be t,Jler'e. We have seen that people have managed 

rather well, or very well, in the meantime, to overcome the problem of a 

grain boundary l'unning through a p-n junction. That is one subject I 

would say I missed. that has not been brought up explicitly around here, 

but it may be a subject for some further meeting because. I think we would 

learn a lot of interesting things. 

SCHWUTTKE: May I answer the previous question, if you don't mind? I think 

that you should not confuse the electrical capture cross section of a 

defect as its capability to getter impurities. These are two totally 

different situations. I think it is possible that you can getter impurities. maybe by some-mechanism that I don't want to go into right now, but 

that the electrical capture cross section for electrons of that particular defect is totally different. You may be just fortunate in this 

respect. 

SIRTL: Your point is well taken. 

242 
N8S-31631 · 

Oxygen and Carbon Impurities and Related Defects in Silicon . 

Charles W. Pearce 

AT&T Technology Systems 

Allentown, Pa. 

Oxygen and carbon are the predominant impurities in Czochral skigrown s i 1 icon. Thei r concentrati ons usually exceedi ng those of any 

intentional dopants. The behavior of these impurities during the heat 

treatments characteristic of device processing generally determines the 

defect morphology of the processed wafer. As a result this topic has 

been considerably researched. This paper will review the topic starting 

with the incorporation of oxygen and carbon during crystal growth and 

proceed to a discussion of device effects. 

Specifically, methods for controlling oxygen and carbon incorporation during crystal growth will be discussed and results supporting a 

segregation coefficient of k=0.5 for oxygen will be presented. The 

nucleation and precipitation behavior of oxygen is complex. This paper 

will focus on temperature and doping level effects which add insight 

into the role of point defects in the nucleation process. In general. 

precipitation is found to be retarded in N+ and P+ sil icon. The types 

and quanti ti es of defects resul ti ng from the oxygen preci pi tates is of 

interest as they are technologically useful in the process called lIin_ 

tri nliic getteri ngll• A compari son will be made between the avail abl e 

defect sites and the quantities of metall ic impurities present in a 

typical wafer which need to be IIgetteredli• Finally, a discussion of the 

denuded-zone, intrinsic-gettered (DZ-IG) structure on device properties 

will be presented • . Introduction 

Oxygen and carbon are important impurities in Czochralski-grown silicon 

as the defect morphology of a processed wafer often depends on the 

behavior of these impurities during the heat treatments used in device 

fabrication. In particular, denuded zone (DZ), intrinsic gettering (IG) 

techniques (1) are used to improve the yield and performance of bipolar 

and MOS devices. These DZ-IG techniques t.ransform oxygen into a 

beneficial impurity. Because of this technological importance the 

subject of oxygen in silicon has been considerably researched and 

periodically reviewed (1, 2, 3). The present state of the art includes 

the following observations. Oxygen is now considered a controllable 

impurity in Czochralski (CZ) silicon. Most supplies of silicon wafers 

will supply material to a specification. Secondly, there is an assort243 

, .. 
ment of published heat treatments which can be used on wafers to develop 

a "denuded zone", i.e., a near surface region free of oxygen-related 

defects, and an interior "intrinsically gettered zone" where the precipitation of oxygen and related defects is promoted. These treatments 

involve heat treatments at different temperatures to outdiffuse oxygen 

for a denuded zone, nucleate and precipitate oxygen, and promote .the 

growth of defects resulting from the precipitation process. Figure 1 

illustrates a typical cycle. Although such methods allow for the control of oxygen during processing, questions still remain as to the 

fundamental aspects of nucleation and precipitation. This is evident in 

the behavior of crystals grown to the same apparent oxygen content, but 

exhibiting markedly different precipitation behavior during device 

processes. To use a practical example we have observed situations where 

given the same level of oxygen content wafers from one supplier will 

readily precipitate during processing, whereas another vendor's material 

remains precipitate-free. Such observations have led to an interest in 

the role of pOint defects (i.e., vacancies and interstitials) in the 

nucleation process. Differences in precipitation behavior are thought 

to be rel ated to the effect of the thermal cycl es, a crystal receives 

in-situ in the grower, on the pOint defect populations (4). ~ The role of 

carbon as a precipitation promoter is also being studied (5). 

Another recent area of interest is the behavior of oxygen in N+ and P+ 

s i 1 icon. The use of N/N+ ,and P /P+ epi tax i a 1 si 1 i con wafers for NMOS and 

CMOS devices (6,,7) has stimulated research into this area. Beyond the 

immediate technological importance studies of N+ and P+ silicon provide 

another avenue to evaluate the role of pOint defects in the nucleation 

process. 

This paper will review the topic starting with oxygen incorporation and 

proceed to devi ce effects wi th oln emphasi s on newer resul ts. 

Oxygen Incorporation 

The quantity of oxygen incorporated into a growing crystal is at any 

point in time a function of the segregation coefficient and the oxygen 

content in the molten silicon (melt). The melt concentration depends on 

the erosion rate of the quartz crucible and the evaporation of SiO from 

the melt-ambient interface (8). Although the erosion rate is temperature dependent it iss i gnifi cantly increased by the presence of convection currents in the melt. In large crucibles characteristic of 

industrial-scale growers thermal convection effects are usually larger 

than those from forced convection. Given the Grashof number as an index 

of thermal convection (9). The melt turbulence tends to be reduced as 

the level of the melt decreases in the crucible during growth. Also, 

the surface area which is eroding simultaneously decreases •. The net 

result is a decrease in the oxygen content of the melt. However, methods to alter the erQsion rate or otherwise control the melt oxygen content have been found. These include the use of magnetic fields to suppress convection currents in the melt (10), double crucible techniques 

" (11) which provide a constant erosion rate and surface area of an inner 

crucible, and reduced ambient pressure growth (12). In short, techniques exist which improve the uniformity of oxygen in an as-grown CZ 

crystal by lOX compared to unrefined CZ growth processes. 

244 
Beyond mel t dynamics the infl uence of impurities on crucible erosion 

needs to be considered. The carbon reduction of Si02 into CO and SiO 

has already been shown to be a favorable reaction (8). Thus, higher 

levels of carbon in the melt increase the erosion rate. Note that since 

carbon has a low segregation coefficient (k=.07) it tends to enrich in 

the mel t as growth proceeds thus increasing the crucible erosion rate. 

We have noticed a similar effect for boron. As seen in Table I crystals 

grown with high levels of boron tend to exhibit a higher oxygen content 

when grown under otherwise identical conditions. This is attributed to 

the glass forming properties of boron because similar melt levels of 

antimony a non-glass former do not increase the level of oxygen. This 

fact needs to be considered when comparing the behavior of P-, P+ and N+ 

crystals. It cannot be tacitly assumed identical growth conditions 

result in identical oxygen levels. 

Fundamental to understanding dopant incorporation is an accurate value 

for the segregation coefficient. For many years the value for oxygen 

was generally accepted as k=1.25. Such a value was extracted from the 

axial distribution of oxygen in an as-grown crystal. However, in hindsight the substantial variation in melt oxygen content due to the convection effects just discussed render such an approach invalid. Recent 

experimental work by Lin (13) suggests a value of k=0.25. We have calculated k from first principles and re-evaluated existing solubility data for the liquid and solid phases and similarly conclude k=0.5 + .25 

(14). ' -

A related issue to the incorporation of oxygen is the method by which it 

is measured. The mos!lcommon method is infrared (IR) absorption measurements at 1106 cm • However", the measurement is sensitive only 

to oxygen in interstitial lattice sites and needs to be calibrated with 

another analytical method. In fact, five cal ibration constants have 

been reported (15, 16, 17, 18, 19). Secondary Ion Mass Spectrometry (SIMS) and Charged Particle Activation Analysis (CPAA) have also been 

used for oxygen determinations. In our experience the CPAA does seem to 

indicate more oxygen than the IR method by about 50% (Table I). However, due to uncertainties in the calibration of each technique and the 

oxygen inhomogeneity within a sample it is unclear whether a real 

di fference is present. Ev i dence of a real di fference comes from 

Jastrzebski (20) who has heated wafers at hi gh temperatures (1200-

1300°C) and observed increases in the IR oxygen content of up to 2X. 

This indicates a substantial amount of oxygen in non-interstitial sites 

in the as-grown crystal. However, we have not observed a similar 

increase upon heating in our crystals. This leaves open the question of 

whether prec.ipitation differences in ,material are due to nucleation 

effects or simply a difference in oxygen content. If the latter is true 

it means any calibration constant for IR measurements is good only for 

the material on which it was produced. 

Nucleation and Precipitation 

The particulars of the nucleation process have been a source of controversy for some time. Discussions have centered on whether the nucleation is homogeneous or heterogeneous and if heterogeneous the nature of 

the nuclei. Specifically, the role of interstitials and vacancies. 

245 
Insight into these questions can be gained from a study of N+ and P+ 

sil icon. 

We have observed (6) as has De Kock and van de Wijgert (7) t~At precipi~ 

tation is suppressed in N+ silicon above a doping level 1x10 atoms/cm 

when heated at high temperatures (T=1000°C). However, given a suitable 

heat treatment (24 hr-700°C, 24 hr-900°C, ref196) preciPjtates can be 

formed. At still higher N+ doping levels (5x10 atoms/em) no precipitates are observed even given the heat treatment just described. Furthennore, the lack of precipitation in N+ silicon is not due to a lower 

oxygen content as discussed in the prior section. Additionally,we have 

found that precipitatipj' is reta~ed, but not totally suppressed, at 

doping level s l~f 5x10 3atoms/cm) for boron-doped sil icon. Doping 

levels 029x10 atoms/cm still exhibit precipitation, but at densities 

up to 10 less than densities in P- samples given the same heat treatment (Figure 2). These results are consistent within a framework of a 

vacancy model. Vacancies in silicon exist in three charge states and a 

neutral configuration (21). The levels are shown in Figure 3. For 

n-sil icon a movement of the Fermi level towards the conduction band 

means negatively charged vacancies become the dominant point defect. If 

these negative vacancies pair with oppositely-charged dopant atoms then 

they are unavailable for nucleation as proposed by De Kock (7). In p 

silicon a similar movement of the Fermi level will not produce a 

dominance of positively-charged vacancies as the energy level for the V+ 

1 i es much closer to the val ence band edge. So even at hi gh P dopi ng 

levels some neutral vacancies still exist so some precipitation does 

occur. The available data does not conclusively prove the role of 

vacancies, but does indicate the role of point defects having asymmetric 

energy levels within the band gap. 

Device Issues 

.DZgI~ i'Cfeatmen1f produce bul k stacki ng faul t (BSF) densities in the 

10 -10 BSF/cm ran~~. l~ical met~llic impurity contents of processed wafers are in the 10 -10 atoms/cm (22). At either 2xtrame complete 

capture (gettering) of impurities by defects requires 10 -10 atoms/BSF. 

Given a ty~ica12BSF ci~cumference of 10 microns a fault need only 

capture 10 -10 atoms/A. Thus, the fault need only retain a relatively fell' atoms along its perimeter. This does not appear to be the 

limiting feature of intrinsic gettering. The limitations of IG probably 

stem from other sources. First, although BSF do exhibit a net capture 

of impurities it is not known how efficient this process is compared to 

other capture processes such as ion pairing in phosphorous gettering. 

Secondly, the capture of a metallic impurity at a BSF does not neutrali ze it electrically. Rather removal of a metall ic impurity from the 

depletion region of a device to a BSF in the interior of the wafer 

results in the impurity being changed from a factor in diffusion rather . than generation curr:ent. As such a net improvement in junction leakage 

will result, but the leakage current will now be a function of DZ width. 

Increasing the DZ width can only be accomplished up 'to half the thickness of the wafer at the expense of the number of gettering sites. The 

IG region remains a region of high recombination for photoexcited 

carriers. 

246 

1 
Conclusion 

In spite of considerable research into this topic full and final answers 

to some questions are still not obtainable, but there exists a sufficient body of data and information to successfully control the 

behavior of oxygen in CZ silicon. In particular, the study of.heavily- doped silicon offers new insights into nucleation and precipitation 

processes. 
n+ 

n+ 

pppp+ 

p++ 

p++ 

Comparison of Oxygen Contents of Silicon 

as a Function of Doping Level and Type 

Table I 

IR 

(.02 ohm-em.) 

(.02 ohm-em.) 

(5 ohm-em.) 1.lxlOl8 

(5 ohm-em.) 0.8xlO18 

(5 ohm-em.) 1.0xlO18 

(.01 ohm-em.) 

(.001 ohm-em.) 

( .001· ohm-em.) 

248 

CPAA 

1.5xlOl8 

1.9xlOl8 

1.5x10l8 

2.1xlO18 

l.lxlO18 

1.3xlO18 

2.7xlO18 

2.5xlO18 
References 

1. C. W. Pearce, L. E. Katz and T. E. Seidel, "Semiconductor Silicon 

1981", edited by H. R. Huff and R. J. Kriegler, The Electrochemical 

Society, Pennington, N.J., p. 705. 

2. J. R. Patel, ibid, p. 189. 

3. W. M. Bull is and L. C. Kimmerl ing eds., "Defects in Sil icon", The 

Electrochemical Society, Pennington, N.J., 1983. 

4. H. Nakanishi, Jpn. J. Appl. Phys., !!, 561 (1980)~ 

5. J. Leroueille, Phys. Stat. Sol. (a) 67~ 177 (1981). 

6. A. J. R. De Kock and W. M. van de Wijgert, J. Crystal Growth~ 49, 

718 (1980). 

7. C. W. Pearce and G. A. Rozgonyi, "YLSI Science and Technology - 1982", edited by C. J. Dell'Oca and W. M. Bullis, The Electrochemical Society, Pennington, N.J., p. 53. 

8. S. M. Sze, editor, "YLSI Technology", McGraw Hill, N.Y., 1983, p. 26. 

9. J. R. Carruthers et al, "Semiconductor Silicon 1977", H. R. Huff 

and E. Sirtl eds., The Electrochemical Society, Pennington, N.J., 

p. 61. 

10. T. Suzuki et al, "SemiconductorSilicon 1981", H. R. Huff and R. J. 

Krieglel4 eds., The Electrochemical Society, Pennington, N.J., 1981, 

p. 90. 

11. W. Lin and C. W. Pearce, J. Appl. Phys., ~ (10), 5540 (1980). 

12. W. Lin and D. W. Hill, "Silicon Processing", D. C. Gupta ed., The 

American Society for Testing and Materials, Phila., Pa., 1983, p. 24. . -

13. W. Lin and D. W. Hill, J. Appl. Phys., 54, 1085 (1983). 

14. c. W. Pearce and R. J. Jaccodine, "Defects in Silicon", W. M. 

Bullis and L. C. Kimmerling eds., The Electrochemical Society, Pennington, N.J., 1983, p. 115. 

15. Y. Yatsurugi et al, J. Electrochem. Soc., 120, 975 (1973). 

16. W. Kaiser and p'. H. Keck, J. Appl. Phys., 28, 822 (1957). 

17. K. Graff et al, Sol. State Elec., ~ 887 (1973). 

18. J. A. Baker, ibid, ~, 1431 (1970). 

249 

-------------------- . 
19. T. Sizuka et al, "Defects in Silicon", W. M. Bulli~ and L. C. 

Kimmerling eds., The Electrochemical Society, Pennington, N.J., 

1983, p. 265. 

20. L. Jastrzebski et al, J. Electrochemical Soc., 124 1638 (1982). 

21. J. A. Van Vechten and C. D. Thurmond, Phy. Rev. B, 14, 3551 (1976). 

22. P. F. Schmidt and C. W. Pearce, J. Electrochem. Soc., 128, 630 

(1981) • 

250 
1200 

1000 

800 

600 

-

ORlGiNAL PA~I"~ 

OF. "OOR QUAtrry, 

_ ORVOX II OO·C 

ffffI 

o 10 

DENUDE 

I- +, 

2 - 8 hra 

N2 

700n

C 24 hrs 

I 

20 

I 

30 

TIME Ihrsl 

NUCLEATION 

losonc 

24 hrs 

N2 

i I 

40 50 

PRECIPITATION -I 

Figure 1. Hi-La-Hi Thermal Cycle for Intrinsic Gettering 

106 

n ---........ 

p'\ 105 I 

I N 104 

E I (J 

II.. "- I 

\ en 103 II) 

\ 

102 \ 

10' 

10'5 

Figure 2. Doping Density Effect on Defect Density 

~Ee v--.11 ev :: 

Figure 3. Estimated Vacancy Energy Levels in Silicon 

251 
DISCUSSION 

SAH: The denuded zone gettering -- can you have a heavily doped region there 

that also could be used as the region for intrinsic gettering, like the 

region you are talking about where eventually you have a large concen- . 

tration of metallic impurities? 

PEARCE: Are you asking if you can have a denuded zone in something very 

heavily doped? 

SAH: Yes. Denuded zone in front of a very heavily doped region; that heavily 

doped region is the region that would getter. 

PEARCE: The structure that I mentioned earlier, the pp+. One of the reasons 

that it works so well is that we form a denuded zone in the p+ substrate, and then the heavy doping plus the precipitation there captures 

all the impurities. That turns out to be a very efficient structure for 

impurity capture. The heavy doping then reduces minority carrier concentrations so there are very few electrons available using the doping level 

for diffusion current. This is why we get these fantastic lifetimes. 

LESK: Could you not measure the distribution coefficient of oxygen in silicon 

directly by using one of the melt refreeze techniques, where within a 

matter of five or 10 seconds you have melted and refrozen, and just look 

at the difference in oxygen content on either side of the interface? 

PEARCE: Yes. I guess you could. We were looking for a fast answer and did 

some of the things we had done and when elected to do the variation of 

pull rate -- it's just amazing that we had the wrong number for so many 

years. 

SWANSON: Some one, years ago -- I think it was Rohatgi -- reported that he 

was able to lower the oxygen concentration with HCl oxidations below the 

solid solubility at l2500C where the oxidations were being done. We 

took some Cz wafers, 100 micrometers thick, and repeated his treatment, 

which according to the report would have depleted the oxygen almost completely from the wafer, and also gave a float-zone wafer the same treatment. The float-zone wafer had a high lifetime after this and the Cz 

wafer did not. Do you have any feeling maybe why that would be the case, 

or what we did wrong? 

PEARCE: The work with the Hel -- I was involved in that with George Rozgonyi 

and we had d9ne some stuff each way. We did it with and without HCl 

and at that time it looked like the Hel did give a pronounced improvement. We even had some charged-particle data that seemed to support 

that. I think, in retrospect, we were just seeing some samples of sample 

fluctuation. Maybe the. role of the HCl wasn't as large as we had origin--

ally expected. There is a recent paper out of Penn State, and some 

others, which shows that in the presence of chlorine, at high temperatures, the diffusivity of oxygen is increased,'and they have an interstitial vacancy model, so I guess it does have an effect. I guess it is 

an effect mostly on the diffusivity rather than on anything else. 

252 
SWANSON: Then you really see no st~ong evidence that the oxygen concent~ation 

is below solid solubility at the processing temperatu~e? 

PEARCE: It is probably not below the solid solubility. 

RAI-CHOUDHURY: There is some evidence that this oxygen precipitates, although 

these precipitates behave as recombination sites or generation sites. 

Especially if you put in diodes, looking at the diode characteristics. Do 

you have any data to show what kind of elect~ical activity these precipitates have? Can you comment on that? 

PEARCE: We don't have any direct evidence on the precipitates. There was some 

early EBIC work by Kimmerling at Hurray Hill that showed decoration or 

impurities around the circumference of, the fault, so that has been mo~e or 

less proved. There was also some wo~k by -- I think it was Varkel', out 

of Hotorola -- doing some diode measurements on things that were precipitated with no extended defects and it did show a degradation in lifetime. 

1 personally have not done anything, but there are some data that support 

that the precipitates apparently att~act metallic impurities as well as 

gettering centers and show the same effect. 

LANDSBERG: Do you have any views about the incorporation of defects as you 

lower the temperature? After you hav~ had a high solubility at a higher 

temperature, some of these oxygen -- or defects of some kind -- will get 

incorporated? I am'looking for people who know how to describe this or 

whether there are some rules or some laws on that. 

PEARCE: One of the things we felt, at least with metallic impurities, is that. 

-- we call them saucer pits, fog, haze, things like this -- you go through 

an oxidatio~, do an etch, you find a small density of pits. One of the 

things we have found is that metallic impurities will precipitate very 

rapidly, so that if you cool the material fairly slowly, starting at some 

high temperature down to some low temperature, you can precipitate the 

metallics, or so-called saucer pits. But now, since they are not in 

solution, the lifetime tends to go up in many cases. On the other hand, 

if you quench the malerial -- very rapid cooling keeps all the metallics 

in solution -- the lifetime is low. So a lot of the effects people see 

with leakage currents and lifetime in .silicon deal with how they cool the 

material out of the furnace, and the particulars of the metalllcs that 

they have present. But even very small changes in pull rate will dramatically affect the amount of precipitates that form. 

LANDSBERG: Right. Are there any sort of systematic studies with this? 

PEARCE: There is some good work in some of the semiconductor silicon series, 

like 19B1 Electrochem Socht,Y f on defects in silicon -- out of the San 

Francisco meeting, 1 guess, ).~~t year. Yes, there are some papers 1 can 

give you the references.on. 

LANDSBERG: But there is no single law that kind of transpires as a result of 

all this, like in my talk I used -- a number of times -- E to some enerS1 

divided by some temperature? 

253 
PEARCE: Well, there is some work by Graff and co-workers who look at how these,_ 

things precipitate as a function of solubility and diffusivities. You can 

start with that kind of information and see how something like a titanium 

would precipitate relative to an iron, and he has been able to preaict 

that some of the metallics will be haze formers, etc. That is pretty good 

work. That is published in a 1981 volume. . . 

CHENG: I just heard you mention that the wafer can be denuded up to 100 

micr:ometers. This seems to ring a bell for solar-cell people ,since 

people can make a four-mil cell thickness. Could you say some more·how 

that is processed? 

PEARCE: Yes. It basically is a time-temperature thing. We did a lot of 

denuding up at 12500C, and at tha't temperature, if you go for something 

20 hours, or whatever, one can denude into some very high thicknesses. 

On this grapb here, Curve No.1, is the work we did at 12500 C and at 

several hundreds of minutes you can get up over 100 micrometers denuding. 

There is a book out, VLSITechnolosy, edited by S.M. SZfi, and the first 

chapter has the experimental data at 12500C verst!s time. 

SAB: I have just one more question: p-p process gave very good results, so how 

~bout nn+ or pn+ or np+? Is there any indication that you would 

expect the same or different results? 

PEARCE: The problem with n on n+ is that it doesn't precipitate, of course, 

and we had a paper that we published, ttVLSI,tt it was in the Electrochem 

Detroit meeting, the first VLSI Symposium, in 1982. The problem with n 

on :1+ is that there are no intrinsic getter sites, so all the impurities 

tend to go to the surface and you get a lot of precipitates at the surface, and it is very poor material. To get the so-called intrinsic gettering to work in nn+ you have togo up to something above 5 x 1019 . There has been some work published on phosphorus gettering as to what 

concentration level you need. It is around 5 x 1019 , so you have to 

get a substrate level up to there. There was some work at RCA where they 

did that. They grew some layers on some' n++ material and the lifetimes 

were quite high. It is just difficult to, routinely grow epitaxial layers 

arid grow background doping at those high levels of arsenic or phosphorus. 

Furthermore, the ~~'t;'ystal growers don' t like to grow crystals like that 

because of the hazards. But, yes, it does work if you get up to that 

level. 

SIRTL: You mentioned this distribution coefficient of oxygen. I would have 

aome mixed feelings if you would call it theoretical distribution coefficient. If it is the effective distribution coefficient for Czochralski 

pulling, that would certainly be all right. 

PEARCE: I would agree' with that. 

3!RTL: The work of a Japanese scientist was an outstanding contribution to 

this particular point. What exactly he did was, he avoided escape of 

oxygen during zoning so that he got the i'deal conditions in terms of 

oxygen incorporation. And if you'll just remember the diagram I showed 

durins my talk: in this case, ingot solidification in a mold is a nearly 

254 
ideal condition in this respect. You may have seen that we indeed have 

found a distribution coefficient higher than 1. and that was not just 

once. so I think that from the ideal standpoint, the Japanese work is 

really the true theoretical value. 

PEARCE: Yes. I think one of the things that make people accept that is that. 

if you take the slope of that one plot that we presented with the 

unrefined Czochralski growth. seed versus tail, and then use classic 

solidification theory to extract a k from that. you usually do get 

something greater than one. So that tended to reinforce that, even 

though what is called the effective value in Czochralski is probably 

something lower and was clouded by all the variation of oxygen within the 

melt. So I would agree with your comments. 

255 
l

\ .' 

~ 

I 

I 

~ '/ 

~ 

I 

I 

N85 - 3163 2 

CURRENT UNDERSTANDING OF POINT DEFECTS AND DIFFUSION PROCESSES IN SILICON 

T. Y. Tan 

IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 

U. Gosele 

Max-Planck Institut FUr Metallforschung, Stuttgart, FRG 

ABSTRACT 

In this paper we first discuss the effects of oxidation of Si which established that vacancies (V) and Si self-interstitials (I) coexist in Si at high 

temperatures under thermal equilibrium and oxidizing conditions. Some essential 

points associated with Au diffusion in Si are then discussed. Analysis of Au 

diffusion results allowed a determination of the I-component and an estimate of 

the V-component of the Si self-diffusion coefficient. A discussion of theories 

on high concentration P diffusion into Si is then presented. Although presently 

there still is no thoery that is completely satisfactory, significant progresses 

are recently made in treating some essential aspects of this subject. 

1. INTRODUCTION 

Atomic diffusion in Si can proceed via both direct and indirect mechanisms. 

Impurity atoms having no strong bonding interactions with Si atoms, and are 

hence located exclusively in interstices, can jump directly between the+inters-+ 

tices. Species such as H, He (and presumably other noble gases), and Cu and Au 

(presumably the Cu and Au interstitials, respectively) are supposed to diffuse 

in this manner. Oxygen atoms, though possess strong bonding interactions with Si 

atoms, are also believed to diffuse directly by jumping between the bond-centered 

interstitial positions. By contrast, substitutional impurity and self-diffusion 

in Si need intrinsic point defects as diffusion vehicles. The vacancy (V-) 

mechanism is known to control self-diffusion in metals,and in Ge, and, as will 

be discussed, 1n Si below about lOOaoC. Above lOOOoC, however, the interstitialcy (1-) mechanism plays a prominent role in Si self-diffusion as well as in the 

diffusion of substitutional dopants P, B, Al and Ga. 

The nature of the dominant point defect species in Si at high temperatures 

has been a long controversial subject, though it is clear that there can only be 

three possibilities: V only, I only, and I and V coexist. The controversy arises 

for two reasons: (i) Presumably because of the small point defect concentrations 

in Si, direct experimental methods have not been helpful. There is no reported 

absolute measurement (1) results, and there is only one very recently reported 

quenching result (2) which indicated the presence of V (in the opinion of the 

present authors, however, this does not imply that I do not exist); (ii) Theoretical calculations, which are more suitable for low temperature cases, have not 

yielded the needed ~5eV activation enthalpy and the ~lOk (k: Boltzmann constant) 

P.RECEDING PAGE BLANK NOT FrLMED 257 
..:;: ~!' ,')0 :r.--; :. i.:. .. ~ .. , 

activation entropy commonly observed for Si self-diffusion. There were several 

early discussions associated with some aspects of the possibility of I and.Y 

coexisting in Si: Seeger and Chik (3) considered that I and V may be contr~outing equally to Si self-diffusion at aoooc; Prussin (4) considered that I and V 

should reach a local dynamical equilibrium under oxidizing conditions; Hu (5) 

considered that B should be ~iffusing in Si via an I-mechanism 1;.rhile As via a Vmechanism at high temperature,· - In the last few years progesses in two areas 

helped to clarify our underst~rl,',:: -i.ng of the nature of point defects and diffusion 

processes in Si considerably. L~'lalyses of oxidation effects on stacking fault 

(SF) growth kinetics (6,7) and on dopant diffusion (8-10) showed beyond reasonable doubt that I and V coexist in Si at high temperatures under thermalequilibrium as well as oxidizing conditions. Analyses of Au diffusion in Si showed 

that I must exist (11,12) and that the features are totally consistent with the 

idea that I and V coexist (13). Studies of Au diffusion into dislocation-free 

Si allowed to determine the I-component (14) and to estimate the V-component 

(15) of the Si self-diffusion coefficient. In this paper the essential points 

associated with these two areas are first discussed. We then examine theories on 

high concentration P diffusion into Si. For various reasons, we believe that 

there is still no satisfactory theory. However, progresses have been made in 

treating some essential aspects of this subject. 

2. OXIDATION EFFECTS 

Oxidation of Si surfaces leads to the so called oxidation-enhanced and 

-retarded diffusion (OED and ORD) of the substitutional dopants and to the generation of the oxidation-induced stacking faults (OSF). These phenomena need to 

be considered together and are due to the fact that oxidation injects I into Si 

(5,16). It has been shown that a consistent interpretation of the data on OED/ 

ORD phenomena is not obtained if either I or Valone were assumed to be present 

under thermal equilibrium conditions (10). Therefore, for our present purpose, 

we consider that I and V are both present in Si at high temperatures under thermal equilibrium conditions. This requires that we consider I and V have attained 

a local dynamical equilibrium condition (4,17), which was actually fulfilled for 

long time experiments (8-14,18,19). The condition is given by (17) 

, (1) 

where CI and C

v 

denote the I and V concentrations respectively and the superscript eq denotes thermal equilibrium values. Eq. (1) is arrived at via the 

reaction 

I+V:tO (2) 

(where a denotes the ideal lattice) under steady state conditions. Using some of 

the more reliable OSF size data (20-22), phenomenological but satisfactory analyses of the OSF growth/shri,nkage kinetics have been carried out (6,7). Define 

the r and V supersaturation ratios respectively as SI=CI/C~q-l and' 

sv=cv/C~q-l during the oxidation, we obtain (7) 

Q dRSF 

A (dt) a eff 

(3) 

258 
i 

, I 

I 

.~ 

I 

f 

! 

for the QiE wi~h a radius RSF ' Here A is th~23rea3per atom in the fault 

(6.38xlO cm ), Q the atom1C volume (2xlO cm ) and y the stacking fault 

eaergy (0.026eV/atom). The dimensionless quantity a ff has a numerical value of 

~2 and contains all factors related to interaction ~otentials between r and the 

Frank partial dislocation binding the OSF. Emperically, for (100) Si wafers 

oxidized in dry 02' the OSF sizes are fitted satisfactorily by (6,7) 

9 

R l640exp(- 2kiev)t3/4 4.8xlO (5.02eV) SF = - kT exp - kT t cm. (4) 

We use Eq. (1) to relate Sr and Sv by Sv=-Sr/(I+SI)' A comparison of Eqs. (3) 

and (4) then yields (8,9), 

S~2 = 6.6xlO-9 exp(2.52eV/kT) t-l / 4 , (5) 

where the superscript 02 denotes the fact that this quantity is only suitable 

for (100) wafers oxidized in dry O2 , Eq. (5) is a most important piece of information obtained from OSF studies: it is used to obtain quantitative fittings of 

OED/ORD data. S is an instantaneous value, the time averaged value S used in 

the actual OED/CRD data fi!§ing is obtained by replacing the pre-expoAential 

value in Eq. (5) by 8.8xlO and by noting that t then denotes the oxidation 

duration. 

In the presence of both I and V, the substitutional dopant diffusivity is 

given by 

D

S 

= D~ + D~, (6) 

where D~ and D; are respectively the 1- and V-component of the dopant diffusivity. Under an oxidation which perturbs the thermal equilibrium I and V concentrations, the dopant diffusivity changes to 

(7) 

In terms of the normalized diffusivity enhancement defined as ~s =Ds /Ds_l the 

ox ox ' 

use of Eqs. (1) and (7) yields (8,10) 

(8) 

where GI is the fractional I-component of the dopant diffusity under thermal 

equilibrium conditions defined as GI=D~/Ds. Eq. (8) applies t~ an instantaneous 

diffusion enhancement. In experiments tfie time averaged value ~s is measured, 

but Eq. (8) still holds to a good approximation by having 81 usg~ together with 

6s 

• A plot of Eq. (8) is shown in Fig. 1 for three GI values. The value of 6s 

igxeither positive or negative (OED or ORD) depending on the value of GI and ox 

S . In Fig. 2 we show a fitting of available Sb ORD data to Eq. (8). It is seen 

t~at the fitting is quite satisfactory on a quantitive basis with GI=0.02. This 

kind of good fitting indicaces that the model of I and V coexisting and attained 

local dynamical equilibrium is correct, particularly in light of the fact that 

no other reasonably thought of model can be equally satisfactory (10). The use 

of Eq. (8) allows to determine GI for a dopant at a given temperature. Some such 

values have been given elsewhere (15,23,24). To briefly summarize, it is found 

that the I-mechanism plays a prominent role in the diffusion of B, Ga, P and Al 

259 
at high temperatures, i. e., GI~O.S for these dopants at a temperature above 

HOOoe. 

The above discussion applies for experiments with sufficiently long oxidation times. For short oxidation times, a transient exists for I and V to reach 

the local dynamical equilibrium. This is due to the presence of an energy barrier 

against I and V recombinations. The existence of such an en.ergy barrier was suggested by Wertheim (2S) to explain the fact that the rate of A-center (E -0.16eV) 

production by high energy electron irradiation is strongly dependent upoR the 

irradiation temperature (below room temperature). For high temperature cases, Hu 

(26) suggested that such a barrier of a few to several eV may exists, so that to 

a large extent I and V may behave indenpendently. The experiments on ORD of Sb 

(18,19) shown in Fig. 2 demonstrated that for oxidation times longer than a few 

hours local dynamical equilibrium according to Eq. (1) is reached. By performing 

similar experiments for shorter times (S to 60 min.) Antoniadis and Moskowitz 

(9) showed that Eq. (1) is not readily satisfied when oxidation first started. 

At 11000e they found a small OED for a S min. oxidation which gives way to ORD 

for an oxidation longer than 10 min., and, the diffusion retardation approaches 

the value expected for local dynamical equilibrium at about 60 min. Their findings may be rationalized as follows: during oxidation I are injected into Si by 

the Si02-Si interface but it takes about 1 hr at 11000e for I-V recombination to 

proceed to such an extent that local dynamical equilibrium is reached. As a consequence, at the begining there is no V undersaturation so that the oxidation 

induced I supersaturatio~ enhances Sb diffusion via the small I-component of its 

diffusivity (GI~O.02). 

We use Waite's theory of diffusion controlled reaction (27) to obtain from 

(9) 

an estimate of the time Td'f required to establish the local dynamical equilibrium in the Ant§Biad!i5MoS~OWi!r experiment if no recombination barrieE8were 

present. With D ~10 cm sec and the reco~bination radius rIV~SxlO cm, 

Eq. (9) yields Td'fsO.OSsec which is about 10 shorter than observed. We therefore conclude thaf I-V recombination is controlled by the overcoming of a recombination barrier that exceeds the Gigbs free energy of diffusion (of I and V) by 

~G. In this picture the factor of 10 by which the experimental T value differs 

from that estimated from Eq. (9) arises from the Boltzmann factor exp(~G/kT). 

Antoniadis and Moskowitz interpreted their observation in terms of an enthalpy 

barrier corresponding to ~H~1.4eV assuming that in the expression 

~G = AH - TAS (10) 

the entropy contribution is negligibly small. By contrast, Gosele et al. (28) 

proposed that the main part of ~G originates from the term T~S where ~S is negative, f.e., from an entropy barrier, whi§B is due to a consideration of the large 

pre-exponential factor associated with D . 

Irrespective of the detailed origin of the barrier, with ~G~1.4eV, the barrier limited reaction time, Tb ,for establishing the local dynamical equilibrium b'etween I and V is given g§ 

260 
I 

I ! 

! 

! 

(11) 

Eq. ~ll) is plotted in Fig. 3 using DSD=0.5(D Ceq+D ceq) with the quantities 

DIC~ and DvC;q taken from Eq. (21) which will te dXsXussed. It is seen that .Tb 

increases rap1dly with a decrease of the temperature and attained values of 2, ar 

17 and 170 days at 1000, 950 and 9000e respectively. Even if it is assumed that 

these results are over-estimated by a factor of 10, Tb values are still 5hrs, 

1.7days and l7days at 1000, 950 and 9000C respectively~rOne significance of this 

finding is that in the expression 

(12) 

the quantities C

r and C

V' ar1s1.ng from experimental perturbation of the respective thermal equ1librium values, are not related by Eq. (1) in an experiment 

performed in such low temperature range and having time durations much less than 

the appropriate Tb values. For device processing in the temperature range of 

850 to 9500C for aafew hrs, should there be any reason that the point defect 

thermal equilibrium values are perturbed, the change only applies to the perturbed species independently, i.e., r and V need to be considered as not having 

attained the local equilibrium condition. 

The fact that I-V dynamical equilibrium is attained extremely slowly at 

lower temperatures offers the possiblity of measuring the quantities DI and DV 

independent of each other a.nd independent of the I and V concentrations. There 

already exist some OSF and OED/ORD experiments conducted with the intention of 

measuring DI at 11000C or above (29-31). However, because of the temperatures 

and oxidation times involved, I-V local dynamical equilibrium should have been 

reached in these experiments and we have shown that such experiments yield an 

effective diffusivity given as (15,24,32) 

(13) 

instead of D . Depending upon the relative magnitude of e~q and c~q, which are 

unknown quantities themselves, Eq. (13) may yield an approximate value for either 

DI or Dv. We have argued that the diffusivity values obtained from these experiments (29-31) should be interpreted as DV (24,32). However, for the lower temperature range, e.g., 850 to 950o

C, the I-V local dynamical equilibrium will 

not be reached for an experiment involves less than a day's time. For such cases, 

effects associated with dopant diffusion or stacking fault growth would be solely 

due to the point defect species whose thermal equilibrium concentration has been 

perturbed by the experimental condition. This means the other species does not 

contribute to the experimental deviations observed if its thermal equilibrium 

concentration has not been also directly perturbed by the experimental condition. 

We can now suggest an experiment to directly determin~ DI : High concentration P 

diffusion into Si proceeds erficiently in the temperature range noted above and 

the diffusion causes a quite high I supersaturation in the Si interior. Thus, 

·experiments similar to those performed for OED/ORD and OSF (29-31) can be carried 

out at the low temperature range (850 to 950oC) with surface P diffusion replacing oxidation to obtain Dr. Similarly, DV can be determined upon finding an 

interface reaction which injects V into S1. Presently we do not know with 

261 
certainty of such a reaction. 

3. DIFFUSION OF GOLD INTO DISLOCATION-FREE SILICON 

Gold atoms, which under thermal ejuilibrium conditions may b~ incorporated 

in Si either as substitutional (Au :Au -) or interstitial (Au.:Au) atoms, may 

diffuse via either the kick-out me~hanism (11) or the Frank-T~rnbull mechanism 

(33). The two mechanisms have in common that long range transport of Au atoms 

occur via migration of Au. atoms which may either jump from interstice to interstice to remain as Au. at6ms or from interstice to lattice positions to become 

Au atoms. This is tr~e because though the thermal equilibrium concentration of 

Aus is much larger than that of Au., the mobility of Au. is much much larger than 

th~t of Au and hence long range tfansport of Au may b~ ignored. However, the 

two mechan~sms differ in the ways Au. and Au at8ms interchange. In the kick-out 

mechani"'ill the interchange involves I1.accordiitg to (11) 

Au. :t Au + I. 1. S (14) 

This mechanism creates an I supersaturation in the crystal which is balanced by I 

out-diffusion. This means if the mechanism is operative than I are involved in 

Si self-diffusion but it does not a priori mean that V are not contributing to 

Si self-diffusion. In the Frank-Turnbull mechanism the interchange process involves V according to (33) 

Au. + V t. Au . 1. S (15) 

This mechanism creates a V undersaturation in the crystal interior which is 

balanced by V in-diffusion. If operative, it means that V are involved in Si 

self-diffusion but it does not mean I are not contributing to Si self-diffusion. 

We now assume that local dynamical equilibrium betweem I, V, Au. and Au is 

established .• The necessary and sufficient condition for this as§umptionSto be 

true is that the three ~eactions (2,14,15) have reached their equilibrium state. 

This requires that two out of the three reactions to be sufficiently fast. It is 

not required that the third reaction be equally fast, since if equilibrlum conditions are satisfied by two of the reactions, then the third is automatically 

under equilibrium conditions. Under this assumption the normalized Au concentration C=C /Ceq to be measured in an experiment on Au diffusion into sdislocation-free SSiSmay be approximately described by 

~ = ~(D ~) at ax eff .ax 

(16) 

with the effective diffusion coefficient given by (l3) 

(17) 

In Eq. (17) contributions to the Au.-Au interchange process due to both kick- . 1. s ) out and Frank-Turnbull mechanisms are accounted for. In deriving Eq. (17 the 

262 

1, 

f; 

II 

, 

! 

! 

; 

, 
following approximations are used 

c. = ceq ~ i' (c.: Au. concentration) J. ~ 

(18a) 

(18b) 

(18c) 

If only V and no I are present Eq. (17) yields a constant effective Au diffusity 

(11,33) s 

The same result holds if DIc~q is not zero but among the reactions (2,14,15) only 

(15) operates sufficiently fast. If only I and no V are present Eq. (17) yields 

a strong concentration dependent diffusivity 

The same result holds if. DvC~q is not zero but among the reactions (2,14,15) only 

(14) operates sufficiently fast. As observed by Stolwijk et ale (14), Au concentration profile after diffusion into dislocation-free Si at and above 800°C can 

not be described by the constant diffusity given by Eq. (19) but are satisfactorily fitted by the use of Eq. (20). Fig •. 4 shows a typical experimental profile 

due to Sto~wijk et ale It can be seen that an erfc-function type profile as expected for D ff failed to fit the data while the use of D ff is quite satisfactory. 

This showsetliat I are contributing to Si self-diffusionefiut it does not mean that 

V are not contributing for the reasons that: (i) It can not be certain that this 

is not only due to the fact that of the reactions (2,li,15) on!2 (14) operates 

sufficiently fast; and (ii) The strong dependence of D ff on C reduces the 

effec!.20f D ceq by this factor for mo.st part of the ex~eriment for which C<l 

and C «1 KoYd. Indeed Morehead et ale (13) found that while almost perfect fitting were obtained for short time diffusion profiles small but observable deviations occured if Eq. (20) were used but a much better fitting is obtained by the 

use of Eq. (17). This not only shows that V are contributing to Si self-diffusion 

but also allowed to estimate that DvC~q~DIc~q at 10000C. The quantity DIc~q has 

been determined by Stolwijk et ale ~14) as 

DIc~q = 9l4exp(-4.84eV/kT) 2 -1 

cm sec (2la) 

o We have already shown that at T$900 C reaction (2) is expected to become ineffect.ive. At still lower temperatures, as will be discussed, reaction (14) is also 

expected to become ineffective. In that case only reaction (15) will be operating 

and an erfc-fgnction type. p~ofile should show up. Wil~cox et a!22(34~ fo~£d such 

a case at 700 c. With their data we obtained that DVC q~8.8xlO cm sec at 

. 7000 C (15). This together with the data of Morehead e¥ al. (13) yields the rough 

estimate 

263 
DvC~q = 0.6exp(-4.03eV/kT) 2 -1 

cm sec (2lb) 

Eq. (21) is plotted in Fig • .5 in which a data point on D c~q obtained by analysing the Ni precipitation behavior (15) of Kitagawa et aY. (35) is also shown. 

An important point is, as rough estimates, the sum of the formation and migra-tion 

entropies are now obtained from Eq. (21) as 3k for V and 10k for I. That is, 

wgble I are quite extended (3), V are fairly point-like. Experimentally observed 

D 3 values from relatively higher temperature measurements are usually of 

10 exp(-5eV/kT) while those from relatively lower temperature experiments are 

of lexp(-4eV/kT) (36..,.40). These values are quite compatible with Eq. (21). 

We now make an estimate to show that at very low temperatures the kick-oJt 

mechanism, reaction (14), can become ineffective, wh1.le the Frank-Turnbull 

mechanism, reaction (15), still operates. It is important to note that if this 

can not be true then it can not be explained why Au diffuses into dislocationfree 8i apparently via the kick-out mechanism at higher temperatures but the 

Frank-Turnbull mechanism at a very low temperature. Eqs. (19) and (20) show that 

Au2diffusion would appear as dominated by the kick-out mechanism in SQ long as - eq eq -L. C D CI /DVCV >1 holds. Because for a large part of the experiment C »1 holds, 

the lick-out mechanism may still appear as dominating the diffusion process even 

for a case for which the frequency of the kick-out events is less than that of 

the Frank-Turnbull events. On the other hand, the frequency of the kick-out 

events should decrease more rapidly than that of the Frank-Tuenbull events with 

a decrease in temperature because the former involves the creation of I which is 

charaterized by an activation enthalpy (the I formation enthalpy) while for the 

latter there is not yet a good reason for assuming that a high enough energy 

barrier exists to prevent an Au. atom drops in a V. In the following we show that 

under thermal equilibrium conditions a quantitative estimate can be made which 

indicates that the above discussed situation can be true. 

For the Frank-Turnbull mechanism, if an Au. atom and a V meet, there is a 

definete probability r$l that reaction (15) will go forward to produce an Au 

atom. Under thermal equilibrium conditions, we obtain the rate of increase iR C 

via this mechanism as s 

(22) 

For the kick-out mechanism, reaction (14), the AUi atom has a certain frequency 

v. by which it produces Au and I. We do not know this frequency but if Au and 

II'meet there is a definiteS probab1.1ity 8$1 for reaction to produce Au. andsunder 

thermal equilibrium conditions this reaction balances that due to v .• 

1

Therefore 

1 

we have, 

From Wilcox et al. (34) we have 

D.C~q = 1.8xlO-2exp(-1.13eV/kT)Ceq 

1 1 s 

2 -1 

em sec 

(23) 

(24) 

Eqs. (2la) and (22) to (24) yield for the rate of converting Au. into Au via 

1 s 

264 
the kick-out mechanism to that via the Frank-Turnbull mechanism as 

(25) 

where a is a constant of the order of 105. We do not know the quantity c~q but it 

can be seen from Eq. (25) t~at r decreases with a decrease of temperature unless 

the V formation enthalpy ~HV· is equal to or larger than 3.71eV, which, judging 

from Eg. (21b), is un!ike1y. In Fig. 6 we show the calculated values of r(T)/ 

r(1000 C) assuming ~H;. is in the reasonable range of 1.5 to 3eV. It is seen that 

the effctiveness of tfie kick-out mechani,sm decreases much more rapidly with a 

decrease in temperature than that of the Frank-Turnbull mechanism. 

With this discussion, it becomes understandable why Au diffusion can appear 

as dominated by the kick-out mechanism (related to I) at higher temperatures, 

while by the Frank-Turnbull mechanism (related to V) at lower temperatures. It is 

expected that other metals may also exhibit a similar kinetica1 behavior in Si 

for experiments involving their diffusion: in- and out-diffusion experiments, 

precipitation and precipitate dissolution experiments. We suggest that by now 

the following rule should be kept in mind: in an experiment if it is found that 

I in Si appears as dominating the diffusion process of an impurity, it means that 

I exist as a species of Si point defect under thermal equilibrium conditions and 

the experimental conditions are suitable for I to appear as dominating, it does 

not mean that V do not a~so exist as a species of Si point defects under thermal 

equilibrium conditions; the reverse is also true. The diffusion experiments of 

Kitagawa et a1. (41) on Ni (dominated by V) and of Mantovani et a1. (42) on Pt 

(dominated by I) are good examples. 

4. ON'THEORIES OF HIGH CONCENTRATION PHOSPHORUS DIFFUSION INTO SILICON 

Diffusion of group-III and -V dopants shows several anomalous features that 

are quite thoroughly discussed in the literature (43-47). To summarize, 

Willoughby (45) and GBse1e and Strunk (47) mentioned that the most prominent 

features are: (i) The emitter push effect, which is the extremely rapid diffusion 

of base dopant (B or Ga) of the doubly diffused npn transistor structure which 

results in an enhanced movement of the base-collector junction; (ii) The kinktail structure of the in-diffusion P profile, which is resulted from the use of 

high concentration surface sources. This is shown in Fig. 7a with conveniently 

designated surface and tail regions. In the tail region the P diffusion rate is 

much higher than expected for isoconcentration studies or OED studies; (iii) 

Movement of burried dopant layers can be extremely rapid if the surface P concentration is high. There exist ample evidences that P rich precipitates form during 

Pin-diffusion (48-55), we therefore add to the above list by (iv) During P indiffusion, the P concentration in the Si surface region exceeds its normal solubility limit. We consider tl1at the following facts have been established: (i) 

The dnpant diffusivity enhancement, are caused by supersaturation of intrinsic 

point defects. The enhancement are much larger than that due to oxidations; (ii) 

The point defect supersaturations are, related to high surface concentration of P, 

and, in some cases, of B or As (56-58); and (iii) Mechanisms involve dislocations in an essential manner, e.g., dislocation climb, are not the origin of the 

point defect supersaturations. 

265 

~ .. ----~---~--~--:-----------,---:_rc_:-~------------~--_:_....,,.,.,_,_~'"" . -'?:~~ -.,---~ 
Since untill recently it was widely believed that V are the dominant thermal 

equilibrium point defect species in Si, earlier models (59-61) put forth to explain the P anomalous diffusion have been based on calculating the V supersaturations. Among these mociels, that of Fair and Tsai (61) gave a most complete treatment and was apparently able to calculate quantitatively the kink-tail structure 

in the P diffusion profile. Even if V were the only point defect species present 

in Si at high temperatures, the model still can not be'regarded as satisfactory 

because of: (i) As pointed out by Kroger (62), the analytical development is questionable with respect to the relation between the total P concentration and the 

total carrier concentration on the one hand, and with respect to the derivation 

of the electrical field on the other; and (ii) As pointed out by Mathiot and 

Pfister (63), the V supersaturation was accounted for by a multiplication factor 

for deriving the fast diffusing tail region P diffusivity instead of solv~~g the 

V diffusion equation. By correcting these problems Mathiot and Pfister (64) found 

that the model of Fair and Tsai can not give a good qualitative description of 

the P diffusion profile. Here we mention two fundamental objections generally 

applicable to these modelsi (i) Formation of P-rich precipitates (48-55) is notaccounted for; and (ii) By now there also exist ample evidences that during P indiffusion an I and not V supersaturation is present in the Si interior, (55,64-67) 

but the V based models can only predict a V supersaturation. 

Recently, two new models have been proposed. One is a vacancy percolation 

(modified E-center) model due to Mathiot and Pfister (68), which has also been 

extended to include an I~component in the diffusivities of both dopant diffusion 

and Si self-diffusion (69). The other is a model due to Hu et ale (70) who proposed that a substantial part of P occupies interstitial positions which we shall 

call interstitial P model. Unfortunately, these two models seems are also not 

satisf~ctory. In the following (Sections 4.1 and 4.2) we discuss some essential 

points of these two models and give some detailed reasons for arriving at this 

conclusion. In section 4.3 we discuss a possible reason for P diffusing into Si 

in a supersaturated concentration. 

4.1. The V Percolation Model 

By correcting the problems of the model of Fair and Tsai and by incorporating the idea of V percolation (71), Mathiot and Pfister were able to quantitatively fit some P diffusion profiles (68). Later on they were also able to exted 

the model to include an I-component in the dopant and Si self-diffusion coefficients with an apparently even better success (69). Their earlier model (68) can 

be straight forwardly regarded as unsatisfactory since it is purely V based. The 

incorporation of an I-conponent in the dopant and Si self-diffusion coefficients 

(69) is a good step forward, but the model is not satisfactory because: 

(i) Formation of P-rich precipitates is not accounted for; 

(ii) They concluded that GI-O.l to 0.3 for the dopants B, As and P from 900 to 

l2000C for low and high concentration diffusions. For the cases of higher 

temperature experiments', we expect that local dynamical equilibrium between 

I and V to be reached, this can only result in a net V supersaturation in 

the Si interior. This is in contradiction with experimental results (55,64-

67) that can only be explained by a net. I supersaturation; 

(iii) The finding that GI<0.5 for P, which requires that the observed ORD of P 

for (111) Si wafers oxidized for long times be explained without assuming a 

266 
net V supersaturation (as Francis and Dobson (72) and the present authors 

(8) have assumed), is in contradiction with the Sb OED result (10,19) which 

was observed under an almost identical experimental condition for obs~rving 

the P ORD. A qualitatively consistent interpretation of these results is 

not obtained unless GI >0.5 for P and GI<0.5 for Sb and under the experimental conditions a net V supersaturation exists. 

(iv) The observation of ORD ofB at l2000 C by Hill (73) can not be explained by 

their finding G <0.5 for B, since in that experiment a 6% HCI was used. By 

analysing the OSF data of Shiraki (21) the present authors have shown that 

for this exp~ental condition a net V should have been injected (7,10). 

If GI <0.5 for B, then it should have resulted in an OED ifistead of the 

observed ORD. 

The present authors believe that the V percolation idea is a very important 

point for which the full significGuce seems have not yet been realized. This subj ect is cert;}inly a. nice contribution of Mathiot and Pfister and is weI}. worthy 

of some discussions. To invoke the V-mechanism for the diffusion of a substitutional impurity sp~cies which exhibit a higher diffusivity than that of selfdiffusion of the host crystal at~ms, it is necessary to assume that the diffusion 

proceeds in the form of. i-V pairs (i denotes a substitutional impurity atom), and 

a pair has to partially dissociate during its migration process. In Si the saddle point for the i-V pair dissociation process corresp(j~lds to having a V on the 

third nearst neighbour position of i. The remaining binding- energy between i and 

V determines the cohesion of the pair. For the case of having a very high impurity concentration, the impurity atoms effectively form a network or cluster in 

the crystal lattice in the sense that now each impurity atom would have some 

other impurity atoms situated at its fifth or even closer neighbour positions. 

The i-V pair diffusion process changes now since upon reaching the saddle position 

of the pair partial dissociation process, the V can also be at a third neighbour 

position of another i. Now V can migrate to the other i atom with a potential 

barrier smaller than that needed for the isolated i-V pair case. This means with 

a sufficiently high impurity concentration, V can freely diffuse through the i 

network or cluster, which does not only enhance the V diffusion but also the i 

diffusion. This is the idea used by Mathiot and Pfister in their models (68,69). 

We now mention a few points associated with the percolation idea that have not 

yet been explicitly considered: 

(i) We believe that the percolation idea is equally applicable to an I-mechanism; 

(ii) In the presence of a high impurity concentration, and hence the percolation 

network, we believe it is sensible to also suggest that the point defect 

formation energy is also lowered. This means the thermal equilibrium point 

defect concentrations are increased because of the presence of a high impurity concentration (not to be confused with that due to electrical charge 

effect) ; 

(iii) The presence of the percolation network necessarily changes the i-I and i-V 

pairing potentials, and hence GI for low and high impurity concen.tration 

cases are in principle of different values. 

267 
4.2. The Interstitial Phosphorus Model 

Hu et al. (70) have recently criticized most of the V models (59-61) and 

proposed a new model to remedy the situation. An important contribution of their 

work is that.formation of P-rich precipitate during P in-diffusion is very much 

emphasized and therfore in the model this is accounted for and hence removing 

one major shortcomings common to all other models. They have written down the 

basic equations but not yet performed the needed calculations and .it is therefore not possible to see whether a net I supersaturation in the Sf interior can 

result from the model or not. An'examination of the basic assumptions involved in 

this model has led the present authors to believe that the model in its present 

form is probably also not satisfactory. Their major assumptions are: (i) A portion of the P atoms in Si occupies the substitutional sites (P ) while the rest 

occupies interstitial sites (P.); (ii) Mutual conversion betwe~n P and P. is 

very slow; and (iii) Both P aftd p. are shallow donors. Assumptions(i) is1needed 

since they invoked a two st~eam diffusion mechanism as the a priori reason for 

obtaining the kink-tail diffusion profile. The best way to see what is a two 

stream diffusion is to imaging that there are two distinct chemical speci~s A 

and B diffusing into Si simultaneously but otherwise independently and we are 

looking for CA+B=CA+CB, see Fig. 7b. Now there is only one P species chemically 

but in Si they can occupy different sites, e.g., P and P .• In so far as diffusion is concerned, P and P. can behave independen~ly. As§umption (ii) is needed 

since if P and P. a~e conv~rting into each other rapidly enough then their individual ide~tity wIll be .lost and a kink-tail structure in the P concentration 

profile can not be obtained. Assumption (iii) is needed since atomically dissolved P atoms in Si is known to be electrically active. The assumption that a substantial portion of the P atoms occupies interstial sites is very different from 

that invoked conventionally: P atoms occupy substitutional sites only. By definition, P

f diffuses primarily via an I-mechanism. Thus, there will always be a substantia number of P atoms on interstitial sites whether they are migrating or 

not. In the converntional picture, P atoms can diffuse via an I-mechanism and 

hence those migrating P atoms are on interstitial sites temporarily but there 

will only be a negligibly small fraction of P atoms that are migrating at any 

instant in time and hence for practical purposes all P atoms are occupying substitution9l sites. 

In the following we present four arguments which jointly constitute as a 

strong indication that the above mentioned assumptions involved in the model of 

Hu et a1. do not form a realistic enough basis for regarding the.model as satisfactory (admittedly, though, each argument individually may be only constituting 

as a weak indication): 

(i) The fact that there is but one shallow donor level associated with P doping 

is generally accepted. While it is legitimate to postulate that Pi is also 

a donor, it is difficult to believe that the donor is also a shollow one, 

and, in particular, its energy level needs to be almost identical to that 

due to P ; . s 

(ii) High concentration P diffusion into Si can induce the formation of a dislocation network to accomodate the Si lattice parameter change in the diffused 

layer due to the incorporation of P atoms to a large concentration. Analyses 

of such dislocation networks indicated that the P diffused layer has a smaller lattice parameter (74) which is consistent with the knowledge that P 

atoms are all on the substitutional sites (the ratio of the covalent radii 

268 
of P atoms to Si atoms is 0.94). In order to explain the P diffusion profiles by the two stream mechanism, it needs to be assumed in some cases 

C . can be almost equal to Cp • If this is so, it seems that by now there 

sh5uld be some indication tha~ the opposite, i.e., the P diffused layer has 

a lattice parameter larger than that of the undiffused Si, is true; 

(iii) The requirement that Pi and P are converting into each other very slowly 

is an extremely stringent cond~tion. Considering the diffusion times involved in a typical experiment, a simple estimate would show that the energ7 

barrier against the P.-P conversion needs to be higher than 3eV and quite 

likely in the neighbo~rh~od of 4 to 5eV. This is the same energy barrier 

prevent the interstitialcy pai.r from dissociation, and hence the pair needs 

to be regarded as very stable. If so, it is not easy to understand why Pi 

can diffuse so fast, which is also required in the model; 

(iv) In an Au gettering experiment, Lecrosnier et al. (75) found that the Au 

concentration in the P diffused layer developed a kink-tail profile similar 

to the P profile. This phenomenon is consistent with the interpretation 

that all P atoms occupy substitutional sites but not equally consistent 

with the interpretation that a substantial portion of P atoms occupies 

interstitial sites.* The interstitial P model requires that the surface region P atoms be mostly P, (diffusion slow) while the tail region P atoms be 

mostly P. (diffusion fas~). We first mention that in the Au getterinij experiment abo the gettered Au atoms should be Au since normally ceq»ci holds 

and' since if they were Au. then we expect t~e P and Au concen~ration profiles follow a complementa~y rather than a similar distribution pattern 

since the charge states of the P and Au atoms should result in a repelling 

force (P is a donor in spite of whether in substitutional or interstitial 

positions, and, Au is also suppose to be a donor, i.e., Au+). Assuming 

that Au atoms are indeed Au atoms, then the best interpretation is that P 

at~ms are all P atoms sinc~ now charge compensation occurs between p+ and 

Au - (presumabl~ Au ) atoms and atomic size compensation also occurs (covalent radius of Si a~om is larger than that of P but smaller than that of 

Au ). If the P atoms are Pi then we expect a la~ge compressive stress to 

de~elop in the 8i which tends to result in a complementary distribution 

pattern between the Pi and Au concentrations. The worst case is that both 

P and Au atoms occupy interst~tial sites since then it will result in a 

compressive strain as well as a charge repelling situation. 

4.3. Physical Reasons for P Difftlsing into Si in Supersaturation 

While the kink-tail diffusion profile of P has been recognized as an outstanding feature for a long time, it is only recently that the equally outstanding (and undoubtly related) feature of P diffusion into Si in supersaturation 

is also recognized. Why is it so? Hu et al. (70) provided one possible reason 

which is dynamical in nature: P diffusion (using a P-rich oxide source) is usually carried out in a partial oxygen ambient and hence oxidation, i.e., a chemical reaction, occurs. They suggested that the excess chemical potential responsible for P entering Si exceeding its solubility limit derives from this chemi-

. cal reaction (oxidation). However, this may not be the primary reason because 

*This problem was brought to the attention of one of the present authors (TYT) 

by Dr. T. E. Seidel. 

269 

....... --.-..,.---------------:-c,,-~--..."=·,~; ... ··-. ~--... -------. 
of: (i) The I supersaturation associated with high concentration P diffusion far 

exceeds that due to an oxidation of Si, and, in particular, this seems to be 

true at very low temperatures, e.g., 750oC, for which an oxidation of Si ceases 

to function; (ii) There are some indications that P can diffuse into Si in a 

supersaturated amount for cases that the annealing ambient is inert. Nobili et 

al. (54) concluded that the electri~~ll~oact!~e P concentration limit (presum~­

bly the solubility l~mit) is about 4xlO cm at 1100~£, b~S at the same temperature P can enter S1 to a concentration of about lxlO cm in an N2 drive-in 

annealing using a P-rich oxide source (76). 

As an alternative possibility, we suggest a mechanism due to phase-equilibrium requirements to explain the phenomenon of P diffusing into Si in supersaturation. This mechanism is readily understandable if the materials involved 

constitute as a binary alloy system. Therefore, for our present purpose we 

discuss the case that the source of diffusion is gaseous P (P ) at the standard 

presure instead of the more commonly used P rich oxide. In Fi~. 8 we show the 

phase diagram of the Si-P system and an appropriate free energy diagram in the 

temperature range of our interest. The significance of Fig. 8 is that, under 

phase-equilibrium conditions: (i) the two primary phases, a (Si containing atomically dissolved P) and y (P ), and the binary intermediate phase SiP, can each 

exists alone; (ii) The a phas~ and SiP can coexist; (iii) SiP and P can coexist. 

This means for a diffusion experiment using P as source, to start iith, the 

materials (Si and P ) do not exist in a phasegequilibrium state. Hence, the materials will procee~ to reach the appropriate phase-equilibrium states by creating coexisting ph~ses permitted by the phase-equilibrium conditions, i.e., the 

above discussed possiblities (ii) and (iii). We coined the term that, before the 

phase-equilibrium state is reached, the materials are in a diffusion-transient 

state. A primary phenomenon associated with this transient state is that P will 

diffuse into Si in excess of its normal .solubility limit which is defined per 

coexistence of the a and SiP phases. Refer to Fig. 8b, the normal P solubility 

in Si is represented by concentration A. The material near the Si surface is now, 

however, not coexisting with SiP but with r which gives a P solubility in Si 

represented by concentration B. Since B>A h~s to hold, we see P enters Si at a 

concentration exceeding its solubility limit A. That is, by the very fact that 

now Pg and Si coexist, the material Pg directly exerts a chemical potential on 

Si to maintain a P concentration in excess of the P solubility deverived per coexistence of S1 and SiP. If kinetical conditions permit, SiP precipitates can now 

form inside the Si crystal or alternatively a continuous layer of SiP can form 

at the Si surface. Before a sufficiently thick continuous SiP layer forms, the 

supersaturation phenomenon will persist. 

Per this discussion, we see that there is a thermodynamic reason for P 

to diffuse into Si in supersaturation. For experiments for which a P rich oxide 

layer is used as source, the argument is also applicable. The analysis leading 

to this conclusion is, however, considerably more complicated than the binary 

example just discussed. This complexity arises because a Si-O-P ternary situation 

is involved. We have carried out the analysis for this ternary situation and the 

details will be given elsewh~re (77). In that analysis we have also shown that 

the 0 solubility limit is also changed. There'exists one experimental result (76) 

indicating that this seems to be the ·case. 

270 

., 

, 

I 

) 

\ 
~\;.~ 

~.~, 

S:~ " 

",t. 

'~, , , 

f 

5. CONCLUDING REMARK 

In this paper some essential points associated with oxidation effects and 

Au diffusion in Si are discussed. Progresses in these areas in the last few years' 

seems to have established beyond reasonable doubts that I and V coexist in Si 

under thermal equilibrium conditions. Within the frame work of coexisting I and 

V species, some new understanding is now emerging. We look forward for more progresses in our understanding of the nature of point defects and their roles in 

the materials transport properties in Si in the near future. 

REFERENCES 

1. R. Simmons and R. W. Ba11uffi, Phys. Rev. 129, 1532 (1963). 

2. A. Chantre, M. Kechouane and D. Bois, Physica ll6B, 547 (1983). 

3. A. Seeger and K. P. Chik, Phys. Stat. Solidi 29, 455 (1968). 

4. S. Prussin, J. App1. Phys. 43, 2850 (1972). 

5. S. M. Hu, J. App1. Phys. 45, 1567 (1974). 

6. B. Leroy, J. App1. Phys. 50, 7996 (1979). 

7. T. Y. Tan and U. GBsele, J. Appl. Phys. 53, 4767 (1982). 

8. T. Y. Tan and U. GBse1e, App1. Phys. Lett. 40, 616 (1982). 

9. D. A. Antoniadis and I. Moskowitz, J. Appl. Phys. 53, 9214 (1982). 

10.·T. Y. Tan t U. Gosele and F. ~10rehead, App1. Phys. A3l, 97 (1983). 

11. U. Gosele, W. Frank 'and A. Seeger, App1. Phys. 23, 361 (1980). 

12. U. GBse1e, F. Morehead, W. Frank and A. Seeger, Appl. Phys. Lett. 38, 157 

(1981). 

13. F. Morehead, N. Sto1wijk, W. Frank, W. Meyberg and U. GBsele, Appl. Phys. 

Lett. 42, 690 (1983). 

14. N. Stolwijk, B. Schuster, J. HB1zl, H. Meher and W. Frank, Physica l16B, 335 

(1983). 

15. U. GBse1e and T. Y. Tan, in 'Defects in Semiconductors II'S. Mahajan and 

J. W. Corbett eds. (North-Holland, NY 1983) p45. 

16. P. S. Dobson, Phil. Mag. 24, 567 (1971); 26,1301 (1972). 

17. E. Sirtl, in 'Semiconductor Silicon 1977', H. R. Huff and E. Sirt1 eds. (The 

Electrochem. Soc., Princeton, 1977) p4. 

18. S. Mizuo and H. Higuchi, Jpn. J. Appl. Phys. 20, 739 (J.98l). 

19. T. Y. Tan and B. J. Ginsgerg, App1. Phys. Lett. 42, 448 (1983). 

20. S. M. Hu, Appl. Phys. Lett. 27, 165 (1975). 

21. H. Shiraki, Jpn. J. App1. Phys. 15, 1 (1976). 

22. S. P. Muraka, J. App1.Phys. 48,5020 (1977). 

23. S. Matsumoto, Y. Ishikawa and T. Niimi, J. Appl. Phys. 54, 5049 (1983). 

24. T. Y. Tan, in 'Electron Microscopy of Materials', W. Krakow, D. A. Smith and 

L. W. Hobbs eds. (North-Holland, NY, 1984) in press. 

25. G. K. Wertheim, Phys. Rev. 115, 568 (1959). 

26. S. M. Hu, J. Vac. Sci. Techno1. 14, 17 (1977). 

27. T. R. Waite, Phys. Rev. 107, 463 (1957). 

28. U. 'Gose1e, W. Frank and.A. Se~ger, S014 State Commun. 45, 31 (1982). 

29. S. Matsumoto, Y. Ishikawa and T. Niimi, J. App1. Phys. 54, 5049 (1983). 

30. K. Taniguchi, D. A. Antoniadis and Y. Matsushita, Appl. Phys. Lett. 42, 961 

(1983). 

31. S. Mizuo and H. Higuchi, Jpn. J. App1. Phys. 21, 272 (1982); 22, 12 (1983); 

J. E1ectrochem. Soc. 129, 2292 (1982). 

271 
32. T. Y. Tan, F. Morehead and U. GHsele, in 'Defects in Silicon' W. M. Bullis 

and L. C. Kimer1in eds. (The Electrochem. Soc., Pennington, 1983) p325. 

33. F. C. Frank and D. Turnbull, Phys. Rev. 104, 617 (1956). 

34. W. R. Wilcox, T. J. LaChapelle and D. H. Forbes, J. Electrochem. Soc. Ill, 

1377 (1964). . 

35. H. Kitagawa, K. hashimoto and M. Yoshida, Jpn. J. Appl. Phys. 21, 276 (1982). 

36. J. M. Fairfield and B. J. Masters, J. Appl. Phys. 38, 3148 (1967). 

37. H. J. Mayer, H. Mahrer and K. Maier, in 'Lattice Defects in Semiconductors 

1976' (Inst. Phys. Conf. series 31, London, 1977) p186. 

38. L. Kalingnowski and R. Seqin, Appl. Phys. Lett. 35, 211 (1979); 36, 141 

(1980). 

39. I. R. Sanders and P. S. Dobson, J. Mat. Sci. 9, 1987 (1974). 

40. A. Hirvonen and J. Anttila, Appl. Phys. Lett. 35, 703 (1979). 

41. H. Kitagawa, K. Hasimoto and Y. Yoshida, Jpn. J. Appl. Phys. 21, 276 (1982). 

42. S. Mantovani, F. Nava, C. Nobili, M. Conti and G. Pignatel, Appl. Phys. Lett. 

44, 328 (1984). 

43. s. M. Hu, in ' Atomic Diffusion in Semiconductors', D. Shawed. (Plenum, NY, 

(1973) p2l7. 

44. A. F. W. Willoughby, J. Phys. DlO, 455 (1977); Rep. Prog. Phys. 41, 1665 

(1978). 

45. A. F. W. Willoughby, in 'Impurity Doping Process in Silicon' F. F. Y. Wang 

ed. (North-Holland, NY, 1981). 

46. A. Seeger, W. Frank and U. Gosele, in 'Defects and Radiation Effects in semicpnductors 1978' (Inet. Phys. Conf. Series 46, London, 1979) p148. 

47. U. Gosele and H. Strunk, Appl. Phys. 20, 265 (1979). 

48. M. C. Duffy, F. Barson, J. M. Fairfield and G. H. Schwuttke, J. Electrochem. 

Soc. 115, 84 (1968). 

49. P. F. Schmidt and R. Stickler, J. Electrochem. Soc. Ill, 1188 (1964). 

50. T. W. O'Keefe, P. F. Schmidt and R. Stickler, J. Electrochem. Soc. 112, 878 

(1965). 

51. E. Kooi, J. Electrochem. Soc. Ill, 1383 (1964). 

52. R. J. Jaccodine, J. Appl. Phys. 39,-3105 (1968). 

53. A. Armigliato, D. Nobili, M.Servidori and S. Solmi, J. Appl. Phys. 47, 5489 

(1976). 

54. D. Nobili, A Armigliato, M. Finnetti and S.Solmi, J. Appl. Phys. 53, 1484 

(1982). 

55. R. J. Jaccodine, in 'Defects in Semiconductors II'S. Mahajan and J. W. 

Corbett eds. (North-Holland, NY, 1983) p101. 

56. J. E. Lawrence, J. App1. Phys. 37, 4106 (1966). 

57. C. L. Claeys, G. J. Declerck and R. J. Van Overstraeten, Revue de Physsique 

Appliquee 13, 797 (1978). 

58. H. Shibayama, H. Masaki, H. Ishikawa and H. Hashimoto, J. Electrochem. Soc. 

123, 743 (1976). 

59. F. N. Schwettmann and D. L. Kendall, Appl. Phys. Lett. 19, 218 (1971); 

App1. Phys. Lett. 20, 2 (1972). 

60. M. Yoshida, Jpn. J. App1. Phys. 19, 2427 (1980). 

61. R. B. Fair and J. C. C. Tsai, J. E1ectrochem. Soc. 124, 1107 (1977). 

62. F. A. Kroger, J. E1ectrochem.Soc. 125, 995 (1978). 

63. D. Mathiot and J. C. 'Pfister, J. Appl. Phys. 53, 3053 (1982). 

64. c. L. Claeys, G. J. Decl.erck and R. J. Van Overstraeten, in 'Semiconductor 

Characteri.zation Technique' P. A. Barnes and G. A. Rozgonyi eds. (The 

Electrochem. Soc., Princeton, 1978) p336. 

65. H. Strunk, U. Gose1e and B. 0 Ko1besen, Appl. Phys. Lett. 34, 530 (1979). 

272 

'''''''',:' .r. 
[ 

66. R. M. Harris and D. A. Antoniadis, J. App1. Phys. to be published. 

67. P. Fahey, R. W. Dutton and S, M. Hu, App1. Phys. Lett. 44, 777 (1984). 

68. D. Mathiot and J. C. Pfister, Physica 116B, 95 (1983). 

69. D. Mathiot and J. C. Pfister, J. App1. Phys. 55, 3518 (1984). 

70. S. M. Hu, P. Fahey and R. W. Dutton, J. App1. Phys. 54, 6912 (1983). 

71. D. Stauffer, Phys. Reports 54, 1 (1979). 

72. R. Francis and P. S. Dobson, J. App1. Phys. 50, 280 (1979). 

73. C. Hill, in 'Semiconductor Silicon 1981' H. R. Huff, R. J. Kreig1er and T. 

Takeishi eds. (The E1ectrochem. Soc., Princeton, 1981). p988. 

74. W. F. Tseng, S. S. Lau and J. W. Mayer, Phys. Lett. 68A, 93 (1978). 

75. D. Lecrosnier, J. Pangan, F. Richou, G. Pe1ous, F. Beniere,-J. App1 ~ Phys. 

51, 1036 (1981). 

76. D. Heck, R.E. Tressler and J. Monkowski, J. App1. Phys. 54, 5739 (1983). 

77. T. Y. Tan and U. Gose1e, App1. Phys. A, to be puab1ished. 

_l~--~----~--~----~--~--~u 

-1 0 4 5 

273 

Fir. 1. Prediction of dopant dif.-

fusivity changes due to an oxidation. The model assumes that I and 

V coexist in Si in thermal equilibrium and in oxidation at high 

temperatures and that during the 

oxidation I and V attained local 

equilibrium. 
t 

.8 

1<1 

-o.s 

-1.0 '----~--~=--~1"=.S~~ 

11 -

Fig. 2. Quantitative fitting of available 5b ORO data from (100) wafers 

to the calculated Gr=0.02 curve per 

Eq. (8). Unfilled circle: Mizuo and 

Higuchi [18]; filled circle: Tan and 

Ginsberg [19]. 

I 

0.5 

n u 

-

J 

0.1 

....... 

" , 

\ 

\ 

\ .' 

~ \\. 

\ \.. 

\ \. 

\ \ " .'. 

\ '. 

\ 

2 5 10 20 50 100 

_[!-1m) -

Fig. 4. Gold concentration 

profile after a lhr diffusion 

into dislocation-free 5i at. 

o 900 C [14]. Dash line: an 

erfc-function fitting per Eq. 

(19); solid line: fitting 

per Eq. (20). 

274 

7 8 9 

Fig. 3. The recombination barrier limited time constant, 

Tbar' for I and V to reach 

dynamical equilibrium as a 

function of reciprocal tempt:-

rature calculated per Eq. (11). 
, . 

900 800 

1

'0'11 \ 0 c·q 

, \ , \1 1 , 

, \ 

" " " \' 

~ 

'\l 

10"24 

n c·q /-v v 

• 5." ..... at. (t • .,:~ o Mor.lwod .t 01.(983) \ 

'100 

~ Wilcox .t al. (1964 ) " 

t Kitagawa .t 01 (19820) " 

1T6 7 8 9 10 

'0'1 T[K"') .. Fig. 5. D ceq eq recip- I I and DVCV VB. 

roeal temperature. 

(a) 

C 

II 

u c: • 0 ...... • ... liD t 

:t II .... • 

: ta:l1-

I relion 

x 

1000 900 800 700 10~--~--~--~--~~----~ 

1 

7 

-tJ 

o 

o 

o 

o 

.... 

-... 

'" 

-

E-4 -... 

8 9 

104iT 

10 11 

Fig. 6. The function r(T)/r(lOOOoC) 

vs. reciprocal temperature, r is the 

ratio of the efficiency of converting 

AUf into Au due to the kick-out meI chanism to fhat due to the FrankTurnbull mechanism. Numbers above , each curve are the possible A~ 

values. 

~ 

, B (b) . 

\ 

C , 

-... \ 1", 

\ , 

\ , A 

'\ \ , \ 

, \ 

, \ 

• 

x 

F1g~ 7. (a) Schematic drawing of the kink-tail structure of P .profile, 

which, hypothetically, may be obtained by adding (b) profiles of phyaically diatinluishable A and B atoms diffusing independently. 

275 

,r ---1r-----
Si 

6G 

Si A B 

a+SiP 

" ..... . . .. 

L+P 

g 

.. .. .. . ... 

SiP 

(a) 

.. 

(b) 

SiP+P 

g 

... 

" 

P 

g 

... 

" " • 

P 

P 

Fig. 8. The Si-P binary system phase diagram (a) and an appropriate free 

energy diagram (b) showing the thermodynamic origin for P to,diffuse into 

Si in excess of its normal solubility limit. The solubility limits A and 

B are obtained from the usual connnon tangent constructions per coexistence 

of the a phase with the ,sip and Pg phases respectively. 

276. --...... 
DISCUSSION 

ROSI: On one of your viewsraphs you showed during the phosphorus diffusion, 

something like 401 of it is electrically active. I wonder if you might 

comment further on what physical form does it take? 

TAB: It takes precipitated form. A small part of it, about 15~, is identified 

as SiP structure. About 85~ of them are only observed in terms of no more 

than 15-A-sized precipitates. They are too small to.be identified by 

transmission electron microscope. Therefore they are only inferred to be 

SiP precipitate, but not proven. . 

277 
• E1~~rica1 and Structural qharacterization of Web Dendr1te Crystals 

G. H. Schwuttke 

Arizona State University 

Tempe, AZ 85287 , 

K. Kol1wad and K.A. Dumas 

Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 

Abstract 

Minority carrier lifetime distributions in si11con web dendr1tes are 

measured. Emphasis is placed on measuring areal homogeneity of lifetime, show 

its dependency on structural defects, and fts unique change dur1ng hot 

processing. The internal gettering action of defect layers present in web 

crystals and their relation to m1nority car~ier lifetime distribut10ns is 

discussed. Minority carrier lifetime maps of web dendr1tes obta1ned before ana 

after high temperature heat treatment are compared to s1mf1ar maps obta1ned from 

100 mm diameter Czochra1ski silicon wafers. Such maps indfcate sim11ar or 

superior areal homogeneity of m1nority carrier lifetime in webs. 

Introduction 

Recently, calculations have been made wh1ch show that the presence 'of areal 

inhomogeneity of minority carrier lifetime in si11con wafers can devastate solar 

cell efficiency (1). For instance, it was shown that for no more than 5% of the 

solar cell area being inferior compared to the rest of the eel I area, solar cell 

efficiency can be as poor as ft would be if the entire area ~ou1d be of inferfor 

quality (1). Thus areal homogeneity of m1nority carr1er 11tetime is an 

important requirement for high efficiency solar ce1 IS. 

This paper reports measurements of minority 

"distributions" made on silicon web dendr1te sections. 

compared to similar data obtained from 100 mm diameter 

wafers. 

Structural Aspects Of Silicon Web 

carrier 11fetlme 

Such measurements are 

Czochra1sk1 5i11con 

A brief description of the as-grown web geometry and dis1ocat10n structure 

is needed to describe our electrical measurements clearly. For detailed results 

we refer to the original papers on web growth (2) and dis1ocat10n structures (3-

5>' 

The web surface 1 s ·paralle1 to the <111> p1 ane, and the web pu111 ng direction is [2iil. A cross-sectfon of web shows its most prom1nent structural 

feature: multiple twin lamellae in the center of the web covered by two thick 

(100 pm) surface layers which are also in twin relation. An example is shown in 

Figs. 1a,b. . 

PRECEDING PAGE BLANt( NOT FILMED 

279 
• 

Dislocations in web are generated through "melt entrapment" caused by 

"wing" growth along the dendrites (Fig. 2). Propagation of such dislocations 

depends on the curvature of the solid-liquid interface of the web during growth. 

An interface curvature of concave downward concentrates the dislocations in the 

center of the web (Fig. 3). Webs grown with a straight interface concentrate 

the dislocations in the fillet region. Thus the web grows free of any 

dislocations (4). Fig. 4. Most webs_..<>f today contain bundles of very long 

dislocation lines parallel to the [211] direction (Fig. 5). They are piled up 

against the twin planes. In addition. annealed web contains large area stacking 

faults. The electrical activity and the influence of these faults on sol ar cell 

efficiency has not yet been investigated. Such an influence is assumed to be 

relatively small but it may be of importance for high efficiency solar cells. 

These defects are described in more detail in References 3 and 5. examples are 

shown in the x-ray topographs of Figs. 6. 

If excessive stresses are present during web growth (buckling) large 

numbers of slip dislocations and small angle grain boundaries may occur. Such 

defects degrade minority carrier lifetime. An example is shown in the x·-ray 

topographs of Figs. 7. 

Minority Carrier Lifetime Measyrement In Web 

Silicon web dendrite sections of various quality (Figs. 5.6,7) were 

evaluated through minority carrier lifetime "mapping" using 1.5 mm diameter MOS 

capacitors. The total number of MaS capacitors per web section was 300. The 

MaS dots were arranged into 15 rows. The dendrites were i ncl uded f nto the 

evaluation. The dimensions of the web sections were 2 inches long and 32 mm 

wide. The webs were e~aluated after each oxidation cycle <15 min wet-liO min 

dry-15 min wet at 1000 C. Three or four consecutive oxidation cycles were used. 

Minority carrier lifetime maps of the total web section were obtained after each 

oxidation cycle by measuring the lifetime under each capacitor as described by 

Fahrner & Schneider (6). Subsequently. the lifetime was computer plotted versus 

its position on the web surface. Local lifetime degrading defects revealed by 

such lifetime maps were analysed by advanced characterization techniques. A 

result typical for web sections of quality as shown in Figs. 5 and 6 is given in F·~g. 8. This figure summarizes the influence of high temperature heat cycles on 

minority carrier lifetime. The lifetime data are displayed in 6 maps. Each map 

represents a matrix of 300 capacitor dots. The maps on the 1 eft si de of the· 

figure carry -the label oxidation 1 to 3 and represent the lifetime data obtained 

after the first. second. and third oxidation cycle. The devices were obviously 

stripped before every successive oxidation step. The z~5cale represents the 

measured lifetime values in microseconds. The range of lifetime data present on t~e web section is also included in the label. For instance. the minimum 

lifetime obtained at a spec1fic location (capacitor) after the fi rst oxi dati on 

was 0.274 microseconds. The maximum lifetime is 207 m1croseconds. The lifetime 

map shows a relatively smooth plateau. Noteworthy is, that this plateau extends 

over the total web section surveyed. Accordingly. this web is of ~xcellent 

crystal quality and compares well with the best Czochralski silicon as available . today. Interesting is a comparison of the maps obtained after the first. second 

and third oxidation •. The lifetime plateau obtained after the second oxidation 

is well above the one obtained after the first oxidation and tne same is true 

for the third oxidation. The third plateau is a little bit lower than the 

second one. Using Czochralski wafer qu~lity as a standard. the 

280 
f1\ ,;.~ ,\ ". \~. 

'"~{ ':i - '. ' \. 1. 

~ ~\ \., 

\ 

: "". . 

" 

" " . ; \'I~ , . 

t 

material obtained after the th1rd oxidation shows very uniform l;fetime 

distribution data. 

The maps on the r1ght side of Fig. 8 are labeled DECREASE or INCREASE. The 

DECREASE map shows the degradation of lifetime as a result of the second or 

third oxidation cycle. The INCREASE map shows the area where the 11tetime 

increased after the third oxidation relative to the f1rst ox1dat10n. These maps show clearly the improvement of 11fetime as a result of ox1~ation. Th1s 

improvement is fairly un1form and covers pract1cally the total web area. 

Decreases in lifetime occur only along the dendr1tes, the. f111et region or along 

the edges where the web section was cut by the d1cing saw. This result 1s 

unique and rel ates to the spec1 al crystal structure of the "perfect" web. The 

defect pl anes, sandwiched between the perfect web surtace layers, provide for 

"internal" gettering during high temperature heat cycles. Thus a substantial 

improvement of minority carrier lifetime can result. 

Web mater1al of the quality as d1splayed in the topographs of Figs. 7 do 

not g1ve comparable results. It was found that the "s11p" dislocations - wh1ch 

result from buck11ng stresses - degrade m1nor1ty carries 11fet1me substantially. 

These dislocations are of the same type as the "process" induced slip dislocat10n encountered during IC processing. It is known that the electr1cal 

activity of these d1s10cations is high. The lifetime map shown in Fig. 9 

corresponds to the sample shown in Fig. 7b. Note the good correlatl0n between 

low lifetime and defect area in the center of this sample. 

Minority Carrier Lifet1me Measurements in CZQChralsk1 Silicon 

Recently, we conducted an evaluat10n of 100 mm oiameter Czochralsk1 si11con 

wafers as availabe from major vendors throughout the world. The evaluat10n 

concentrated on m1nor1ty carr1er lifet1me mapping as descr1bed for the web 

crystal. Four consecutive oxidation cycles were used. The MOS dot ma~r1x 

cons1sted of 25 times 25 MOS capaCitors of 1.5 nm diameter. A result typ1cal for the evaluated Czochralsk1 wafers is shown 1n F1g. 10. The 11fetime data 

shown 1n F1g. 10 are d1splayed 1n 4 maps. The maps on the left carry aga1n the 

oxidat10n number. The data obtained after the f1rst ox1dation indicate 

excell ent wafer qua11ty. The map has a pl ateau at approx. 250 to 300 

m1croseconds and extends pract1cally across the total wafer area. This wafer 

represents si11con of the best quality. Nevertheless, success1ve ox1dation 

results 1n steady degradat10n of 11fetime. Th1s is seen by compar1ng the maps 

obtained after the f1rst and fourth oxidat10n. 

Interesting are the DECREASE and INCREASE maps shown on the r1ght of F1g. 

10. The decrease mapconf1rms that degradat10n occurs uniformly across the 

total wafer area. After the fourth oxidation cycle small l1fet1me increases are 

observed only at 9 locations. In all other areas 11fetime degraded 

substantially. 

Discussion and Summary 

The data given in Figs. 8 and 10 aro representative of "perfect" web and 

Czochralski silicon wafers. We note a basic difference botween these two 

materials. Oxidation increases generation lffetime in Web but decreases the 

281 
same lifetime in Czochra1ski material. The decrease in lifetime in Czochra1ski 

wafers correlates with the precipitation phenomena of oxygen in s11 tcon (7). 

The large extent to which areal inhomogeneities exist in todays sil1con. ana 

influence device performance (1) is not well known. However, uniform m1nority 

carrier lifetime distributions are a pre-requisite to high performance solar 

cell technology. Solar cell efficiency in excess of 151 for large area single 

crystal silicon cells (10 cm x 10 cm) will be very difficult to achieve without 

proper control of minority carrier lifetime distributions during large scale 

manufacturing. 

References 

1. F. A. Lindholm et a1., Solid State Electronics, 23, 967, (1960). 

2. S. O'Hara and A. I. Bennett, J. App1. Phys., 35, 409, (1964). 

3. S. O'Hara and G. H. Schwuttke, J. Appl. Phys., 36, 2475, (1965). 

4. T. N. Tucker and G. H. Schwu'ttke, App1. Phys. Letter, 9, 219, (1966). 

5. E. S. Meieran and 1. B1ech, IJ. App1. Phys., 38, 3495, (1967). 

6. W. Fahrner and C. P'. Schneider, J. E1ectrochem. Soc., 123, 100, (1976). 

7. G. H. Schwuttke, Semiconductor Industry Association (SIA) Lecture, Stanford 

Univ., Sept. 1981, Palo Alto, CA. 

282 
F1gure Capt10ns 

Fig. 1 a. Web Crystal Geometry b. SEM-micrograph of cleaved web cross-section after preferential 

etching. Note twin lamellae in center. 

Fig. 2 SOT X-ray topograph of 2 cm wide web dendr1te. Note w'ng growth (arrows) at dendrites below web leading to liquid entrapment ana 

dislocation generation during growth. 

Fig. 3 SOT X-ray topograph of 3 cm wide web dendr1te. Note disl'ocatl0n 

generation at stress centers and propagation of dislocat10ns during growth toward center. 

Fig. 4 SOT X-ray topograph of perfect 1.5 cm wide web. Dislocat10ns are 

trapped in fillet region. 

Fig. 5 SOT X-ray topograph of high performance web 22D-reflection. Note long dislocations, 73 degree type; Burgers vectors [lOll, [110l. Low 

electrical activity. 

Fig. 6 SOT X-ray topographs of high performance web. Width 3.2 cm. 

a. (111) reflection: Surface twin lamellae 

b. (iii) reflection: Bottom twin lamellae 

Note difference in crystal perfection: Bottom lamellae contains large 

area stacking faults. Topographs recorded after th1rd oxidation. 

Electrical activity of defects low. Electrical data in Fig. 8. 

Fig. 7 a. SOT X-ray topograph of low quality web. Note slip dislocat10ns. 

Electrical activity high. Lifetime range: 0.01 - 1 psec. b. SOT X-ray topograph of medium quality web. Electrfcal data in 

Fig. 9. 

Fig. 8 Minority carrier lifetime maps of h1gh performance web. Lifetime 

range: 0.2 - 207 psec. 

Fig. 9 Minority carrier lifetime map of low performance web. Corresponding SOT topograph is shown in Fig. 7b. Note correlatl0n between 

dislocation density and low lifetime. Lifetime range: 0.1 - 50 psec. 

Fig. 10 Minority carrier lifetime map of Czochralski wafer for comparison. 

Lifetime range: 4 - 478 psec. 

283 
Growth Di recti on 

win mella 

Fill t 

(Ill) Face 

of Web 

Cleavage Surface 

Typical Regions of Liquid Inclusion 

Fig. la Web Crystal Geanetry 

284 
ORIGINAL PAGE' 

OF POO QUAL r( 

Fig. Ib SEM-micrograph of cleaved web cross-section after preferential 

etching. Note twin lamellae in center. 

285 
Fig. 2 SOT X-ray topograph of 2 em wide web dendrite . Note wi ng growth 

(arrows) at dendrites below web leading to liquid entrapment ana 

d1s1ocation generation dur1 ng growth. 

286 

ONGiNAL PAoE' 

OF POOR Q ALrrY 
Fig. 3 SOT X-ray topograph of 3 cm wide web dendr1te. Note dislocation 

generation at stress centers and propagation of dislocations during 

growth toward center. 

281 
Fig. 4 SOT X-ray topograph of perfect 1.S em wide w.b. Dislocations are 

trapped in fillet region. 

288 
Fig. 5 S T X-ray topograph of high performance web, 22o-reflect10n. Note long dislocations, 73 degree type; Burgers vectors [101], [110]. low 

electrical activity. 

289 
Fig.6a SOT X-ray topographs of high performance web. Width 3.2 cm. 

(111) reflection: Surface twin lamellae. 

Electrical data in Fig. 8. 

290 
Fig. 6b SOT X-ray topographs of high performance web. Width 3.2 cm. 

(lIT) reflection: Bottan tw i n lamellae 

Note di fference in crystal perfection: Bottan lamellae contains 

large area stacking faults. Topographs recorded after thlrd 

oxidation. Electrical activity of defects low. 

291 
Fig 7a SOT X-ray topograph of low quality web. Note slip dislocations. 

Electrical activity high. Lifetime range: 0.01 - 1 ~sec. 

292 
o L P 

OF OOR QUALITY 

Ffg 7b SOT X-ray topograph of medfum quality web. Electrfcal data fn Fig. 9. 

293 
Oxidation 1 

NO. OF OXIDATIONS: 1 

DATA RANGE: .2740 207 

Z.sCALE: MICROSECONDS 

-... 

400 

eb Dendrite Silico 

Lifetime Distribut= Data 

D as 1 to 2 

OXIDATION NUMBERS: 1 2 

DATA RANGE: .5000 200 

Z-8CALE: MICROSE 0 0 

---

.. 

::]

~~ 

. A _~~ ::~. ~@@mI~ 

~I~ """""'" 

------ Oxidation 2 

NO. OF OXIDATIONS: 2 

DATA RANGE: .2120 808 

L SCALE: MICROSECOND 

-... 

o ...... ............. .. " uu",a, ~~-.--

Decrea$e 1 to 3 

OXIDATION NUMBERS: 1 3 

DATA RANGE: .1000 183 

Z-8CALE: MICROSECO DS 

--

-

.. 

o ......-......... 

.. :100 

:100 

100 

O~~~ ... 

• 

.. ~~~~~ii~~~~~~~ ,. o' • 

.. ""I' ..... ··· .. · 

tL. ..-... ___ _ 

Oxidation 3 

NO. OF OXIDATIONS: 3 

DATA RANGE: .,.,0 452 

Z·SCALE: MICROSECOND 

-... 

400 

:100 

:100 

100 . 

0-

• 

.. .,."., ........ , .. &.------ ...... .. . 'f ... ...... 

Increa e 1 to 3 

OXIDATION NUMBERS: 1 3 

DATA RANGE: .,.,0 305 

Z-8CALE: MICROSECOND 

---

.. 

o 

.. 

-: W~~~~~~RX 

o 

Fig. 8 Minority carrier lifetime maps of high performance web. 

lifetime range: 0.2 - 207 ~sec. 

294 

~ ......... , ...... 

....... ... ........ 
Fig. 9 Minority carrier lifetime map of low performance web. Corresponding SOT topograph is shown in Fig. 7b. ~ote correlation between 

dislocation density and low lifetime. Lifetime range: 0.1 - 50 ~sec. 

295 
Lifetime Data Distribution Map 

Vendor B 

Oxidation 1 

NO. OF OXIDATIONS: 1 

DATA RANGE: 4.0000 478 

Z-SCALE: MICROSECO D 

p.er.r.r .001 ... , ..... 

Oxidation 4 

NO. OF OXJDATIONS: 4 

DATA RANGE:.53OO 121 

Z-SCALE: MICROSECONDS 

-

.. 

-

:III 

.. ,. o 

p ........... ....... ... . 

o --... _ ... 

o ..... ..,. 

Decrease 

OX.IDAnoN NUMBERS: 1 4 

DATA RANGE: 7.0000 442 

Z-SCALE: MICROSECO D 

--

--

-, . 

• 

Increase 

OXIDATION NUMBER.S: 1 4 

DATA RANGE: 2.0000 41 

Z-5CALE: MICROSECONDS 

--

--

-

,. 

• ,. '0 

• 

Phall"'" 

• • o 

..... -----... 

'1 

'0 

..... _ ... _ ... 

Fig. 10 t4inority carri er:- lifetime map of Czochra1ski wafer for comparison. 

Lifetime range: 478 ~sec . 

29 
1 

DISCUSSION 

BANOKA: Do you have any idea why the grown dislocations seem to be not electrically bothersome, whereas the stress-induced ones are? 

SCHWUTTKE: First of all, the core structure of this grown dislocation is very 

benign. It .akes an angle of 730 , and this type of dislocation has been 

described in the literature. This structure is very benign, while a 600 

dislocation, which is a ~lip dislocation, is very active due to its core 

structure. 

297 
N85-31634 

ERIC Characterization and Hydrolen Passivation in Silicon Sheet 

ABSTRAcr 

lack I. Banoka 

Kobil Solar EnerlY Corporation 

Walth ... Kassachusetts 02254 

As a leneral qualitative tool. the electron be .. induced current (EBIC) 

method can be very useful in imalinl recombination in silicon Iheet used for 

solar celli [1.2]. In this paper. work usinl ERIC on EFG silicon ribbon will be 

described. In particular. soae efforts at makinl the technique more 

quantitative and hence more useful. some limitations of the method. and finally 

specific application to hydrolen passivation will be treated. AI an 

introduction. soae brief remarks will be made relardin, tho technique itself. 

The EBIC Technique 

FiBure 1 shows a schematic of the ERIC procell. An electron be .. i~inles 

on a semiconductor sa~le containins a junction of soae sort. The ener,y of the elect~ons in the beam typically ranles from 1 to 50 keV while the miniaum ener,y 

to create hole-electron pairs in a semiconductor is the band lap. which is on 

the order of 1 eVe As a result. a sinlle hilh enerlY electron incident on the 

seaiconductor produces many hole-electron pairs. on the order of 10. to 10· per 

incident electron. The electron-hole pairl are created within the material in a 

volume termed the leneration volume. The important carriers here are the 

minority carriers -- electrons in the p-type layer and holes in the n~type 

layer. If the diffusion len,th of the lenerated ainority carriers is lon, 

enou,h. they will diffuse to the p-n junction and be swept across it by the 

stron, field present. thus producin, a current that can be aeasured externally. 

This is the electron-b ... -induced current. This current can then be amplified 

even further and the amplified si,nal used to drive the CRT display of the SBM. 

while it is scanned synchronously with the electron be... The result is a 

aappinl of the current collected at every scanned point. If a defect such as a 

srain boundary or a dislocation is prelent. the relultins recoabination at such 

a defect will produce less collected current and a darker iaa,e (correspondin, 

to les. current collection) in the CRT di.play. Exaaple. of EBIC iaases of 

recoabination at srain boundaries and at dislocationa will be shown in later 

fi,ures in this paper. 

The de.cription above indicates that ERIC is an electron-be .. analo, of 

the photovoltaic effeot. The i.a,e. one obtains usin, li,ht be .. induoed 

current (LBIC) are. in fac~. siailar to tho.e seen fro. EBIC. LBIC ,enerally 

ha. poorer re.olution than BlIC but offer. the ability to ,enerate carriers at 

varyin, dista.oes aooordi., to the wavele.,th of the li,ht oho •••• 

With BlIC. the d.pth of pe •• tratio. or the ran,. R. of the .l.otzo. b ... 

is a funotio. of the .l.otro. b ..... er,y. E. with thia fora for .ilioo.: 

PRECEDING PAGE BLANK: NOT mMED 

299 

• 
• 

R - (0.032) B

1 •

67 (1) 

where R ia in aicrona .nd B ia in keV. The r.Dle-enerIY rel.tion dependa on the 

IIOde1 choaen •• nother cOllllOnly used aoelel lives R - 7 .... t 30 keV [1]. 

A re.aonable .nd uaeful .pproxia.tion for ail icon ia to conaider the 

electron-hole p.ir lener.tion vol .. e to be • aphere t.nlent to the aaaple 

aurf.ce. R ia then the di .. eter of thia aphere. Por a 30 keV be .. , R - 9 .... R ia alao • ae.aure of the reaolution obtai.able. It ia i~ort.nt to note th.t 

the reaolutt~~ ia only we.kly dependent on the ainority c.rrier diffuai9n lenlth 

.nd is aalnly f;eterained by the value of R. 

There ia • conaider.ble body of liter.ture now .v.ilable on qu.ntifyin, 

BlIC. but we w1ll concern ouraelves with two or three techniquea in particul.r' 

which we h.ve found uaeful in atudyin, lol.r cella. 

Low Teaper.tpre EPIC 

Aa aentioned above •• n BaIC ia.,e providel • recoabin.tioD a.p. In 

.ddition to aiaply taowiDI the Ipati.l loc.tion of recoabiD.tion aitea. it ia 

iaportant. p.rticul.rly fro. the point of view of aakinl hilher efficiency 

silicon ribbon sol.r cells. to further underat.ad wh.t ia takin, pl.ce .t theae 

recoabin.tion aitea. 

Accordinlly. we have iDveati,.ted the use of EBIC .t low teaper.turea [3]. 

In lener.l •• conaider.ble .aount of recoabin.tion contraat eah.nceaent ia aeen 

in EFG ribbon ailicon when loinl fra. roo. teaper.ture to. a.y. 200-E. Throu.h 

the uae of • trappinl aodel. it w.a ahown that the experiaent.l resulta obtained 

could be interpreted .a due to sh.llow enerlY at.tes loc.ted below the 

conduction band .nd th.t the .ctiv.tion enerlY of thea. levela could be 

c.lculated fro. the low te.perature BBIC d.t •• 

Purther.ore. the beh.vior of these tr.ps aa • function of therm.l 

processinl .nd [Oi] h.s been atudied .nd will be dilcusaed below. 

The ribbon a •• plea atudied here were p-type, with p - 1 O-c.. Both Al 

Schottky barriers and PII. diffu.ed junctions "ere used •• collectinl junctions 

for the EBIC work. The low teaper.ture BaIC w •• done usinl ~ liquid 

nitro,en-cooled apeciaen .ouat which wa. fitted to • C •• brid,e 84-10 SIK. The 

ribbon ... ple aDd • .in,le cryat.l CZ ref.rence .~le were .ounted on a thick 

copper block with. theraocouple b.twe.n the two a.~le.. With this 

arr.n,.aent, the el.ctron be.. induc.d current .t a p.rticular defect could be 

•••• ur.d by .dju.tin, the condenser l.n •• s on the SIK to liv •• pr.-s.l.cted 

v.lue of the DIC for the CZ ref.r.nce oell. No sipifio.nt def.ct. w.r. 

observed in th.CZ ref.r.nce cell .t 300-E or down to 200-E. An ..... pUon u.ed 

in aakin, the ae •• ureaent. ia th.t the DlC of the reference oell i. independent 

of teaper.ture. 

The ,ener.l re.ult ob.erv.d i. ahown in Pi,. 2 "ere the eDb.noed 

reooabin.tion .lon, .Dd between the linear bound.rie •• t low t .. per.ture o.n 

re.dily be .een. In the roo. t.aper.ture photo,r.ph in Pi,. 2 (top photo,raph), 

the prototypic.l defect. s.en by DIC on BPG ribbon .re evident. Th •• e .re 

line.r bound.ries p.r.ll.l to the ,rowth direotion .Dd .rr.ys of di.loo.tion. 

300 
within b.nds bordered by line.r bound.rie •• 

QuantifyinS the .bove is done by aea.urins the EBIC sisnal .t a particular 

defect a •• function oftemper.ture. U.inS the sinsle cry.t.l reference cell 

.nd the v.lue of the EBIC sisn.l .t the defect, • diffu.ion lensth L, could be 

a.sisned to the reaion enclosins the defect [3,4]. 

A model w •• developed in which the enh.nced recoabination .een .t lower 

temperatures wa. viewed •• due to tr.ppins of electron. at .h.llow level. below 

the conduction b.nd [3]. Fiaure 3 .how. the scheme used 'for the aodel. If .uch 

• level is .t an enersy AB below the conduction b.nd, then it was possible to 

.how that 

(2) 

Thus, ae.surins the v.lue of L .t a particular defect as a function of 

temperature would permit the calculation of the trap activ.tion energy, AB. In 

this way, three shallow tr.ps were found, E - 0.04 eV, E - 0.10 eV, and E -

0.13 eVe C c c 

The behavior of the.e traps indicate. con.iderable .en.itivity to both the 

p.rticular srowth conditions (quartz or sraphite crucibles), addition or 

non-addition. of ODs to the srowth ambient u.ed, .nd also to the temperature 

employed for the n-type ~iffusion. • 

A feature common to .11 the above cases is the spatial anchor in, of these 

tr.p. at di.location. or at linear boundarie.. The location of those tr.ps i. 

not .ffectod by diffu.ion temperature. up to 10S0oC, at lea.t within the EBIC 

.p.tial resolution liait of -9 ~ for a 30 keV electron beam. Fisure. 4 aDd S 

illu.trate .ome difference. in EDIC temperature behavior (increa.ins 

recombination with decreasins teaper.ture) for the as-srown quartz crucible and 

as-srown sr.phito crucible .ilicon ribbon. The sraphite material (FiS. S) .hows 

• s.turation at temperatures below 1530 K indica tins th.t below this temperature 

electron. do not detrap back into the conduction b.nd but underso • tr.nsition 

to a deeper level .t which recoabin.tion take. place. Thi. l.tter proce •• t.ke. 

pl.ce with relatively little teaper.ture sensitivity .s oppo.ed to the 

exponenti.l beh.vior of the detr.ppina prooe.s. The qu.rtz-srown •• teri.l (Fi,. 

4), on the other h.nd, .how. either no saturation down to 1400K or the tr.p 

distribution ch.n,e. at -lSsoK fro. the 0.04 level to a domin.nce of either the 

0.10 1ev.e1 or the 0.13 level. 

Tt.p behavior in .ol.r cell. m.de froa the araphite crucible a.teri.l in 

which the [Oi] w •• v.ried by chana ina the ODs p.rtial pre •• ure in the arowth 

aabient .how.d • tr.n.ition froa t~. 0.04 .V l.vel to the 0.10 eV lev.l only 

when [Oi] > IOU cm-I • Also, in c ... s .t hip.r diffusion t.mper.tures (10400C, 

inste.d of 900°C), .11 sh.llow tr.p l.v.l. could b. suppressed. These r.sult. 

are ..... riz.d in the four c.ses shown ia Fia. 6. Fiaur. 6 also indicat.s that 

we believe that the, •• h.llow stat.s o088unic.t. ia soa. way with d.eper mid-,ap 

stat,., but little oan b ••• id .bo~t this at this time. 

Th. r.sult •• u •••• t that SGa •• ort of ozya.a-related coaplez i. formed at 

thes. el.ctrically aotiv. di.looation.. Th. ooapl.x th.a di.solv •• or br.ak. up 

whea T > 1040oC. For [Oi] ) lOS. om-I, th.r. is .a iat.raction with the 

301 
.h.llow •• t tr.p .t Ec - 0.04 .Dd tr.p •• t E - 0.10 .Dd Ec - 0.13 .V the. , ••• if •• t th .... lv... Th •• ff.ct of c.rbo. i •• 11 this r ••• i •• to b. uncov.r.d. 

but .l.c. c.rbo. i. pr •••• t i. co.c •• tr.tio •• of the ord.r of 101 • 0.-'. it 

prob.b17 h ••••• jor role to pl.y. 

I.c •• tly. w. h.v. b •• u. u.i •• low t •• per.tur. EBIC to .tudy di.loo.t10 •• 

which .r. fora.d u.d.r known .tr •••• Dd t •• p.r.tur. oo.ditio... I. ord.r to 

•• t.bl1.h • r.f.r •• c •• i.it1.1 work h •• b ••• do •• o •• 1.,1. ory.tal •• t.r1.1. 

Th. utility of low t •• p.r.tur. EBIC i •• Db •• o1 •• recoabi •• t10. at the . d1.loc.t10 •• fora.d i. this c ••• by pl •• tic d.fora.tio. c •• be •••• i. Pi •• 7. 

Sh.llow tr.p l.v.l. h.ve .ot y.t b ••••••• ur.d h.r. but the h1ihly .Db •• c.d low 

t .. p.r.tur. EBIC co.tr •• t of th ••• d1.100.t10 •• i. quite .vid •• t froa PiS. 7. 

Diffu.io. L •• ,th .nd Surface I.coabi.atiop velocity M ••• "oa •• t. 

Th. iDhoao •••• ou. di.tributio. of the two typ •• of d.fect. which ar. 

e •• ily i •••• d by EBIC ..... ly di.loc.tio ••• Dd ,r.i. bound.ri •••••••• th.t the 

diffusion l •• ,th. L •• 1.0 v.ri •• sp.ti.lly i •• ate.ri.l which oo.t.i •• th ••• 

def.ch. 

I ••• alyzi •• the curre.t coll.ctio. i. EBIC when d.fects or r •• io •• of 

di.ini.h.d value. of L ar. pr •••• t ••• v.r.l .ppro.ch ••• r. po.sibl.. On. 

appro.ch is to treat the d.f.ot ••• p.rturb.tio. such th.t L cha .. e. abruptly 

wh •• a d.f.ct i ••• couat.r.d. With this .ppro.ch to the probl... • •••• ly.is 

built up ual.S poi.t d.tectl oa. bo don •• 0 th.t Ii •• d.f.ct •• Dd pl.nar d.f.ct. 

c •• b •• tudi.d. Do.ol.to [5) h •• u.ed this .ethod ext •• siv.ly in hi. p.p.rs •• d 

w. will .how how it ca. b. utiliz.d furth.r o. i. this sectio •• 

An .pproach which repr •••• tl •• oppo.it •• xtre •• c ••• lso b. t.ke. [4) 

wh.re o.e ....... (1) th.t the d.fect •• re di.tribut.d over .,fi.ite volua ••• d 

i. f.ct fill the .e.er.tio •• phere. ..d (2) th.t L varies i •••• oother .Dd I ••• 

• brupt f •• hion i •• ovi., froa • d.fect to • d.f.ct-free re.io •• 

Both of th •••• pproach.s will b. illu.trat.d with .xp.ri.e.t.l ex .. ple. 

which will .1.0 .how the adv •• t.,e ••• d di •• dv.nta,ea of e.ch appro.ch. \ 

The .h.llow tr.ppi •• level .odel utilized i. the int.rpr.t.tio. of the low 

t •• p.ratur. BaIC d.t. iaplicitly u.ed the •• oo.d .ppro.ch where the def.ot i. 

visualiz.d •• fUU •• the .e •• ratio •• ph.r.. This. of cour.e. is • alaplistic 

a .... ptio. but it allow. u. to ••• i ...... b.r or diffu.io. lenath at a.y 

p.rticul.r poi.t .10., •• EBIC Ii ••• c... Pi.ur. 8 .how. EBIC .icro.r.ph. of 

the •••• r •• 10n of •••• pl. of EPO .ilioo. ribbon b.for ••• d.ft.r th.ra.1 

proo ••• 1... I. Pi •• 9 .re .hown Ii ••• c ••• throuah the .... r •• io. b.for •• nd 

aft.r th.ra.l proo ••• i ••• 10., with the deor •••• i. 4iffu.10. leaath v.lu ••• t 

v.rlou. poi.t. followi •• the th.ra.I- proo ••• l... Th. r.coabi •• tlo •••••• ft.r 

the th.raal prooe •• i •• ooour. at the ••••• It •• which .xhibit .Db •• o.d 

r.oOllbi •• tio •• t low teap.r.tur...Thia type of dat ••• well •• the low 

t.-p.ratur. BlIC d.t. l •• d.·to • piotur. of the i.tr •• r •• ul.r 4i.loo.tlo •• rr.y. 

AI b.l •• the .It ••• t whloh r.ooabl •• Uo. oh ••••• t.t. plaoe. i.o1u41 •• oh ..... i. the shallow .l.otro. tr.p •• 

Th. firat .ppro.ch to •••• uri •• L, th.t u •• 4 b~ Do.ol.to [5J, .110w. 0 •• 

to •••• ur ••• urf.c. r.ooabia.tic. veloolty, S,.t •• lY •• bO'iuld.q •• w.ll .i 

302 
the diffusion lensth for intrasranular resions on either sid~ of this boundary. 

ORe takes a line scan throu,h the ,rain boundary and by aeasurins simple 

seoaetric properties of the line scan related to the half width. these 

par .. eters can be extracted. This method is more accurat,e than the one 

described above. but requires a relatively "clean" boundary 1j'ithout extremely 

dense dislocation arrays adjac~nt to it. a situation which is often found in 

silicon ribbon. In the followin, section on hydroaen passivation. an 

application of this method will be described. 

HYdroaen Passivation 

In the early work on hydrosen passivation of srain boundaries. it was 

demonstrated that the el~ctrical properties of srain boundarien could be 

draaatically altered after hydrosen passivation (6],. This was a perfof3t 

application for EDIC. and. in fact. draaatic befo~e and after BBIC photos of 

hydrosen passivation of srain boundaries ".sre obtai~,Gd [7]. nona with 

imprelsive improvements in solar cell efficiency. , 

An example is shown in Fig. 10. EDIC photos such as these indicated th&t 

in some cases hydrogen p~ssivation could virtually eliminate any EDIC contrast 

due to srain boundary recombination. These EDIC photos were made at 30 keY. 

where R - 9~. Thus, passivation proceeded down to this depth, but did it 

proceed any further? 

To answer this question. a technique was developed to measure the depth of 

penetration of hydroaen passivation down arain boundaries [8]. Fisure 11 is an 

illustration of the confisuration used. The sample is cleaved and the cleaved 

surface is exposed to hydrogen ions. A blocking layer of PH. diffusion-produced 

glass .ubsequently covered with a thin layer of evaporated Ti is used to confine 

the hydroaen penetration to be normal to the cleaved surface. After 

passivation, the sample is turned 900 and EDIC is done on the side with the 

blocking layer. Tho Ti layer is thin enough to permit penetration of the 

electron beam. A typical result obtained with this technique is shown in Fig. 

12. In this way. passivation depths of anywhere from -5 pm to -200 pm were 

found. This variation was due to great differences in the recombination 

properties of different boundaries. Using the method of Donolato, referred to 

above. to aeasure S, a rou,hly linear relationship for In S vs. the passivation 

depth. x, was found for x i 35 pm and S 1 2 X 10· cms/sec. This is shown in 

FI,. 13. 

Exploitin, this technique even further, it was found that diffusivities of 

hydro,en down ,rain boundaries could be measured at 4000C and ran,ed frOB 10-' 

to 10-1 • cms/sec. These values were the first direct diffusivity aeasureaents 

of hydroaen diffusion down grain boundaries and show the power of EDIC in better 

understandinl hydro,en passivation. 

Sp'ary 

The utility of EDIC in study!n, rocoabination in silicon ribbon has been 

described. Efforts at quantifyin, the technique have be,un to yield soae fruit. 

The behavior of shallow electron trappin, levels associated with dislocations in 

the .aterial has been monitored. The situation. while undoubtedly coaplex. does 

show that there are three basic traps and that they are especially sensitive to 

303 
[0 1 aad theraal processia,. Thus. the aethod could be of ule in better 

unAerltaadia, the role of oZYlea aad theraa1 proceslial ia this .aterial. The 

use of low te.perature BBIC ia Itudyia, thele trap.. aad. ia ,eaera1. ia 

Itudyia, the electrical .behavior of dislocatioal hal beea dilculled. 

Bydro,ea pallivatioa of dofectl ia·li1icoa ribboa il a particularly apt 

applicatioa of BBIC aaalydi. EDIC work hae: already .howa that pa .. ivatioa 

depthl caa vary fro. 5 to 200 ~ alonl Irain boundariel aad that hydrolea 

dlffulivitiel a10al luch boundaries can vary fro. 10-' to 10-10 c.s/lec. 

Reference. 

1. 1.1. Banoka and R.O. Boll. Ann. Rev. Mater. Sci~. !!. 353 (1981). 

2. 1.1. Banoka. Solar Celli. !. 123 (1979/80). 

3. 1.1. Baaoka. R.O. Bell and B. Bathey. in: Proc. of Syapolia on Electronic 

aad Optical Propertiel in Polycrystalline or Iapure Semiconductorl aad Novel 

Silicon Growth Techniques. ed. by ~.V. Ravi and B. O'Mara. The Electrochea. 

Soc •• Princeton. 1980. 

4. R.O. Bell aad 1.1. Banoka. 1. Appl. PhYI •• 53, 1741 (1982). 

s~ C. Doaolato. Appl. PhYI. Lott •• H, 80 (1979). and C. Donolato. Sca.-inl 

Electron Microlc •• Part I (1979), p. 257; al.o, C. Donolato and R.O. Bell. 

Rev. Sci. Iastr1lll., H( 8), 1005 (1983). 

6. C'.B. Sea.er and D. S. Ginley, Appl. PhYI. Lott., ~.!, 5 (1979). 

7. 1.1. Banob, C.B. Sealer, D.l. Sharp, and 1.~.G. Paaitz. Appl. PhYI. Lott., 

~(In. 618 (1983). 

8. C. Dub'. 1.1. Baaoka, and D.B. Saadltroa, Appl. Ph,.I. Lott •• ij,(4). 425 

(1984) • 

304 
ONGINAL PA 

OF. POOR QUALITY 

,-

,-nPi 

ICllICOIiOUCTIit 

Pi,. 1. oh .. atio of t e IC proo •••• 

Bl.otron- ole pair. ar. e erat. 

within the .haded re,ion. In the 

p-type re,ion, eleotron. diffu.e to the 

Junotion, ar. oolleot.d, aad then fora 

the be..-induoed ourre.t. 

M.D lA, lTATl1 

? 

Iy-----------------------------

IeHIMI POll SHALLOW itA"'''' MODIL 

Pi,. 3. 

Pi,. 2. Roo. t.aperature (top) a.d low 

teap.rature BBIC (lower photo) of the 

.... re.ion. Direction of ,rowth of 

the ribbon i. Tertical. 

., ... , 

Pi,. 4. BBIC teaperatare b.haTior for 

quarts oruoible-,rowa ribbon. 

305 
140 II) no 

TI .. ' - Fi,. 5. BlIC t .. p.r.tur. b.h.vior for 

,r.phit. crucibl.-,rowa ribboa. 

Fi,. 7. Di.loc.tioa 1 CZ .la,l. 

cry.t.l •• ~l •• tr •••• d .t 1300'C u.ia, 

four-poiat b.adia,. Top: roo. 

t .. p.r.tur.; botto.: 150'K. 

0..,. .w 

QJO oW 

.. 

11.1 .AP ITATU 

? 

• ...., - 111M .w II IDIIIIIATII .., 

0.10 . W -'T Cot]~. 

• _"C- G04 .w" 0Ftt1l e-- _ .., mill. QJO. 01 cua .W 

AT T'I .... 

Fi,. 6. 

beh.vior. 

• ry of .h.llow tr.p 

THERMAL 

PROCESSING 

Fi,.'. BlIC .ioro,r .ph. of the •••• 

r.,ioa b.fore .ad .ft.r th.ra.l 

proo • .,.a,. 

306 
200 

Ca ERE CE CELL 

I 

I 

I 

:' II 

r.-t 

DISTANCE (p.) 

800 1000 1200 1400 1600 1800 

Fil. 9. Line leanl for the two calel in Fil. 8. 

Fil. 10. IBIC photol of a ribbon lolar cell before and after pallivation. 

307 
-

OIWGWAL P , 

OF 'OOR QUALI 

Fi,. 11. Sch •• e u •• d f or p ••• iv.tion 

d.pth .... ur ... nt •• 

Fi,. 12. p ••• ivat ion depths u.in, the 

t.chnique of Fi, . 11. 

I 

• 

4··S- ".t ..,., II. 

• 

. .,... 

Fi,. 13. ..l.tion bet.een .urf.ce recoabin.tion 

velocit7 S ... p ••• iv.tion depth, z. 

308 
DISCUSSION 

RORATGI: When yuu showed the diffusivities of 10-8 to 10-10 , I take it you 

ara saying that this is the diffusivity in the grain boundaries, but not 

noeessarily in the bulk silicon. 

HANOKA: That is right. 

RORATGI: You also indicated that you think that hydrogen went in the bulk, 

also through one of your measurements. Did I read you right? 

HANOKA: That is right. 

RORATGI: Bow deep was the detection of the hydrogen? 

HANOKA: In fact, it is not something I am discussing here, but we have a considerable amount of evidence to indicate that the hydrogen goes down in 

the bulk rather deeply also. We will be publishing some data on that very 

soon. 

RORATGI: This is in contrast to what Larry (Kazmerski) said in his talk this 

morning, that hydrogen doesn't go through the bulk silicon. 

HANOKA: It is not a simple bulk diffusion. Through ordinary good non-defectfree silicon, because there isn't much data on the diffusion of hydrogen 

down bulk silicon, but data indicate that the diffusivities are something 

like 10-14 , so you don't expect -- it's only Angstroms that you would 

expect the hydrogen to be going that way. So it has to be a defectassisted diffusion down the bulk region. 

RORATGI: Then I take it this range of 10-8 to 10-10 that you had was 

based on this range of passivation that you sawall the way from 5 to 100 

micometers. 

KAHOKA: Yes, that is right. 

ROBATG!: That is the reason for this big range? 

HANOKA: Yes. Generally, the boundaries that show the shallowest passivation 

are the one that have the highest surface recombination velocity. 

LESK: Can you please .antion your beam current densitiel and whether or not 

you had atteapted to control the temperature during the iaplant? 

HANOKA: The current densities were about 2 milliamps/cm2 and the temperature -- it is hard to aeasure the temperature and there is soae controversy about this -- but,I think the temperatures of our samples are fairly 

high, soaething on the order of 4000C to 5000C when we passivate. 

DAUD: Could you ca..ent about your numbers for the diffusion length? If the 

distance between the grain boundaries is less than the diffusion length 

in this area, is your measurement correctt 

309 
~OKA: You .re probably risbt but sener.l1y what you find is tbe distance 

between tbe electrically .ctive bound.ries on tbe order of .ever.1 bundred 

aicra.eter. on .verase, and our diffusion 1enstbs unfortun.te1y are not 

•• v.ral bundred aicraaeters. So I don't tbink tbat is a problea in moBt 

c ••••. 

SIRTL: You aentioned tbese trap levels, and pattlcu1ar1y tbe one correl.ted 

witb oxysen. Is this Boaetbins tb.t has been reported tbe first time by 

you? 

HANOKA: Actually, I save it at tbe ECS aeetins in Hinneapolis about two or 

tbree years aso, but I bave not pub1isbed it. It was just an oral pre--

.ent.tion, but I am p1annins to publisb it Boon. 

SIRTL: So far nobody else bas. 

HANOKA: Hot tbat I am .ware of. 

310 

J 

, 
ABSTRACT 

H85-811as -. 

MEASUREMENT OF ELECTRICAL PARAMETERS AND CURRENT COMPONENTS 

IN THE BULK OF SILICON SOLAR CELLS 

Arnost Neugroschel 

Department of Electrical Engineering 

University of Florida 

Gainesville, FL 32611 

A review and illustration of electrical measurements for determination of 

the bulk parameters in silicon solar cells is given. The presentation 

concentrates on transient and small-signal admittance measurements. These 

measurements yield accurate and reliable values of the base lifetime and the 

surface recombination velocity at the back contract without inaccuracies that 

normally results from electrons and holes in the pIn junction space-charge 

region. This then allows the determination of the recombination current in 

each region of the cell. As an exampl e, current components in the emitter, 

low-doped base, high-doped base and junction space-charge region of the backsurface field cell are obtained. Such analysis is essen'!:ial in determining the 

relative importance of, the base and the emitter and, thus, the region that 

limits the cell efficiency. 

I. INTROOUCTION 

The efficiency of state-of-the-art sol ar cells is determi ned primari ly by 

the mi nori ty-carri er diffus i on 1 ength in the base of the cell and for some 

cells also by the surface recombination velocity at the back contact. It is, 

thus, very important to have measurement methods for fast and reliable 

determination of these two parameters. 

Various methods are available at the present, some of which were reviewed 

by others [1]. In this presentation we concentrate on, two methods only: 

(1) the short-circuit-current decay method [2], and (2) the small-signaladmittance methods [3-5]. It wH 1 be demonstrated that these two approaches 

yield reliable results directly from the data without any adjustable parameters 

which are usually taken from the literature when using some other techniques. 

The methods also allow the determination of the relative importance of the base 

and the emitter regions of the cells. 

II. SHORT-CIRCUIT CURRENT DECAY (SCCD) 

This is a relatively new method described in detail in [2]. We will 

describe it here only briefly. A solar cell is forward-biased with voltage V 

causing forward current If. At time t=O, the cell is short-circuited through a 

fast and very low resistance MOS transistor, by applying a voltage pulse to the 

311 
gate, see Fig. l(a). The current transient measured across a small resistor R 

is displayed on an oscilloscope. The current transient can be expressed as an 

infinite series of exponential decays 

CD -t/ 'C . -t/ 'C 

i(t) ~ 1. ii(O) e dl:: i(O)e d + 

i =1 

CD -t/ 'Cdi Y. ii(O) e 

i=2 

(1) . 

where 'Cdi is the decay time constant of the i-th mode and ii (0) is the 

corresponding initial value at t=O. As shown in [2] the first mode is dominant 

and the higher decay modes can be neg1 ected. The value of the fi rst-mode 'Cd is 

obtained simply from the 10gei(t) vs t plot, and the corresponding i(O) is 

obtained b'y extrapolating the straight portion of the plot to t=O. This 

extrapo1atlon is necessa~ partly ~ecause the delay time constant of the 

measurement circuit prevents accurate measurement immediately after the closing 

of the switch. The resulting plot is schematically illustrated in Fig. l(b). 

Figure l(c) shows the measured current decay for a n+ /p/p+ back-surface-fie1d I (BSF) solar 3 cell with 'Cd ~ 6.4 posec yielding Ln ~ 180 1JI11, 

i Seff ~ 1.3 x 10 cm/sec. 

I 

I 

i 

The two measured quantities, i(O) and 'Cd' are both functions of the 

minority-carrier base lifetime 'C and the effective surface recombination 

velocity Seff at the back contact. Simultaneous solution of these two 

dependencies (see Appen~ix A) yields the desired parameters: 'C and Seff. 

The discharging of the excess electrons and holes in the junction spacecharge-region (SCR) occurs within a time of the order of ---10-11 sec. The 

discharging of the excess carriers in the emitter occurs within a time about 

equal to the emitter 1 ifetime or emitter transit time, both of which are much 

smaller than the first-mode 'Cd. As a result, the SCR and the emitter do not 

affect the transient observed on a time scale about equal to 'Cd. 

This fact is one of the main advantages of this method of measurement of 

the base properties in comparison with more conventional transient methods, 

such as the open-ci rcuit voltage decay (OCVD) and the reverse-step recovery 

(RSR). As discussed in detail in [2], both the OCVD and the RSR methods suffer 

from distortions caused by the recombination within the SCR and the emitter 

that persist throughout the entire decay. 

The sensitivity of the SCCD method to the bulk lifetime and to the surface 

recombination velocity is illustrated in Figs. 2(a) and 2(b). These figures 

show that for thin cells with W « L, the SCCD method is very sensitive to Seff 

but rather i nsensiti ve to 'C. For cells with W » L, the method is very 

sensitive to 'C but insensitive to Seff. This behaviour can be explained by 

rea1hing that if W « L, then most of the minority carriers recombine at the 

back surface. However, if W » L, then most of the recombination occurs in the 

bulk. 

In the two limiting cases above, the SCCD technique will yield only one of 

the desired parameters, ei ther L or S. In order to determi ne the other 

parameter for these two cases, the SCCD measurement has to be supplemented by 

312 
some other external charcteristic of the cell dependent on both Sand L. For 

example, one can use the dark saturation current 10 or the open-circuit voltage 

Voc for this purpose. Both 10 and Voc ' however, may be affected by the emitter 

regi on and the combi nat i on of SCCO - 10 or SCCO - V oc may gi ve mis 1 eadi ng 

results for the base parameters. 

In the next section we explore small signal admittance techniques that are 

sensitive primarily to the base properties. The combination of the SCCO and 

the admittance techniques gives the base parameters' (S, l) for any cell 

regardless of the W/l ratio. 

III. SMALL-SIGNAL ADMITTANCE IEASUREMENTS [3-5] 

Small-signal admittance measurements can be used to analyze a variety of 

semi conductor devi ces. We di scuss here specHi cally the appli cat ions for 

analyzing the solar cells, namely measurement of the base land Seff and the 

separation of the emitter and the base current components. The small-signal 

measurements can be performed either at low-frequencies (w't « 1) or high 

frequencies (w't »1). The choice of a particular frequency range will depend 

on the W/l ratio. 

A. Low-frequency Ethod (LF) [3,4] 

Consider a n+/p/p+ BSF solar cell shown in Fig. 3(a). For a low-frequency 

signal with w'tn « 1, where 'tn is the minority-carrier electron lifetime in the 

p-type base, 1i=derive the expressioi~ for the small-signal quasi-neutral base 

capacitance CONB and conductance GDNB , respectively (see equations (B1~Fand 

(~~) in Append1x B). Equations (B1r aniF(B2) contii" four unknowns: CONB' 

GONB ' In' and Seff. The parameters CONB and GQNB are measured and' the 

cam5ination of (B1) and (B2) yields In and"Seff. 

and 

It is worthwhile to discuss in more detail a few special cases: 

A .1 long di ode: W > l 

For this case, (81) and (B2) yield a simple expression for C~~B 

2 

IF ..Jl Aqn i In ~ CQNB = kT 2N [exP(iT) - 1] AA 

IF _ 2CQNB 'tn - LF GQNB 

• 

and 'tn 

(2) 

(3) 

The base diffusion length is obl~ined eith~F from (2) or from (3). The details 

concerning the deduction of CONB and GQNB from the data are di~cussed in 

[3]. As an illustrative exampfe, we show fn Fig. 4 the measured CQNB(V) and 

313 
G~~B(V) plots for the p+/n device with NO~ = 1.25 x 1015cm-3• The analysis 

uSfng (3) or (3) gives Lp = 80 ~. 

• 2 A.2 BSF solar cell. Wp ~ Ln, WpOn/Ln < Seff < (On Wp) 

In this case, (B1) and (B2) are solved to yield Ln and Seff. FigurOe 5 

shows the measured C(V) and G(V) dependencies for a p+/n/n+ BSF solar cell from 

which we derive Lp = 500 ~ and Seff = 80 cm/sec. 

LF The method fails, however, for S ff «0 W/L~; in thh case 

GONB = KW /~n yields ~n' but Seff cannot be found. ~nother limitation exists 

fOr high P values of Seff » 0n/Wp; in this case both. (B1) and (82) are 

independent of Ln and Seff. 

The above difficulties with the LF method can be largely eliminated by the 

high-frequency approach. 

B. High-frequency _thod (HF) [5] 

We treat the high frequency method for two special cases. 

B.1 w~n> 10 and 0.1 ~ Wp/Ln ~ 1 

The small-signal admittance then is 

HF KOn w~n 1/2 . ~n 1/2 HF . HF 

YQNB = -L- [(-2-) + JW(2) ] = GQHB + Jw CQNB (4) 

n 

The important conclusion fran (4) is that the w1/ 2 dependence gives the range 

of 0.1 ~ Wp/Ln ~ 1 regard1~s of the value of Seff. To obtain the desirable 

parameters, we measure GONB vs w for w~ ~ 10 and extrapolate to lower 

frequencies to obtain an int~rcept wI with G~~B given by (B2). This gives 

2 W2 ° 1/2 ° 1 + (SeffLn

2

/ OnWp) L 2 = ( p n ) (..1!.) ---,.,~~~.:...-_.:;.... n wI Wp (O/Wp J + Seff (5) 

Equation (5) cannot be be solved for Ln and Seff except for the following 

cases: 

a) Seff < 0nWp/L~ < Dn/Wp 

( 2 )1/4 Ln = 2Wp20n/wI 

b) 0nW/L~ < Seff < 0n/Wp 

Seff = (wIOn/2)1/2 • 

(6) 

(7) 

The method is illustrated in Fig. 6 for the p~/n/n+ solar cell of Fig. 5. 

G~~ follows the w1/ 2 dependence for f ~ 104 Hz with the intercept at wI = 

314 
, .~'" ( '-sh 

:.\ 

'l 

. ',-'. 

: f 

" . 

'. 

(21t)103 1/sec. Us1ng (5) and combining w1th Seff ~ 80 cm/sec 

LF method, we have ~ ~ 503~, which is in excellent 

L ~ 500 ~ using the Lf' method alone. p . 

obtai ned by the 

agreement with 

Even though the general solution (5) cannot give Land Seff exactly, and 

only one of the parameters is obtain~ either fran (6) or fran (7), the method 

h very us~ful b'T"Se: (1) the GON vs w1/ 2 dependence shows. that L > W; 

(11) the G N vs w dependence i n<ll cates that the emi tter cont rl but 1 on to 

the conduct~nce (and dark current) is negligible (this point is discussed 

further below); (lii) the SSCD for L > W yields an accurate value of Seff only 

and using this value in (5) we obta1n an accurate value for L. The combination 

of these two methods gives Land Seff for practically any cell. 

The sensitivity of the HF method to t!m: emitW com!lW'ent GH~E of the 

total measured quasi-neutral conducwce G ~ = G NB + G N is ~xPlored in 

Fig. 7. The time constant 'tE of GQNE is ~1Ven b~ eithe~ ihe Auger lifetime 

'tA in the heavily doped emitter, or by the combination of 'tA and the 

transit t1me [6]. H~he emitter time constant is much shorter than the base 

1 ~ f et i me, thus HrQNE- HF is ftffquency i ndepe~dent uP. to f ~ tV 'tE ~? 1/ 'tB • 

Flgure 7 shows GQN =liQNB + GONE for an arbltrary cholce of GONE/GONB. The 

reglon far. away from the Rnee can be fitted to Hr straigllt nne with 

G a w1/m, where m > 2. .~ice, however, that wy for G NE > Po is close to the 

1 ntercept value wI for GONE = O. Furthermore, s 1 nce e a w} 4, a H~a 11 Rfror 

ln wI gives O&y a negl1g1ble error in L. For example, for GQNE = GQNB , 

wI ~ 1.5 wI (GQNE = 0), th1s gives an error in L of only about 1~. 

B.2 w'tn > 10, Wp/Ln ~ 0.1 

The condition W /Ln ~ 0.1 may apply for the thin cells (50 - 100 1JI11) 

with a very long lifet~me. For this case we have 

(iW:/3) + Seff (On + SeffWp) 

(On + SeffWp)2 

For BSFce 11 s, Seff < Dn/Wp and ( 8) yields 

(8) 

HF 2( 3 GQN ~ K[w W / 3Dn) + Seff] • (9) 

Figure 8 shows the G~~ vs w dependence for a 8 ~ thick epitaxial n-type 

layer w1th dop1ng dens1ty ~DD = 5 x 1015 cm-3• The w2 de~endence for f> 1.5 

MHz immediately gives Lp > lOW> 80 IIJI and al so Seff « W W3/3Dn « 1.2 x 103 

cm/sec. More accurate analysis of the knee reg10n below the w2 dependence 

gives Seff ~ 120 cm/sec and using th1s value 1n (B1) gives more accurate 

Lp := 90 IJIII. 

Note, that the HF method for L > 10 W gives only the lower l1m1t of Land 

the upper l1m1t of Seff. A comb1nat10n of this techn1que with either the LF 

method or the SCCD can give more accurate results. 

315 
8.3 w~ .... 10 , W /l .. " 0.1 n p n 

For the previ o"~ two 2speci al cases we have obtai ned G~~B a }/2 for 

W /l ~ 0.1 and GDN8 a w for W /In ~ O.lAF Obviously, there flas to be an 

iRtePmedhte range fbr Wp'/ln .... o.f where G N8 a J1 ( < m ~ 2). One possible 

approach here ~~ to oHtain Seff from th~ SCCO method and then fit the 

theoretical GoN(Seff' In) with the experiment. A very reasonable 

approximation of ~n can be made, however, by realizing that the GQN vs w 

dependence begins to increase from its low-frequency value for 

W = wI = 10/~n [5].lF Thus, ~n = 10/wl , where w1HFcan be app·roximated as the 

intercept of the GQN line wlth the extrapolated GQN a w

m dependence. 

IV. REGIONAL MAl YSIS OF SOLAR CELLS 

It is important to analyze the contributions of each region of the cell to 

the total dark current (or Voc ). Such an analysis is demonstrated here for a 

n+/p/p+ 8SF solar cell shown in Fig. 3(b). The analysis is based on the 

determination of the base parameters ~n and Seff by one of the methods 

discussed in Section II and III. This is sufficient to calculate the profile 

of the mi nori ty elect rons in the base. The recombi nat ion losses in the base 

are given by (82) and the recombination losses in the p+ -8SF portion of the 

base are 

(10) 

The SCR recombination current ISCR can be determined graphically [7] and the 

emitter contribution IE is obtained by realizing that the total dark current is 

+ 10 = I E + I SCR + I B + 18 ( 11) 

For example,such analysis of the p+ /n/n+ BSF cell of Fig. 5 gave [4]: 

l., = 500 I-II11t Seff = 80 cm/sec, 18 = 0.8 10 , ISCR = 0.2 10 , IE« 10 , 

18 « 10 • 

V. SUMMARY 

Table I gives a summary of results for a number of different cells. A 

comparison of results obtained by different methods, shown for some cells, 

demonstrates very good agreement. Notice, in particular, the last cell in 

Table I, which 1"5 a thin cell (Wbase - 92 ~) with In »WB• For this cell, 

the SCCO method gives Seff- = 180. cm/sec, but the metho~ is inse~sitive to In 

(see Fi g. 2( a) ) • We have to combi ne the SCCD method W1 th the h, gh-frequency 

. small-signal admittance method and then use (5) with Seff obtained from the 

SCCO method to determine In. 

The main conclusion of this study is that the SCCO method and the sma1lsignal admittance methods yield a rapid and reliable determination of the base 

316 
parameters. They also allow the detenmintion of the relative importance of the 

base and the emitter regions with regard to cell efficiency. Identification of 

the region limiting the efficiency is a key to an informed cell design. 

Acknowledgement: This work was supported in part by NSF Grant No. ECS-8203091. 

APPENDIX A 

To obtain the base diffusion length l and effective surface recombination 

velocity Seff at the back contact we have to solve the following two equations 

for the first-mode decay [2]: 

1 + (OpKI/lpSeff )cot (WQNBKI/lp) = 0 (AI) 

. qopP(O,O-)Kl cot(KIWQNB/lp)- (OpKI/lpSeff) 

1 (0) = - S l 2 2 • 

1 P ('&p/2Kl) + (WQNB/2Seff )[cosec (K1 WQNB/lp )](A2) 

Here Kl = (-1 - Sl'&p)I/2~ SI = -1/'&01' WQNB is the width of the quasi-neutral 

base, and P(O, 0 ) = (ni/NOO)[exp(qV/kT) - 1] where V is the steady forward 

voltage applied for t < O. 

APPENDIX B 

The small-signal quasi~neutral base capacitance and conductance are given 

by [4]: 

+ '& 

n 

where K = Aq(q/kT)(ni/NAA)exp[(qV/kT) - I]. 

317 

(Bl) 

(B2) 
Table I: 

CELL 

n+ /p/p+ 

BSF 

n+ /p/p+ 

n+ /p/p+ 

BSF 

* obtained from G~~ 

t obtained from GLF 

ON 

Summary of results for some typical solar cells. 

The values for Lbase and Seff were obtained using the SSCD method, unless mar~ed otherwise 

Pbase 

(oem) 

10 

10 

10 

0.15 

10 

10 

227 

103 

360 

295 

320 

92 

318 

454 

450* 

250 

512 

100 

503 * 

soot 

",,(;00* 

Seff 

(cm/sec) 

105 

2.9x103 

2x105 

.... 180 
REFERENCES 

1. J. H. Reynolds and A. Meulenberg, Jr., J. Appl. Phys., 45, 2582 (1974); 

A. Azim Khan, J. A. Wool am, and A. M. Hermann, Appl. Phys. COl1l11un., 1" 

17(1982) • 

2. T. W. Jung, F. A. Lindholm, and A. Neugroschel, IEEE Trans. Electron 

Devices, ED-31, 588(1984). 

3. A. Neugroschel, P. J. Chen, S. C. Pao, and F. A. Lindholm, IEEE Trans. 

Electron Devices, ED-25, 485(1978). 

4. A. Neugroschel, IEEE Trans. Electron Devices, ED-28, 108(1981). 

5. F. N. Gonzalez, A. Neugroschel, IEEE Trans. Electron Devices, ED-31 , 413(1984). 

6. M. A. Shibib, F. A. Lindholm, and F. Therez, IEEE Trans. Electron Devices, 

ED-26, 959(1979). 

7. A. Neugroschel, F. A. Lindholm, and C. T. Sah, IEEE Trans. Electron 

Devices, ED-24, 662~1977). 

319 
v 

(.) 

Fig. 1. (a) Electronic circuit used in the SeeD method. The switching time 

of a power MOST is less than 10Q nsec • 

• ,------4 

(b) 

(b) Schematic illustration of the current decay displayed on a log 

scale. 

320 
(c) Expe rimental current decay for a n+ /p~ BSF sol <1r cell 

(Pb = 0.3 Cc~t Wb = 367 ~t 'td = 6.4 ~ect L = 180 ~t 

Sef~s~ 1.3 x W crn/~~~). The vertical scale is loB rnA/division. 

321 
300 

240 

1 110 

! 

J 120 

10 

0 

0 100 200 300 500 

T("Me) 

(a) 

Fi g. 2. (a) Plot of S ff vs 't for a thin n+ /p/p+ BSF solar cell 

(Pbase '" 10 &!m Wbase '" 92 1JIll). 

20 

I I I 

1. 

12 

i f1d-Upeec - .!-

l- e 

V 

4 

0 I I I 

0 2.51(104 51(104 7.51(104 105 

Ie" (cmlMC) 

(1)>) 

(b) Plot of 't vs Seff for a thi ck n+ /p/p+ BSF solar cell (Pbase '" 

0.15 Qcm, Wbase '" 295 ~). 

322 
~ '" I i n+ I I 

~ I 

ORIGINAL PAot'lit 

OF POOR QUALITY. 

P 

ba •• 

.1 - 1+ 

v 

(8) 

I I 

I I p+ I 

I lba .. 

OHMIC 

CO NTACT , 

'--

I = IE + ISCA + ~ i'N(X)dX + 1.+ 

o 

X.o 

(b) 

Fig. 3 (a) Schematic diagram of an n+/p/p+ BSF solar cell. 

(b) Qualitative sketches of minority-carrier distributions in the 

dark. 

323 
Fig. 4 

164 103 

- 105 IJ.. 

- 102~ 

i(: I " U I!, Gg 

- ~ N 

/If 

l!) 

10-6 /i CQN 

(b) 10' 

I 

I~ i 

167 i 

i 

v- -IJ.. 

..s 

168 

u , 

I 

I 

0.6 0.65 

V (Volts) 

10-9 

0 05 0.6 0.7 

V (Volts) 

Measured conductance and cagacl tance vs forward-bl as V for along ;;p+ /n 

diode with NO~ = 1'.25 x'101 cm-3 and Wbase <= 250 IJ1l (from Ref. (3]). 

324 
Fig. 5 

10° 107 

- / - f. I&. 

- - / u 

CJ / 

10' //GSCR 10-8 1/ 

10-2 /1 

~/ 

108 

J GQN 

-3 10 

0.1 0.2 0.6 0.9 

Measured capacitance and conductance YS forward bias for a p+/n/n+ BSF 

solar cell (from Ref. [4]). Here, NO~ ::: 6 x 1014 cm3, Wbase ::: 320 

~. 

325 
iii 

! 

ILZ 

:z:a 

<:J 10 

10 103 104 

Frequency (Hz) 

Fig. 6. Measured high frequency conductance G~~ vs freqency for the p+ /n/n+ 

solar cell of Fig. 5. . The conductance was measured at forward bias 

V = O~5 V and shows w1/ 2 dependence. 

326 
i 10 

& 

i GOHf/GoHs- 3 

-e 

C 

ILZ 

- 1 :Z:cf 

0.5 

1.0 0 

1~ 1~ 

0) (Arbitrary Scale) 

HF HF HF Fi 9 • 7. Plot of a GQN = GQNB + GQNE 0, 0.5, 1, 3. 

for di fferent rat; os of 

327 
-o 

~ 

E 

-

au 

CJ 

Z 

C 

... 

CJ 

!:) 

Q 

1 

~ Y-SeO mY 

CJ 0.1 

10 

FREQUENCY (Hz) 

Fig., Frequency dependence of .high-frequency conductance for a thi n (8 !.1111~ 

n-type epitaxial layer (from Ref. [5]). The conductance follows w 

dependence. 

328 
DISCUSSIO. 

YO. IOOS: You .. de one com.ent I would to talk about, and that wal the diffusion 1enath -- if "it i. auch 1arser then the width of the cell, it cannot be .. asured by any other .. ani. .ow, that il not quite correct. 

There is another .. ans to do that, and that il with the EBIC or 

aap1itude-aodu1ated electron be __ i aealurins the phale shift will indeed 

sive you the 1ifeti .. , and therefore the diffusion lensth -- also in the 

case where the ratio of width over diffusion 1ensth is very small. 

329 
SESSION V 

MODELING 

R. Schwartz, Chairman 
N85-31636·. 

Current Status or One and Two-Dimensional Numerical Models: 

Succeues and LImitations 

by R. J. Schwartz, J. L. Gray, and M. S. Lundstrom 

Purdue University 

School of Electrical Engineering 

West Lafayette, IN 47g07 

Abstract 

tal 

The capabilities of one and two-dimensional numerical solar cell modeling programs 

(SCAPID and SCAP2D) are described. The occasions when a two-dimensional model is 

required are discussed. The application of the models to design, analysis, and prediction 

are presented along with a discussion of problem areas for solar cell modeling. 

Introduction 

Accurate numerical models for single crystal silicon solar cells have proven to be very 

reliable in the simulation of the performance of these cells. These models have proven to be 

extremely useful in: the interpretation of experimental measurements; the identification of 

processes which limit cell performance; the prediction of benefits which will result from 

design and materials changes; the comparison of various cell designs; and the prediction of 

efficiencies which may eventually be obtained in silicon solar cells as various technological 

barriers are overcome. 

. The capabilities of a one-dimensional (SCAPID) and a two-dimensional model 

(SCAP2D) are described and examples of their use for each of the above purposes are 

given. 1-3 It will be shown that there are circumstances under which cells which appear to 

be one-dimensional require a two-dimensional model to properly simulate their behavior. 

As cells become more efficient the requirements on the accuracy of the physics used in 

the model become more stringent. Effects which are of little significance in poor or 

moderately good cells can take on major significance in high efficiency cells. A number of 

problem areas which are of concern in the modeling of high efficiency cells are discussed. 

These include heavy doping effects, metal-semiconductor boundary con.ditions, minority carrier mobilities, high injection lifetimes, and carrier-carrier scattering. Each of these may 

liave a major impact on the performance of the cell under certai~ operating conditions. 

The Model 

Physical E8'ecte or Importance 

One of the major advanta.ge~ of a numerical model is that it affords one the opportunity to include the very large number of'physical effects which may be acting simultaneously 

within a solar cell. The complexity of the phenomena and their interactions with each other 

preclude analytic solutions in anything except highly idealized situations, which are not 

indicative of actual cells or operating conditions. An attempt has been made in the formulation of SCAPID and SCAP2D to include as many of the physical effects which are known 

to influence cell performance as possible and to do this in a manner which represents our 

33l 
present knowledge of these effects. One of the goals in writing these codes was to have 

them be sufficiently accurate in their representations so that they could be used in a predictive mode. This is possible only if all of the pertinent physical effects are included. 

In those cases where the physics is questionable, we have attempted to include options 

which allow one to choose between various models. For example, in the case of heavy doping effects, one is able to choose between the models of Slotboom, Lanyon-Tuft, and 

Mahan, or to supply a subroutine of one's own choosing. . 

We have attempted to choose materials parameters which in our. estimation are the 

most reliable. These materials parameters are used as default values. The user can easily 

change these parameters to values that he views as more reasonable. 

The following physical effects are included in the codes: hole and electron mobilities, 

including their doping and temperature dependencies; heavy doping effects, using the formulation of Lundstrom, Schwartz, and Gray; absorption coefficients, including their temperature. dependence; recombination, including Auger, Hall-Shockley-Read, and surface 

recombination. Surface recombination is handled through the specification of the surface 

recombination velocity. In the case of SCAP2D, the effects of surface potentials are also 

included. 

Semiconductor Equations 

The programs perform' a full simultaneous numerical solution of the two continuity 

equations and Poisson's equation subject to the boundary conditions appropriate to one and 

two-dimensional cells. The equations are formulated as shown in equations 1-3. 

'VeJp = q(G-R), 

'VeJn = q(R-G). 

The generation term in equations 2 and 3 are given by 00 

G(x) = 10 4Jll'e-QXd~ 

and the recombination term is given by equations 5, 6 and 7. 

Tno 

~ = ----(-N~D-+-N-A-)-

1 + ------- Nc 

The hole and electron current densities which appear in equations 2 and 3 are given by 

332 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 
J p = -qpppVvp-kTppVp 

I n = -qpnnVvn +kTpn Vn 

~G v = v-(I-,),)- p q 

. ~G 

vn = v+')'-- . q 

(8) 

(g) 

.(10) 

(11) 

where v p and v n are the effective potentials defined in equations 10 and 11 and ~G and ')' 

are parameters which account for variations in the band structure, such as density of states 

and band gap, and account for Fermi-Dirac statistics. 

No low injection assumptions are made. The equations are solved from contact to contact with appropriate boundary conditions so that the solutions are valid for all ranges of 

operation and include minority and majority carrier flow. The latter places some restrictions on the CPU word size required for solution. 

These codes have been extensively tested Cor accuracy by comparing the results of 

their predictions with experimental results obtained on very carefully and extensively 

characterized cells for a wide range of cell design,s and operating conditions. The agreement 

has been such that a high degree oC confidence has been developed in results computed 

using these codes. 

Code Description 

Figure 1 is a block diagram oC the structure oC SCAPID and SCAP2D. The operator 

must supply information about the materials parameters, a description oC the device to be 

analyzed, the type oC analysis which he wishes to perform, and the spectrum, if appropriate. 

He also can, iC he wishes, control some oC the details of the numerical solution; the amount 

oC inCormation supplied while the program is converging to an answer and how the output 

information will be stored or displayed. 

The results of the computation are presented in printed summary form and the 

detailed results oC the calculation are stored on magnetic tape. A separate plotting routine 

is used to access the inCormation on tape and to display the appropriate parameters. The 

plotting capability is one of the most valuable features of the code, in that it allows one to 

effectively have a microscopic view of most of the parameters of interest in the interior of 

the cell under operating conditions. We will show some of the available graphical output as 

we discuss the capabilities oC the code. Table I shows the input control offered to the 

operator. In every case deCault parameters are specified if the operator chooses not to supply a parameter. 

Table IT contains a listing oCplots which are available through the plotting program. 

In this case the operator specifies the type oC plot which is required and the region of the 

cell for which he desires that plot. Most of the figures which follow were obtained directly 

·from this plotting routine. 

In addition to the reliability of the output, the utility of codes of this type will depend 

on their ease oC use and efficiency of computation. For example, in a design mode, it is 

333 
Cell 

DeKI'iption 

Typeot ro- An.IY8ia 

. Print Spectral Soh·e for 

Choice n,p,Vand Results 

requested type 

of analysis 

Materials f-- Parameters r---

Optical Filters 

and Reflection I--

Store Results Plotting 

on Tape for Future Programs 

Use Numerical Solution I Control Parameters 10-

, 

Output Inlormation Type otPlot 

and Range Control 

Figure I Block Diagram of the Structure of SCAPID and SCAP2D 

Table I - Input Parameters 

Device Description 

Doping Profiles 

Step junction 

Erfc (Ns'x j) 

Experimental Profile 

SUPREMn 

Dimensions 

Materials Parameters 

Lifetime (T and energy) 

Surface Recombination 

Auger . 

Bandgap narrowin~t 

Slotboom 

Mahan 

Lanyon-Tuft 

User supplied 

334 

Spectral Choices 

AMO 

AM 1.0 

AM 1.5 direct &, global 

Monochromatic 

Uniform generation 

User supplied 

Optical Filters &, Reflection 

Filter (Ge, Si, Si02, GaAs) 

Back surface reflector 

Types of Analysis 

Dark I-V 

Illuminated I-V 

Solar Cell 

Spectral Response 

Plots 
I 

I 

Table n - Plotting Options 

Carrier concentration 

Hole and electron current densities 

Change in potential (from equilibrium) 

Doping density 

Energy band diagram 

Electric field 

Hole and electron quasi-electric fields 

Effective fields (electric plus quasi-elect.ric) 

for holes and electrons 

Optical generation 

Hole current density and components 

Electron current density and components 

Mobility 

Lifetime 

Ratio of nie/nio 

Potential 

Recombination rate 

Charge density 

Excess carrier concentration 

advantageous to be able to make mult.iple runs in a rea.sonable lengt.h of time and at reasonable cost. While SCAPID can be run effectively on nearly any mainframe computer (a 

typical run on a CDC 6600 requires 100-300 CPU seconds)! SCAP2D requires a very fast 

machine with a large amount of a.ctual or virtual memory. On a Cyber 205, 300 CPU 

seconds are required for a typical run. 

Situations Requiring Two-Dimensional Analysis 

In many situations a one-dimensional simulation is quite adequate and there is no need 

to use the more complex and expensive two-dimensional simulation. On the other hand, 

there are a number of situations which only a two-dimensional simulation will suffice. 

Some of the situations which require two-dimensional analysis are quite obvious, while 

others appear to be one-dimensional in nature, but, in fact, require a two-dimensional solution for proper description of the cell performance. Most of the cell structures which have 

been proposed as high efficiency silicon cells fall into the obviously two-dimensional analysis 

category. Among these structures are the Interdigitated Back Contact cell, the Vertical 

Multi-Junct.ion cell, the Etched Multiple Vertical Junction cell, the Polka Dot cell, and the 

Grating cell. As an example of the use of SCAP2D in the analysis of these two-dimensional 

cells, we show figures 2 through 4 for an mc cell. In Figure 2 we show the total short circuit current flow under one sun .. conditions. In Figures 3 and 4 we show the majority and 

minority carrier flows for this same cell operating under the same condition. 

Less obvious applications of the two-dimensional code are shown in Figures 5 through 

6 in which a conventional solar cell has been analyzed. In Figure 5 we show the potential 

distribution along the emitter from a point half way between the grid lines up to the grid 

lines under open circuit conditions. This figure illustrates that there is a lateral voltage 

drop along the emitter, even under open circuit conditions, as a result of the current which 

is injected in the vicinity of the grid line. Figure 6 shows the circulating currents which 

exists in the vicinity of the grid line. 

335 
" VI 

C 

0 

L 

U 

.... 

e 

v-

:1' 

Figure 2 

" 

~ 0 

L 

U 

.... 

e 

v-

:1' 

n+ contact p+ contact 

300.0 . 1 \ \-.....--./' ? , f r 

l \ '- ~ 

-,., "" ~ f t 

M.O 

.~ \r " ... ... ~ ,JI I' ,. t 

• .. • " • .. " • • .. 1 •• 0-

• .. • " • .. • • .. • 

• .. • " .. .. • • .. .. U!.o.O 

.. .. • " .. .. " • .. .. 

.. " " .. .. .. " • .. .. 60.00 

.. !I .. .. .. .. " • .. .. 

" " .. .. .. • .. " • .. 0.000 

0.000 25.00 50.00 15.00 100.0 125.0 

)( (micl"ons) 

Total Short Circuit Current for an mc Cell 1 Sun AM1.0 

300.0 1 

2'10.0 1 

! 

! 

1 •• 0 

! 

! 

1210.0 

! 

1 

60.00 

1 

! 

0.000 

0.000 

p+ contact 

t \ ~"- '" """ 

~ \ \ \ \ \ 

1 ~ \ \ ~ ~ 

1 1 1 1 1 ~ 

! ! 1 1 1 1 

! ! ! ! ! 1 

! 1 1 1 1 1 

1 1 1 1 1 ! 

1 ! ! ! ! 1 

! ! .! L ! ! 

25.00 50.00 75.00 

)( (micl"ons) 

... .. \, \ 

~ ~ 

1 1 

! ! 

1 1 

1 1 

1 1 

! ! 

! ! 

100.0 

.. 

.&. 

~ 

L 

1 

1 

1 

1 

! 

! 

125.0 

Figure 3 Majority Carrier Current Flow for the Cell of Figure 2 

336 
"II I~L PAG . QUALITY 

n+ contact 

,. ~ /' /'/I r T T r 

r f , , / ! l T T r .... . 0 

t r r T f f T T r r 

" r r r T T T ! T T T 

~ T T T r rT f f r T 

t • . O 

L 

T f f f iT f i T i 

f T f T T T T T i T 

u 

... 

Ii 

.., t • . O 

:::p 

T T Ti T i i T T i 

".00 

T 1 iii T T T T T 

t t T T t t t t T T 

0 .000 

0 .000 25.00 50 .00 75.00 to .0 125.0 

X (microns) 

Figure 4 Minority arrier urrent Flow for the Cell of Figure 2 

• 

Figure 5 Pot nti 1 i tributi n in he Emitter of a ooveotiooal Solar Cell Operating at 

400 suns. 

337 
1.000 

-~~ "-.. "- ~ '\ \ ~ .;t .-'f 

.• 00·' 

~ .;t ~ 

~--"'-"-".\.\ ., ~ ,.t -A __ "-..'\.'\. \ \ 

., )I .;t ..,A -....,. , \. \ \ \ " 

~ .1000 

0 t JI )I /I ...... '\. \ \ \ \ L 

U 

.... t t ,. JI e \ \ \ \ \ .,. v .'1000 • ::J' t t t t • l. 1 1 1 1 

t t t t • '" ~ ~. ~ ~ .eooo· 

t t t t • '" '" '" '" '" 

• • • • • + .. .. .. .. 0.000 

O.O~ 6.000 le.OO 11.00 1!'f.00 30.00 

Grid x (micl"ons) 

Line 

Figure 6 Circulating Current in the Vicinity of a Grid Line for a Conventional Solar Cell 

An even less obvious problem with one-dimensional simulation occurs when one tries to 

properly model the front surface of a conventional cell. This surface is composed of a 

Si02-Si interface and a metal-semiconductor contact. In a one-dimensional simulation, one 

is forced to aggregate the two effects with some equivalent front surface recombination velocity! SF' Figure 7 illustrates the difficulty with this approach. Under short-circuit conditions the proper value of SF is equal to the surface recombination velocity of the Si02-Si 

interface. However, near open circuit conditions, the proper value of SF may be 3 to 4 orders of magnitude larger. This is a result of the fact that the metal semiconductor contact 

may be a very effective recombination site for minority carriers. It. is particularly important 

as the operating voltage of the cell increases. For proper operation of a one-dimensional 

code, the front surface recombination velocity should be a function of operating condition. 

The two-dimensional code does not have this problem, since the surface recombination velocity at the Si02-Si interface and the metal semiconductor interface are specified separately, 

and the recombination along the entire surface is properly accounted for under all operating 

conditions. 

At high operating condition~, such as are found in concentrator solar cells, even the 

conventional cell behaves in a two-dimensional fashion and must be modeled using the 

two-dimensional code. Minority carrier current flow for a conventional cell operating at 800 

suns is shown in Figure 8. If this cell is modeled using the one-dimensional code under 

these operating conditions, serious errors are encountered in the computation of the fill factor which can not be compensated for by including an external series resistance in the 

model; as the effect is nonlinear. 

338 
" U 

II 

U\ 

, 

e 

u 

..., 

'La.. 

en 

10" 

S 

103 S 

102 S 

10' 

S 

ORIGINAL PAGE"fS 

OF. POOR QUALITY 

- 10" CM.lS.C 

II 103 CM.lSK 

II 100 CM.lsec 

-10 CMoIsec 

339 
Modes of Utilization" . 

As we mentioned previ9usly, a carefully prepared solar cell model is useful in a.number 

of modes. In this section we will discuss the use of SCAP.ID, and SCAP2D a;; 3; desIgn too~, 

a sensitivity analysis tool, an aid in the analysis of experImental da~a,. an aId m the prOVIsion of insight into the operation of the cell, and, final~y, ~s a predIctIve tool for. the comparison of proposed cell designs and as a means of p,roJ~ctmg performance as varIOUS technological barriers are removed. For the sake of contmUl~y, we .have ch?s~n to use t~e Sandia high concentration cell operating at 1 sun as a base lme desl~. ThIS, IS a c~ll whIch has 

exhibited 18% conversion efficiency at one sun, and 20% converSIOn efficIency m the 50-100 

sun range for an AM 1.0 spectrum. 

Design 

As a simple example we show, in Table ill, the effects of va~iations in the base doping 

about the present design doping of 2.29 x 1016, on the performance of this cell. We see that 

the present base doping is nearly optimum for the design parameters used in the other 

parts of the cell. 

Tablem 

Solar Oell Performance Dependence on Base Doping " AM 1.0 (one sun) . 

Base D~:Fing Voc ~c F.F. Efficiency 

cm volts rna cm2 %" 

5 x 1015 .634 35.1 .828 18.35 

1 x 1016 .640 34.8 .833 18.46 

2.29 x 1016 .649 34.4 .836 18.55 

1 x 1017 .656 33.3 .838 18.21 

5 x 1017 .650 30.2 .836 16.37 

Sensitivity Analysis 

'> 

By utilizing a computer code such as SUPREM to simulate fabrication conditions one 

can model the sensitivity of device performance to fabrication parameters. Here, as an 

extreme case, we examine the effects of changes in the emitter doping profile on cell performance. The Sandia cell was simulated using the two emitter profiles shown in Figure g. In 

Table N, a comparison of these simulations is shown. Note that the erfc emitter profile 

simulation predicts a higher Voc' This is due to the lower net recombination hi the emitter 

as compared to the SUPREM n emitter profile simulation, as shown in Figure 10. Recombination is higher in the SUPREM n emitter because the doping is higher over most of the 

emitter volume, and therefore Auger recombination is correspondingly higher also. . ' 

If the results of a process 'simulation program such 'as SUPREM are coupled with 

SCAPID or SCAP2D as shown above the·sensitivity of the cell to process variations can be 

readily esta.blished. 

34.0 
en 

~ 

U 

0:: 

W 

£L 

a: 

z 

I 

0 

z 

1021 

1020 

" '\. 

10 19 

10 18 

10 17 

1016 

\ 

\ 

\ 

\ 

\ 

Erfc \ 

\ 

\ 

ORIGINAL PAGE' Iti" 

OF. POOR QUALITY 

10 15+-______ ~------~----.--~----~~-----_+ I I 10 15 

0.000 .200 4-00 .600 .800 1.000 DISTANCE IN MICR~NS 

Figure g Emitter Doping Profiles as Determined by SUPREM n and Complimentary Error 

Function 

0,000 .::'00 .1100 .finO 

ITl .2000 -I----.....L---·----... - J -.----. " - I 

"noo 

I. 

) .noo 

1.UUU 

C\J 

o 

..... 

x 

en 

~ .1500 

U Erfc 

0:::: 

. W 

a... 

w 

.f- .1000 

a: 

0:: 

z 

0 

...... 

fa: .0500 z 

I 

/ 

/ 

SUPREM .",,----------------- / . 

Erfc ...... ------------------• 

:z 

a 

....... 

fa: 

z 

,'750 ;n 

::E 

a 

u 

w 

0:::: 

...J ,SODa: 

fa 

fLL 

a 

,250~ 

...... ...... m f- ~ U 

o a: 

U 0:::: 

W LL 

0::::0 .OOOO·-fio.---~-.--.;:..---,---.----.------.------'- 0.000 

0,000 .200 ,4-00 .600 .800 1.000 DISTANCE IN MICRQNS 

Figure 10 Emitter Recombination for the Two Doping Profiles Shown in Figure g 

341 
Table IV 

Dependence of cell performance on emitter doping profile . AM 1.0 (one sun) 

Type of Profile Voe i

e FF Efficiency 

volts ma cm2 % 

Erfc .648 34.3 .836 18.6 

SUPREMll .632 33.9 .833 17.75 

Analysis 

It is possible, by adjusting the parameters entered into the code, to obtain a fit 

between the model generated results and experimental dark I-V, solar cell, and spectral 

response curves. If this fit can be obtained for a single set of parameters, then one has a 

reasonable expectation that these are the correct parameters describing this device. 

Insight 

With the ability to observe most of the parameters of interest as a function of position 

and operating conditions anywhere within the cell, it is possible to achieve a great deal of 

insight into the limiting factors on any cell design. Examination of the model for·.the 20% 

Sandia. cell very quickly establishes that the cell appears to be emitter limited, and, in fact, . 

that further efforts in improving the performance of the cell should be devoted to reduction 

of the metal-semiconductor contact recombination and in reducing the volume of the 

heavily doped emitter. 

Prediction 

Potentially one of the most valuable, and also one of the most risky, uses of the 

numerical models is as a predictive tool. The models have already been shown to be quite relh~,ble in comparing the relative merits of different cell designs. One particularly attractive way to utilize the code is to use it to identify limiting phenomenon in a particular cell 

design and then to remove that limitation and observe the effect on cell performance. In 

this fashion, one can predict benefits which will accrue through various advances in technology, and, in fad, can make some reasonable est.imates of the ultimate performance of silicon single crystal solar cells. This latter use of the code is particularly risky since as the 

performance of the cell improves, physical effects which may have been insignificant in their 

effect on cell performance before, may suddenly become the dominant limitation. 

Problem Areas 

There are a number of areas in which there is concern about existing solar cell models 

either because the physics is not well u~derstood, available data is thought to be unreliable, 

or because the effect has not been include in the model. These areas of concern are discussed below. 

342 
Heavy Doping Eft'ects 

There is a controversy. over the origins and magnitude of heavy doping effects. There 

is a great deal of scatter in the measured effective band ga.p narrowing, particularly in the 

very heavily doped samples where we have our major concern. In order to alleviate . this 

situation somewhat, we have provided the operator with the option to choose between most 

of the popular band gap narrowing models. This remains an area of major concern and is 

probably the least reliable area in the modeling of silicon solar cells. 

Auger Recombination 

Some uncertainty exists about the reliability of published Auger coefficients. At least 

two groups (Sandia and General Electric) have indicated that published Auger coefficients 

may be too large. 

Minority Carrier Mobility 

Reliable measurements of minority carrier mobility do not exist. Various authors have 

proposed that the minority carrier mobility is larger, smaller, and the same as the majority 

carrier mobilities of the same type carrier. As a consequence, SCAPID and SCAP2D 

assume that the minority carrier mobilities for electrons are the same as they would be if 

electrons were majority carriers. A similar assumption is made for holes. 

Metal-Semiconductor Contacts 

In well designed high efficiency solar cells, the metal semiconductor contact limits the 

open-circuit voltage. The removal of this high dark current source, through the use of tunneling contacts or through the reduction of the metal-semiconductor contact area, has 

already demonstrated a significant improvement in open-circuit voltage. Further advances 

in this area may well employheterojunction structures in addition to the present tunneling 

structures. SCAPID and SCAP2D allow for specification of a finite minority carrier surface 

recombination velocity to model this effect. 

Doping Profiles 

We have already seen that device perfOl'mance can be a strong fu.nction of the shape of 

the emitter doping profile. SCAPID and SCAP2D a.llow for the use of a complimentary 

error function, a computed profile based on the Fair diffusion model for phosphorus, doping 

profiles obtained from a process simulation program such as 'SUPREM, or experimental 

data. The use of data from SIMS measurements has the problem that it includes the total imp~rity concentration not just the electricaUy active dopants. If any precipitation is 

present in the highly doped region, SIMS will overestimate the amount of active dopant. 

Spreading resistance measurements are a measure of the free carrier concentration. Near 

the depletion region this can lead to significant errors in the doping prome if the spreading 

resistance profile is interpretated as being the same as the doping profile. 

~. 

343 
Spectral Response 

Spectral response meas~rements are par~icu!arly usef~l for obtaining informa~ion abo'-!t 

the base lifetime and the surface recombmatIOn velocity. However, some difficulty IS 

experienced in matching long wavelength response with computed response. This difficulty 

has been traced to the fact that small changes in device temperature can lead to large 

changes in the long wavelength response as a result of changes in the absor.ption coefficients 

due to a shift in the band edge. 

In order the determine the surface recombination velocity of the Si02-Si interface, it is 

also highly desirable to have spectral response measurements in the very high absorption 

regime of .35 - .4 pm. Accurate measurements of the internal quantum efficiencies are 

difficult to obtain at these wavelengths. . 

Eft'ects of Band Gap Narrowing on Long Wave Length Absorption CoefBcients 

At the present time no corrections for the effect of band gap narrowing are made to 

the absorption coefficients. 

Carrier-Carrier Scattering 

Carrier-carrier scattering can be a significant effect in high concentration solar cells, 

and will become a significant effect in one sun solar cells as the efficiency is increased. 

High Injection Lifetime 

J\t the present ~ime very little data is aV!lil~ble on ~aj?ritr ca~rier lifetime. A typical modelIng approach IS to assume that the majority carrier hfetime IS the same as minority 

carrier lifetime. This seems to give reasonably good agreement with cell performance under 

high injection conditions, but direct measurement of the high injection lifetime would be 

highly desirable. . 

Conclusions 

. One ~nd ~wo-dimens.ional de,!i~e. models h.ave been qU.ite. successfully employed as an 

aid to deSign, mterpretatIon, sensitivity analysIs, and predictIOn. However, the predictive 

capability of any device code is only as good as the physics which is modeled and the data. 

which is supplied; If further improvements are to be made in the performance of single crystal silicon solar cells, careful attention will have to be paid to both of these areas and a 

great deal of effort will have to be devoted to measurement techniques which will allow the 

independent determination of the parameters which must be supplied to the device code. 

Acknowledgment 

. SCAPID and SCAP2D were developed under the sponsorship of Sandia National Laboratories on contract number 52-5675. 

344 
1. 

2. 

3. 

RerereDeea 

M. S. Lundstrom R.' J. Schwartz, "Annual R~port on Interdigitated Back Contact 

Solar Cells," TR-EE 80-14, School of Electrical Engineering, Purdue University, West 

Lafayette, IN. _ 

R. J. Schwartz, M. S. Lundstrom, J. L. Gray, "Annual Report on High Intensity Solar 

Cells, TR-EE 82-5, School of Electrical Engineering, Purdue University, West Lafayette, IN. '. ' 

R. J. Schwartz, J. L. Gray, M. S. Lundstrom, "Report on High Intensity Solar Cells," 

TR-EE 83-21, School of Electrical Engineering, Purdue University, West Lafayette, 

IN. 

f1 

345 

, 
DISCUSSION 

SAH: I would like to ask you about that particular example you gave, the complementary error function, also the SUPREMo There is quite a difference 

in the results. What is the basic mechanism? WhAit are the recombination .. chanis.s that give you the difference? 

SCHWARTZ: What's included in the code is Hal1-Shock1ey-Read and Auger using 

Schmidt Auger coefficients, and for that particular run -- thank you for 

asking -- I should have mentioned at the time: for that particular run we 

used the Slot-800m band-gap narrowing model, so there is a significant 

amount of band-gap narrowing occurring, and recombination mechanisms. For 

that particular run, Auger and Hall-Shock1ey-Read, and I didn't bring the 

plot along. The plot shows the split between them. I don't recall what 

t .. e spli t was. 

SAH: For the particular profile, was it the Auger that causes the one to be 

better than the other one? 

SCHWARTZ: Yes, I believe that it was Auger, but I don't have the plot with 

me. 

NBUGROSCHBL: You said that the published Auger coefficients don't agree with 

the experiment. In'order to get agreement, do you need larger lifetimes 

or shorter lifetimes? 

SCHWARTZ: The recombination wants to be reduced. I should qualify that a 

little bit. I was repeating what is said in a couple of publications by 

Posene at GB and Weaver at Sandia. It is possible that the problem lies 

in the band-gap narrowing model and not in Auger, so one wants to be a 

little careful. There is a problem in the emitter, and that's clea~, and 

people have tended to blame Auger. I guess I'm not ~ompletely convinced 

that it is Auger -- it may well be related more to the band-gap narrowing. 

DAUD: I would like to follow up on Sah' s question. You have the same carrier 

density at the surface for the SUPREK-and for error function. So, normally you have much larger field right at the surface in case of complementary function, and I would expect less recombination there. Would you 

give some reason why? 

SCHWARTZ: Yes. There are a number of reasons. One is that the recombination 

not only depends on the Auger coefficients and lifetime,. but also on the 

excess ainority carrier concentration, and if I had shown the plot, what 

you would have seen is that many of the carriers are recombining in the 

case of SUPRIH as they moved, and the axis cure was lower at the surface. 

The other difference is in the way that the band-gap narrowing effective 

field is distributed. The minority carriers in the emitter don't see 

just an electrostatic driving force due to the gradient. There is another 

component, which is associated with band-lap narrowing itself, and it 

tends to reduce the effect of pulling minority carriers away from that 

surface or keeping them out of the emitter. 80th are operating ,ndthey 

are distributed differently. 

346 
DAUD: Tbe second question bas to do witb actually runninl tbis prOlram. We 

find tbat one of tbe items tbat one bas to put in is tbe TpO and 

TnO' .ormally when we measure, we eitber measure tbe lifetime or 

diffusion lenltb where tbe dopinl is already tbere. How does one 

reconcile witb tbis? Wbat kind of numbers one sbou1d put for TpO 

TnO' 

SCHWARTZ: I'. sorry. You say you noraally .. a sure whaU 

DAUD: Say we bave a cell where we measure tbe diffusion lenltb or the lifetime. We cannot directly put tbat in your model because your model 

corrects it for the doping. 

SCHWARTZ: Yes. Tbere were a lot of features tbat were not talked about bere, 

and since we bave sent a copy of tbe code out to JPL, be is asking. You 

bave tbe option of turning on what amounts to a Kandel fit to doping. If 

in fact you bave tbat turned on and if tbe base doping is above tbe 

transition dopinl for tbe tbe Kandel fit, tben you bave to correct tbat. 

If you bave measured tbe lifetime at that particular dopinl level, you 

eitber bave to correct it or just turn Kandel fit off and enter tbe value 

you measure. It·s your cboice. It is under your control on tbe input 

deck. 

LINDHOLM: I have tbree questions. Tbey are all, I tbink, fairly quick. Just 

to remind tbe audien'ce: you recast some of the -- what you might say, 

equations whicb wer~ truer to tbe pbysics -- into a form tbat one is more 

used to seeing in a conventional treatment of semiconductor device 

pbysics. In so doing, you introduce tbe parameter tbat you called small 

IUlla, lowercase gaDlDa, and I tbink tbat tbat parameter was supposed to 

bave taken care of various tbings tbat were being violated by tbe density 

of states. You made a big point, whicb is an extremely valid point -- tbat tbe parameters tbat go into tbe model bave to be measurable. So 

witb tbat preparation for tbe audience, I could bavejuat asked you what 

success bave you bad in measuring gaDlDa, and bow do you do it? How don·t 

you do it, if you can't do it? 

SCHWARTZ: I tried to stay away from tbe equations, Fred, and I apologize for 

tbe poor quality bere. The g8DIDa that Fred is talking about entered into 

tbe effective potential tbat we sbowed. Here is tbe electrostatic potential, and bere is tbe term wbicb I said was an effective aSYDIDetry factor, 

and tbat term is not normally known. AS one gets measurement of tbe 

effective band-lap narrowing, whicb in fact looks like tbis -- tbe band 

gap plus all tbe degeneracy and band structure effects. Gamma, in fact, 

bas electron affinity divided by tbe delta G minus terms fo~ degeneracy. 

The answer to your question is', you don't know. But before I let tbat 

go, it turns out tbat for solar cells you seldom care, and tbe reason for 

tbat is tbe following: GB observed tbis first, tbe ranle on tbat numbers 

fro. 0 to 1 and one can run tbe full range and see almost no detectable 

cbanse in tbe deyice cbaracteristics. On tbe otber band, if you look 

inside tbe device, tbere are radical differences in tbe electric field 

dbtribution in tbe .. itter, in tbat resion. There are buge differences. 

But it turns out, and you can do tbis in closed form, tbat if you are . ~~ealinl with a resion whicb is quasi-neutral and low injection, as tbe 

347 
emitter is under anything except extreme conditions, you can show in 

analytic fo~ that, in fact, terminal characteristic is independent of 

that parameter. There are places where it makes a difference. It does 

make a difference in junction cap~eitance; you can show that fairly 

readily. It makes a difference in the electric field. And a dramatic 

one if, for instance, you are concerned with avalanche, not in a solar 

cell, but calculations of ,avalanche, and you are in a heavily doped 

condition. Then possibly one should be worried about present~day 

avalanche coefficients if they are based on classically calculated 

electric fields. But the answer is that it doesn't affect the terminal 

characteristics. 

LINDHOLK: The rea~on I asked that is twofold. First of all it would seem to 

me that for diagnostic purposes it would be desirable to k~ow what you 

call gamma, or what I would rather just call the electron r-finity, 6nd I 

know about the comment you made about the quasi-neutral region. But as 

you start entering a little bit into the junction transition region, then 

I think it becomes more important. And the reason I asked that is, if I 

correctly read your earlier paper with Mark Lundstrom, that you indicated 

a method for measuring gamma. And so I come back to my original question: 

what degree of success have you had in measuring gamma? 

SCHWARTZ: Very little. We're still working on it. 

LINDHOLK: I think it is 'a good thing to work on, actually. The reason is that 

it's very easy, even though you did not intend to do this -- in fact, your 

wording was very careful -- but people will take sort of special cases and 

say it doesn't matter, but it does matter from a diagnostic point of view 

in finding out what's going on with.the profiles ,how you can improve the 

device, that kind of thing. I'm very glad you used such careful wording, 

so congratulations on that. 

SCHWARTZ: I'm glad you read the paper, very few people have. 

LINDHOLK: Its a very interesting and very good paper. I was extremely interested in your measurement of gamma. 

SCHWARTZ: I have a Ph.D. student who is extremely interested too. 

LINDHOLK: The other thing that I noted that you said, and since you wo~d 

things so carefully, I was noticing that you said that most of the people 

who made electrical measurempnts in effect were measuring the p-n product. Now, I think that thstis probably true of the Slot-Boom graph you 

use, the transistor struct'i!r~, I think it's not true of EBIC people. 

Would you agree with that? A '\good portion of the data now coming out is 

BBIC data and the guys from GE who aren't here are talking about p-n 

product and I think that they can't do that. The fundamental reason is 

that Fe~i levels have to remain sensibly, spatially invariant over a 

significant region of the device in order for that me.surementto yield 

the p-n product. 

SCHWARTZ: That's absolutely ri!ht, and from a physics point of view is very 

p1eadng. And from a modeUng point of view it's difficult, because now 

348 
in the intermediate region, where one worries about what happens to the 

band shape, you've got a problem in using it. 

LINDHOLM: One last one. You keep mentioning two-dimensional programs, and I 

would like to know about three-dimensional programs, and why you can get 

away with two-dimensional. 

SCHWARTZ: It's not so much getting away with two-dimensional, it's really a 

level of difficulty. In our case -- one thing I didn't mention, and I 

neglected it inadvertently -- I told you that it cost a,bout $5.00 and 

takes 100 to 300 seconds on a 6500 CDC if you run the l-D code. It ,takes 

about 300 CPU/second on our CYBER 205 Supercomputer to run the 2-D code. 

Now, what I mean by that is to run a full analysis, something like 10 

points, and do all the associated stuff. That uses about 2,000 mesh 

points. So right now it's about what we are capable of tackling. If 

Purdue will put anoth~r two million words into the main memory of that 

computer then we will look at the three-dimensional. 

LINDHOLM: If the next speaker is successful in cutting the computer time 

significantly by his technique, as'he suggests, would you then strongly 

advocate three-dimensional steady-state modeling as a highly useful, 

moderately useful or rarely useful vehicle for solar cell design optimization and for monitoring manufacturing processes? 

SCHWARTZ: I think thats 'a very good question, whether it's Ii',sked about one, 

two or three-dimensional, and the answer lies in how ea51 it is to use, 

whether it's fast, are the turn-arounds quick, and what is reasonably 

cheap. Because you do have to make a lot of runs, and if it's very 

expensive or very time-consuming, the utility becomes a lot less. 

LINDHOLM: Suppose it doesn't cost anything? 

SCHWARTZ: Then its very useful to do even for one sun. Is that what you 

think? 

LINDHOLM: I haven' t t~wught enough &bout it. 

SCHWARTZ: If you want to do a cell like Dick Swanson's. 

LINDHOLM: A more conventional' cell is very useful t.here? Or is it moderately 

useful? 

SCHWARTZ: I doubt it, I can't see the benefit to a conventional cell with 

three dimensions. 

QUESTION: Dick, a quick question. Did you decide that radiative recombination and trap Auger effect could be neglected safely? 

SCHWARTZ: No, we didn't. I told you the status of the code as it was. It is 

a fairly straightforward matter to add those components to it, we just 

haven't driven things, we haven't made any runs where the other lifetimelimiting mechanisms were low enough to do that. But clearly, if you do, 

that's a limiting mechanism that is not present and needs to be added. 

349. 
QUESTION: And on the surface recombination you might also have trap Auger 

effects, or do you wrap it all up in a surface recombination velocity? 

SCHWARTZ: Well in the one-dimensional code it's wrapped up in the surfaee recombination velocity. I didn't talk about how it's handled in two 

dimensions. In two dimensions you could either do it by integrating 

through the trap states and capture cross-sections, or you could do it by 

a lumped parameter, which is probably not as good -- and you do have to 

control surface potential, which we do by setting the charge in the oxide. 

QUESTION: Now, a last question: capacitance. Do you work it out or do you do 

current-voltage, capacitance voltage? 

SCHWARTZ: No, JPL doesn't know if their version of the code does have capacitance in it, we just didn't tell them. It is the equivalent of very 

low-frequency capacitance. I'll tell you what it is and you can name 

it. It is the integ~a1 of either the electrons or holes with the appro--

priate voltage term put in, I!.nd you are quite right. 

QUESTION: It can miss by a factor of three or four? 

SCHWARTZ: Yes. We don't use it that way. 

350 

iJ = 
_____

N8S - 31687' 

APPLICATION OF CLOSED-FORM SOLUTIONS TO A MESH POINT FIELD IN SILICON SOLAR CELLS 

M. F. Lamorte 

Research Triangle Institute 

Research Triangle Park, NC 27709 

Abstract 

A computer simulation method will be discussed that provides for equivalent 

simulation accuracy, but that exhibits significantly lower CPU running time per 

bias point compared to other techniques. This new method is applied to a mesh 

point field as is customary in numerical integration (NI) techniques. The 

assumption of a linear approximation for the dependent variable, which is 

typically used in the finite difference and finite element NI methods, is not 

required. Instead, the set of device transport equations is applied to, and the 

closed-form solutions obtained for~ each mesh point. The m~'sh point field is 

generated so that the coefficients in the set of transport equations exhibit 

small changes between adjacent mesh points. In contrast to the NI linear 

approximation, the closed-form solutions more accurately represent the physical 

system and the device physics incorporated in the transport equations. 

Application of this method to high-efficiency sil-icon solar cells is 

described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing~ carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been 

investigated using Fermi-Dirac statistics, and these results show that bandgap 

narrowing is more pronounced and that it is temperature-dependent in contrast to 

the results based on Boltzmann statistics. It is also suggested that carrier 

diffusivity relationships that apply to degenerate materials in thermal equilibrium may also be applicable to regions in which high injection exists even in 

nondegenerate material. 

Impo$ing the appropriate boundary conditions on the closed-form solutions 

results in a set of equations which require simultaneous solution. This results 

in obtaining the solution of all constants of integration, from which, in 

principle, all cell characteristics may be derived. It has been demonstrated 

that recursion relationships exist between the constants of integration. Trial 

or "guess" solutions are not required in this new method for devices operating 

at any injection level, because the closed-form solutions obtained at each mesh 

point, in fact, fulfull th~s role. This carries over to those devices operating 

at high injection levels, but the inclusion of Auger recombination introduces 

nonlinear terms in the continuity equations, and special attention must be 

devoted to satisfyi.ng Poisson's equation. Under these conditions, an initial 

estimate must be made of the value of the independent variable for inclusion in 

the continui,ty equations at the initial mesh point. An iterative procedure is 

. then used to obtain a consistent solution. 

351 
Il-4'"TRODUCTION 

Computer modeling simulations have been shown to be very useful in the 

development of semiconductor d.evices in those cases where the simulation is an 

accurate representation of th,' ohysica1 device. However, to be an effective aid 

to the experimentalist and to bEcome an equal partner in the technologies used 

in device development, it may 't.e required to operate the computer program 

frequently each day in an active developmental program. For frequent use, as 

required in solar cell development, CPU costs must be lew. Moreover, low CPU 

cost allows for engaging in computer experiments, which can be,made to ~e a very 

useful and powerful technique. 

Computer modeling using numerical integration (NI) methods in Si device 

technology have usually shown fair-to-good agreement with experimental data. 

However, CPU costs for the execution of computer programs that are based on 

numerical integration methods are prohibitively high for their use as a laboratory or manufacturing tool [1]. The number of bias points that are required to 

study optimized device designs usually exceeds 5,000 runs. Similarly, a comprehensive study involving device structures or new types of devices may exceed 

10,000 runs. Increased CPU cost results if convergent problems arise. In most 

cases, the cost of such studies, for the benefits gained, may not be attractive. 

Simulation accuracy is determined by both the accuracy of the a1gorithm/ 

analytical method representing the device transport equations, and the accuracy 

of the phenomena submodels in representing the corresponding experimental data 

related to material properties. For most efficient use of the CPU, the accuracy 

of the algorithm/analytical method and of the phenomena submode1s should be 

commensurate. For example, even if the algorithm/analytical method accurately 

represents the device, simulation results may not agree with experimental data 

if the phenomena submode1s are accurately represented. The reverse is also 

true. In solar cells, the phenomena submodels that produce first-order effects 

in terminal characteristics are: absorption curve, built-in and induced electric 

fields, bandgap, lifetime, mobilities, diffusivities, photoexcited carrier 

concentrations, surface recombination velocities, junction transport, etc. The 

representation of the phenomena submodels must take on an importance equal to 

the analytical method used to represent the system. 

Under some operating conditions and for a number of solar cell structures, 

two-dimensional modeling may be required to obtain improved agreement between 

simulati,on'resu1ts and experimental data. Although the results presented above 

apply generally to one- and two-dimensional modeling, the CPU execution time is 

significantly grea'ter for two-dimensional simulations. 

In this paper, a new method is described which has been used to simulate 

semiconductor device characteristics. Although this method shares similarities 

with some aspects of NI methods, it differs markedly in other aspects. 

Abbreviated, forms of analytical relationships representing the solution of solar 

cell transport equations that are obtained using this new method are presented 

and discussed. The similarities and differences between the methods are also 

discussed. 

352 
• ~, I 

-?,,< 

~< f#; 

~~' ..... 

SIMULATION METHODS 

In this section, the transport equations are discussed as they relate to 

the simplifications and approximations that are required to be made in order to 

use NI methods and the new method, which is the application of closed-form . 

solutions applied to a mesh point field. The finite difference (FD) and finite 

element (FE) methods, which are considered NI methods, are briefly discussed 

because they are most similar to this new method. An outline of these methods 

is presented and the procedures are developed to apply them. 

Numerical Integration Methods 

The most commonly used transport model in semiconductor devices is due to 

Van Roosbroeck and is represented by the set of equations: 

an = 1 v • j + (G-R) at q n (1) 

~ = - 1 v • j + (G-R) at q p (2) 

j 

n 

-+ 

= qll nE + qD Vn 

-n n (3) 

j = qll pE - qD Vp P p P (4) 

v • E = 51 (p-n + N -N ) e: D A (5) 

The above set of relationships is applicable to nondegenerate and degenerate 

materials, low and high injection levels, dc and ac operation, and to most 

semiconductor device structures. 

The Van Roosbroeck transport equations comprise a system of coupled partial 

differential equations that describe a semiconductor carrier concentration and 

current density in position and time. The net balance of generation sources and 

recombination sinks of electrons and holes are described by the respective 

continuity equations, and the Poisson equation describes the electric field 

distribution that is' produced by the charge distribution within the semiconductor. 

For solar cells, the steady~state condition is assumed. which greatly simplifies 

the transport set because an/at and ap/at vanish. Device phenomena submodels 

may be added to the transport equations to accurately describe a variety of 

carrier dynamical and other internal physical processes. 

However, the Van Roosbroeck equations must be significantly modified in 

order to describe the effects arising from velocity overshoot, ballistic transport, and very thin surface layers [3]. In solar cells, only the latter may 

need consideration. The phenomenon in thin n-type surface layers, where an 

oxide charge insulator (OCI) produces an electron accumulation, may introduce 

sidebands within the conduction band, where each sideband corresponds to a 

quantized level for electron transport in a direction normal to the surface. 

l. 

353 
Solution of the transport equations is more difficult for higher order 

models; i.e., time-dependent requirements, and two- and three-dimensional 

geometries [2-11]. Moreover, this difficulty is brought into sharp focus in 

two-dimensional modeling when comprehensive phenomena submodels are considered 

[2,12]. 

In comprehensive representations, the complexity of the Van Roosbroeck 

transport equations does not allow for closed-form solutions which accurately 

simulate semiconductor devices~ Accurate solution of the transport equations 

requires a method that simplifies these equations. The most pop~lar approach is 

to divide the device structure into small parts [2-15]. In one-, two-, and 

three-dimensional solutions, these small parts are 'defined as infinite slabs, 

areas, and volumes, respectively. Each of these small parts is assigned a mesh 

point, which is identified by one, two, or three indices corresponding to a one-, 

two-, or three-dimens.ional representation of the device. These small parts must 

be made sufficiently small so that all dependent variables in the transport 

equations exhibit small changes in value between adjacent mesh points [2,4,5,8, 

15]. In addition, the coefficients in the transport equations also exhibit 

small or negligible changes between adjacent mesh points [15]. If either of 

these conditions is not met, a solution is not obtained because convergence does 

not occur. NI methods and the closed-form solutions may be applied to mesh 

point fields. 

In applying the FD method, all derivatives are replaced by finite differences 

between discrete points in an active domain in the interior of the structure. 

The residue of the newly established difference equation is set to zero at each 

mesh point. Thus, the differential equations are transformed into difference 

operator equations. The value of the dependent variable is determined at each 

mesh point from the set of equations obtained [2,4]. 

For example, the differential equation to detel~ine the temperature distribution is given by [4] 

(6) 

The difference operation is represented by 

(7) 

where Ti , Ti+l , and Ti+2 are the values of the dependent variable, T, at the 

mesh points i, i+l, and i+2, and ~x is the independent variable representing the 

separation of the mesh points i and i+1, and 1+1 and i+2, assumed to be equal. 

A corresponding equation is' constructed at each mesh point. The resultant set 

C?fequations 'requires. the simultaneous solution for T l' T 2' --, Ti' --. Thus, 

the value of',the dependent variable, T, is obtained only at .the mesh points 1, 

2, --, i,The' ,value for T in the x:egion between the mesh points is not 

354 
obtained. explicitly and may only be approximated by one of the established 

methods. Typically, a linear approximation is used. 

In the FE method, a,typical assumption made is that the dependent variable 

is a linear function, where, for the system discussed above involving tempera~ure 

[4], 

Ti+l - Ti 

T = T~ ... + Xi (x - Xi) xi +l - (8) 

This relationship is substituted into an equation, called the "iunctional'," that 

describes the system to obtain a set of equations. Simultaneous solution of 

this set results in discrete values of the dependent variable at each of the 

mesh points. Between the mesh points, the dependent 'variable is governed by a 

linear relationship similar to that represented in Eq. (8). 

The full numerical solution of partial differential equations as described 

above, which is applied to a physical system and which describes all regions of 

this system in a unified manner, was first suggested by Gummel [51. In this 

work, Gummel',applied his method to a one-dimensional bipolar transistor. 

Subsequently" the method was further developed by DeMari [6,7] who applied it to 

p-n junctions, and by Scharfetter and Gummel [8] to IMPATT diodes. Although 

this initial work was confined to one-dimensional structures, the Gummel approach 

has also been adapted to ~wo-dimensional modeling [3,9-12]. However, the twodimensional algorithm requires excessive CPU execution time [3,12]. 

Phenomena submodels may be imposed on the coupled nonlinear partial 

differential equati'Clils' which may result in nonlinear transport equations; Le., 

band-to-band Auger recombination introduces a term involving n

2 

or p2, and the 

electric field in the quasi-neutral region depends on the injection level. In 

NI numerical methods, the transport relationships are linearized. Two schemes 

have been used and both require initial "guess" solutions. The decoupled method 

proposed by Gummel [5] is to assume the coupling is weak so that the equations 

are solved serially. While the method is not difficult to implement, it fails 

to give accurate results for highly nonlinear systems. The coupled method, 

proposed by Hachtel et al. [14], solves the transport equations simultaneously. 

However, this is more difficult to implement. The implementation of the 

algorithm becomes complex when recombine.tion-generation and electric field drift 

terms are included'[4]. In addition, this results in significantly higher CPU 

execut:ion,'time and increased main memory requirements. 

As discussed above, using NI methods results in values for the depende.nt 

variables, such as the carrier concentrations and electric field, at discrete 

points in the semiconductor; Le., at the mesh points. Thus, the cOlltinuum of 

the dependent variabl:es, des'cribed by the transport equations, is transformed 

into a discontinuous or discrete set of values repres.enting these variables at 

each of the .mash points.' In contrast. the method that is proposed in this paper 

does not resort,to this transformation. 

355 

I~· I 

"
Closed-Form Solutions Applied to a Mesh Point Field 

The major point of departure between the algorithms of the new method and 

NI methods is that the new method uses a closed-form solution which is applied 

to a mesh point field that defines the system in space and in time [15]. This 

requires the application of the transport equations to each mesh point. In . 

order to obtain a closed-form solution to the transport equations, the mesh 

point field is generated so that the equations accurately represent each mesh 

point. The closed-form relationships represent analytical solutions and result 

in a continuum of values for the dependent variables in the reg~on between 

adjacent mesh points. Analytical solutions of adjacent mesh points also provide 

a continuum of values for the dependent variables in their corresponding regions. 

Analytical solutions of neighboring mesh points satisfy the usual boundary 

conditions that are demanded in semiconductor devices in accordance with the 

electronic/optical model under consideration. The analytical solutions representing the dependent "variables at each mesh point contain constants of integration, which are determined by imposing the boundary conditions on each of the 

solutions. 

A procedure has been established in applying the closed-form solutions to a 

mesh point fie·id. The procedure is as follows [15]: (1) establish the electronic/optical model of the solar cell within the generic transport equations; 

(2) impose the phenomena submodels, represented in analytical or tabular form, 

on the transport equations; (3) develop mesh point field distribution of order f 

which reduces the complex'ity of, and makes the coefficients that are present in, 

the continuity equations constant or nearly constant, so that a closed-form 

solut.ion is obtained at each mesh point with minimum restrictions; (4)' establish 

2;f-boundary conditions on the mesh pOint field; (5) apply the 2f-boundary 

conditions on the f-closed-form solutions; and (6) solve the resultant 2fequations simultaneously to obtain the 2f-constants of integration through 

recursion relationships. In prinCiple, the transport equations are uniquely and 

completely solved after the relationships for the 2f-constants of integration 

are obtained. Electron current is calculated at the depletion region edge; the 

hole current is determined by a similar relationship. Adding the electron and 

hole 'currents results in the J-V relationship from which most of the terminal 

characteristics are recovered. 

The well-established solar cell electronic/optical model ~s imposed on the 

transport equations; i.e., optical pair generation of carriers, and minority 

carrier collection and transport across a p-njunction. This is followed by 

imposing the phenomena submodels which 'are subsequently discussed. A mesh point 

distribution is established so that the electric field, lifetime, mobility, 

diffusivity, absorption coefficient, and bandgap exhibit small changes between 

adjacent mesh points. Ffgure 1 shows the subdivision of a one-dimensional solar 

cell structure. The n-region (0, X2) and the p-region (X3, XS) are subdiv~4ed 

into;fn-. and fp -mesh points, respectively. To illustrate the method, the pregion transport solution is discussed below. The electron continuity equation 

is represented by 

+ l.I E 

n p 

356 

dn (x) n (x) - n 0 pe _ p p 

dx '( 

n 

= 0 , (9) 
hJl 

w_ 

\11 

.... 

Depletion 

OCt Region 

..--

-- n-Type i~"'" I- I 

I I I I I ~ I I I 

I I 

I I 

-I I 

I I 

I , I , I I 

i = 1~ ------fn j= 1 

x=o x=2 x=3 

J p2 = t1I-&p2Pn2En2 - q DP2 dPn2 dx I 

Pn2 = A12ec.J12X + A22ec.J22.X + A32(x) 

p-Type 

~------- ------f;( 

x=5 

L..-__ I J n4 = q,Ln4n~Ep4 + q Dn4 d~~ 

np4 = B14ec.J14X + B24ec.J24X + B34(x) 

Figure 1. Discretization of 1-dimensional solar cell structure. 

~ 
where the Poisson equation takes its usual form. The symbols have their usual 

definitions, where nand n represent the total and photoexcited electron 

p pe 

concentrations, respectively. Implicit in Eq. (9) is that the subdivision 

results in a condition in which the slope of the electric field, dE /dx, is 

p 

small and may be neglected in a region between adjacent mesh points. Although 

the electric field slope is assumed to be negligible, the electric field itself, 

in general, is allowed to vary from mesh point to mesh point. Moreover, under 

these conditions the remaining material properties also exhibit small changes 

between neighboring mesh points for low injection levels. These changesbe~ome 

large under high injection levels, in which case a more dense mesh point field 

may be required to maintain comparable changes. As a result, a near-exact 

closed-form solution is obtained at each mesh point for the photoexcited electron 

concentration, which is an exact solution of Eq. (9) and is represented by 

n ,(x) = Bl,exp (wI'x) + B2 ,exp(w2 ,x) + B3 ,(x) peJ· J . J. J J J , 

where the terms comprising Eq. (10) are given in Table 1. 

liit 

(10) 

The subscripts, j, in Eqs. (10)-(30) represent the jth mesh point in the pregion as indicated in Figure 1. Correspondingly, in Eq. (10), Blj and B

2j 

represent the constants of integration, and B3j in Eq. (11) represents the 

photoexcited electron concentration, produced by photon absorption in the region 

of the jth mesh point. In the context of the conditions imposed on the continuity 

equations at each mesh point, wlj and w2j in Eq. (14) are constants. Photoexcited electron concentration, Eq. (10), is governed by the exponential terms 

and B3j which are all functions of position; in addition, B3j is also a function 

of wavelength through Eqs. (12) and (.13). Eq. (10) provides for con.tinuous 

values of n through the assignment of values to x, where the range of x is 

pe 

restricted to the region bc:tween the (j-l) and j mesh points. In contrast to 

numerical integration methods, the continuum of values describing the behavior 

of n is preserved in the closed-form scheme as was the original inten.t pro- pe 

posed by the Van Roosbroeck concept related to the use and the' interpretation of 

the transport equations. 

It is clear that the relationship used in the closed-form method, to 

represent thephotoex~ited electron concentration, Eq. (10), is an analytical 

solution that is demanded by, and has its support in, the tran.;port equations. 

Moreover, this relationship may also incorporate a comprehensive set of phenomena 

submodels as dictated by the transport equations, imposed boundary conditions, 

and the representations of the material properties coupled with the mesh point 

field. The phenomena submodels that influence Eq. (10) are represented in the 

relationships for the parameters, Eq. (1)-(30), that describe their behavior in 

the region bo~nded by the (j-l) and j planes in Figure 1. Eqs. (11)-(13) describe 

the photon absorption generation rate and the redistribution of the photoexcited 

electron-hole pairs, while Eq. (14) governs the electron effective diffusion 

length in the presence of an electric field. Drift an.d diffusion components of 

the electron current are represented in Eq. (15), and the electric field used in 

358 
Table 1. List of relationships of terms appearing in the solution of 

the electron concentration, Equation (10). 

(11) 

x A (x') x' 

Glj(x) = Dl i exp(-wl·x') I c a.No·exp(- i a.dx")dAdx' (12) nj J J J J 

o 0 0 

where 

:= _ llnjEpj 

2D '. nJ 

±J(llnj Epj ) 2 + L .-2 

2D • nJ nJ 

n 

E = (b t')~ E . pBNj pj - ~p rpj pBNoj 

kT 2 dniej 

EpBNoj = - q n

iej dx 

359 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

(19) 
Table 1 (continued). 

E TP' = [(b.- p-- J PJ 

n. N] ~ )...E9.l+ ~ .-& E 

P r. p r. pIPoj PJ PJ 

(20) 

(21) 

kT b . - ~ dn . E = _ - PJ . P peJ 

pPEj q r. dx 

PJ 

(22) 

r . - (b • + ~ )n . + ~ NA. PJ llJ P PJ P J (23) 

(24) 

(25) 

\lj :: J.lnj (26) 

llpj 

D • 

kT =-ll .b (27) nJ q nJ nJ 

(28) 

(29) 

(30) 

360 
the drift term is given by Eq. (16). The electric field components are defined 

in Eqs. (17)-(2.7), arising under equilibrium and nonequilibrium conditions, and 

include effects produced by ohmic voltage drops in the quasi-neutral regions, 

bandgap narrowing, impurity concentration profile, and photoexcited electron 

concent'ration distribution. Eq. (29) describes the intrinsic concentration with 

respect to temperature and bandgap narrowing. . 

In contrast, the relationship that is used in NI methods, corresponding to 

Eq. (10), is typically linear and is of the form given by 

n (xj ) - n (xj 1) 

n (x) = n (x" 1)' + pe _ pe - - ( ) x - x(J'-I) pe pe J- Xj - x(j_l) (31) 

where x is the independent variable in the region bounded by the (j-l) and j 

planes. The photoexcited carrier concentrations, n "and n ("+1)' do not peJ pe J 

normally represent algebraic expressions, but represent discrete values and 

require initial estimates of the ~oncentrations at their designated positions. 

The richness of Eq. (10) and its associated parameters , defined in Eqs. (11)-

(30), in representing dev'ice physics is clearly evident in contrast to the 

repr.esentation in Eq, (31). This relationship, Eq, (31), is used in NI methods 

because it simplifies the matrix equation that requires solution, but it is 

artifical in its representation of the photoexcited electron concentration 

because it has been const·ructed independent of the transport equations, 

The difference in the results obtained by applying Eqs. (10) and (31) to 

the same mesh point distribution, which defines the solar cell structure, is 

significant. Applying Eq. (10) results in the determination of the constants of 

integration. B1" and BZ"' assigned to the carrier analytical relationship at 

J J 

each mesh point. Substituting Blj and BZj in Eq. (10) provides for an analytical relationship at each mesh point, describing the behavior of n "for a peJ 

continuum of values of x in the range x(j_l) and xj . In contrast, the results 

of applying Eq. (31) is a set of discrete values for n "at each mesh point. peJ 

In the work reported in this paper, the general case is treated as it 

relates to injection level. The information of injection level is contained in 

the electric field and its components, Eqs. (16)-(30), lifetime through the 

diffusion length, L , and boundary conditions at the depletion edges bounding . n 

the p-n junction, and in the carrier mobilities and diffusivities. Application 

of Eq. (10) requires negligibly small changes in electric field between adjacent 

mesh points. Under these conditions, Eq, (10) is an excellent approximation to 

the exact solution at the assign.ed mesh point region. The measure for which. 

Eq. (10) approaches the exact solution is the self-consistency obtained from the 

solution of the Poisson equation using the analytical relationships for n "and peJ 

the number of iterations required to obtain values of B1j and B2j • 

The £ -mesh point distribution in the p-type region of the solar cell 

p 

comprises (fp-l) internal boundaries, and external boundaries at x3 and xs' At 

the external boupdaries, the usual p-n junction boundary condition on minority, 

361 

~ 

t
carrier concentration applies. At each of the (f -1) internal boundaries, the 

p 

electron concentration and electron current, separately, are continuous and are 

represented by 

where 

and 

k, 

J 

lIEcj/kT 

e 

J ,(y ,) = J ('+1)(0) nJ OJ n J 

(32) 

(33) 

(34) 

where y , is the separation between the (j_1)th and jth mesh points. A surface 

OJ 

recombination velocity boundary condition is imposed at the Xs boundary. This 

results in 2f -boundary conditions, from which 2f -equations are obtained that 

p p 

must be solved simultaneously to obtain the solution of the 2f -constants of 

p integration. 

Applying the boundary conditions using Eqs. (10) and (15) results in 2f -

equations which are represented in matrix form by p 

I "'~, 1 0 0 0 

T1kl -1 -1 0 

61"1 E1T1 -02 -E2 0 

• 0 0 "2k2 T2~ -1 

0 0 62"2 f2T2 - °3 

-1 

-f3 

"1kl Tiki -1 -1 

01"1 flTI -01+1 -EI+1 

362 

6 11 

6 21 

6 12 

6 22 

6 13 

6 23 

npe(x3) 

F01 

F02 

F03 

F04 

Fos 

F0(21-1) 

F0(2i) 

(35) 
••• 

The constants of integration are denoted B11 , B12 , ---) B1f ' B2f ' and the 

relationships for the other factors contained in Eq. (35) a¥e thePmaterial and 

structure properties at corresponding mesh points. The Fletcher boundary 

condition [16] is used at x3 , because it represents the boundary for the complete range of conditions that may exist: from equilibrium (i.e., the photovoltage V

Jph = 0) through increasing positive values of VJph up to and including 

high injection levels where VJph ~ Vbi. 

In Eq. (33), l1E " represents the band edge discontinuity located at the j CJ 

mesh point. If ~E " is positive, the boundary condition describes minority cJ 

carrier confinement (i.e., electrons confined to the junction region). 

The factors wlj and w2j ' Eq. (14), are the reciprocals of the effective 

electron diffusion length in the p-type region, and describes the recombination 

of electrons in the presence of an electric field in the region bounded between 

the (j-l) and j mesh point. It describes the recombination related to those 

electrons entering this region across the planes defined by the (j-l) and j mesh 

points as well as those photoexcited carriers produced by photon absorption 

within that region. If the electric field, E " = 0, then WI" = -w2 " and are 

PJ J J 

equal in magnitude to the reciprocal of the diffusion length, L = ~ . n n n 

Similarly, for degener'ate material or for high injection levels, low values of 

the electric field are obtained, and wlj ~ -w2j o In bath cases, electron drift 

toward the junction occurs by means of diffusion rather than a combination of 

diffusion and field-assisted drift. Eq. (10) reduces to the more familiar form 

to represent photoexcited carriers. 

The constants of integration are obtained by solving Eq. (35). While the 

matrix in Eq. (35) may be inverted to obtain the solution, a recursion relationship exists between the constants of integration. As a result, there is a 

significant reduction in CPU execution time to obtain the values of these 

constants through the recursion relationships. For example, in certain iteration 

procedures, some of the terms in these relationships that depend on geometry and 

mater.ials pr.operties may not change and need not be calculated for every 

iteration. There are probably other benefits, which will be revealed as more 

experience is gained in using this type of modeling program. 

The recursion relationships for the constants of integr.ation are given by 

the following equations: 

F(2f )-SnB3f (YOf ) - af enf (of +Sn) 

- ----p~~---~p~~p~----~p~~p~~p---­

L f (Ef +Sn) - Ynf a f (of +Sn) 

p p p p p 

363 

(36) 
and 

e .-y .B2 . nJ nJ J 

B22(02-E2)+FOl02-F02-G18nl(02knl-Ol) 

Tl (sl-02knl)-YnlGl(ol-o2knl) 

(37) 

(38) 

(39) 

(40) 

(41) 

There also exists recursion relationships for the e . 's and the y . 's which are nJ nJ 

functions of material properties at their assigned mesh points. 

Having obtained the constants of integration and 

relationship representing the appropriate mesh point, 

relationships which fully describe the behavior of n 

pe 

substituting them into the 

there results f -

P 

in the p-region. In 

principle, all device properties may be recovered through the manipulation of 

n .s. Using Eqs. (10) and (15) and the corresponding relationships for holes peJ 

in the n-region, the hole current Jl , Eq. (28), is obtained. Eq. (28) represents 

a relationship relating photocurrent versus photovoltage. The photovoltaic JVJph curve may be obtained from which maximum power and efficiency is calculated. Moreover, the effects on the J-VJph curve of the phenomena submodels, 

and material and structure parameters may be investigated through Blj , B2j , 

and B3j . 

SUMMARy 

A new computer modeling method is described and is applied to silicon solar 

cells. The method is similar to numerical integration (NI) methods in that 

364 
" 

''\. 

.. t· . 

I 

both require the use of a mesh point field. The set of transport equations 

is applied to each mesh point, and through a judicious selection of the mesh 

point distribution, an accurate closed-form analytical function is obtained at 

the assigned mesh point. Application of the boundary conditions, to an f-mesh 

point field, results in 2f-equations that require simultaneous solution. This 

solution is manifested through the determination of the 2f-constants of integration, where each closed-form solution, representing a mesh point, contains two 

constants of integration. Solar cell transport solution is represented by the 

complete set of constants of integration obtained in the n- and p-regions. 

Substituting the constants of integration into the corresponding closed-form 

analytical function, representing an assigned mesh point, results in a set of 

analytical functions that is applicable only to its assigned region in the mesh 

point field. As a result, the complete set of closed-form functions describes 

the behavior of the photoexcited carrier concentration for a continuum of xvalues in the n- and p-regions. The photoexcited carrier relationship is used 

to obtain the current-voltage relationship, from which the maximum power point 

and conversion efficiency are determined. Effects of temperature, solar concentration, submodel parameters, and structure parameters may be studied through 

changes at each mesh point in wlj ' w2j ' Blj , B2j , and B3j , 

REFERENCES 

1. T. Wada and J. Frey,. IEEE Trans. Electron Devices, ED-26, 476-90, 1976. 

2. P. Antognetti, Editor: Process and Device Simulation for MOS-VLSI 

Circuits, S. Selberherr, A. Schiitz, and H. Potzl, 490, Martinus Nijhoff 

Publishers, Boston, 1983. 

3. T. Wada and J. Frey, "Physical Basis of Short-Channel MESFET Operation," 

IEEE Trans. Electron Devices, ED-26 , 476-90, 1979. 

4. J. J. H. Miller, Editor: An Introduction to the Numerical Analysis 

of Semiconductor Devices and IrttegratedCircuits, E. M. Buturla, 

9-15, Boole Press, Dublin. 

5. H. K. Gummel~ itA Self-Consistent Iterative Scheme for One-Dimensional 

Steady-State Transistor Calculations," IEEE Trans. Electron Devices, ED-II, 

455-465, 1964. 

6. A. DeMari, "An Accurate Numerical Steady-State One-Dimensional Solution of 

the P-N Junction," Solid-State Electron., 11, 33-58, 1968 • . . 7. . ·A. DeMari, "An Accurate Numerical One-Dimensional Solution of the P-N 

Junction Under Arbitrary Transient Conditions," Solid-State Electron., 11, 

1021-1053, 1968. 

8. 

9. 

D. L. Scharfetter and H. K. G~mmel, "Large-Signal Analysis of a Silicon 

Read Diode Oscilla.tor," IEEE Trans. Electron Devices, ED-16, 64-77, 1969. 

D. P~ Kennedy and R. R. O'Brien, "Computer Aided Twa-Dimensional Analysis 

of the Junction Field Effect Transistor," IBM J. Res. Dev., 14, 95-116, 

1970. 

365 
, " 

10. M. Reiser, "A Two-Dimensional Numerical FET Model for DC, AC and LargeSignal Analysis," IEEE Trans. Electron Devices, ED-20, 35-45, 1973. 

11. K. Yamaguchi and H .. Kodera, "Drain Conductance of Junction Gate FETs in the 

Hot Electron Range," IEEE Trans. Electron Devices, ED-23, 545-53, 1976. 

12. J. L. Gray, uTwo-Dimensional Modeling of Silicon Solar Cells," Ph.D. 

Dissertation, Purdlle University, August 1982. 

13. D. P. Kennedy and R. R. olBrien, "Two-Dimensional Mathematical Analysis of 

a Planar Type Junction Field-Effect Transistor," IBM J. Res. Dev., 13, 662-

74, 1969. 

14. G. D. Hachtel, M. Mack, and R. R. O'Brien, ilSemiconductor Device Analysis 

via Finite Elements," Eighth Asilomar Conference on Circuits and Systems, 

Pacific Grove, Calif., 1974. 

15. M. F. Lamorte and D. H. Abbott, Final Report No. AFWAL-TR-8l-l0l6: "III-V 

Detector Modeling,it March 1981, WPAFB Contract No. F336l5-79-C-1828. 

16. N. H. Fletcher, "General Semiconductor Junction Relations," J. Electronics, 

~, 609-610, 1957. 

366 

... ---_ .. _ ... _._ •. .,.....-------.,.---,--....,..-----........,----
DISCUSSION 

(LAMORTE) 

LINDHOLM: I have a number of small questions. You put your attention on the 

dependent v"ariables. which you treat as the hole and electron densities. 

I'm wondering how you enter the external boundary conditions since you 

are not feeding in hole and electron densities at the ends of the 

device. 

LAMORTE: At the junction side of the end region, for example, meaning the 

emitter, the boundary condition becomes the Fletcher boundary condition 

for the photo-excited holes, because we are treating the general case of 

high injection level. At the surface region we are calculating the recombination velocity, by means of a ~x divided by the lifetime at the 

center of the first mesh point. And we have gotten some interesting 

results there, in that it appears that even for calculating the surface 

recombination velocity in that manner, it may not be consistent with the 

slope of the photo-excited holes at the surface. If you don'trecalculate the surface recombination velocity, the solution will oscillate. 

We're just putting a fix in that, and the fix is that you want to update 

the surface recombination velo~ity at the surface by the exact relationship. Keaning the product of the surface recombination velocity times 

the photo-excited hole concentration at the surface, and that is equal to 

the surface r~combination current, which includes a drift field component 

and a diffusion component. So that becomes the left-hand boundary. 

LINDHOLM: I have a related question. If you are going to do a non-illuminated 

analysis where you apply a voltage, then how do you get into the external 

boundary conditions? I'm not now concerned with the edge of what you call 

the depletion region but rather the contacts of the device. 

LAMORTE: I don't know whether it will work for that, but we can probably make 

it work. We have not given that any consideration. 

LINDHOLM: Would you integrate the electric field? Would that be the way of 

doing it? Getting integrated, the electric field through the material, 

and setting that equal to zero, and then you would have to iterate, I 

suppose. 

LAUORTE: Yes, we have that in the model because under high injection level 

you want to determine. what the voltage drop is aCL"oss the quasi-·neutral 

region. 

LINDHOLM: When you say the Fletcher boundary condition, you mean the Fletcher 

Kasawa boundary condition as modified by Houser? 

LAMORTE: No, the Fletcher and Kasawa conditions are separate. They account 

for the same thing, but they'require different information. The Fletcher 

boundary condition applies to the edges of the depletion region and thats 

what we are using. The Kasawa uses the right-hand edge of the depletion 

region and the left-hand contact. 

367 
LINDHOLM: How do you define the edge of the depletion region in your numerical 

analysis? 

LAMORTE: We calculate the depletion region for either a graded case or the 

abrupt case. 

LINDHOLM: You calculate it how? Depletion approximation? 

LAMORTE: Yes. 

LINDHOLM: That won't work, I'm afraid, because you probably need to make a 

correction because of the free electrons and holes in that region. We 

could discuss that privately. That is probably an updating of the physics 

that goes into the model. 

LAMORTE: Well, that is updated. 

LINDHOLM: Oh, I see. You don't use the depletion approximation to calculate 

the depletion thickness? 

LAMORTE: We use it to get it started. 

LINDHOLM: Oh, I see, then you update. Okay. Then how do you define the edge 

of the depletion region once you get it updated? Somehow you have to use 

some criterion to de'fine the edge of the depletion region. 

LAMORTE: Then we use the depletion approximation. 

LINDHOLM: Okay, I don't understand the answer to that, but maybe we could 

discuss that privately, unless you want to elaborate on it now. What I 

thought you said was, as your starting point to get the edge of what you 

call the depletion region, you would use the depletion approximation and 

then you would iterate up in, including the electron hole densities, in 

order to redefine the depletion approximation. Then I asked you what the 

criterion was after you did the updating. 

QUESTION: Maybe that's something the two of you could discuss. 

LINDHOLM: I have one last question. This is a very interesting idea to me. I 

have been sounding very negative; I'm sorry to sound negative. I just 

was looking at some small points. I don't do numerical analysis, but I'm 

somewhat familiar with what Mike did, and Gummel, and all these other 

people, and the only place I have ever seen this done previously, similar 

to this, is in a book by some Russians. I wonder if this is the first 

time this method has been used? 

LAMORTE: I have not seen it anywhere else, and I have spoken to about a dozen 

people who have done computer modeling in 'Other areas, other thari semiconductors, as well, and they claim that they have not seen it. And I 

have not seen it elsewhere. 

LINDHOLM: This Russian book is not quite numerical analysis, so I guess I 

haven't seen it either, but that's as close as I have come to seeing it. 

368 
It's very interestJlng. 

LAMORTE: One of the thi.ngs that this does for you, and what we showed in the 

avalanche photo diode -- because you're reflecting a lot of the physics 

in the closed form solution -- when you look at the convergence of the 

solution as a function of mesh points, you find that you do not need as 

many mesh points, for example, in the avalanche photo diode. We didn't 

need to go above 15 to 20 mesh points when we had a half-micrometer 

depletion width, and we went all the way up to 80 mesh points, and at 15 

to 20 we were within l~ of the asymptotic solution with 80 mesh points. 

I'm fully convinced that since you have a closed-form solution, which is 

a good approximation, the physical system, that it's forgiving in tet~S 

of using a lesser number of mesh points. And so, therefore, that combined 

with the recursion formulas, the CPU time is reduced greatly. 

LINDHOLK: I was wondering if you could describe the output that you got from 

your model and do you have it set up to give you graphs of carrier distributions and so forth? 

LAMORTE: No, we haven't done that yet. We almost have the model working, 

meaning that with one of your cells we got something like 38 milliamperes, and it's about 20~ too high, so we have gotten it that far and 

we are still trying to debug and determine where that is. And it may be 

just a simple matter that the lifetime we are using is too high. 

LINDHOLM: So the code doesn't give you plots of carrier distributions and 

things that help one see what's going on in the physics of the device. 

LAMORTE: We get discrete points, for example, of carrier concentration, okay, 

at the mesh points, and we get it at two points actually, we get it at 

each of the mesh points and in between. But if you wanted to, by taking 

the relationship that applies to that particular region of the cell in 

combination with the appropriate constants of integration, you could plot 

the entire thing on the continuum if you wished. 

369 

"'F-. - .. -------,-,.:<""_~_-. ~""'·~---------.,-rll ...... ',-::-· -::---,---~ 
N85-31638 

PHENOMENA SIMULATION FOR HEAVY DOPING 

AND SURFACE RECOMBINATION VELOCITY 

Fred A. Lindholm 

Department of Electrical Engineerin~ 

University of Florida 

Gainesville, FL 32611 

1. Introduction 

2. Basics 

2.1 Quantum 

2.2 Statistics 

3. High Concentrations 

3.1 Fermi Level 

CONTENTS 

LIST OF SYMBOLS 

3.2 Einstein Relation for Majority Carriers 

3.3 NP Product if There is No Energy Gap Narrowing 

3.4 Slope of Mobility Edge for Minority Carriers 

3.5 Energy Gap 

3.6 Minority Carrier Diffusivity and Mobility 

3.7 Trapping Model 

3.8 Other Parameters 

4. Moderate Concentrations 

4.1 Fermi Level Saturation and Consequences 

4.2 Einstein Relation for the Majority Carriers 

4.3 Einstein Relation for the Minority Carriers 

4.4 Past Treatments 

4.5 Unsolved Problems and Consequences for Computer Simulation 

5. Basic Equations for Simulation 

5.1 Importance of Time Variations 

5.2 Conventional 

5.2.1 Counting 

5.2.2 Remark on Quasi-Fermi Potentials or Levels 

5~3 Modified Basic Equations 

5.3.1 Modifications for Computer Solution 

5.4 Modifications Needed But Not Available 

6. Areal Inhomogeneity and Multi-Dimensional Flow 

7. Recommendations and Conclusions 

8. References 

9. Figure Captions 

10. Figures 

P ,.:noE m-;ANK NOT m;MED PRECEDING fiV 

371 
a 

div 

o 

e 

E 

EI 

EG 

F 

g 

grad 

kT 

kT/e 

1 

j 

m 

m* 

NAA 

NC 

NO~ 

ni 

n 

p 

T 

QOS(E) 

QFL 

V 

v 

vN 

w 

a 

LIST OF SYMBOLS 

NOT DEFINED IN TEXT 

cutoff distance in derivation of energy-gap model 

divergence operator 

diffusivity or displacement flux density (context determines) 

magnitude of electron charge 

energy of electrons or electric field (context determines) 

kinetic energy of free carriers normalized by kT 

energy gap 

Fermi 1 evel 

generation rate from external source (does not include thermal 

generation rate) 

gradient operator 

thermal energy 

thermal voltage 

Fermi integral of order one half 

convection current density, augmented by subscript N or P means 

electron or hole current density 

rest mass of electron 

effecti ve (or crystal) ma.ss 

ionized acceptor atom concentration 

effective density of states of conduction band 

ionized donor concentrations 

intrinsic carrier concentration 

electron concentration (also used as subscript) 

hole concentration (also used as subscript) 

absolute temperature 

quantum density of states 

quasi-Fermi level 

applied potential or internal potential (content determines) 

total time-varying applied or internal potential 

quasi-Fermi potential for free electrons, equals quasi-Fermi level for 

free electrons when multiplied by -e, prime denotes normalized with 

respect to thermal voltage, N subscript replaced by P subscript means 

hole quasi-Fermi potential 

energy of bound electron in derivation of model for energy-gap 

narrowing 

optical absorption coefficient 

kinetic energy of free electrons, normalized by kT 

energy-gap narrowing 

dielectric permittivity 

optical wavelength or screening length (context determines) 

electron affinity 

space charge density 

recombination lifetime or relaxation time (when symbol is augmented) 

372 
1. INTRODUCTION 

We survey the theoretical models now available that characterize heavily 

doped (highly conducting) regions in silicon and analytical and numerical 

approaches that try to determi ne the i nfl uence of such regi ons on . the 

conversion efficiency of solar cells. Heavily doped regions are bounded by 

adjoining regions. As one example, a physical surface bounds the front 

surface. This physical surface may consist of a mixture of ohmic-contact metal 

with either an anti-relection coating or with a thermal or deposited oxide. As 

another example the adjoining surface may define a transition between heavily 

doped and more lightly doped silicon. The interplay between the heavily doped 

and adjoining regions constitutes a key to designs for improved performance. 

This will receive attention, as will the multi-dimensionality of variables such 

as current and mobile-carrier density. 

Although dilutely doped silicon is well characterized except for some 

disagreement about optical absorption coefficients, what exists now for heavily 

doped silicon and its interplay with adjoining regions is an incomplete theory 

in whi ch not all contri buters to transport, recombi nati on, generati on, and 

trapping are defined. Further the parameters relating to these mechanisms and 

their values as determined by experiment are subject to various 

interpretations. The presentati on will bear in mi nd these uncertai nti es and 

wi 11 treat the characteri zati on of heavily doped s il i con not as a theory but 

rather as an imperfectly articulated and incompletely formalized body of 

experience. This view is intended to help point the way toward the attainment 

of a more compl ete theory of heavily doped sil i con and thereby toward more 

informed designs of solar cells. Because computer programs constitute tools 

both for design and for estimating performance limits, the review will include 

some remarks pertinent to existing and developing programs. 

2. BASICS 

Highly doped silicon differs fundamentally from silicon of dilute doping 

in several main respects. 

2.1 Quantum 

As the concentration of shallow impurity atoms increases, their groundstate orbitals begin~ to overlap (Fig. 1), resulting in a distorted quantum 

density of states which includes an impurity band (Fig. 2). From an 

experimental viewpoint, one sees the resulting metal-insulator (or Mott) 

transition occuring for common dopant species at about 1018 cm-3 (Fig. 3). The 

theoretical interpretation of Mott and Davies (1967) involves the warped 

quantum density of states shown in Fig. 4. 

At concentrations above about 1019 cm-3, the abundance of majority free 

carriers and the associated screening yields a quantum density of states that 

more closely approximates the standard dependence, QDS(E) ~ ;-(kinetic 

373 
· energy), which applies for dilute concentrations of the impurity atoms. 

Experimental evidence supporting this conclusion comes from electronic specific 

heat and other observations (Keyes 1979) and (Shibib and Lindholm 1980). 

The random component of the atomic potenti al introduced by the approximate 

random positions assumed by the impurity atoms in the host lattice results in 

band tails, as Lifshitz (1942) first notes. A portion of these band tails 

comprises bound quantum states where trapping of majority and minority carriers 

can occur. 

Macroscopic lattice strain introduced by a high concentration of impurity 

atoms, and the accompanying structural imperf\\=ctions, in principle can also 

i nfl uence the quantum density of states, rna; nly through changes in the energy 

gap. 

Thus we conclude: (a) the warped quantum density of states at the lower 

end of the range of high doping concentrations may decidedly affect device 

performance, particularly near the edge of the pin junction transition reg'ion 

and particularly if the device design emphasizes avoidance of high impurity 

concentrations, as in recent cell designs advanced by Green and Blakers, by 

Wolf, by Spitzer and co-workers, by Rohatgi and by others 1); (b) the 

prevalence of a near standard quantum density of states for concentrations> 

1019 cm-3 admits treatment of the majority carri ers as a Fermi gas, and 

associated simple screening models enter; (c) the existence of bound states 

near the minority-carrier band edge may introduce trapping as an important 

mechani sm if many such states exi st. 

These conclusions receive attention in the sections that follow. 

2.2 Statistics 

Electrons (and holes) are fermions. Thus their distribution in energy is 

described by Fermi statistics. At low enjough carrier concentrations, the 

Fermi functi on tends to\'/ard a Maxwell-Boltzmann function (Boltzmann 

statistics). Fermi statistics contain Boltzmann statistics.. Thus there is no 

fundamental reason to argue the issue whether Botlzmann or Fermi statistics 

apply, as many workers have done. The answer is that Fermi statistics always 

apply. From a practical viewpoint, however, some need exists for further 

consideration. As one example, if past work has used Boltzmann statistics, 

correctly or incorrectly, as a vehicle for framing such experimental results as 

energy-gap narrowing 8EG, then one must take care in the introduction of Fermi 

statistics when using these results. If raw data exist, however, then one can 

USI~ Fermi statistics to reframe the parameters of interest. Such a parameter 

is energy-gap narrowing and its dependence on impurity concentration. As 

1) See the special issue of the IEEE Transactions Electron Devices, May 1984. 

374 

-----~~~~--.-----.. ~.- ,~,--".~,-~--
another example, one may wish to avoid Fermi statistics to obtain expressions 

that yield more easily to analytical or numerical treatment. For numerical 

sol uti on of the fi nite-difference or fi nite-el ement counterparts of the basi c 

differential equations, however, the availability of a variety of accurate 

approximations to the related Fermi integrals (Blakemore 1982) apparently makes 

this unnecessary. 

As a fundamental point, one may remember that Fermi statistics always 

describe electrons or holes. This is not true for Boltzmann statistics which 

introduce considerable error if the majority-carrier density > 1018 cm-3 • 

Incorrect temperature dependence of vari abl es may be one result of mi suse of 

Boltzmann statistics. We would not belabor this issue if it had been discussed 

less in the literature. 

Fermi statistics also describe the occupancy in equilibrium of bound 

states, such as those in band tails. But a difficulty enters here because the 

Fermi statistics must be altered to contain the degeneracy of the bound state. 

This degeneracy apparently is unknown for band tai 1 s. The same diffi culty 

prevails, of course, if one uses Boltzmann statistics. 

Finally we define explicitly the term, Fermi gas, used in Sec. 2.1. The 

concentration of such a. gas ;s determined by the integral of the product of the 

standard Fermi function for delocalized states and the standard quantum density 

of state, QDS~/-(kinetic energy). This integral, the Fermi integral to order 

one-half, will enter later into models for ~EG through the screening length of 

a Fermi gas. 

3. HIGH CONCENTRATIONS 

By high concentrations of shallow acceptor or donor states we mean 

> 1019/cm3, approximately. For such concentrati ons, as suggested above, the 

quantum density of delocalized states of both conduction and valence bands 

obey, 

ODS(E') oc ;-(E')dE' (3.1) 

where Eli s the ki net i c energy measured from the mobil ity edge of the band. 

For developments that follow, note that an electron, or hole, at this band edge 

has only potential energy, according to quantum theory. Thus the band edge 

corresponds to the energy reference for kinetic energy. 

Thus the hole or electron concentration in thermal equilibrium is the 

integra 1, from the band edge to i nfi ni ty, of the product of (3.1) and the 

standard Fermi-Dirac function. For the majority carriers this integral, the 

Fermi integral of order" on~-half, describes a Fermi gas. Because the Fermi 

function goes into a Boltzmann distribution for low particle concentrations, 

the Fermi gas becomes a Boltzmann gas for the minority carriers. 

375 

. -
3.1 Fenmi Level 

The Fenni level F or Fermi potential of a Fenni gas follows from standard 

expansions (Kubo, 1966, p. 231); the Fermi level shows only a slight 

temperature dependence, which for terms up to the order T4 is 

F(T)/F(T = OK) = 1 - (i/12)[kT/F(O)]2 - (n4/80)[kT/F(0)]4 + ••• (3.1.1). 

The weakness of this temperature dependence will prove useful in the discussion 

below concerning the energy gap, measured electrically. 

3.2 Einstein Relation for Majority Carriers 

For a position-dependent doping concentration, the principles of detailed 

balance requires oppositely directed majority-carrier drift and diffusion 

currents, equal in magnitude, for thermal equilibrium. This requirement, 

together with the position independence of F and with the association of a band 

edge with potential energy (discussed in regard to Eq. 3.1), establishes the 

slope of the majority-carrier band edge and hence the drift field acting on the 

majority carri ers. The energy-gap narrowi ng t£G(x) then determi nes the drift 

field (or quasi-field) acting on the minority carriers (Fig. 5). In general, 

the majority-carrier and minority-carrier fields differ in magnitude and may be 

opposite in sign. This has central importance in the analysis of the 

performance of devices. 

Because of the balance, and for other reasons, the ratio of diffusivity D 

to mobility ~ is significant. For the Boltzmann gas of the minority carriers, 

D/~ = kT/e (3.2.1) 

which is the standard Einstein relation of 1905. If trapping influences the 

transport of minority carriers, as later we shall suggest, the Einstein 

relation remains valid because trapping is spontaneous and random. 

For majority carriers, the Einstein relation of the Fermi gas shows that D 

has a stronger dependence on particle density than does~. Lindholm (1984) has 

suggested that this behavior originates in the kinetic pressure dependence of a 

Fermi gas, the gradient of which is related to the gradient of the chemical 

potent i a 1 and hence to di ffus ion. For T = 300K, the dependence is shown in 

Fi g. 6, fi rst plotted by Lindholm and Ayers (1968). Landsberg (1952) fi rst 

derived the D/~ relation for a Fermi gas as a ratio of Fenni integrals, a 

simple yet accurate approximation of which is due to Kroemer (1978). 

3.3 NP Product if there is no Energy Gap Waff09ri~ 

The hole concentration product with the electron concentration for thermal 

equi 1 i bri urn enters semi conductor devi ce phys i cs because excitations may often 

be assumed to provoke a small perturbation (quasi-equilibrium) of the 

equilibrium condition. Thus use of the PN product in equilibrium often yields 

a pre-exponential constant multiplying a tenn of the form, exp[V/(kT/e)] - 1. 

376 

--
For a Boltzmann gas, 

PN = nr(T), (equilibrium) (3.3.1) 

which is often called the law of mass action. For a Fermi gas, the PN product 

falls with increasing majority carrier density. Kleppinger (1970) first 

plotted this dependence (Fig. 7). Because 

, (3.3.2) 

one might think that Fig. 7 implied an increase in energy gap as the majority 

carrier concentration increases. But the construction of Fig. 7 assumed 

independence of the energy gap on majority carrier concentration. Thus the 

result shown deri ves only from use of Fermi rather than the more famil; ar 

Boltzmann statistics. 

Many previ ous workers have interpreted experimental results usi ng 

Boltzmann stati sti cs to deduce the carri er concentrati on dependence of the 

energy gap. Because of the dependence shown in Fi g. 7, when a Fermi gas is 

used to describe majority carriers, larger energy-gap narrowing is inferred 

from experimental data. Thi s partly expl ai ns the di screpancy between the 

results of Neugroschel, Pao, and Lindholm (1982) and those of many other 

workers. A related elaboration appears below. 

3.4 Slope of Mobility Edge for Minority Carriers 

We have discussed this issue above in Sec. 3.2, relating to the inequality 

between the drift fields acting on the majority and the minority carriers. For 

a diffused junction, for example, a huge drift field acts on the majority 

carriers. If this same field were to act on the minority carriers, those 

injected over the pIn junction barrier into the quasi neutral emitter, or front 

layer, would be so signifiantly drifted back toward the junction transition 

region that the probability of reaching the surface would be low (Lindholm, Li 

and Sah, 1975). Experimental evi dence i ndi cates that such mi nority carri ers 

reach the surface in great abundance where they vani sh, if the front surface 

recombination velocity is high, without contributing to current in the external 

circuit (Iles and Sockloff, 1975), (Fossum, Lindholm and Shibib, 1979). The 

inequality of the majority-carrier and minority-carrier quasi fields helps 

explain this result. 

3.5 Energy Gap 

If we restrict consideration to donor or acceptor impurity atom 

concentrations high enough (Sec. 2.1) that a Fermi gas description becomes 

adequate, then an approximate model for the energy-gap narrowi ng t-EG as a 

function of majority-carrier concentration (n or p) emerges. The central 

parameter entering this model is the Debye or Thomas-Fermi screening length A, 

as first suggested by Sah and collaborators (1981) and discussed systematically 

by Landsberg, Neugroschel, Lindholm and Sah (1984). 

377 
The model starts from the view that the highly doped semiconductor is, to 

some extent, a neutral dielectric continuum in which positive and negative 

particles are smeared out over macroscopic vol~me. This model continuum 

consists implicitly of particles in complicated and correlated motions, the 

correlation coming from the forces among the particles. The correlated motions 

of the actual many body problems incorporate the long-range part of the Coulomb 

forces between the electrons (assuming for concreteness n+ silicon) and between 

them and other charges, both those fixed in the lattice (ions) and those that 

are mobile. The most significant forces are short-range which one can view as 

forces altered by screening of the many electrons. These forces one can 

characterize, with no additional approximation involved, as a screened 

potential, the relation being the equality between the gradient of the scalar 

potential and the vector force field. The introduction of the screened 

potential simplifies discussion, as will be seen. 

We treat the screening length for this potential as a constant, which is 

an approximation (Landsberg, et. al., 1984). Then we consider the creation of 

an electron-hole pair, which at the first instant are in a bound state at 

r = 0, to fix the reference position. Then we imagine the hole to remain 

trapped and the electron to be removed to infinity against the screened Coulomb 

attracti on. The total energy to create the pai r, and to separate it, is 

(Fig. 9) 

ENERGY:: W + (e2/Ea)exp(-M) (3.5.1) 

where W is the energy requi red to create the pai r in the bound state and the 

second term on the right side is the energy required to separate the pair. The 

sum of these two energies then yields a created free electron and free hole. 

Thus this sum is the energy gap,which depends on nand p through the screening 

length "II.. The consequent energy gap narrowing, ENERGY(O,O) - ENERGY(n,p), 

illustrated in Fig. 9, depends only on ~(n,p) because subtraction cancels Wand 

the cut-off distance a (Landsberg et. al., 1984), which are regarded as 

concentration independent. The energy W is concentration independent because 

the model employed attributes energy-gap narrowing only to carrier screening. 

The question remains as to the choice of ~, a parameter that enters many 

part of physics (Landsberg, 1981). Using Debye or Thomas-Fermi screening gives 

the same result in the limit of extreme degeneracy. The result, which in cgs 

units is 

(3.5.2) 

is a function of the effective mass of the majority carriers, E, and n for n+ 

silicon. If one assumes equality between the effective mass and the rest mass, 

E = 11.7, one obtains 

(3.5.3) 

378 
Ii I I I 

I 

This energy-gap narrowing exceeds that of Lanyon and Tuft (1979) who 

adopted a different screening model and used a different physical picture 

following the suggestion of Hauser (1969). The difference is a factor of 1.33. 

We note the prediction of an energy-gap narrowing of 215 eV for a car~ier 

concentration of 1020/cm3• 

For a general value of n, and for a parabolic band (Sec. 2.1), the energy 

gap becomes 

(3.5.4) 

where I is the Fermi integral of order one-half and y is the kinetic energy of 

the electrons normalized by kT. If both holes and electrons are numerous, one 

need only add a similar Fermi integral for the holes multiplied by the 

effective density of states for the valence band. 

This last formula we shall adopt for comparison with experiment. Though 

it applies for all levels of concentrations, we shall recall our previous 

discussions (particularly that of Sec. 2.2) emphasizing the inappropriateness 

of the assumed parabolic bands that underlie the origin of the Fermi integrals 

of order one half. MorE;!over, because of physi cs rel ated to the cutoff di stance 

a in (5.3.1)~ the expression holds with good accuracy only for concentrations 

up to 5 x 10~O/cm3 (Landsberg, et al., 1984). 

If we now compare with experiment (Fig. 10) obtained by electrical 

measurements, we note the excellent fit of this theory with the values obtained 

for Si:As by Neugroschel, Pao, and Lindholm (1982), (full circles), and for 

Si:B by Landsberg, Neugroschel, Pao, Lindholm and Sah (1984) (full triangles) 

by the same method. We note that the agreement is good only for majority 

carrier concentration> 5 x 1019/cm3, as expected from the discussions of Sec. 

2.1 and elsewhere above. In constructing Fig. 10, we have assumed for the 

experimental results in full circles and triangles an effective mass of 

electrons and holes that is a factor of 1.1 larger than the electron rest 

mass. The effective masses have uncertain values for highly doped silicon, 

t"hough the assumption just stated agrees with the val ues usually advanced for 

the effective electron mass of dilutely doped silicon. In regard to most of 

the rest of the measurements of energy-gap narrowing in the literature, some of 

which are shown in Fig. 10 without explicit identification, Boltzmann 

statistics were used. We have recalculated these data so as to allow a fair 

comparison. 

The agreement between the model above and the various experiments 

approaches the agreement between different experiments. The agreement tends to 

be better for larger concentrations, as expected (Sec. 2.1). 

The experimental results of workers other than those mentioned are smaller 

than ours cited above. Apparently several reasons exist for this 

disagreement. In some of the work of others, the impurity concentration was or 

379 
may have been markedly dependent on position. Thus enters the effect of the 

quasi-field on the minority carriers (Sec. 3.4); moreover these workers used 

some spatial average of the impurity concentration. Another significant 

difference between the work referenced above and that of others involves 

assumpt ions about the mi nority carri er mobil ity \.1. The energy-gap narrowi ng 

from electrical measurements pictured in Fig. 10 comes from the minoritycarrier current, which depends on the product ~Xp(LlEG/kT). Other workers have 

assumed an equal ity between the mi nority carrier and majority carrier mobil ity, 

which has the convenience that the majority carrier mobility is perhaps 

adequately known from conventi onal measurements. In contrast, in the work 

ci ted above, we assumed only a near temperature independence of iJ. and LlEG ina 

small range of temperatures near 300 K. This leads to evidence that iJ. is about 

one order of magnitude smaller than the majority carrier mobility for 

concentrations of about 1020/cm3 in Si:As (Neugroschel and Lindholm, 1983). 

This contributes to the differences noted. Controversy about these issues 

exists, as evidenced by the communications exchanged between del Alamo and 

Swanson (1984) and Neugroschel and Lindholm (1984). 

Figure 11 compares our model predictions (Eq. 5.3.4) with the recent 5 K 

photoluminescence and photoluminescence excitation data of Wagner (1984). At 5 

K and for these doping concentrations, the effective masses for holes and 

electrons are unknown •. Thus we introduce the noncommital symbol m*/m for the 

effective mass ratio with the electron rest mass. For intrinsic silicon at 

5 K, the ratio is about 1.06 (electrons) and 0.59 (holes). Using the 

temperature dependence implicit in our model above! we find that best agreement 

with Wa!~ner's data occurs for m*/m = 0.45 (Fig. 11). 

3a6 Minority-Carrier Diffusivity and Mobility 

Ex.pl oiti ng temperature dependenci es, Neugroschel and Lindholm (1983) have 

present.ed evi dence, as noted above, for a much lower mi nority-carri er mobil ity 

and diffusi vity than that assumed previ ously. They obtai ned these results for 

Si :As having a doping concentration of about 1020/cm3, for which a customary 

Fermi integral of order one-half was assumed to describe the majority 

electrons. This fixes the electron quasi-Fermi level approximately 100 meV in 

the conduction band above the band edge. In a simple physical picture advanced 

to explain these results, Neugroschel and Lindholm supposed the trapping of 

minority carriers at the bound states of band tails (or at acceptor states in 

the compensated n+ silicon). Holes while trapped do not contribute to current 

of the hole Boltzmann gas. Thus for this mechanism to enter significantly, the 

characteristic time for thermal emission of a hole from a shallow bound state 

must be of the same order as the scattering time of holes within the valence 

band. Although band tails appear near both conduction and valence-band edges, 

trapping of the majority electrons is a negligible mechanism because the 

electrons contributing to curent lie near the Fermi level, about 100 meV away 

from the nearest band tail state. An illustration of the pertinent hole 

trapping appears in Fig. 12. 

- 380 
3.7 Trapping Model 

To explore this mechanism from a theoretical viewpoint, it is useful to 

generalize the Boltzmann equation to include band-bound transitions. This 

generalization, discussed, for example, by Smith, Janak, and Adler (1967) and 

worked out in detail by Sah and Lindholm (1973), involves approximating 'the 

collision integral~ for small departures from equilibrium, by the sum of two 

terms of the form, (f - fo)/'t;{relaxation). This first term is the customary 

relaxation time approximation for the nonequilibrium distribution function f in 

which .. (scattering) = .. (relaxation) is the scattering time that characterizes 

intraband transitions. In the second term, .. (trapping) instead appears, which 

characterizes the mean trapping time of holes for localized states near the 

valence-band edge. Thus .. (trapping) enters into the description of the hole 

current and of f.l(holes), as described by Sah and Lindholm (1973). In 

principle, this enables detailed investigations of the trapping model and of 

the bound states of the minority-carrier band tails. 

3.7 Other Parameters 

Besides the functional dependencies of the energy-gap narrowi ng and the 

minority-carrier mobilities and diffusivities, emphasized in the preceding 

discussions, other par?meters important for solar-cell analysis and design 

remain uncertain for silicon having donor or acceptor atom concentrations in 

the moderately high and high ranges. We point to the absorption coefficient 

a(A), which has importance not only for the obvious reason of detailed 

calculation of photogeneration in the emitter or front layer. It also has 

importance in schemes for measuring other parameters. We have not touched on 

the lifetime in the volume of the heavily doped emitter and have referred only 

tangentially to the front surface recombination velocity. This is intentional, 

based on the assumption that other authors in the JPL Research Forum will focus 

on parameters relating to these mechanisms. In an extensive recent review of 

electri cal current and carri er density in degenerate semi conductors, Marshak 

and van Vliet (1984) have emphasized the need for better knowledge of such 

parameters as the effective masses, dielectric permittivity E, and electron 

affinity x. He agree with their assessment, and refer the reader to thei r 

paper for details. 

4. MlDERATE CONCENTRATIONS 

For impurity concentrations approximately ~ 1Q18/cm3, the metal-insulator 

transition impl ies that the majority-carrier quantum density of states will 

differ sharply from the standard dependence. This occurs partly because of the 

exi stence of impurity bands, accordi ng to the theory that interprets thi s 

transition. 

Thus many aspects of the physical electronics become more difficult and 

less precise. 

381 
4.1 Fenmi level Saturation and Consequences 

The severe wa rpi ng of the quantum dens i ty of states from the ri gi d-band 

model (parabolic band) results in far less penetration of the Fermi level into 

the majority carrier band as the doping concentration increases. Indeed for a 

range of doping concentrations one may anticipate that the Fermi level nea"rly 

saturates. This leads to (a) a smaller energy-gap narrowing than 

interpretation of data on emitter recombination current by the rigid-band model 

would imply, a.nd (b) a stronger quasi-field on the holes (minority carriers) 

that drifts holes toward the surface. This in turn yields a stronger 

dependence of emitter recombination current (and open-circuit voltage if 

emitter recombination current (and open-circuit voltage if emitter 

recombination current is important in a cell design on the front surface 

recombination velocity. 

Figure 13 illustrates result (b) for a concentration of free electrons 

decreases in the n+ silicon with x from its value at the surface (x=O). 

4.2 Einstein Relation for the Majority carriers 

In its simplest derivation, the Einstein relation for OIl! derives from 

detailed balance between drift and diffusion tendencies in thermal 

equilibrium. Diffusion "depends on the gradient of chemical potential, which is 

related to the kinetic pressure. The kinetic pressure of a Fermi gas having a 

non-standard band differs considerably from that for a standard band. Thus so 

also does the Einstein relation differ from that pictured in Sec. 3.2. 

4.3 Einstein Relation for the Mjnority Carriers 

The mi nority carri ers are a Boltzmann gas, and the Ei nstei n rati 0 is 

standard: D/I! = kT/e. 

4.4 Unsolved Problems and Consequences for Computer Simulation 

These issues are treated in Sec. 5.3. 

5. BASIC EQUATIONS FOR SIMULATION 

The basic equations for analysis or for computer simulation follow from 

the foregoing discussion of the physics for high concentrations of impurities 

(Fermi gas for majority carriers). As the discussion has indicated, these 

equations involve approximations, especially for such parameters as energy-gap 

narrowing and the minority-carrier diffusivity and mobility. The approximation 

becomes more severe for the moderate range of dopings, between approximately . 1018 to 1019 per cm3, where impurity bandi ng warps the quantum density of 

states for majority carriers from its standard dependence on energy. Thus the 

position of the Fermi level and consequently the quasi field for the majority 

carriers and the temperature dependence of these variables become more 

• 

382 

I 

I 

1 

'I' 

I 

! 

i 

! 

t 
uncertain than they aj'l~ f1r the· higher range of doping concentration. The • '. 1 

Einstein ratio for the majority carrier's, the energy-gap narrowing, and other 

quantum and transport paraemters also becomes less accurately known. 

5.1 I~ortance of Time Variations 

Although when delivering power a solar cell operates in the steady-state, 

time variations of the carrier concentrations, quasi-Fermi levels, potential, 

and particle current still have significance for several reasons. Fir:-st, for 

exampl e, many methods of measuri ng parameters such as 1 ifet ime 't i nvol ve either 

a transient or an exp(iwt} variation. As a second example, trapping of 

minority carriers at bound states in the band tails or at impurity states in 

compensated silicon may play a role in determining the minority-carrier 

diffusivity 0 and mobility~. As a third example, inclusion of the full set of 

the Maxwell equat ions among the bas i c equations, when combi ned with 

phenomenological parameters such as E, in principle yields reflection and 

transmission at the heavily doped surface. 

5.2 Conventional Equations 

In the absence of the effects i ndi cated in the precedi ng sections that 

make the physical electronics of heavily doped silicon differ from the phYSical 

electronics of dilute silicon, the conventional equations are: 

'on/ot = div(jN/-e } - Rn + g(external) (5.2.1) 

op/ot = div(jp/e} - Rp + g(external} {5.2.2} 

j = N e~nE + eOngrad(n} (5.2.3) 

= -e~Nn grad (v N) (5.2.3a) 

jp = e~pE - eOp grad(p} (5.2.4) 

= -e~pp grad(v p} (5.2.4a) 

div(O} = p (5.2.5) 

= e(p - n + NO~ - N

AA} (5.2.5a) 

j = j N + j P + aD/at (5.2.6) 

If recombi nat ion domi nates, the. remova 1 rates, Rn and Rp become equal. For 

electrons and holes from quasineutral regions, this equality defines the 

1 i fetime 't: (R -+- M/'t). 

A seventh equation will describe, for the steady state, some assumed model 

for the recombination rate and hence the lifetime 'to Sah (1977) has expressed 

this equation in its most general form to unify impact-Auger, Shockley-Read383 
Hall and othe.r mechanisms. For greater generality, the kinetic rate equation 

for the time variation of particle density on traps (Sah 1971) supplements the 

equation of the steady state recombination rate. This then provides a 

quantitative characterization of the minority carrier diffusivity D and 

mobil i ty IJ. when the trappi ng rate at bound states becomes comparabl e to .the 

scattering rate within the minority carrier band (Sah and Lindholm, 1973), as 

discussed earlier. This equation, or equations, not given explicitly here, is 

numbered (5.2.7). 

To these seven equations are added auxiliary relations to enable or aid 

solution. 

di v(j + cO/ct} = 0 (5.2.8) 

E = -grad(V} (5.2.9) 

E = O/e: (5.2.10) 

n/n. = exp(v' 1 

v' ) N (5.2.l1) 

p/n. = exp(v p - v' } (5.2.12) 1 

diffusivity/mobility = kT/e (5.2.13) 

Here the primes denote normalization by the thermal voltage kT/e to yield a 

dimensionless variable. Eq. (5.2.8) assures the position independence of the 

total current, which becomes the position independence of convection current j 

for the steady state and j * f(x) in a one-dimensional model. This relation 

simplifies analysis. Maxwell's other three equations are added, but not shown, 

for reasons given directly above. 

We omit detailed discussion of the lifetime ~ for heavily doped silicon, 

assuming that other authors in this Research Forum will provide this. 

5.2.1 Counting 

To' assess the possibility of solution, we now count unknowns and 

equations. The first two equations, (5.2.1) and (5.2.2), the continuity 

equations for holes and electrons, introduce four unknowns: the electron and 

hole densities and current densities. The optical excitation determines the 

generation rate through a relation of the form, 

g(external} a !exp[-a(A)x]dA (5.2.14) 

where the constant of proportionality depends on the fraction of the sunlight 

transmitted past the surface into the volume of the solar cell. For a given 

solar-cell design, g(external} is assumed known. 

384 
1 

I 

I 

~ 

I 

1 

~ i 

I 

If we deal with the current densities as expressed in terms of drift and 

diffusion components, we introduce one more. unknown: the electric field E(x) :: 

-grad[v(x)]. Assuming E is known in (5.2.10), (5.2.5a) then becomes Poisson1s 

equation for v(x), the fifth equation in five unknowns. 

If we deal with the electron and hole currents expressed in terms of the 

gradient of their quasi-Fermi potentials, we have as unknowns, in the two 

current density and two continuity equations, the following: the hole and 

electron densities, and the hole and electron quasi-Fermi potentials,. and the 

hole and electron current densities. This gives six unknowns in four 

equations. But (5.2.11) and (5.2.12) introduce only a single additional 

unknown, v(x), the electric potential. Thus adding Poisson1s equation, from 

combining (5.2.5a), (5.2.9) and (5.2.10), yields in principle a solvable set of 

equations. 

The equations are nonlinear. To illustrate this, note that the product of 

nand grad(-v(x)) appears in the equation for the electron current density. 

But n and v are related through (5.2.5) when put in the form of Poisson1s 

equation. Assuming analytic functions, one can express this relation by a 

Taylor series. Thus the equation for electron density involves a sum in which 

234 5 n, n , n , n ,n ••• appear. 

Because of nonlinearity, solution of the basic equations requires either 

approximations for special cases that yield analytic solutions or numerical 

solutions of the finite-difference or finite-element counterparts of the basic 

equations. 

5.2.2 Remark on Quasi-Fenmi Potentials or Levels 

Solar cells must contain ohmic contacts to enable power delivery. An 

ohmic contact is a union between metal and semiconductor that allows electrons 

and holes to flow freely between the metal and the semiconductor. Hence, at 

the contact, electrons and holes can neither accumulate or become .depleted, 

their densities stay at equilibrium values (assumed known), ·and the hole and 

electron quasi-Fermi levels converge to the Fermi level F.' This impl ies that 

at an ohmic contact the merged quasi-Fermi levels in the semiconductor join the 

Fermi level in the metal without discontinuity. But the Fermi level at any 

pOint in a metal is the electric potential at that point. Thus the potential 

difference between two ohmic contacts in a solar cell or any semiconductor 

devi ce equals the difference between the merged quas i-Fermi 1 eve 1 sin the 

semiconductor at the two contacts. 

As a result, a potential difference in an external circuit causes an equal 

potl~ntt.A~ difference in the quasi-Fermi levels at the two contacts. Hence use 

of tne" quasi-Fermi level description of hole and electron currents allows a 

simple introduction of the boundary conditions on electric potential. The 

alternate description in tenns of drift and diffusion ccmponents requires 

sati:sfaction of the boundary conditions on potential by setting a line integral 

of the electric field through the semiconductor equal to the potential 

difference appearing at the terminals. 

385 
• 

Advantages thus apparently resul t for numeri cal simul at i on. Moreover a 

preference for description in terms of quasi-Fermi levels enables a 

straightforward introduction of trapped particles at bound states in the 

forbidden gap. This is done by use of quasi-Fermi levels (or occupancy 

probabilities) for each of the bound states. If then one restricts attention 

first to variations in the potentials at the terminals and hence to variations 

in the quasi-Fermi potentials within the volume of the semiconductor device 

that are much smaller than the thermal voltage kT/e, the set of basic equations 

become linear. To these linear equations corresponds a electric circuit 

representation. That circuit representation often can be simplified by using 

the theory of electric circuits; for example, Y to /::,. transformations can yield 

simplifications. Thus numerical solution of the finite difference equations 

becomes easier. To obtain solutions to the nonlinear equations, one simply 

adds the consequences of successive small-signal responses to potentials small 

relative to kT/e. 

Sah has advanced and utilized computer algorithms related to those just 

described; for example, see Sah (1971) and Sah, et al. (1981). 

5.3 Modified Basic Equations 

We now consider the modifications needed to include the phenomena occuring 

in highly doped silicon treated in the foregoing sections. The reader may 

refer to Sec. 5.2 on the conventional basic equations, which we now modify. 

The continuity equations remain intact; they serve the bookkeeping purpose 

of summing all contributors to changes in particle density with time. 

Because carriers at the mobility edge have only potential energy, we see 

that the electric field E governing the drift component of the majority-carrier 

current becomes grad[mobility edge/-e]. This is the same relation prevailing 

in the convent i oan 1 equations except that the mobil i ty edge has replaced the 

band edge. If we take n+ material for concreteness of discussion 

E + -grad[Ec

/ -e] (5.3.1) 

where 

grad[EC/-e] = grad(v) + grad( xl - e) (5.3.2) 

as in Sah and Lindholm (1977) and Marshak and van Vliet (1984). 

Typically majority carrier concentrations will be perturbed only slightly 

in nonequilibrium; that is, the low-injection condition will prevail. Thus we 

anti ci pate a near pos ition independence of the majority-carrier quasi -Fermi 

level, and we anticipate that the energy separating this quasi-Fermi level from 

the mobility edge for the majority-carrier band will remain as in equilibrium, 

to a good approximation. Thus the left side of (5.3.2) will be determined; the 

right side will become unimportant to the majority-carrier drift component. 

386 
For a Fermi gas (parabolic band), the diffusion component of the majority 

carriers remains intact; the D/IJ. ratio reflects the Fermi statistics, as 

discussed in Sec. 3.2. For a moderately doped region, we have emphasized the 

warping of the quantum density of states, in accord with the metal-insulator 

transition. The diffusion current then depends on the random force (Prigogi.ne, 

1980) or ki netic pressure appropri ate to thi s quantum density of states. To 

dccount for this the diffusion component of the majority carrier current, a 

term involving a gradient in addition to the gradient of n appears (Marshak and 

van Vliet, 1984). 

We note that these complications concerning the majority-carrier diffusion 

current vanish if one deals with (S.2.3a) in which this current is simply the 

electron conductivity times the gradient of the electron quasi-Fermi potential 

(electrochemical potential). The electrochemical potential is a basic 

thermodynamic variable whose gr'adient is linear in the particle current except 

for large deviations from equilibrium. The vanishing of the complications 

referred to is only apparent, however, because they will reappear in the 

relation between the quasi-Fermi levels and the particle densities, as we shall 

soon see. 

Equation (S.3.1), for the majority carriers, relates to the drift 

component of hole current (minority current) through 

grad[EV/-e] = grad[EG/-e] - grad[Ec/-e] (5.3.3) 

The product of this gradient (left side) times the hole conductivity determines 

the hole drift current (minority-carrier drift current) in terms of the 

gradient of the majority-carrier mobility edge (known through Eq. (S.3.1)) and 

the energy gap dependence, assumed known through the model of Sec. 3.S or 

through experimental determination. 

If we assume that the band tails of the minority-carrier band are mainly 

bound. states, the hole (minority-carrier) current is the conventional sum of 

drift and diffusion components, with D/IJ. = kT/e, for a Boltzmann gas. 

Thus the conventional description for the minority-carrier current 

survives except that the gradient of the quasi-field, influenced by the 

gradient of the energy gap, replaces the conventional electric field. This 

replacement has key importance, as we have emphasized earlier. But the 

survival of a simple description of the minority-carrier current permits, for 

the quasi-neutral emitter, many approximations that give simple relations for 

the quasineutral emitter recombination current. Examples· include the 

transparent-emi tter model of Shi bi b, Li ndholm, and Therez (1979) extended by 

del Alamo and Swanson (1984), the field-free model introduced by Fossum, 

lindholm, and Shibib (1979), etc. 

387 

R nld a ea J!Jt. ~'.j; 
i _ 

5.3.1 Modifications for Computer Solution 

Having just discussed anlaytic solutions for the qusineutral regions, we 

now turn attent i on agai n to contact-to-contact computer sol uti on by fi nitedifference or equivalent formulations of the basic equations. 

Consider Poisson's equation, resulting from combining (5.2.5a) with 

(5.2.9) and (5.2.10). The key issue becomes the relation of potential v(x) to 

n(x)and p(x) in view of (5.3.2). Consideration tllat p and n are proportional 

to integrals of the form, f[QoS(E)](probabilfty~E,QFL)]dE, will show an 

asymmetry in the expressions for nand p not present in the standard relations 

(5.2.11) and (5.2.12). This occurs because the probability function in the 

integral will be Fermi-Dirac form for electrons (majority carriers) and 

Boltzmann form for holes, and because the QoS may contain the effects of 

impurity banding for the electrons but not for the holes. In principle, 

knowledge of the QoS for both bands will permit replacing the standard relation 

by 

(5.3.1.1) 

p = B f*[v p - (Ev(-e)] (5.3.1.2) 

These are the most general re"lations. If we assume that the bandtail states of 

the minority band are localized, f* becomes an expontial function and B becomes 

the standard density of states for the val ence band. If, for highly doped 

semiconductors, we assume impurity-banding effects are negligible, f becomes 

the Fermi integral of order one-half and A becomes the standard density of 

states for the conduction band (we allow for a deviation of the effective mass 

from its standard value). Otherwise f, f*, A, and B become determined by the 

integral indicated above, and are known only if QoS is known. 

To these two equations, \fie add sev.en more to yield ten equations in ten 

unknowns, suitable for finite-difference, contact-to-contact computer solution: 

on/ct = -div(jN/-e) - R(n,p) + g(external) 

cp/ct = -div(jp/e) - R(n,p) + g(external) 

jN = -elJ.

n

n grad(v N) 

jp = -elJ.p P grad(v p) 

riv = -(e/e:)[p - n + NO~ - NAA t ~ trapped particles] 

Ec - Ev = EG ' grad(Ec) - grad(Ev) = grad(EG) 

grad(Ec/-e) = grady + grad( x/-e) 

j = jN+ jp + cO/ct , 0 = e:E , E = -grad(v) 

388 

(5.3.1.3) 

(5.3.1.4) 

(5.3.1.5) 

(5.3.1.6) 

(5.3.1.7) 

(5.3.1.8) 

(5.3.1.9) 

(5.3.1.10) 
These equations are basic for exact computer simulation. Apparently they 

have not appeared as the identified basic set before, though Marshak and van 

Vliet (1984) discuss many relevant issues. 

The equations requi re know1 edge of many parameters such as energy~gap 

narrowing, minority-carrier mobility, and charged bound states. The last of 

these will be most important near the metallurgical junction for low forward 

voltage. They require also knowledge of the position dependence of the 

electron affinity x(x), which apparently has received little attention, and of 

the quantum density of states of the majority-carrier band for moderately high 

concentrati ons (roughly rv lOIS /cm3) whi ch has received most attenti on for the 

metal-insulator transition at approximately 4K. 

Approximations simplify the basic equations for the quasi-neutral 

emitter. Just below (5.3.2) we noted that the gradient of the majority-carrier 

mobility edge is known, partly because of the position independence of the 

majority-carrier quasi -Fermi 1 evel • In the quasi -neutral emitter, low 

injection implies that the dependence of electric potential v(x) will remain to 

a good approximation as it was in equalibrium. Thus Poisson's equation and the 

resulting entry of x(x) can be ignored for the quasi neutral emitter. This 

simplified computer solution. This adds emphasis, however, to a need for 

precise determination of the edge of the quasi neutral emitter. 

6. AREAl INHlJ40GENEITY AND KJlTIDIMENSIONAl Fl()l 

Apparently all detailed analyses of the highly doped emitter of silicon 

solar cells are based on a one-dimensional model. But the emitter surface in 

the best solar cells will be a mixture of ohmic-contact metal (S rv 107 cm/s) 

and of a surface passivated over perhaps 95% of the area by thermal oxides or 

other methods that reduce the surface recombination velocity S there to orders 

of magnitude below 107 cm/s. 

At least two cases of relevance exist. If the emitter is doped in the 

moderately high doped range (rv101S/cm3) '~o avoid the so-called degrading heavydoping effects, then the relatively long diffusion lengths in this region will 

lead to three-dimensional minority-carrier flow. The ohmic contact metal will 

so reduce the ,minority carrier density that large minority-carrier 

concentration gradients will exist. Even if the design includes an n//meta1 

contact system, partly with the motive of providing an n/n+ low/high junction 

to ward minority carriers away from the ohmic contact while permitting the 

majority carriers to pass by the usual dielectric relaxation mechanism, this 

will likely not work. Because of energy gap narrowing on the n+ side, no 

significant barrier in the energy band can exist at the n/n+ junction when the 

dopi ng concentrati on of the n side is of the order of lOIS /cm3• Thus three 

dimensi ona1 flow enters, and the open-ci rcuit voltage decreases as a 

consequence. 

389 
In the other case, the design includes n+ silicon over the great majority 

of the emitter volume. Then the diffusion length of minority carriers in the 

emitter wi 11 be short enough to admit estimates by neg1 ect i ng three- or twodimensi ona1 flow. In the resulti ng model, one-dimensional flow prevail s. But 

over the 5% of the area covered by the ohmic contact the diode there will have 

a high reverse saturation current, r'esulting from vanishing of minority 

carriers at the surface. Over the remaining 95% of the area, the reverse 

saturation current will be much smaller because of the low S over that area. 

Thus, in good designs in which the recombination current of the quasi neutral 

base is small enough that the emitter enters significantly into determining the 

open-circuit voltage and the effiCiency, the importance of a relatively bad 

diode over 5% of the area becomes potentially important. 

Lindholm, Mazer, Davis and Arreola (1980) have considered this issue 

quantitati ve1y. The I'esult, for thei r type 1 areal inhomogeneity perti nent to 

this discussion, is that 5% of ohmic contact metal gives performances that 

nearly approaches that of a solar cell for which no thermal oxide is present to 

passivate the front surface. This is not seen experimentally. Perhaps the 

reaons for this lies in the quasi-fields and in the low D and !.l treated in 

earlier sections. Thus the work of Lindholm, etal. (1980) needs updating to 

help toward informed design. This updating will help decide whether decreasing 

ohmic contact area can· lead to high efficiencies in already highly efficient 

silicon solar cells. 

Note that the issue here is not metal shading of the incident light. 

Rather it is the fraction of the surface area that is covered by ohmic contact. 

7. CONCLUSIONS AND RECOMMENDATIONS 

The main findings discussed here are: 

(a) The quantum density of states for moderately doped silicon (approximately 

in the range 5x1017 to 1Q19/cm3, deviates sharply from the standard quadratic 

dependence on kinetic energy. This can lead to pinning of the majority-carrier 

quasi -Fermi 1 eve1 and produce thereby, for a positi on-dependent impurity 

concentration, a quasi field on the minority carriers that drifts them toward 

the surface. The modeling of many pertinent variables in this moderate 

concentration range is incomplete, although other workers, particularly 

Slotboom and deGraaf (1975), have emphasized this doping range. The 

incompleteness results from the model they and others have used, which combined 

Boltzmann statistics with an implicit quadratic relation between the quantum 

density of band states and the free-carrier kinetic energy. The meta1-

insulator transition dramatically illustrates the inadequacy of this quantum 

density of states for moderate doping concentrations. As a potential benefit, 

note that the long and continuing interest in the metal-insulator transition, 

both experimental and theoretical, provides clues for the modeling of this 

range of moderate doping concentrations. 

390 
(b) For higher doping concentration, experimental evidence suggests the 

adequacy of describing the majority carriers by a Fermi gas, that is, by a 

Fermi integral of order one-half. This admits use of a majority-carrier 

screening model, which, though much less ambitious than the many-particle 

computations that have and are emerging, gives simple theoretical dependencies 

of 'energy-gap narrowing on impurity concentration and temperature. These 

dependencies agree favorably with the experimental results on energy-gap 

narrowi ng of several different groups of workers. Compared with the manyparti cle model, the carri er-screeni ng model has the vi rtues of simp1 i city and 

of yielding an analytic expression. This carrier-screening model in its 

earl iest form ((Sah, Chan, Wang, Sah, Yamakawa, and Lutwak) 1981) and in its 

more detailed form (Landsberg, Neugrosche1, Lindholm, and Sah, 1984) ,differs 

substantively from earlier carrier-screening models (Hauser, 1969), (Lanyon and 

Tuft, 1979). 

(c) The randomness of the atomi c potential cont ri buted by the assu,med 

random positioning of the impurity atoms leads to the formation of tails on 

both the conduction and valence bands. The characteristic time associated with 

trapping at localized states in the tail adjoining the minority-carrier band 

may involve a mechanism that contributes to low minority-carrier diffusivity 

and mobil i ty of the Boltzmann gas desc ri bi ng the mi nority carri ers. 

Experimental evidence 'exists to support this conclusion (Neugroschel and 

Lindholm, 1983), although contrary suggestions appear in the literature. 

Computer simul ati on of sol ar-ce1l performance regui res detail ed knowledge of 

Illi nority-carri er di ffusi vity and mobil ity just as much as it regui res such 

knowledge of the energy-gap narrowing. Moreover, experimental interpretation 

involving electrical response also requires such knowledge. 

(d) The optical absorption coefficient 0:(A.) in moderately and highly 

doped silicon is highly uncertain; apparently it is also uncertain for silicon 

having dilute doping concentrations. Because the absorption coeffient provides 

suggestions about the energy-momentum relation of heavily doped silicon, it has 

fundamental importance to the unravelling of the detailed transport and optical 

properties of the material. This use we view as more significant than is the 

moderate need for knowing 0:(A.) for detailed computer simulation of solar-cell 

performance parameters. 

(e) The results of simple models for a heavily doped region containing 

ohmic contacts mixed with thermal oxide suggests that the one-dimensional model 

convent i onally used may not" accurately predi ct the performance parameters of 

the emitter. reg.ion, parti cu1arly the open-ci rcuit voltage. Other sources of 

areal inhomogeneity also exist, such as impurity clustering ( •••• 1984). 

(f) The basic equations for computer simulation of solar cells containing 

heavily doped silicon require inclusion of all of the effects described 

above. Present computer programs are based on eguati ons that fall short of the 

status aimed for by this recommendation. Continual updating is needed as 

experiment and theory reveal more about the dependence of transport and quantum· 

parameters on doping concentration, chemical species, temperature, etc. The 

, 391 
" • 

most severe need exists at the moderately high doping concentrations defined 

above. There the conventional treatment as a Fermi or Boltzmann gas fails. 

(g) In their greatest generality, the basic equations for the simulation 

of solar-performance must include time variations. This need arises 

particularly because time variations of response exist in many measurements 

used to determine parameters. For greatest generality, one may add the 

Maxwell's equatiQns to 'the customary continuity and current equations. 

Maxwe ll' s equations admit the vi ew of 1 i ght as a wave' phenomenon; when combi ned 

with the phenomenological material paramaters normally introduced, reflection 

and transmissi.on results. (Absorption and the optical generation rate in the 

continuity equations involve, at least fundamentally, the particle model of 

light as incident photons ,that produce. quantum transitions between the bands or 

to bound states in the forbidden bands.) 

(h) The basic equations include a kinetic equation of the time-rate 

change of occupancy at a bound state re~ulting from transitions from band 

states. This kinetic equation, emphasized by Sah (1971), is absent in most 

formulations of the basic equations for computer simulation. It enters 

markedly into such issues as the detai 1 ed model i ng of mi nority-carri'E!r mobil ity 

and diffusivity, discussed above. For the steady state inclusion of trap 

occupancy in the Poisson equation is highly important near the metallurgical 

pin junction, where the donor and acceptor dopant ~oncentrations nearly cancel 

(u'ndholm and Sah, 1977). It is im,portant al so for' work aimi ng toward high 

conversion efficiency using relatively thi'n and inexpensive silicon, such as 

th~t deriving from the WEB proc~ss. Most computer programs neglect the 

trapping mechnaism" even in the steady state. the notable exception appears to 

be the computer simul ations of Sah and co-workers (1981). 

(i) The rec~nt work' of Neugroschel and Li ndholm (1983) on low mobil ity 

and diffusivity of minority carriers 'in Si:As of doping concentration about 

~o~o Icm3 suggests a novel method of pr'otect i on from surface recombi nat i on at 

both the front and back surfaces. These arise from the possibility of 

significant gradients in minority-carrier 0 and ~ provoked by very highly doped 

silicon (""1021 /cm3 or above) in thin layers (.....sOO A or less) near the 

surfaces. The. work now evolving in non-equilibrium growth following,eximer 

laser radiation (and melting) may provide a method of sealing the surfaces 

against minority-carrier loss. This sealing mi~ht occur despite the large 

impact Auger recombination rates in such' n++ or "p'+ siUcon. Experiment will 

decide this. The issue is the inhibiting 'of flow by the gradients of 0 and ~ 

versus the oppos i ng effects, of energy-gap narrowi ng and Auger recombi nat ion. 

" As one aspect of ttre issue, we may expect that the Auger recombination,' if 

Dand-band, wlll have a rate that is prQP~ortiona1 to n2 (for n-type material) 

whereas the gradients in minority-carrier 0 and ~ may have sufficient strength 

to offset this 'n2 dependence by warding minority carriers away from the volume 

of the n++' region. We note tha't nothing is known of the physical electronics 

of n++ or p++ silicon, as defined above. Essenti,ally no, detailed experimental 

data are available about tile physical ,e1ectronics,and the model for enf'rgy-gap 

narrowing of Sec. 3.5 does not apply for cpncentrations greater than about 5 x 

1Q201cm3, according to Landsberg, et al.(1984J. 

392 
I 

I 

I 

~ I 

I 

(j) From the discussion in Sec. 5.3.1, it follows that apparently the 

formulation of the basic equations for finite-differenct computer solutions 

from contact to contact remains far from complete. By this we mean to suggest· 

that apparently computer programs now developed cannot accomodate important 

aspects of heavily doped silicon that physical theory and experimental studies 

have identified and in the future may yield values of relevant parameters. 

8. REFERENCES 

Blakemore, J. S., 1982, Solid-State Electronics, 25, 1067. 

del Alamo, J. A., and R. M. Swanson, 1984, IEEE Trans. Electron Devices, 31, 

123; Reply by A. Neugroschel and F. A. Lindholm, ibid, p. 124. 

del Alamo, J. and R. M. Swanson, 1984, Proc. 18th Photovoltaic Conf., Orlando, 

FL. 

Fritzsche, H., 1979, The Metal-Nonmetal Transitions in Disordered Systems, 

Proc. 19th Scottish Summer School in Physics. 

Fossum, J. G., F. A. li ndholm, and M. A. Shi bi b, 1979, IEEE Trans. Electron 

Devices, 26,165. 

Hauser, J. R., 1969, NSF Final Report. 

Iles, P. and I. Socklorf, 1976, NASA Final Report. 

Keyes, R. W., 1979, Solid-State Communications, 32, 179. 

Keyes, R. W., 1981, Comments Solid State Phys., 10,23. 

Kleppinger, O. D., 1970, An extension of the engineering theory of 

semiconductors,with applications, Ph.D. dissertation, University of Florida, 

Ch. 2. 

Kubo, R., 1971, Stat; st; ca 1 Mechan; cs : An Advanced Course with Problems and 

Solutions (North-Holland, Amsterdam, London). 

Landsberg, P. T., 1952, Proc. R. Soc. London, Sere A, 213, 226. 

Landsberg, P. T., 1981, Europ. J. Phys., 2, 213. 

Landsberg, P. T., A. Neugroschel, F. A. Lindholm, and C. T. Sah, 1984, Proc. 

18th Photovoltaic Specialists Conf., Orlando, FL, IEEE, New York. 

Lanyon, H. P. D. and R. A. Tuft, 1979, IEEE Trans. Electron Devices, 26, 1014. 

~; 393 
Lifshitz, I. M., 1941, J. Exp. Theor. Phys., 2, 117, 137, 156. 

Lindholm, F. A. and R. W. Ayers, 1968, Proc. IEEE, 56, 371. 

Lindholm, F. A., S. S.· Li, and C. T. Sah, 1975, Proc. 11th Photovoltaic 

Specialists' Conf., Phoenix, AZ, 32, IEEE, New York. 

Lindholm, F. A. and C. T. Sah, 1977, IEEE Trans. Electron Devices. 

Lindholm, F. A., J. A. Mazer, J. R. Davis, and J. 1. Arreolla, 1980, SolidState Electron., 23, 967. 

Lindholm, F. A.~ 1984, Solar Cells, 12, 131. 

Marshak, A. H., and C. M. van Vliet, 1984, Proc. IEEE, 72, 148. 

Mott, N. F., 1949, Proc. Phys. Soc. (London), 62, 416. 

Mott, N. F. and W. D. Twose, 1961, Adv. Phys., 10, 107. 

Mott, N. F. and E. A. Davis, 1971, Electronic Processes in Non-Crystalline 

Solids (Clarendon,Oxford). 

Neugroschel, A. and F. A. Lindholm, 1983, Appl. Phys. Lett., 42, 176. 

Prigogine, I., 1980, From Being to Becoming: Time and Complexity in the 

Physical Sciences (Freeman, San Fran~isco). 

Sah, C. T., 1971, Physica Status Solidi (a), 7, 541. 

Sah, C. T. and F. A. Lindholm, 1973, Solid-State Electron., 16, 1447. 

Sah, C. T., 1977, IEEE Trans. Electron Devices, 24, 410. 

Sah, C. T., 1977, IEEE Trans. Electron Devices, 24, 358. 

Sah. C. T., P. C. Chan, A. C. Wang, R. L. Y. Sah, K. A. Yamakawa and R. Lutwak, 

1981, IEEE Trans. Electron Devices, 28, 304; also see references therein. 

Shibib, M. A., F. A. Lindholm, and F. Therez, 1979, IEEE Trans. Electron 

Devices, 26, 959. 

Shibib, M. A. and F. A. Lindholm, 1980, IEEE Trans. Electron Devices, 27, 1304. 

Slotboom, J. and H. de Graaf, 1975,' Int. Electron Devices Meeting; also 

Solid-State Electron., 29, 857. 

394 

" 

! 

I 

I 
9. FIGlME CAPTIONS 

Fig. 1 Overlapping impurity states give rise to 

Fig. 2 impurity band in the energy gap. 

Fig. 3 The resistivity p in Q cm at 4'2K of Si:P plotted as. a function of 

donor concentration (Alexander and Holcomb, 1968). 

Fig. 4 Density of states for an electron in an n-type semiconductor showing 

the splitting of the impurity band into the E3 band (a), and the E2 

band (b). (c) is the conduction band. 

Fig. 5 Illustrating that grad(Ev '" grad(Ec) in the n+ emitter. The 

conduction- and valence-band edges, EC(x) and EV(x), are mobility 

edges, the boundaries between localized and delocalized states; EG(x) 

is the mobility gap where disorder exists. 

Fig. 6 

Fi g. 7 

Fi g. 8 

Fi g. 9 

Fi g. 10 

Fi g. 11 

Fi g. 12 

The Einstein diffusivity-to-mobility ratio for majority carriers, 

under the assumption of a square root dependence of the quantum 

density of states on the majority carrier kinetic energy. 

The equilibrium product of the hole concentration P and the electron 

concentration N normalized by the standard square of the intrinsic 

concent rat i on as a funct i on of the reduced Fermi 1 eve 1, under the 

constraints of no energy gap narrowing and a square root dependence of 

the quantum density of states on the majority carrier kinetic energy. 

The increasing values on the abscissa correspond to increasing dopant 

con cent rat ion. 

Not present in manuscript (because of oversight). 

Schemat i c di agram showi n9 the decompos i t i on of the band-gap energy 

into Wand the work done against attraction. More carriers are 

assumed present for curve 1 than for curve 2. 

Gap shri nkage t.EG as inferred from transport measurements for n-type 

1 ayers from vari ous sources at a mean temperature of ~ 340 K. The 

upper curve is for m*/m = 1.45, the lower curve is for m*/m = 1.10, 

and E = 11.7 (Si) has also been used. The horizontal axis is the 

majority carrier concentration. 

Comparision with recent optical data at 5 K. 

Qualitative illustration of the band edges of heavily doped 

n+-si1icon. The broken lines show the unperturbed parabolic bands. 

The positions of both the electron and hole quasi-Fermi levels is also 

indicated. The arrows near EV indicate hole capture and emission by 

395 
the tail states and by the acceptor level from the p-type substrates. 

The penegration of the tail states into the forbidden gap is assumc~d 

to be very small in comparison with the bandgap EG = EC - EV. 

Fig. 13 The band edges for the n+ silicon in which the donor dopant 

concentration decreases sharply with x (x = 0 is the surface): , 

band edges corresponding to the rigid band model (these illustrate a 

deep penetration of the Fermi level and a modest force field (nearly 

zero) acting on the holes); , band edges co.rresponding to a 

majority carrier quantum density of states warped relative to that of 

the rigid band model (these illustrate Fermi level saturation and a 

consequent strong force field drifting holes toward the surface). 

396 
10-3 ::-

• • 

• • 

• 

Fi g. 1 

• • 

• .. • 

Fi g. 3 

• • 

i

Q,DS(,i) -+ 

Fi g. 2 

(h)O-----(e-') ----I': 

:., .. 

,I 01 

Fi g. 4 

397 
10 

.£!l!... 

kTle 

SPACE-CHARGE REGION 

Fi g. 5 

/'" 

/' 1---=====----=---~--

I I 

1018 1019 1020 5x 1020 

CONCENTRATION (cm-3, 

Fi 9. 6 

398 
-4 -2 

EF - Ec 

liT OR 

Fi g. 7 

OR'G\N~l p~G"£;'~ OF. POOR QUAU"rl 

0 2 

Ev - EF 

kT 

~i g. 10 

399 

wI ---±a--- . r 

o n-lype \ • p-typ. 

Fi g. 9 

! ;: 102'L-----------~~------~--~--------j w " 

<I 

• 0 

Fi g. 11 
_____ E

fP 

-<l------ E" laccaplor 1 ••• 11 

II II Hoi. Trappl"" 

E a I V t- _ III .... , 

DENSITY OF STATES 

Fi g. 12 

--EC l---~----EF ,,/ 

...- 11- '<.-- --

-- EG(x) 

EV 

----~-...... ...,,,,, • X 

Fi g. 13 

400 
DISCUSSION 

QUESTION: Fred, I just have a couple of simple questions. You talk about the 

definition of the ohmic contact. Have we seen any such ohmic contacts? 

LINDHOLM: Yes, I think in Martin Green's cell contact, the tunneling junction 

has a hetrojunction such that there is a blocking barrier for the holes 

in the end-type material, yet the electrons tunnel freely into the conduction band of the metal. That would be one example. Another place 

I might just mention a very good book on contacts, which is called 

Photoconductivity and Allied Problems, by Albert Rose, is very good, 

because it is so thin. I think we should think a lot about contacts. 

QUESTION: Some 30 years ago, when the effort was solving t~~ junction equations, I worked with a mathematical physicist named Pau: Wise. His 

opinion, unshakably, 'was that the quasi-Fermi level was a mathematical 

artifact. In other words, if your carrier concentrations were constant 

then you could say, yes, quasi-Fermi level was constant; if they weren't, 

they werentt. Rather than give a physical significance and work from 

there, he insisted that you just can't use it. I haven't followed the 

literature since then. I'm wondering if he is wrong? 

LINDHOLM: Yes, he is completely wrong. The electrochemical potentials are 

basic thermodynamic variables. This question was asked of Peter Landsberg 

in a heavy-doping workshop some time ago, and I remember his answer. The 

electric potential we all know about; if you look in any book on the 

theory of beat or thermodynamics you'll find the chemical potential. And 

it's the algebraic sum of the two. So there's no problem, except with 

your friend. Oldwig (von Roos) said only in local thermal equilibrium, 

and it is true that the linearity between the current and the gradient 

and the quasi-Fermi level will not work if you have extraordinary variations in the quasi-Fermi level, but that's not surprising, because 

linearity -- as we know -- only applies for small perturbations, anyway. 

On the other hand, small perturbations can be very large currents of the 

sort we get with 1,000 suns with no problem at all. 

SCHMIDT: You still believe in the rigid band approximation? 

LINDHOLM: No, I don't. Only for doping concentrations above, say, 5 x 1019 

to 1020 it is pretty good. Except the band edges on the minority 

carrier bands would be important there, even for the high doping 

concentration~. 

SCHMIDT: You mentioned a variable electron affinity and if it affects the 

forces acting on carriers. Now the electron affinity is very little 

known, so that's a problem. However, I found some time ago that if you 

have lOW-level injection conditions and you have a variable chemical 

composition or .doping or other facts, then the force on minority carrier 

is strictly the gradient of the band gap. Plus, of course, the potential 

force. 

401 
LINDHOLM: That is absolutely correct. 

SCHMIDT: So there is no influence of the electron affinity? 

LINDHOLM: This is absolutely true in low injection, and other workers have 

found that also and have published it. However, the low injection impli~s 

that you have a minority carrier, and that implies that you are in a 

quasi-neutral region. So when you get out of a quasi-neutral region and 

get into what people call a depletion region -- which I don't lii~ to 

call it, I like to call it junction-transition region or space-charge 

region -- then if the gradient in the electron affinity is present, then 

it will introduce an effect. I can discuss that with you with this very 

simple picture. You probably know that anyway. 

SCHMIDT: With this background, I like the way you deduced your points and you 

came to some conclusions. And just to make a test of it, my question is: 

do you question the present ideas about the Auger recombination correlated with the concentrations of certain dopants? Because, for a practical person, this is an extremely important thing. We had not been sure 

up to now: the correlations that you often had seen, up to the present 

time, of carrier concentrations or doping concentrations and the boundary 

of Auger recombination seem to be, let's call it, rigid. Do you think, 

from your point of view no~. that that can be questioned? 

LINDHOLM: Yes. I'm heavily opinionated on this issue also. My opinion is 

that the Auger coefficients are open to question. Since there has been a 

single experiment done at rather high doping concentration, and some of 

these other things I have talked about could influence these things. I 

would say on a theoretical level that the primary person who has worked 

on the theory of those Auger combinations is Peter Landsberg. And his 

physics is impeccable, but it involves many, manyapproximati<cms. So he 

can only give us an estimate. So we will have to find the results from 

experiment, and I think it's an open question. Mainly when people talk 

about Auger recombination, they think about band-to-band Auger recombination but, as you know -- you have pointed out in your talks -- there are 

many recombination states in a diffused junction and, therefore, the 

Auger process may be extremely important, and that should not be overlooked. And that is only estimated, as far as I know, from a theoretical 

viewpoint, and by Peter Landsberg and Robbins first. You bring attention 

to a very important point. 

SCHMIDT: 

body 

tant 

good 

I think you may have sensed why I asked you that question. 'For somewho is responsible to prepare semiconductors, it is extremely importo know what kind of doping level could be tolerated and still make 

solar cells. 

LINDHOLM: That' s fill excellent point. The band-to-band Auger process gives you 

an ultimate upper bound. For higher doping concentrations, certainly the 

band-to-band Auger recombination gives you an upper bound. That needs to 

be looked at carefully, and experimentally, again. 

SCHMIDT: Do you think that the situation may be changing again in case you 

have a highly counter-doped material? 

LINDHOLM: Could be. 

402 
SESSION VI 

HIGH-EFFICIENCY DEVICE 

PROCESSING 

P. Rai-Choudhury, 

Chairman 

-, 
N85~31639 HIGH EFFICIENCY LARGE AREA POLYSILICON SOLAR CELLSt 

S.M. Johnson and C. Winter * 

Solarex Corporation, Rockville, Maryland 20850 

ABSTRACT 

Large area (100cm2) polysilicon solar cells having efficiencies of up to 

14.1% (100mW/cm2 , 250 C) were fabricated and a detailed analysis was performed 

to identify the efficiency loss mechanisms. The I-V characteristics of the 

best cell were dominated by recombination in the quasi-neutral base due to the 

combination of minority carrier diffusion. length Cand base resistivity. An 

analysis of the microstructural defects present in the material an~ their 

effect on the electrical properties is pres~nted. " 

IN'J;'RODUCTION 

Developments in the fabrication of 4cm2 single crystal solar cells have 

yielded efficiencies'exceeding 18% under standard terrestrial test conditions 

[1,2]. More recently, single crystal cell efficiencies exceeding 19% have 

been reported [3 J • In comparison, 4cm2 polysilicon solar cells have been 

fabricated having terrestrial efficiencies up to 17% [4]. Based on these 

successful results an effort was made to determine the maximum efficiency 

achievable on large area cast polysilicon material. 

MATERIAL AND DEVICE CONSIDERATIONS 

Short-Circuit Current 

Earlier analyses of short-circuit current limitations in polysilicon 

solar cells have indicated that for an effective grain diameter (based on 

electrically active grain and subgrain boundaries) exceeding 1-2 mm, the 

short-circuit current is essentially determined by the minority carrier 

diffusion length within the grain volumes [5,6]. Recently it was shown that 

polysilicon material can be modelled using the concept of an effective 

minori ty carrier diffusion length, which depends on the grain diameter and 

grain boundary surface recombination velocity, incorporated together with 

single crystal device models [7] ,. 

t Work supported by DOE, Cooperative Agreement No. DE-FCOl-80ET23l97 and by 

Solar ex Corporation 

*Current Address: Maryland National Capital Park and Planning Commission 

1403 
" 

Figure 1. Theoretical Maximum' Short-Circuit-

.current- D~nsity Versus Minority C.arrier 

. Diffusion Length For a Long-Base Solar 

Cell (I>' > >Ln), AMl.5, IODJuW/cm2 , 

400!..llOO nm 

Figure 1 is a graph of the theoretical maximum obtainable short-circuit 

current density, in the wavelength range 400 - 1100 nm, versus the minority 

carrier diffusion length, Ln , in a long-base solar cell (cell thickness W, 

where W» Ln), calculated using a recently published AM1.5 global spectral 

irradiance curve (97mW/cm2) [8J. The calculated values were then increased by 

3% to approximate IOOmW/cm2 conditions. Figure 1 shows that for' diffusion 

lengths exceeding approximately 100 ].lm, in a long-base solar cell, the shortcircuit current increases asymptotically with increases in diffusion length. 

For an effective grain size of 1-2 mm, intragrain diffusion length of 250].l m, 

and an infinite grain boundary surface recombination velocity, the effective 

diffusion length in polysilicon material would be approximately 120 - 170 ].lm 

and grain boundary effects on short-circuit current are minimal [7J. 

The material used in this study has average grain diameters of 2 - 10 mm, 

however the presence of dislocation subgrain boundaries wi thin some of the 

large grains locally reduces the effective grain size and the effective 

minority carrier diffusion length. A detailed study of the origins and 

electrical properties of subgrain boundaries in cast polysilicon material has 

been performed [9J. For typical subgrain diameters in the range 0.1 - 0.3 mm 

the effective diffusion length can be reduced to 40 - 90 ].lm, using the 

previous values of intragrain diffusion length and surface recombination 

velocity, and reduce the short-circuit current [7 J • A decreased effective 

lifetime in regions containing subgrain boundaries, revealed using a Secco 

etch, has been reported earlier [IOJ. Thus it is important to obtain polysilicon material which has a long intragrain diffusion length and has a 

minimum density of subgrains. 

Open-Circuit Voltage and Fill Factor 

Neglecting series resistance and shunt conductance the dark I-V 

characteristics of a solar cell can be written as 

Jd = Jsco[exp(qV/nkT)-I] + jqno[exp(qV/kT)-IJ (1) 

where the first term is the current component arising from recombination in 

the space-charge region (with a diode ideality factor, '0) and the second term 

is the current component due to recombination in both the quasi-neutral 

emitter and quasi-neutral base of the solar cell [IIJ. With the use of single 

crystal base material and high quality, careful, cell processing, the spacecharge component is usually negligible. 

404 
I 

In order to maximize the open-circuit voltage most workers have first 

minimized the quasi-neutral base recombination component by using boron-doped, 

high lifetime, low resistivity (0.1-0.3 Q-cm) float-zoned single crystal 

silicon as a base material and then minimized the quasi-neutral emitter 

recombination by a combination of tailoring the emitter doping profile and/or 

passivating the 'surface with a thermally grown oxide [12-17,2]. The most 

successful work to date is the MINP solar cell design [18-19]. 

Empirically it has been found in the past that the minority carrier 

difjusion length in cast polysilicon material decreases rapidly for base 

resistivities below approximately 1 Q-cm and that good quality material can be 

grown in thel-2Q-cm resistivity range. Thus in order to apply these results 

the recombination current in the quasi-neutral base must first be estimated 

for this range of base resistivity. The quasi-neutral base recombination 

current, J qno ' can be calculated for two different conditions [14], (1) the 

long-base solar cell (W~>Ln): 

Long-base 

2 

J qno = qnjDn 

NALn 

(2) 

and (2) the perfect back surface field (BSF) condition (back surface recombinati.on velocity is zero): 

BSF J qno = (qJjDn ) tanh(W/Ln ) 

\NALn 

(3) 

where q is the electronic charge, ni is the intrinsic carrier concentration, 

Dn is the minority carrier diffusivity, NA is the base doping concentration, 

Ln is the minority carrier diffusion length and W is the base thickness. 

Using Figure 1, and equations (2) and (3) the maximum, base-limited, opencircuit voltage under 10OmW/cm2 , 250 C conditions was calculated as a function 

of minority carrier diffusion length for p = 1 Q-cm, W = 150 1.1 m and p= 1. 7Q-cm, 

W = 225 l.1m, and is shown in Figure 2. These resistivity/thickness combinations correspond to base parameters for a high efficiency 4cm2 and the 100cm2 

polysilicon solar cells respectively discussed later. 

Figure 2 shows that for a 1 Q-cm, 150 ~m thick cell the minority carrier 

diffusion length must be, for a base-limited open-circuit voltage to exceed 

60OmV, greater than 170 l.1m for a BSF cell and greater than 240 1.1 m for a longbase cell. For a 1. 7 Q -cm, 225 l1m thick base the minority carrier diffusion 

length must be greater than 300 l.1m for a BSF cell and greater, than 400 l.1m for 

a long-base cell. Thus, the use of high base resistivity material puts a 

large lower limit on the range of the minority carrier diffusion length 

necessary to reach a base-limited open-circuit voltage of 600 mV and places 

further emphasis on obtaining material with a minimal lifetime inhomogenit'y. 

It was recently demonstrated experimentally that reduced open-cir~uit voltages 

in large-grained polysilicon solar cells were due to a lower minority carrier 

diffusion length in the base substrate material [20]. As discussed previously, the effective minority carrier diffusion length in regions containing subgrain boundaries can be as low as 40-90 l.1m. In these localized regions, using 

Figure 2, the open-circuit voltage can range from 550 - 575 mV for 1 Q -cm 

material and from 530 - 550 mV for 1. 7 Q-cm material. Open-circuit voltage 

degradatiofl due to increased quasi--neutral base. recombination associated with 

405 
subg ai 0 nd r 

inhomo ni ct 

obtained by summing 

different regions of 

F ur 2. B S - lilli t d, 

rsus inority 

V r ious 

Flgur 

I 0 d r 

3. S cco-Etched IOc.. x 

afer Serial Section 

IOc Polya1l1con 

In ord r to mini 1z r co bina ion in th waf r 

selec ed on a basis of having reasonably to 

the -carri r lif i e , m asur d ith a contac Ie modulat d micro av 

reflec ance chniqu (lOJ and having a mini al numb r of subgrain boundari s. 

Figur 3 sho s a pho ograph of a S cco- ched 100cm2 polysilicon ser al 

sec ion used in his effort and Figure 4 is a micrograph of a typical region 

containing ubgrain bounda i ith spacings of 0.1 0. 5 mm. Subgra n 

boundari s hav al ays been found to caus minori y carri r r combina tion as 

se n in both fin light spot scanning (lOJ and EBIC [9J measurements. It was 

stimated by in p ction of the S cco- tched 100cm2 wafer that approximately 8% 

o the total waf r surface is comprised of regions similar to Figure 4. 

406 

Figure . 

Micrograph Showin A Dens Array of 

Subgraln Boundarie s 
cru • C( LS SlArtsTlC lac oc: F.r. rr lCIfJICT 

ccr, ' M/ttl! '1iY! III 

- 10.' S7'I 0.111 ~ 

fT 0 •• S.t o.Ott O.J.I 

31 . 3, SI'! 0.111 I~ l 

]11.' lOt OJ1t I • . ' 

Tabl 1. P01ysil1con So ar C 11 Illuminat d 1-

Chars t r tics (100 Ie 2 2S 0C) • 

Pi ur S. 100c 2 Cell ShDwin Grid Design 

thou h co bina ion in pac -charg region is no ally n gligibl 

in sin 1 crys al si icon solar c lIs, i can, if pr sen, seriou ly r duc 

the fill factor and op 'n-circu voltag. Increas d spa -charg r combination is associated with ubgr~in bou daries in polysilicon solar cells and has 

the largest influence on f11 l factor rather than open-circuit voltage [21]. 

Thus there was a further r ason to minimize the area of such regions in a 

large a ea polysilicon solar cell. 

CELL FABRlCATIO AND RESULTS 

A 0 al 0 fi y 100c fabrica d u ing pac -quality c 11 

proce sing chnology. Th rs r thinn d to a nominal thic n ss 

of 225 1.I using a CP giv n a shor tch in aOH 0 y1 ld a 

sligh ly further reduction in hickn ould 

a110 for a he difficulty in proce ing a 100cm2 

wafe inner grea for h scop of the 

exp rim nt.) di fused to a h r sistanc 

o approxima cr n pr1n d, alloy d, and h 

r sidual pas Con ct r pho olithographically· 

d in d and h on con i ted 0 vaporat d/ el c ropla d Ti/Pd/ Ag. 

Figur S i photograph 0 a 100cm2 c 11 showing th grid m ta11iza ion 

d ign. our bus conductors were used to help minimize the m allization 

shadowing. A wo-lay r vapo d antireflection coating wa applied, 

consis in 0 Ta20S a th irst layer and MgF as h second lay r, follow d 

by a bri in ring t p. 

Th short-circuit current as measur d outdoor at lOOmW/cm2 illumination, ref renced to a global pyranome er. measurement (Eppley PSP) , and the 1-

curves were then completed on a filtered' xenon simulator at 2S0 C. The average 

and standard deviation of the illuminated I-V characteristics of the fifty 

cells is given in Table 1. These cells had an average efficiency of 13.5% and 

401 

~ ... 
the best ~ell had an efficiency of 14.1%. Table 1 also summarizes the illuminated I-V characteristics of the best large area cell together with the 

characteristics of a small area (4. 03cm2) 16.2% efficient polys!licon solar 

cell fabricated during an earlier study [41. The efficie~cy .of . the small area 

polysilicon solar cell was independently confirmed. at .. ' the Solar Energy 

Research Institute [221. 

ANALYSIS 

Short-Circuit Current 

In order to quantify the efficiency loss mechanisms, a detailed loss 

analysis of the best large area cell together with a' high efficiency small 

area cell was performed. Figures 6 and 7 show the internal' and external 

quantum efficiencies of the 16.2%, 4.03cm2 cell and the 14.1%, 100cm2 cell 

respectively in the wavelength region 400 - 1100 nm. Of particular note is 

that both cells exhibited a spectral response which varied with light 

intensity [23]. The observation of a minority carrier diffusion length which 

is dependent on injection level has been studied previously in other silicon 

materials [24,25]. The quantum efficiency of the 16.2% cell was measured with 

a chopped monochromatic beam and a steady white light bias of approximately 1 

sun intensity [231. The large area cell was measured with a white light bias 

of approximately 0.1 sun bias intensity due to measurement limitations. Thus, 

although it is possible that the near infrared quantum efficiency measured for 

this cell is inaccurate, no significant variation was found in the range of 

0.05 - 0.1 sun bias indicating that the traps dominating the low injection 

lifetime were saturated. 

Figure 8 shows the internal quantum efficiency measured, at approximately 

1 sun bias, in a regipn containing subgrain boundaries and an ad~acent region 

free of subgrain boundaries (both regions are in the 14.1%, 100cm cell). The 

effective minority carrier diffusion length in the subgrain region was calculated from the linear plot of inverse quantum efficiency versus inverse 

absorption coefficient [26] to be 80 1-1 m. This value is approximately onethird of the base thickness so that ignoring BSF effects in the diffusion 

length calculation is justified. In contrast, a calculation of the diffusion 

length in the subgrain-free region, or for the curves in Figure 6 and 7 using 

this method yields diffusion length values close to or exceeding the base 

thickness. Thus the analysis assumptions are violated and these values are 

inaccurate. 

1.0 

0.9 

> 0.8 !!! 

'" 0.7 ;:; 

ii: 0.6 II. 

'" :Ii 0.5 

::> 

1-' 0.4 z 

ct 0.3 ::> 

a 0.2 

0.1 

400 500 600 700 800 900 1000 1100 

>. (nM) 

Figure 6. Internal and External Quantum 

Efficiency Versus Wavelength For the 

16.2%, 4.03cm2 Polysilicon Solar Cell 

(~ 1 sun bias condition) 

1.0 

0.9 

~ O.B 

~ 0.7 

tE 0.6 

:Ii '" 0.5 

~ 0.4 z 

~ 0.3 a 0.2 

0.1 

400 500 600 700 800 900 1000 1100 

>. (nm) 

Figure 7. Internal and External Quantum 

Efficiency Versus Wavelength For the 

14.1%, 100cm2 Polysilicon Solar Cell 

(~ 0.1 sun bias condition) 

408 
~ 1.0 

0.9 

!;l '"0.8 ... 

... 

'" 0.1 

~ 0.6 ..... 

~ 0.5 => 

o 0.4 

~ 0.3 

~ 0.2 

~ 0.1 

). (nm) 

Figure 8. Internal Quantum Efficiency in LargeGrain and Subgrain Regions of the Large 

Area Polysilicon Solar Cell ('\r I sun 

bias condition) 

16.21 Cq.03C,.z, Iq.1I C100c,.z, 

LOSS FRACTIOI! lCCI"A'~~' FRACTIOI! 1.cl"Alc~' 

ItECIWIISfI AVAIlA81.E AVAILA8I.E AVAILABLE AVAILABlE 

MTER LOSS AFTER lOSS AFTER LOSS AFTER LOSS 

THEOIIETICAl 1.0 '13.2 1.0 Q3.Z 

IlAXI .... 

IHTEIIIIAL ClUANTIJ! 0.81 31.6 0.85 36.1 

EFfICIENCY LOSS 

AHTIBEFL[CTIOI! 0.91 . 36.5 0.91 35.6 

COATING LOSS 

GIIID SHADOIIlHG 0.95 3q.6 0.88 31.3 

LOSS 

HET 0.80 3~.6 0.13 31.3 

Table 2. Short-Circuit Current Losses for the 

Small and Large Area Poly silicon Cells 

in the Region 400 - 1100 nm 

By separately integrating the product of each quantum efficiency curve 

with the AMl.5 solar spectral irradiance curve [8] over the wavelength range 

400 _. 1100 nm, and by measuring the percentage grid shadowing, the percent 

losses in short-circuit current due to internal quantum efficiency, antireflection coating, and grid shadowing were calculated. This short-circuit 

current loss analysis is summarized in Table 2. The short-circuit current 

associated with the internal quantum efficiency of the small area cell is 

approximately 2% greater than the large area cell partly due to a reduced cell 

thickness (150 ~m versus 225 ~m), which enhances BSF effects, and the addition 

of a back-surface reflector (BSR) which was not used for the large area cells. 

From an analysis of Figure 8 a total internal quantum efficiency loss in 

short-circuit current of only approximately 1% can be attributed to the 8% 

area of the cell containing subgrain boundaries. Antireflection coating 

losses were identical. The major difference between the two cells was the 

percentage of grid shadowing, representing approximately 5% for the small area 

cell and 12% for the large area cell. The grid shadowing is approximately 

twice the design value for the large area cell and was due to excessive grid 

line broadening during the photolithography and metallization processes. 

Open-Circuit Voltage and Fill Factor 

The. dark I-V characteristics of both cells were generated by measuring 

Isc-Voc at different illumination levels to eliminate the effect of series 

resistance and then subtracting the shunt conductance contribution (determined 

from reverse-bias measurements). This data was then fitted to equation (1) 

using a computer program designed to minimize the differences between the measured data and the I-V characteristics calculated from equation (1) [27]. The 

series resistance was calculated from the difference in the Isc-Voc and dark 

forward-bias I-V characteristics. The base resistivity waf';: calculated from 

junction capacitance measurements., These results are summarized in Table 3. 

Using the shifting approximation, the illuminated I-V characteristics 

were calculated from the short-circuit current and dark I-V characteristics in 

Table 3. This calculation was done by starting with the quasi-neutral 

component alone, calculating the illuminated I-V characteristics, and then 

sequentially adding the space-charge component, . shunt conductance, and series. 

409 
PARNfT£R 

SHUNT CONOOCTAHCE 

GI IIVtcn2 I 

SERIES R£SISTAHCE 

RI!IL-cn21 

SPACE -CHARGE DIIIlE 

OUALITY FACTOR. H 

SPACE -CHARIit CURR£~'T 

l,cal "A/c"21 

OUASI -It[UTRAl CURR£HT 

Jo"al "Alc"21 

EOUIVALENT VOl TAG[ 

V[("VI 

BASE RESISTIVITY 

II\-C" I 

0.11 

0.38 

5.5 

2.5 I 10-9 

522 

1.0 

I~.n 

ll00cn21 

0.90 

0.32 

2.0 

6.3 J 10-~ 

3.6 J \O"~ 

1.7 

Table 3. Dark I-V Characteristics for the Small 

and Large Area Polysilicon Solar Cells 

IHCLlf)£O nARK I -v CHARACTERISTICS CAlCIl.ATED rRlJ! 

~~~~ENlliTS~ ________ ~I~K~LUM~O~C~ARK~I'~Y~~~~sruHT~S __ 

Vac F.r. !I.. ,I\. I !!VI CJ) III 

IlIIASI-fj[UTAAl 602 0.129 17.2 

AtC(J1!INATIIII 

OUASI-tI£UTRAL , 1lAQ:- S?I 0.796 16.~ 0.1 

CHARGE REClJelNAImI 

WASI -N£UTRAL. Sl'ACE -CIWlIit 599 0.793 16.~ 0 

, SlfllNT COfC1UCTAKE 

QUASI -N£UTRAL. SPACE -CHARGE. StUlT 599 0.775 16.1 0.5 

COI«lUCTAHCE , gRlES AtSISTANCE 

I£ASURED tlL§BAmmms 601 0.779 16.2 

hll( ~A 

IHCLlf)£O DARK 

I -y to!!'DN£NTS 

I-V CHARACT£RISTICS CAlCll.AT£D FR(JI 

IHCLUMD OARK I -y t!l!'DN£NTS 

Vac F .F.. I\. to.l\. 

leVI III III 

OUASI -!I£UTRAL 511 0.126 15.2 

RmT!!!IfATIDlI 

WASI-I![UTRAL , mkE- 58~ 0.103 1~.7 0.5 

tllABQ[ BEt!l!!lHAUDlI 

O\JASI -I/EUTRAL. SPACE -CHAP'G[ 583 0.791 I~.~ 0.3 

, SliUNT COO/CTAKE 

WASI -!I£UTRAl. SPACE -CIIARG[. SIU!T 583 0.777 1~.2 0.2 

CIINDUCTAHCE , SERIES RmSTANCE 

I£ASUI!ED tllABAmmmS 58~ 0.779 I~.I 

TAIl( qB 

Table 4. Illuminated I-V Losses Calculated Using 

the Shifting Approximation and the Dark 

I-V Characteristics in Table 3 for the 

Small Area (Table 4A) and Large Area 

(Table 4B) Polysilicon Solar Cells 

resistance, and repeating the calculation after ~ach addition. Table 4A 

summarizes the results of this calculation for the 16.2% small area cell. 

Space-charge recombination reduced the open-circuit voltage minimally ("-'3 mV), 

however it caused a 0.8% reduction in cell efficiency (17.2 to 16.4%) due to a 

decreased fill factor. The cause of this increased space-charge component was 

not identified. The shunt conductance was sufficiently low to not affect the 

cell efficiency, however series resistance decreased the fill factor and 

caused a 0.3% reduction in cell efficiency. The uppermost curve in Figure 2 

shows that, theoretically, the open-circuit voltage of a pet'fect BSF cell of 

this thickness and base resistivity must have a base minority carrier diffusion length exceeding approximately 1801..1 m, which may be possible, in order to 

achieve a base-limited open-circuit voltage larger than experimentally 

obtained. The base diffusion length and back surface recombination velocity 

are difficult parameters to measure in a BSF cell and were not measured in 

this study. (Techniques to separately determine the. base and emitter dark 

current components have been recently reported [28,29]l However, based on the 

a.bove analysis of the dark current and Figure 2, the open-circuit voltage of 

the 16.2% cell is approaching the level where recombination in the quasineutral emitter begins to dominate. 

Table 4B summarizes the calculated I-V characteristics of the 14.1% large 

area cell. Space-charge recombination again reduced the open-circuit voltage 

minimally ("-'4 mV) however it caused a 0.5% reduction in cell efficiency due to 

a reduced fill factor. It is reasonable to assume that part of the increased 

space-charge recombination is due to the presence of subgrain boundaries. 

Shunt conductance and series resistance accounted for efficiency losses of 

0.3% and 0.2% respectively due to a decrease in fill-factor. The next to 

lowest curve in Figure 2 shows that, theoretically, the base minority carrier 

410 
diffusion length of a perfect BSF cell of this thickness and base resistivity 

must exceed approximately 200 llm in order to achieve a base-limited opencircuit voltage larger than experimentally observed for the large cell. The 

diffusion length must exceed 300 llm, which is not likely, in order to achieve 

a base-limited open-circuit voltage of 600 mV. Thus it is concluded that the 

open-circuit voltage of this cell is limited by recombination in the qU8sineutral base due to both base resistivity and minority carrier diffusion 

length limitations. This conclusion is consistent with results in 2 Q-cm 

single crystal silicon solar cells [15]. 

The extent of this base recombination due to an approximately ·8% area 

containing subgrain boundaries was calculated from the measured effective 

diffusion length of 80 11m in this region and equations (2) or (3). The 

interesting result is that approximately 40% of the total quasi-neutral 

current results from an region comprising approximately 8% of the cell area. 

This emphasizes the need to eliminate these defects by modification of the 

crystal growth process or possibly by passivation of these defects using, for 

example, atomic hydrogen [30]. 

SUMMARY AND CONCLUSIONS 

Large area (100cm2) polysHicon solar cells having efficiencies up to 

14.1% (lOOmW/cm2, 250 C) were fabricated and a detailed analysis was performed 

to identify the efficiency loss mechanisms. The I-V characteristics of the 

best cell were dominated by recombination in the quasi-neutral base due to the 

combination of minority carrier diffusion length and base resistivity 

(1.7Q-cm). Approximately 40% of the total quasi-neutral recombination current 

was attributed to regions comprising approximately 8% of the total cell area 

containing subgrain boundaries. These subgrain boundaries substantially 

reduced the local effective minority carrier diffusion length which locally 

increases the base recombination current. By comparison, an analysis of a 

16.2% small area polysilicon solar cell (4.03cm2) indicated that the opencircuit voltage of this cell was approaching the level where recombinlltion in 

the quasi-neutral emitter begins to dominate. 

Further efficiency increases in large area polysilicon solar cells can be 

realized by an improvement in the crystal growth, and/or post-solidification 

processes, to reproducibly yield low resistivity material having a long, 

spatially uniform, minority carrier diffusion length. After a suitable 

reduction in the base recombination is accomplished, a' further development and 

application of the surface passivation and emitter formation techniques, 

successfully demonstrated with single crystal material, should allow 

efficiency advances to be made. 

ACKNOWLEDGEMENTS 

The authors wish to express their appreciation to L. Brickman, E. Coccia, 

J. Culik, D. Fardig, T. Migliorini, C. Osterwald and G. Storti for their 

contributions to this effort and to P. Fazio for preparing this manuscript. 

411 
REFERENCES 

1. A.W. Blakers, M.A. Green, S. Jiquin, E.M. Keller, S.R. Wenham, R.B. 

2. 

Godfrey, T. Szpitalak and M.R. Willison, IEEE Electron Device Letters, 

Vol. EDL-5, No.1, 1984. 

M.B. Spitzer, S.P. Tobin, and C.J. Keavney, IEEE Trans. Electron Devices, 

Vol. ED-3l, No.5, May 1984, in print. 

3. M.A. Green, A.W. Blakers, Jiqun Shi, E.M. Keller and S.R. Wenham, Appl. 

Phys. Lett. 44 (12), June 1984. 

4. G.M. Storti, Conf. Rec., 15th IEEE Photovoltaic Specialists Conf., 442, 

(1981). 

5. G.M. Storti, S.M. Johnson, H.C. Lin, and C.D. Wang, Conf. Rec., 14th IEEE 

Photovoltaic Specialists Conf., p. 191, (1980). 

6. S.M. Johnson, R.G. Rosemeier, C.D. Wang, R.W. Armstrong, H.C. Lin, G.M. 

Storti~ Proc. Int. Electron Devices Meeting, p. 202 (1980)'. 

7. S.M. Johnson, to be published. 

8. R.J. Matson, K.A. 'Emery, and R.E. Bird,' Solar Cells, Vol. 11, No. 2 

(1984). 

9. K.C. Yoo, S.M. Johnson, W.F. Regnault, to be published. 

10. S.M. Johnson, J.C. Culik, Conf. Rec., 16th IEEE Photovoltaic Spec. Conf., 

548, (1982). 

11. F.A. Lindholm, J.G. Fossum and E.L. Burgess, IEEE Trans. Electron 

Devices, Vol. ED-26, No.3, March 1979. 

12. J.A. Minnucci, K.W. Matthu, A.R. Kirkpatrik, and A. McCrosky, in ref. 

[5], p. 33. 

13. M.P. GOdlewski, T.M. Klucher, G.A. Mazaris, and V.G. We-izer, in ref. [5], 

p. 166. 

14. R.A.Arndt, A. Meulenberg, and J.F. Allison, in ref. [4], p. 92. 

15. E.S. Rittner, A. Meulenberg, and J.F. Allison, J. Energy, Vol. 5, No.1, 

1981. 

16. A. Meulenberg and R.A. Arndt, xef. [9], 348. 

17. H.T. Weaver and R.D. Nasby in ref. [9], 361. 

lB. M.A. Green, et.al., in ref. [4J, p. 1405. 

412 
19. M.A. Green, et.a1., in ref. [9], p. 1219. 

20. J. Cu1ik, P. Alexander, K.A. Dumas, and J.W. Wohlgemuth, Fifth E.C. 

Photovo1taic Solar Energy Conference, Athens, p. 1090-1094, (1983). 

21. J. Culik, K. Grimes, 17th IEEE Photovoltaic Specialists Conf., in print 

(1984). 

22. C. Osterwa1d, Report No. 296, Solar Energy Research Institute, September 

20, 1983. 

23. L.A. Brickman, unpublished research. 

24. E. Fabre, M. Mautref, and A. Mircea, Appl. Phys. Lett., Vol. 27, pp. 

239-241, (1975). 

25. R. Shimokawa and Y. Hayashi, IEEE Trans. Electron Devices, Vol. ED-30, 

No. 12, (1983). 

26. E.D. Stokes and T.L. Chu, App1. Phys. Lett., Vol. 30, No.8, (1977). 

27. J.C. Cu1ik, unpublished research. 

28. B.H. Rose, H.T. Weaver in ref. [21]. 

29. V.G. Weizer, C.K. Swartz,. R.E. Hart, M.P. Godlewski in ref. [21]. 

30. C.H. Seager, D.J. Sharp, J.K.G. Panitz, and R.V. D'Aie110, J. Vac. Sci. 

Techno1. 20, 430, 1982. 

413 
DISCUSSION 

RAI-CHOUDHURY: I notice your internal quantum efficiencies around 0.4 micrometer were in estcess of SO'!'... Would you cODll\ent. on why you had such high 

internal quantum efficiency without the surface passivation? 

JOHNSON: I think it's strictly due to our thinner junction. We have a fairly 

high sheet resistance of 100 ohms per square -- maybe slightly larger than 

that. 

RAI-CHOUDHURY: What is your surface dopant concentration? 

JOHNSON: I don't know. We haven't measured that. 

RAI-CHOUDHURY: It's not clear why you had such high collection efficiencies. 

There has got to be either low emitter surface dopant concentration or 

somehow your surface has got to be very well passivated, because usually 

even if you take a single crystal material at 0.4 micrometer you see 

internal quantum efficiencies of about 50~ to 60~ at the most, and you 

had 80~ there. 

JOHNSON: All that I can say is that it may be just from the particular way we 

do our diffusions. 

LESK: I was just wondering, ther9 was a paper in your organiz~tion on hydrogen passivation of defects, and I was wondering if you see any passivation 

of the sub-grain boundtiry regions with hydrogen, or can you look at it 

closely? 

JOHNSON: We haven't done that yet. Jerry Culick, who is here, will be doing 

that, and there is a lot of pr~mise for passivation of those regions, 

because the region where you are going to get the passivation is probably 

at the dislocations, where you are going to get diffusion down the boundaries dU6 to the presence of dislocation. 

SIRTL: I have two questions. One is, could you briefly desc~ibe or show the 

crystalline features of the two top cells you were discussing? The secund 

question is, did you -- with the same cell technique -- make solar cells 

from standard monocrysta1 like Czochralski, just to show the dlffer~ncus 

in terms of this sophisticated cell techna1ogy? 

JOHNSON: Yes. For Czochra1ski material, for 2 x 2 cells we can tet 

16 l/2~ - 17~ without too much difficulty. For large areas, we did 

process &. few five-inch wafers, where we cut off the edges. We started 

about four of them; we got two of them finally to the end. On~ Qf the 

cells had an open-circuit voltage of about 600 millivolts liu\d t3.e other 

one tt1aS somewhat less than that, maybe 590 or so. This is dUle mote to 

processing limitations, I think. Efficiencies run in the order of 

15 1/~ for the large area cells. 

srkTL: Could you describe the two samples? Was the 2 x 2 l6.2~ cell largely 

monocrystalline, or how did it look? 

4·14 
JOHNSON: No, the grain size was larger, and I don't have a picture of that 

particular cell. The grain size in that cell was probably closer to half 

centimeter to a centimeter or so in size. I'd say closer to about half 

centimeter in size. The large-area cells, optically visible grain size 

is still in the range of 3 to 5 millimeters. Again, it's not the optically visible size that is important to us, it's the size under a defect. 

That's where we see these small-grain regions and sub-grain regions. 

QUESTION: I'd like to follow up on that. Your 4 cm2 cell had very good 

characteristics; do you have any feeling what is the percentage of grain 

boundaries? What kind of grain boundaries? Earlier you called it 8~. 

JOHNSON: Oh, subgrains in that particular cell. We did not want to destroy 

it, naturally, but I would estimate subgrain boundaries in that particular cell were very minimal. I would say very few are in that region. 

For small-area cells you have the luxury of choosing good areas out of a 

large area. For large-area cells you have to take what the material 

gives you. 

RAO: It's interesting that you have this 8~ of the material having sub-grain 

boundaries, and you showed some nice pictures of that. Is there any way 

that can relate this to location and the sample where you have high 

density sub-grain boundaries, and do you know what happens at the subgrain 

boundaries? Why they are forming? Are they forming because of impurity 

segregation there, perhaps? 

JOHNSON: Impurity segregation would be difficult for us to measure. Someone 

like Larry Kazmerski could probably measure it relatively easily. What 

we have found is that the electrical activity of grain boundaries is 

associated with dislocations at the interface. First-order twins, which 

do not need dislocations to make up the orientation difference, are rarely 

electrically active. Second-order twin boundaries can have regions that 

fit together coherently; there's no dislocations needed. They are all 

relatively aetive electrically. small-angle boundaries that are totally 

compressed at this location are always found to be electrically active. 

We have always seen that to be so. Whether it's impurities, atmosphere 

being formed around these dislocations causing their recombination, is 

not very clear, but as we have seen, a lot of the people have talked 

about low-temperature work. It's not very straightforward why dislocations are electrically active. People have looked at this but whether 

it's impurities or the poor structure of the dislocation -- but again, we 

believe that the recombination at the grain boundary is associated with 

dislocation, whether it's impurities there or the natural structure of 

the dislocation itself. 

DYER: Mine is mainly a COIilment, and it is in response to' Rai-Choudhury' s 

remark earlier, on hOl# come you have this higher quantum efficiency and 

so forth? It just rtH~alls to me a chemical monkey wrench that I want to 

throw into this whole business: that is, the chemical processing of the 

early slice is very important. If you thin the slice with hydroxides and 

then if you texture it with dilute hydroxides there are some things that 

will plate out of solution. For example, iron plates out of solution. 

If you don't do anything to remove that before you diffuse, then you 

415 

I • 
would drive iron into the emitter, and so forth, and I don't think that 

would be very good for the devi~e. So, I just want to remind people of 

this, and of course if you are using acid cleanups, acids plate gold and 

copper out of solutions; you have to guard against the buildup of these 

materials and then replating them out. They are also bad. Just to 

mention this as possible effect on the voc that earlier in the meeting 

someone pointed out was slightly lower from texturing. 

SICKLER: I'd like to comment on the origin of some of these stresses at the 

corners of the grain boundaries. I think it would be valuable if you did 

a thorough study on grain orientation from the freezing· point of silicon. 

I'm sure the stresses you mentioned from the crucible are probably minor 

by the time you get in a few grains and it may submit itself to an analysis. Since you get a dimension change and different directions it may 

focus that force, that strain at those stress points. 

DYER: It may be this, the changes in thermal gradient in the ingot, which are 

not nearly as well controlled as material like Czochralski, that we are 

getting. Now, Yoo at Texas Instruments has done a lot of looking at the 

origin of these stresses and what the effect is on different grain orientations. The approach that he has taken is that if you assume a particular stress direction due to thermal stresses, just based on how the 

ingot is going to cool, what is the resolved shear stress on the grains 

of different orientation? So if you have a grain in the right orientation you are going to get a very large shear. stress on that particular 

grain and you are going to get a slip. 

SICKLER: The analysis that I am talking about would be isothermal cooling, if 

such a thing, theoretically, exists. There still would be a differential 

expansion as a function of grain orientation. You could analyze that 

after the fact. You could look at these samples that you show pictures 

of and see if, in fact, there is any stress or strain. 

HANOKA: I just want to follow up and try get it clear. What you are saying, 

in effect, is that the dislocations that are electrically active and 

giving you a problem are due to thermal stress. And if that's so, it's 

basically the same distinction then that Schwuttke made yesterday also 

with web, with only tb.~ stress locations that seem to be electrically 

troublesome. Is that right? 

DYER: No, what I was saying was that the sub-grain boundaries themselves seem 

to be indications that they are formed from stress in the ingot. In 

other words, the collation of the dislocations there. When they are in a 

particular boundary, then their nature is very difficult to determine. 

We. have always seen the boundaries to be electrically active. Some of 

the dislocations in the material, however, we only saw at low temperature. 

Whether they are formed f~omstress or they have grown into dislocations 

I really can't say. So we see some dislocat.ions electrically active, some 

are not. I have not made a clear distinction. 

QUESTION: A lack of clear contrast at room temperature does not mean that they 

are not adversely affecting you, though. We have seen crystal samples 

that have we have stressed in the JPL program. Those two pictures that I 

416 
showed yesterday: you have difficulty sometimes seeing these ~islpcations 

that you formed by stressing at room temperature. But they do affect the 

diffusion length, so just looking for contrast can be a little deceptive. 

You have to be careful without having any absolute measure of what the 

real lifetime or diffusion length is. 

QUESTION: If you don't see a contrast at a particular defect, I would say 

that at room temperature it's not strongly electrically active, unless 

you have such a high density of defects that you can't tell the difference between the various contrasts. The contrast you see for dislocation 

depends on the recombination efficiency at the particular dislocation and 

also on the diffusion length in the surrounding material. The surrounding material is limited by impurities or point defects or some other 

defect; you may see a very low contrast. It may not be indicative of 

what's happening at dislocations. It may be the bulk material around it. 

QUESTION: I generally would agree with that. But I still think one has to be 

careful, though. If you don't see contrast, you can't state absolutely 

that you don't have dislocations and that it's not affecting your lifetime. 

JOHNSON: Well, I agree. I wouldn't want to say anything absolutely about 

it. I made a statement that if we don't see that they are not a dominating factor as far as efficiency is concerned, I wouldn't argue that 

they are not a factor at all. 

MILSTEIN: I would comment on the two previous discussions. It is all well 

and good to understand how the stress interacts in causing dislocations 

and things of that nature; however, I think the problem that really needs 

to be addressed is what does one do about controlling it. In that sense, 

that's really the crux of what you are addressing. 

JOHNSON: That is the crux of why we are spending a lot of time figuring out 

what fot~s these particular defects. We would like to tailor our particular thermal environment so as not to produce these in the as-grown 

crystal rather than have to try to passivate them later. 

ILES: You are saying you are working on a polycrysta1line material, so by 

definition you have, I take it, grain boundaries and sub-grain boundaries. 

What I would like you to comment on is what you were planning to do in 

the near future to improve the lifetime or the diffusion length, and some 

feel for what kind of a number you expect in some given time frame. Would 

you like to comment on that? 

JOHNSON: I certainly cannot give you a number of what I would expect. What 

we would like to look at in more and more detail is why our lifetime does 

drop off as a function of dopant density, to try to determine where the 

actual limitations are, and it's very important to try to overcome the 

technological limitation of the material. Try to get to lower resistivity. So we are looking at that particular area right now. I don't have 

a feel for what I could say if we cast silicon sheet having resistivity 

of O.S-ohm centimeters that we would still expect our diffusion length 

to be 150 micrometers. I have no basis to make a judgment. 

417 
ILES: The reason i asked that question is you have now 3.2 ohm centimeters 

between your float zones. Everybody's working on it and getting the diffusion length hit and miss; some crystals have it, most of them don't. 

What kind of ultimate limits can we gain in efficiency? If somebody has 

that number. and would like to comment on it? 

QUESTION: I'd like to make a comment on that. It is that we know relatively 

well that our efficiency losses are due to the structural def.ects, such 

as grain and sub grain boundaries. We can minimize the sub-grain boundary 

density; that can be controlled. Independent of that, there is a problem 

with inter-grain minority carrier diffusion, which is r'elated to the 

doping density. It's seen in Czochralski material, not seen in floatzone, in that particular area that we are looking at, and it's something 

that's independent of the fact that there are grain and sub-grain boundaries around. You can separate the two, but it may not be separate from 

the actual method that we grow the crystal. It may be, or it looks to 

be, inherent in Czochralski, and I hope there are some improvements down 

the line. I really can't say what they would be at this time. 

418 , 
N85-3164 

HIGH EFFICIENCY' SOLAR CELL PROCESSING 0 

INTRODUCTION 

F.Ho and P.A.Iles 

Applied Solar Energy Corporation 

City of Industry, California, 91749 

At the time of writing, cells made by several groups are approaching 19% efficiency 

(AMI) (already achieved by the UNSW group). To help focus the forum objectives, we 

have chosen to discuss some more general aspects of the processing required for such 

cells, rather than presenting detailed cell results. 

Most processing used for high efficiency cells is derived from space-cell or 

concentrator cell technology, and recent advances have been obtained from improved 

techniques rather than from better understanding of the limiting mechani~ms. 

Theory and modeling are fairly well developed, and adequate to guide further 

asymptotic increases in performance of "near-conventional" cells. There are several 

competitive cell designs with promise of higher performance (> 20%) but for these de:;igns 

further improvements are required. 

The main trend recently has been the increased number of groups which can combine 

the available technology to fabricate high efficiency cells, and later we will discuss this 

trend in relation to the goals of the forum. 

HIGH TECHNOLOGY PROCESSING 

The available cell processing technology which has been exploited can be listed as 

follows: 

Choice and use of high quality silicon (mostly highly doped, mostly float-zone 

refined). 

Processing to preserve the high quality of the silicon. 

Formation of polished or textured front surface with low damage, accompanied later 

by the formation of a well designed (and carefully deposited) AR coating. 

Formation of shallow, lightly doped, good quality PN junction (usually by diffusion, 

in some cases by ion-implantation). 

Use of contacts with low contact resistance, perhaps with tunnel oxide Jayers to 

reduce recombination. 

Use of grid patterns with low shading (3-4%) and reduced series resistance (few %), 

giving fill factors above 0.80. 

Use of front surface passivation. 

In some cases, use of fields, reflectors or passivation at the back surface. 

In addition, when required, space cell groups have demonstrated the fabrication of 

thousands of thin (50-100um) cells with high efficiency. 

I Tables 1 and 2 show the intrinsic and extrinsic properties required for high 

efficiency cells, along with the process steps which mainly determine these properties. 

We have also indicated the cell parameters most affected. 

419 
TABLE 1 

INTRINSIC CELL PROPERTIES AND PROCESS STEPS WHICH 

INFLUENCE THESE PROPERTIES 

INTRINSIC PROPERTY PROCESS STEPS 

HIGH BULK DIFFUSION LENGTH ST ARTING SILICON, CLEANING, 

PROCESSING 

GOOD JUNCTION QUALITY SURFACE PREPARATION, CLEAN 

DIFFUSION 

LOW BULK LEAKAGE CURRENT JUNCTION, PURE SILICON, DOPING 

OF SILICON. 

LOW SURFACE RECOMBINATION SURFACE PASSIVATION (BSF, FSF, 

OXIDES, ETC.) MIN. METAL (AREA, 

PASSIVA TION) 

SHALLOW JUNCTION DIFFUSION CO~TROL 

TABLE 2 

AFFECT 

Jse 

Voe (CFF) 

Voe 

Voe (Jse) 

Jse 

EXTRINSIC CELL PROPERTIES AND INFLUENCING PROCESS STEPS 

EXTRINSIC PROPERTY PROCESS STEPS AFFECT 

LOW REFLECTANCE AR COA TING, (TEXTURED) Jse (Voe) 

LOW SHADING GRID DESIGN Jse 

LOW RESISTANCE LOSS GRID DESIGN, LOW CONTACT CFF 

RESISTANCE 

INTERACTIONS 

SILICON QUALITY/PROCESSING 

JUNCTION QUALITY/SHALLOW J UNC./PASSIV A TION/GRIDDING 

SURFACE PREPARATION/AR/PASSIVA TION 

420 
./ 

1 

I 

-f 

, 

If can be seen that there is considerable interaction of the process steps. This 

emphasizes the fact that to equal (or exceed) the best state-of-the-art cell performance, 

most of the processes listed must be acquired and combined successfully. In fact the main 

requirement is to minimize the unwanted interactions as far as possible. Often the key 

requirements ego texturing and passivation, are in conflict. 

In some cases, the effect of a different (hopefully improved) process can only be 

evaluated by including it in a cell fabrication sequence with most of the other necessary 

steps. Experience shows that to achieve the best cell performance, all the process steps 

must be applied well. 

In other cases, involving severe conflict of process steps, relief is sought by moving 

to alternate structures. For example, use of mostly back surface structures, can ease the 

shading and pa.ssivation requirements, but may lead to the need for higher carrierdiffusion lengths, and for effective back surface passivation, as well as requiring a more 

complex (interdigitated) contact design. 

In a few cases, the conflicts are resolved by using more complex steps ego the use 

of "dot" contacts to reduce metal Si contact area, and to reduce the need for contact 

passivation. Figure 1 shows pictorially the high technology processes which have been 

combined to give "",19% and it can be seen that a fairly good level of optimization is 

needed for almost all the steps. 

FIGURE 1 

EFFICIENCY ACHIEVABLE WHEN VARIOUS PROCESSES OPTIMIZED 

20 I 

I 

I I 

19 I I 

I I I I 

I I I I I 

18 I I I I I I I I I I I I I I 

I I i I I I 

17 I I I I I I I I I I I I I I I I I I I I 

I C I I I 

16 A B D E F -G H I 

EFF (AMl.5) PROCESS FUNCTION 

(%) 

LEGEND: A GOOD QUALITY SILICON 

B SURFACE PREPARATION 

C QUALITY JUNGTION 

D SHALLOW, LIGHTLY DOPED SURF. LAYER. 

E REFLECTANCE LOW. 

F LOW SERIES RESISTANCE 

G REDUCED SURFACE RECOMBINATION. 

H LOW SHADING AREA. 

I CONT.'\CT PASSIVATION 

421 
If some of the steps (e.g. G or I) are omitted, 17-18% is still achievable (this is the 

level often seen on production runs of space or concentrator cells). 

To exceed 18%, most of the processes shown must be well controlled and combined. 

To reach 19-20%, it is important to make improvements in steps A, G and I. 

Silicon Quality· 

Most of the present high efficiency designs, and most of the projections for further 

increase to -20%, involve the use of very high quality silicon. 

Almost all high efficiency cells have used float zone refined silicon, often with 

multiple zone passes. Such high quality silicon in the high doping ranges required,is not 

readily available (high efficiency solar cells represent a very limited market), and the 

quality is not easily specified or guaranteed. In fact, there is danger that the highest 

efficiencies claimed world-wide could all have been obtained usIng very few (perhaps one 

or two) ingots. This is of academic interest to show the feasibility of the combined 

processes to meet the design goals, but additional action is required if these cell designs 

are to be useful for meeting lon~ term flat plate efficiency goals (array efficiencies in 

excess of 15%, at a price of ~90 per square meter, and with 20-30 years projected 

lifetime). . 

We have had much experience with Czochralski-grown silicon, but limited experience 

with highly doped Cz-Si. G~nerally for equivalent doping concentrations, cell efficiencies 

are lower by 1-2% in conversion efficiency (5-10% lower in power), when Cz-Si replaced 

Fz-Si. However, lightly doped Cz-Si has shown very good quality, and very little work has 

been done to check if the problems at high doping levels are derived from the doping 

pellets used, or from crucible interactions. Although the latter would appear to be the 

cause when comparing to the zone-passing improvements, it is hard to explain why lightly 

doped Cz ingots are so good. Microcircuit technology has made significant improvements 

in the quality of surface devices, by use of internal gettering. It appears that more work 

should be done to identify the causes for reduced performance of highly doped Cz-Si. For 

production purposes Cz-Si has proved capable of high throughput and high quality, and 

although not yet satisfactorily inexpensive, it still is competitive with most other types of 

silicon. 

DISCUSSION 

We have indicated above that: 

a) Continued optimization of cell technology (mostly already used at low "production: 

levels) can provide cells -20% efficient; also most of the same technology can be 

deployed to test new cell designs. 

b) The feasibility of cells which can meet the efficiency requirements for future flat 

plate arrays, has been demonstrated. 

c) At present, in order to demonstrate small improvements, it is necessary for each 

group involved to master most of the proces~Jes required to make a cell. 

d) Most designs rely on use of very special quality silicon. 

422 
However, there are some important areas which require assessment, especially for 

this forum: 

i} More work is required, to widen the choice of silicon which has the chance of 

meeting the long term goals. 

ii) Although it is necessary at present to show successful combination of all the process 

steps, in the long run it is inefiicient to expect various cell development groups to 

acquire all these processes. In some cases, the time spent in such acquisition 

detracts from effort in areas where their real technical strengths can be used, 

whether it is in cell modeling, or in development of new processes. 

The only solution to this appears to be the formationof "teams", wherein the basic 

processing skills are used to complement some of those groups. 

Consideration of this option, leads to the realization that there are several different 

motives which drive cell development, including basic interest in theory and 

practice, commercial interest in the flat--plate array goals, the need to obtain 

financial gain or prestige for establishments or self, or even patriotism. These 

motives must be reconciled to make best use of all available talents. 

iii) Now that the cell technical requirements have reached a competitive efficiency 

plateau (19-20% cells should meet 15% array goals) j t is not too early to begin 

assessment of the cos.t and production limitations, and 'also to demonstrate adequate 

environmental stability. Here again, as in (i) a different set of skills may be needed, 

and it is important that some of the groups developing cells should be attuned to 

interaction with production groups. . 

iv) A minor consideration is offered - that perhaps a cell design should be selected 

which can be used 1n both flat plate and concentrator arrays (with slight known 

modifications for the latter) as the best compromise for short term production 

evaluation. 

v) In parallel with (lin, work should continue to extend the demonstrated feasibility 

(towards 23-25%) either by routes which do not demand utilization of many precise 

technology process steps, and which overcome some physical limitations (eg. high 

doping effects), or perhaps by effective team efforts. 

Some of the areas discussed above can be explored by decisions reached after the 

forum, by suitable direction from JPL or other agencies. 

SUMMARY 

Using near-conventional cell structures, present cell process technologies, when 

suitably combined can give cell efficiency ..... 19%, and with slight improvements, mostly in 

Si quality, 20% seems feasible. 

The successful designs to-date are derived from spac~ ,and concentrator cell 

. technologies which have demonstrated medium scale production levels '( 100KW flat-plate 

output per year), although without meeting the flat-plate array cost goals. 

423 
We feel that already manufacturing assessment should be made for cells operating in 

the 19-20% plateau. 

Some theoretical designs offer the possiblity of exceeding 20%, and should be 

pursued without constraints of costs, etc. 

One non-technical purpose of the forum maybe to combine the various motivations 

involved, to provide an effective program; one area of promise is the deliberate formation 

of balanced teams which include a wide range of skills (and motives). 

424 
~ll .' 

~ 

i 

-I 

t 

f 

! 

~ 

I 

I 

f 

I 

H 

f 

I 

DISCUStION 

(ILES) 

CISZEK: Peter, I'm intrigued by these older space cells that were worked out 

at AKO and a lot of people say they would have done real well under terrestrial conditions. ~sn't it possible to dig some of those out from the 

old Spectrolab or OCLI cells that are textured? 

ILES: Yes, they are still being made. The strange thing is that textured 

cells have only been made for a limited run and a different reason. The 

textured cells run 100C to lSoC hotter in space, and most people in 

the terrestrial areas don't understand that, that we can get a higher 

efficiency on the block but we don't get a higher efficiency when we 

interface with a real system. Space cells are a little more sophisticated, and the customer puts his specifications in there very early on 

and he knows very well what he is going to gain. I'm sure you are 

right. Matter of fact, I think Daud wanted some decent cells, backsurface fields so that he and Fred Lindholm and some other people could 

find out whether there was a voltage drop at the back surface. They came 

and got some Class 2 mechanical reject cells -- we don't make that many 

back-surface fields. He took them back and phoned us the next day and 

said do you know these are 17 something percent, and we said yes, you 

never asked us what, you just wanted some Class 2 cells. 

CISZEK: It would be inte~esting to hear more of the results on some of those 

space cells and sees how they really stack up terrestrially. 

ILES: I think the bottom line is they look very like these other cells; these 

are mainly 10 ohm-centimeter with a good back-surface field. It's hard 

to compare the 0.1, 0.2 ohm-centimeter concentrator-type cells. They are 

not very different in diffusion, gridding -- all those things are very 

similarly done. We can get you some of them if you want to analyze them. 

RALPH: Here I'd like to pin you down, I guess, as you have heard, we all have 

put in bells and whistles and that type of thing to make our cells and we 

all can agree that we could make like l7~ with the bells and whistles we 

put in daily. What would you do different to get the 19~ jump? In other 

words, there has to be something additional. Is it just resistivity 

change. or is it plus the passivation, or is it the material that's 

limiting it? What would you do d1.fferent, what additional bells and 

whistles would you add? 

ILES: At the moment, the material is the driving factor. To look very carefully, you want to get 19~ with high yield -- we are not talking about 

the best of the week or the best of the month. I think you have to 

divide the maximum diffusion length on the material and a reasonably high 

doping level. I don't think at the moment -- the trade-off to having 

lighter doping and a back surface field is not quite competitive" but 

very close when you get to that level. It's not easy in production but 

quite feasible to make shaded areas at one sun less than 3~. I think 

that would be no big deal. It would be a little tricky for a while but 

not unfeasible. The coatings and everything else are fairly straightforward. That's why I get so frustrated -- now we are talking about 

425 
production levels in a solar cell that is largely still hand production, 

but these processes are being automated for very large scales and, in 

different areas like the coatings, as you know, automated by different 

industries. The diffusion and the slicing and the polishing, all that 

stuff is well taken care of. So 1 think that the answer is that it's 

just a matter of putting them together. It depends on the material. 1 

think it's sort of a weaselly answer, but my feeling is it's nice to use 

these nice materials, but if you are going to set up a production line, 

you look at the best material you can buy in production quantities nnd 

then that sets your target as to what your line efficiency would be. 

RALPH: Basically, is it a Green cell design or something different? 

ILES: It's shallow-diffused, probably textured, if you are going to do some 

external cooling of some sort. Probably textured with a multilayered 

coating and presence of contacts. And, I'll point out, without surface 

passivation, and without contact passivation I believe you cannot go over 

177. anyway. 

RALPH: To get to 197. or so are you still going to have to surface passivate? 

ILES: At 197. you are going to have to do surface passivation to get the 

voltage up and if you want to agree there consistently, you have to keep 

the contacts out of it. 

SCHRODER: In the quest for the high-efficiency cell, in your view, what would 

be the three most important problems that you face today, or perhaps the 

most unknowns today? Not 10 or 12, but the top three. 

ILES: 1 think the most important thing would be to find a process sequence. 

Well, first of all, choose the material, you have to choose the material, 

because that fixes your design, and there are several competitive designs. 

The second is quite important -- that you pick a process sequence that 

can really take you up all the way and not sort of falter as you go. You 

don't need super-processing at each stage, but you naed each stage to be 

done very well, and 1 think you choose a sequence maybe where these 

trade-offs are made. There are certain trade-offs, as there are in any 

semiconductor device, and it's how you fit into the trade-off that 

matters. Now in the past, some of those trade-offs have been internal 

technology that -- like a guy has only a shadow mask. so he says I can't 

get very good shading areas so I'll make up for it,I'll do something 

else that's very clever, and I'll stress that I've got some advantage, 

even though 1 don't have a good process. 1 think when you are getting up 

to 197. or 207. you have to have everything working very well -- the whole 

sequence has to work very welL 

SIRTL: Peter, you made a fairly strong point on the material, of course, and 

the worst thing that could happen after the meeting is a strong inflow of 

orders to get the super-material, or something that would come near to 

it. 1 think 1 should cotm\ent a little more on that. On the one hand, 

when you get some extraordinarily good material on the finat-zone side, 

it has to be a byproduct of a much larger portion on a production scale. 

That's where the money has to come from. So in every case, such a kind 

426 
of material would always be very limited. Of course, it could be supported in terms of a project being made out of a long-range task to 

create, under any circumstances, such a super-material. But, on the 

other hand, if you remember, I made a strong point yesterday on the 

subject of gettering. I think the science of gettering still is in its 

infancy. My expectations, at least, go stronger in this direction --

that we would learn, over the years to come, a lot more about gettering 

and to ha.ndle material that can be produced under reasonable cost conditions and give it the final touch by the most appropriate gettering 

syst.em. And that, of course, has to vary from one type of cell, or t.ype 

of processing, to another. . 

ILES: I think that's a good point. It takea us away from the route of having 

to have clean rooms at every stage and building a whole extensive processing sequence. That's philosophically a nice approach. Do you think 

there's no chance of scaling-up for float-zone? There is obviously not a 

large enough market now, but supposing somebody said there was a quarter 

of a gigawat,t market. 

SIRTL: I have my serious doubts with it. economically, that this would ever 

be able to work. 

LOFERSKI: Peter, you made a rather strong point, and I think I agree with it, 

that the significance of what one has to do is to make it happen in the 

real world, on real-world materials. I think my understanding of how the 

process might go is that on the one hand you have to understand all the 

bits and pieces of how -- perhaps in the laboratory -- you would reach a 

20~ level, which might translate in the real world to an 18~ level. In 

that regard, perhaps the Cz material in its finest form might be capable 

of that kind of quality. The point about understanding what is required 

to get to the very highest level you can is also important, and in that 

sense -- having determined that -- now you attempt to apply that with the 

things that are available. I believe that is the next step that should, 

and perhaps will, take place. The float-zone material -- you are putting 

all the load on the guy producing the material -- and the Czochralski. I 

think we are implyir.g some sort of in-line gettering or updating or whatever. I think that's important. If you tell a manufacturing man "Here 

is what we want you to make -- oh, by the way. you are not going to get 

that material, you are going to have to somehow or other 'in that sequence 

put a gettering thing in there," that's not fair to him. I think you 

have to present him with the two options and see which he can, produce. I 

think in a sense you are right, but I think the conception that was held 

at the time when the high-efficiency work that I am supporting was put in 

place was simply: let us, in terms of understanding the details, remove 

as many of the roadblocks as we can. Let's work on the best material 

available to see what comes out. If you know you have a number of defects 

in the materials that are going to be limiting features, no matter how 

well you do the job, and no m~tter how good your understanding, you will 

be hindered by that. Perhaps after you understand what's required you 

then work your way around this one point, and knowing you might get the 

answer is better than saying "We think we can get the answer. Let us try 

to find the way without knowing where the pitfalls might possibly be." 

We area little sensitive, because we are like the guy who can jump 7'9" 

427 
but we can't tell anyone else how to jump 7'9". I'd hate to see a 

sprinter trying to jump 7'9". 

ILES: When you "are talking about a 20~ cell, you cannot put all the burden on 

material; I think your earlier comment was well taken. So it's very 

important that we know how to make this 2~ cell in the laboratory so 

that eventually one can optimize a cost or simplify later. 

SWANSON: Peter, we have seen in selected Czochralski wafers, 10 to 20 

ohm-centimeter resistivity range, as high a lifetime a~ we have seen in 

float-zone, and that was about four years ago. It was very sporadic, and 

averaged more like 20 microseconds to 50 microseconds. I think today, 

perhaps, with much more understanding on controlling oxygen concentration, that a serious effort to go back ~nd try to learn how to get the 

lifetime up in Czochralski would be successful, in light of the better 

material today. What we found is that the gettering procedures that have 

been optimized around generation lifetime considerations are simply not 

appropriate, and generally do not work when you are concerned with 

recombination lifetime in the bulk of the material. 

ILES: If you want to make fast-switching solar cells in good shape. 

428 
PROCESS AND DESIGN CONSIDERATIONS FOR HIGH-EFFICIENCY SOLAR CELLS 

A. Rohatgi and P. Rai-Choudhury 

Westinghouse R&D Center 

Pittsburgh, PA 15235 

ABSTRACT 

This paper shows that oxide surface passivation coupled with optimum 

multilayer anti-reflective coating can provide ~ 3% (absolute) improvement in 

solar cell efficiency. Use of single-layer AR coating, without passivation, 

gives cell efficiencies in the range of 15-15.5% on high-quality, 4 ohm-cm as 

well as 0.1-0.2 ohm-cm float-zone silicon. Oxide surface passivation alone 

raises the cell efficiency to ~ 17%. An optimum double-layer AR coating on 

oxide-passivated cells provides an additional ~ 5-10% improvement over a 

single-layer AR-coated cell, resulting in cell efficiencies in excess of 

18%. Experimentally pbserved improvements are supported by mod~l calculations 

and an approach to ~ "20% efficient cells is discussed. 

1. INTRODUCTION 

The idealized efficiency(l) of a silicon solar cell ~s about 25%, 

assuming the best material and surface parameters achievable to date, although 

present day cells fall considerably short of this limiting value. This is 

largely a consequence of heavy doping effects, bandgap narrowing, and high 

recombination at and near the cell surfaces. The major problems of efficiency 

improvement fall in the above categories; however, there are additional design 

requirements for efficient contacts and antireflective coating. Although 

these areas are well understood, they are not trivial and must be optimized 

consistent with the device structure. In this paper we will discuss the 

design, fabrication, and analysis of 18% efficient surface-passivated solar 

cells on high-quality, 0.1-0.2 ohm-cm float-zone silic.on. Results on 4 ohm-cm 

silicon cells are also shown. Various electrical measurements, along with a 

simple theoretical model which uses internal recombination velocity to assess 

minority carrier losses in various regions of the solar cell, are used to 

analyze the cell data and address the requirements for surface-passivated 20% 

efficient cells on low-resisitivity silicon. 

2. CONSIDERATIONS FOR HIGH-EFFICIENCY SOLAR CELLS 

It is clear that high efficiency is a major attribute that will 

enhance the large-scale applicability of solar photovoltaic systems. Assuming 

5% reflector absorption losses, 1% mismatch losses, and 96% packing factor for 

rectangular cells, 20% efficient cells will be required for 18% efficient 

429 
modules. Current module efficiencies are about 12-13% in production. In the 

last two to three years, solar cell efficiencies have been in the range of 14-

_-17j" ~ven at :.eh~l·~earch level; however, recent breakthroughs have occurred 

;-~irCSi.ngie-crfi'taI "Vcell efficiency at the research level. Cell efficiencies in 

the range of 17-19.1% have been reported by several investigators (Table 1). 

To achieve 20% or greater efficiency cells, a considerable amount of furthe-r 

research will be required in the areas of: 

• Material and carrier lifetime improveme:nts 

• Process development 

• Design improvements such as surface passivation,'reduced heavy 

doping, and multilayer AR coating 

• Tandem cells 

Module efficiencies can be further enhanced by: 

• Improved packing factor 

• Reduced reflection losses from the glass 

• Reduced interconnect losses 

• Reduced mismatch losses by near-uniform cells 

2.1 Material and Carrier Lifetime Considerations 

High carrier lifetime is desirable because it improves both J sc and 

Voc. The best m'easured lifetime values in silicon to date are on the order of 

1 msec, well below the ultimate value based on the radiative band to band 

recombination. Fossum et al.(11) have hypothesized a vacancy-related 

fundamental defect in silicon crystals which limits the lifetime in nondegen·-

erate silicon. Based on our experience, it is difficult to detect any deeplevel defect in good-quality silicon even with the help of the most sensitive 

techniques, such as deep-level transient spectroscopy, that are available 

today. There is some concern about the accuracy of true lifetime or diffusion 

length measurements, especially when diffusion length becomes greater than the 

base width. 

In Table 1, use of very high-quality low-resistivity (0.1-0.3 ohm-cm) 

float-zone silicon was a key factor in 17-19.1% efficient cells fabricated by 

Westinghouse, Spire Corp., and the University of New South Wales. It is not 

clear why these crystals are much better or less sensitive to process-induced 

lifetime degradation compared to the majority of low-resisitivity Czochralski 

or float-zone crystals. Therefore, there is a need to identify, understand, 

and minimize the lifetime-limit.ing centers and develop more reliable 

techniques for measuring true base diffusion length and surface recombination 

velocities. 

2.2 Process Considerations 

High carrier lifetime in the starting silicon becomes academic if 

processing introduces new defects and unwanted impurities. Special care must 

be taken during substrate cleaning, and favorable gettering ambients 

consisting of POCR.3 and HCR. gas should be utilized whenever possible. Slow 

430 
J V 

ml7cm2 m~c 

36.0 625 

36.5 610 

36.2 600 

36.0 627 

35.9 627 

34.9 643 

33.0 653 

34.0 624 

35.1 623 

36.0 653 

Table 1 

Some Recent High-Efficiency Silicon Solar Cells 

Tested Under One Sun AMl Illumination 

n 

FF % 

.805 18.1 

.775 17.2 

.793 17.2 

.800 18.1 

.800 18.1 

.813 18.1 

.810 17.5 

.820 17.6 

.780 17.1 

.811 19.1 

Substrate 

Resistivity 

ohm-em 

0.15 

10.0 

4.0 

0.2 

0.3 

0.2 

0.3 

Concentrator 

Cell 

0.3 

Concentrator 

Cell 

0.3 

0.1-0.3 

Source 

Applied Solar Energy 

Corporaton 

Westinghouse 

Westinghouse 

Spire Corporation 

University of New South 

Wales, Australia 

Sandia National 

Laboratories 

Applied Solar Energy 

Corporation 

Catholic University of 

Leuven, Belgium 

University of New South 

Wales, Australia 

cooling and gradual wafer withdrawals from the furnace could also be important 

in preserving the lifetime of the starting material. 

2.3 Design Considerations 

If a very high carrier lifetime cannot be obtained in the finished 

cell, then a clever cell design can still give h~,h-efficiency cells. As 

suggested by recent model calculations of Sah,(l 20% efficient p+-n-n+ cells 

can be realized with a base lifetime of 20 ~secs provided that cell thickness 

is reduced to 50 ~m and the back-surface field is ~O ~m deep with ND of 5 x 

1018 cm-3• Wolf's(l) design criteria for very high-efficiency cells include 

equal impurity concentration in the base and emitter up to the onset of heavy 

doping effects, coupled with reduced surface recombination velocities on the 

order of 10 em/sec. 

In this paper our own model calculations show that a combination of 

design features such as surface pas'Sivation, reduced heavy doping, and 

431 
~ 

w 

~ 

ID and Cell Design 

No Passivation 

Cell #2 

Front and Back 

Surface Passivation 

Cell U HIEFY 4-5 

Passivation and 

Reduced Heavy Doping 

No Passivation 

Cell UC-2 

Front and Back 

Surface Passivation 

Cell flC-8 

Surface Passivation 

and Double-Layer AR 

Cell f1C-12 

Surface Passivation 

Reduced Heavy Doping, 

Double-Layer AR 

*Assumed 

tJ.Expected 

Table 2 

A Comparison of Measured and Calculated Open-Circuit Voltage for High- and 

Low-Resistivity Solar Cells With and Without Surface Passivation Designs 

Sejb 

cm/sec 

Seje 

cm/sec 

Job 

pA/cm2 

Joe 

2 pA/cm 

NA ~ 3.5 x 1015 , L 400 ~s, W: 250 ~m 

883 4826 7.9 1.5 

517 3340 4.6 1.0 

456 117 4.1 0.04 

N 2 x 1017 L 

A ' 168 ~s, W 375 ~m 

956 12129 0.15 1.3 

953 9301 0.15 0.97 

953 9301 0.15 0.97 

925 332 0.14 0.03 

Job + Joe 

pA/cm2 

9.4 

5.6 

4.14 

1.45 

1.12 

1.12 

0.17 

Measured 

J sc 

mA/cm2 

33.4 

36.2 

36.2~ 

31.7 

33.2 

36.0 

36.0~ 

Calculated 

V oc 

mV 

569 

584 

592 

616 

625 

.625 

675 

Measured 

Voc 

mV 

582 

600 

612 

628 

627 

Cell 

n 

% 

15.2 

17.2 

18. tJ. 

15.6 

17.0 

18.0 

20.06 
1 

; 

! 

f 

I 

n 

I 

, 

I 

multilayer AR coating can give ~ 20% efficient cells on 0.1-0.3 ohm-cm floatzone silicon with base diffusion lengths in the range of ISO to 200 microns. 

3. MODEL CALCULATIONS 

We have developed a simplified analytical model to provide guidelines 

for maximizing V and cell efficiency. This model, which is described 

elsewhere in det~rl,(2,3) includes the effect of bandgap n~rrowing, Auger 

recombination, and recombination at the cell surfaces, but it "neglects the 

electric field effects resulting from the gradient of doping concentrations.(4,S) With the help of this model we can calculate internal recombination velocity (S ) in any region of the cell using surface recombination 

velocity (So), dIffusion length, cell width, and doping density as input 

parameters. The solar cell is divided into several small elements and S is 

calculated iteratively from the surfaces toward the junction using the 

following equation: 

L Sl D + tanh 

L 1 + Sl D tanh 

(1) 

where W is the width of the element; (Sl' Nl , ~VGl) and (S2' N2 , ~VG1 are the 

recombination velocity, doping density, and the bandgap narrowing at the two 

boundaries of the element; and D and L are the diffusivity and diffusion 

length of the minority carriers within the element. The model uses empirical 

equations to calculate diffusivity~ diffusion length, and bandgap narrowing 

primarily from the doping density.,2,j) 

Examples of internal recombination velocity plots are shown in Figures 

1 and 2. Figure 1 shows the calculations for 4 ohm-em cells with a base 

diffusion length of 400 ~m, and Figure 2 is for 0.1-0.2 ohm-em cells with a 

base diffusion length of 168 ~m. Each figure includes the calculation for 

three different back-surface field (BSF) and emitter designs, namely: a) no 

surface passivation, b) surface passivation where So is red~ced to SOO em/sec, 

and c) surfac~ passivation plus reduced he~~y d~~ing whige t~j surface dopant 

concentration has been lowered from 2 x 10 cm ~o 10 em • ~o at the 

metal and bare silicon surface is assumed to be 10 cm/sec and 10 em/sec, 

respectively. A junction depth of 0.3 ~m and a BSF width of O.S ~m were 

determined by spreading resistance measurements on the actual cells. 

Exponential doping profiles are assumed in the diffused regions, and the 

doping density at the emitter depletion boundary in Figures 1 and 2 has been 

estimated to be 1 x 1017 cm-3 and 3 x 1017 cm-3 , respectively. 

Using the values of the internal recombination velocities at the 

depletion region boundaries in Figures I and 2, total reverse saturation 

current (Jo) for any case can be calculated according to: 

S "b (.....tlQ. N 

A 

433 

S " 

+ ~) N 

D 

(2 ) 
Figure 1. 

Figure 2. 

Distance, 11m 

0 0.5 120 249.7 250 

I I I 

106 

l =400 11m 

NA =3. 5)( 1015 cm-3 S =104 

o 20 

~ 106 Ns =2x 10 

E 

u 

-= .... 104 So = 500 Vl Ns =2 x 1020 

z.. 

~ 103 

> 

c: 

.2 

,;; So = 500 ~ 102 

N =1019 E 

§ s 

'" p+ N+ 

101 p- Base Emitter BSF 

Back Junction Front 

Surface Depletion Surface 

Region 

Model calculations and internal recombination velocity plots for 

4 ohm-cm base cells with a base diffusion length of 400 microns. 

0 

106 I 

~ 105 

E 

u 

...: .... 104 Vl 

~ 

l5 

103 0; 

> 

c: 

.2 

,;; 

102 c: 

:c 

E 

0 

&! p+ '" 10 BSF 

Back 

Surface 

0.5 

I 

Distance, 11m 

17 -3 

So = 106 l = 168 Jl m. NA = 2 x 10 ~m 

N=2xl020 50 =10 

s Ns =2 x 1020 

So = 500 

Ns =2 x 1020 

P-Base 

374. 5 375 I I 

N+ 

Emitter 

J unction Front 

Depletion. Surface 

Region 

~~'odel calculations and internal recombination velocity plots for 

0.1-0.2 ohm-cm base cells with a base diffusion length of 

168 microns. 

where J band J represent the base and emitter contribution of J and 

(8 0b' §A) and ~Seje' Nn) are the recombination velocity and the dgping 

de~~ity at the depletion region boundary in the base and emitter, 

respectively. Finally, Voc is calculated from 

v 

oc 

KT = - R.n 

q 

434 

.. 
where J sc is either estimated or measured short-circuit current density. 

Table 2 shows the calculated J o and Voc for various cell designs in Figures 1 

and 2. 

4. EXPERIl1ENTAL WORK 

Following the guidelines of our model calculations, we fabricated' 

oxide-passivated cells on high-quality a) 0.1-0.2 ohm-cm, ,boron-doped, (100), 

15 mils thick float-zone silicon and b) 4 ohm-cm, boron-doped", (Ill) floatzone and dendritic web silicon. The baseline cell structure was n+-p-p+, 

where the n+ emitter was formed by a 8500C POCl3 diffusion which resulted in a 

junction depth of 0.3 ~m and a sheet resistance of 60-80 ohm/square. The p+ 

back-surface field was fabricated by a 9500C boron diffusion. Thermal oxide 

for passivation was grown at 8000 C, which resulted in an oxide thickness of 

~ 100 A on top of the n+ region and ~ 50 A on the p+ surface. About 600 A 

thick single-layer AR coating was applied by a spin-on process on the 

passivated cells. AR coating thickness on the unpassivated cells was ~ 750 A. 

In selected instances a double-layer AR coating was applied on the oxidepassivated cells by a spin-on process. The double-layer AR coating consists 

of 475 A Ti02 and 980 A Si02 layers on top of 100 A passivating oxide. 

Ti-Pd-Ag contacts were m.ade on front and back, and the front grid design had 

an area coverage of 2%. 

Both reflectivity and spectral response measurements were performed 

over a wavelength range of 0.4 to 1.1 ~m to obtain the internal quantum 

efficiency. In selected instances, minority carrier lifetime in the cells was 

measured by the open-circuit voltage decay (OCVD) techntque, where the 

injection current was made equal to the short-circuit current. 

5. RESULTS 

Table 3 shows the data for the 4 ohm-cm float-zone silicon cells, with 

and w~thout oxide surface passivation. Without passivation, J sc is ~ 33 

rnA/cm , Voc is ~580 mY, and cell efficiency is ~ 15%. With both surfaces 

passviated, th~ cell efficiencies are in excess of 17%, with Voc ~ 600 mV and 

J sc ~ 36 rnA/cm. Dark I-V m{~~urements showed that oxide passivation reduces 

J o by about a factor of two. Quantum efficiency plots in Figure 3 clearly 

show that front- and back-surface passivation enhances the short- and longwavelength responses of the cell. OCVD lifetime in the 17.2% cells was 50 

~secs, corresponding to a diffusion length of ~ 400 ~m, which was used in the 

model calculations in Figure 1. 

Table 4 shows the data for the passivated and unpassivated 0.1-0.2 

ohm-cm bas~ cells. Unpassivated cell efficiencies are ~ 15.5%, with J sc of 

31.5 rnA/cm and Voc of 612 mY. ~fter oxide passivation, cell effici~ncies 

approach 17% with J sc = 33 mA{§m an~ V c = 627 mY. Dark I-V data showed a 

decrease in J

o 

from 7.1 x 10- A/cm tg 5.0 x 10-13 A/cm2• Quantum 

efficiency plots in Figure 4 show that oxide passivation on this lowresistivity silicon increases only the short-wavelength response, but has 

negligible effect on the long-wavelength response. OCVD lifetime on these 

435 
Cell ID 

1 

2 

HIEFY 

4-4 

-5 

Figure 3. 

1: 

Q.) 

~ Q.) 

c. 

>. 

u 

c: 

... 

:i;i 

::: 

UJ 

E 

:::l 

1: 

'" :::l 

0 

Table 3 

Solar Cell Data on 4 ohm-em Float-Zone 

Silicon With and Without dxide Passivation 

With Single-Layer AR Coating 

100 

CXI 

80 

30 

20 

10 

0 

J~c rnA/cm2 

33.3 

33.4 

36.1 

36.2 

Voc 

Volts Fill Factor 

WITHOUT PASSIVATION 

0.582 0.767 

0.582 0.780 

WITH PASSIVATION 

0.599 0.794 

0.600 0.793 

Curve 7'.4B'fS-A 

• Without Oxide Passivation 

o With Oxide Passivat/on 

Efficiency 

% 

14.8 

15.2 

17.1 

17.2 

425 525 625 725 825 925 1025 1125 

Wavelength ( nanometers) 

Internal quantum efficiency plots for a 15.2% unpassivated cell and 

a 17.2% efficient oxide-passivated cellon 4 ohm-cm float-zone 

silicon. 

cells was ~ 168 ~m, which was used in the model calculations in Figure 2. 

Table 4 also ~hows that double-layer AR coating increased J sc from 33 rnA/cm2 

to ~ 36 rnA/cm and gave) 18% efficient cells. Figure 5 shows the measured 

spectral reflectivities on single-layer AR-coated 17% efficient cells and 

double-layer AR-coated 18% efficient cells. 

436 
100 

'Xl 

80 

C 

'" 70 :: 

'" 2-60 

>. 

u 

c 

J!! 50 .II! 

E 40 

E 

::I • Without Oxide Passivation 

C 30 

'" o With Oxide Passivation ::I 

0 20 

10 

0 

1125 

Figure 4. Internal quantum efficiency plots for a 15.6% efficient 

unpassivated cell and a 16.9% efficient oxide-passivated cellon 

0.1-0.2 ohm-cm float-zone silicon. 

Curve 74714B-A 

40 

~ II >. 

-.;: Single Layer AR Coated 17% Cell 

:;:; 

Double Layer AR Coated 18. 1"10 Cell u 

Q) 

;:: 20 Q) 

0:: 

10 

0 

0.4 0.6 0.8 1.0 1.2 

Wavelength (microns) 

Figure 5. Measured reflectivities of single-layer AR-coated 17% efficient 

cell and double-layer AR-coated Gell. 

Oxide-passivated cells were also fabricated on 4 ohm-cm dendritic web 

silicon crystals. Table 5 shows that without oxide passivation, good-quality 

web crystals give average efficiency of ~ 14.5%, but with oxide pa3sivation 

the cell efficiencies are ~ 16%. As in the case of 4 ohm-cm float-zone 

silicon eells, an oxide passivat~on-induced 1 to 2% increase in web cell 

efficiency was associated with an increase in J sc and Voc and a reduction in 

J o' 

437 
~l 'j 

I 

54 

1 

I 

" 

1 

I 

1 

I 

Cell ID 

C-2 

C-5 

C-7 

C-8 

C-9 

C-10 

C-U 

C-12 

Cell ID 

W6 

W7 

WI 

W2 

Table 4 

Solar Cell Data on 0.1-0.2 ohm-cm Float-Zone 

Silicon With and Without Oxide Passivation 

31.8 

31.7 

33.0 

33.2 

Voc 

Volts Fill Factor 

WITHOUT OXIDE PASSIVATION 

0.613 

0.612 

0.802 

0.797 

WITH OXIDE PASSIVATION 

0.627 0.815 

0.628 0.815 

PASSIVATION AND DOUBLE-LAYER AR 

34.7 

35.1 

36.0 

36.0 

0.626 

0.624 

0.620 

0.627 

Table 5 

0.810 

0.803 

0.808 

0.800 

Efficiency 

% 

15.6 

15.5 

16.9 

17.0 

17.6 

17.6 

18.0 

18.1 

Solar Cell Data on 4 ohm-cm Dendritic Web 

Silicon With and Without Oxide Passivation 

32.7 

33.1 

34.6 

34.5 

Voc 

Volts Fill Factor 

WITHOUT PASSIVATION 

0.575 0.782 

0.577 0.784 

WITH OXIDE PASSIVATION 

0.584 0.784 

0.586 0.794 

6. DISCUSSION 

Efficiency 

% 

14.7 

15.0 

15.9 

15.8 

Table 2 shows that oxide passivation coupled with careful cell 

processing can produce cell efficiencies greater than 17% (AMI) on highquality 4 ohm-cm float-zone silicon, with Voc ~ 600 mV and Jsc ~ 36 mA/cm2• 

This corresponds to a ~ 18 mV increase in Voc ' 3 mA/cm2 increase in Jsc ' and 

2% improvement in absolute cell efficiency compared to the unpassivated 

cells. Model calculations in Figure 1 and Table 2 for the 4 ohm-cm base cells 

indicate that without any surface passivation, Job and Joe contribute appre438 
ciably to the tota: J o; therefore, both front- and back-surface passivation 

become important in reducing J o or improving Voc. For example, Table 2 shows 

that: a) without any passivation, J o = 9.4 pA/cm2 and the calculated Voc is 

569 mV; b) with front-surface passivation alone, J = 7.9 + 1.0 = 8.9 pA; 

c) with only back-surface passivation, J o = 4.6 + Y.5 = 6~1 pA; and d) with 

both surfaces p~ssivated, J o = 5.6 pA, resulting in a calculated VQC of 584-

mV. Thus, model calculations predict an increase .~f 15 mV in Voc if both 

surfaces of a 4 ohm-cm cell are passivated and its base diffusion length is 

400 Pm. This is in very good agreement with the experimentally observed 

increase of 18 mV in V • However, it should be noted in Table 2 that the oc . absolute values of calculated V are about 15 mV smaller than the measured 

values. This difference can beO~ttributed to a number of assumptions and 

estimated inputs that went into the model calculations, e.g., surface 

recombination velocities, exponential doping profiles, diffusion length 

obtained by OCVD lifetime, and estimated doping density at the depletion 

region boundary in the emitter. More accurate values of the above parameters 

are needed for precise modeling; nevertheless, such model calculations provide 

very useful guidelines as to what should be done to which region of the solar 

cell in order to obtain high Voc. 

Figure 2 and Table 2 show a similar calculation for a 375 pm thick 

cellon 0.1-0.2 ohm-cm silicon with a base(~iffusion length of 168 pm. Unlike 

the 4 ohm-cm cells, here J dominates J, ) with or without surface 

passivation. In addition,Ojob remained ~nchanged (0.15 pA/cm2) after backsurface passivation, because the minority carrier diffusion length in the base 

is much smaller than the thickness of the base. Therefore, back-surface 

passivation in these low-resistivity cells becomes unimportant, and only the 

front-surface passivation contributes to the increase in Voc. A calculated 

increase of 9 mV in Voc is in good agreement with the observed increase of 13 

mV, considering the number of model assuuiptions. Notice in Table 2 that the 

calculated values of V are in much better agreement (± 4 mV) with the 

measured values for th~Clow-resistivity cells. This is probably the result of 

the better estimates for the model inputs for this case. 

In the 4 ohm-~m base cells, we measured a 3 rnA/cm2 improvement in J sc compared to 1.5 rnA/cm in the low-resistivity cells as a result of oxide 

passivation. This can also be explained in terms of the difference in the 

effectiveness of back-surface passivation in the two cells. In the lowresistivity cells, diffusion length to cell thickness ratio·(L/W) is much less 

than one; therefore, reduced recombination at the back surface does not 

improve the collection or quantum efficiency of the carriers generated by the 

long-wavelength photons near the back surface (Figure 4). The improved J c in 

the low-resistivity cells only results from front-surface passivation, which 

enhances the quantum efficiency of the short wavelengths (Figure 4). In the 4 

ohm-cm base cells, (L/W) is much greater than one; therefore, we observe an 

improvement in short- as well as long-wavelength response (Figure 3). 

Table 4 shows that the use of double-layer AR coating raises the lowresistivity cell efficiencies from 17% to 18.1%. Single-layer AR-coated 17% 

efficient cells and double-layer AR-coated 18.1% cells on 0.1-0.2 ohm-cm 

float-zone silicon were analyzed in detail by spectral response and 

reflectivity measurements. Figure 5 shows a comparison of the measured 

reflectivity of the two cells as a function of wavelength. The double-layer 

AR-coated cell has smaller integral reflectivity compared to the single-layer 

439 
l 

j 

AR-coated cell. However, as shown in Figure 6, thei~ internal quantum 

efficiency as a function of wavelength is virtually similar. It is important 

to remember that in the calculation of internal quantum efficiency, the 

effects of reflectivity are removed; therefore, identical internal quantum 

efficiencies imply that the interior quality of the two cells is nearly the 

same. Thus, the difference in the cell efficiency is primarily due to the· 

difference in the reflectivity of the AR coatings. This is consistent with 

the cell data in Table 4, which show that the ~ 2 to 3 mA/cm2 increase in 

short-circuit current is the main reason for increased cell efficiency from 17 

to 18.1%. 

Table 2 also shows model calculations for a cell design with reduced 

heavy doping in the emitter and the BSF regions. In this case d~pant 

con§entration at the surfaces has been reduced from 2 x 1020 cm- to 

101 cm-3• It is interesting to note that reduced heavy doping in a 4 ohm-cm 

base cell gives additional improvement of only 8 mV (592-584) in V ,but in 

the low-resistivity case the calculated improvement is 48 mV (673-gZ5), 

neglecting the drift field effects. This is because reduced heavy doping in 

the BSF region does not change J b very much, but reduced doping in the 

emitter lowers Joe by more than ~n order of magnitude (Table 2). Since the 

Voc of the oxide-passivated 4 ohm-cm cells is controlled by Job' reduced heavy 

100 

90 

80 

C 70 ... 

u '" 

'" Q. 

60 >. 

u 

<:: 50 '" ;g 

-0- Single-layer AR-Coated 17% Efficient Cell 

-0- Double-layer Ar-Coated 18.1% Efficient Cell 

i:U 40 E 

:0 

C lJ to 

:0 

0 aJ 

10 

0 

J/5 tf75 575 675 775 875 975 1075 

Wavelength (nanometers) 

Figure 6. Internal quantum efficiency versus wavelength plots for a 17% 

efficient single-layer AR-coated cell and an 18.1% efficient 

double-layer AR-coated cell. 

doping has little effect on V c' The V of oxide-passivated 0.1-0.2 ohm-em 

cells is controlled by J e; tRerefore, ~~duced heavy doping in the emitter 

increases Voc very signi~ca~tJyu Therefore, use of multilayer AR coating and 

reduced heavy doping can me:\ke these low-resistivity surface-passivated cells 

(Table 4) 20% efficient with \Jocof 675 mY, Jsc of 36 mA/cm2 , and fill factor 

of 0.82. Calculations in Table Z point out that at 20% efficiency, V of 

these low-resistivity cells will become base-limited (Job »J ). Iffferefore, 

in order to obtain greater than 20% efficient cells, eitfier ba~~ thickne~s will have to be reduced or higher base diffusion lengths will be required. 

Some experiments are being conducted to verify this model desigit. 

440 
CONCLUSIONS 

Consistent with our model calculations, we were able to improve opencircuit voltage and short-circuit current by oxide passivation of the cell 

surfaces. Oxide-passivated cell efficiencies on 4 ohm-cm as well as 0.1-0.2 

ohm-cm float-zone silicon were 17% compared to 15 to 15.5% without surface 

passivation. Use of double-layer AR coating raised the low-resistivity cell 

efficiencies from 17% to 18.1%. In 4 ohm-cm cells, both front- and backsurface passivation was imp~rtant, and their combined infl,uence increased Voc 

by 18 mV and Jsc by 3 rnA/cm. In 0.1-0.2 ohm-cm cells, where diffusion length 

was much smaller than the cell thickness, back-surface passivation did not 

help significantly. In these cells, V went up by 13 mV and J increased by 

1.5 mA/cm2• Our model calculations in8rcate that in low-resisti~ity cells, 

Joe dominates J o; therefore, back-surface passivation does fiot improve Voc. 

However, front-surface passivation reduces J and improves the shortwavelength response quite significantly. Mo~el calculations indicate that 

oxide passivation coupled with reduced heavy doping in the emitter can give a 

very substantial increase in V in the low-resistivity'cells with 

efficiencies of 20%. oc 

REFERENCES 

1. M. Wolf, Proc. of 14th IEEE Photovoltaic Specialists Conf., p. 674 (1980). 

2. J. R. Davis and A. Rohatgi, Proc. of 14th IEEE Photovoltaic Specialists 

Conf., p. 569 (1980). 

3. A Rohatgi and P. R~i-Choudhury, IEEE Trans. on Electron Devices, ED-31, 

No. 5~ p. 596 (1984). 

4. M. Wolf, Proc. of 14th IEEE Photovoltaic Specialists Conf., p. 563 (1980). 

5. M. P. Godlewski, C. R. Barona, and H. W. Brandhorst, Proc. 10th IEEE 

Photovoltaic Specialists Conf., p. 40 (1973). 

6. A. Rohatgi, J. R. Davis, R. H. Hopkins, P. Rai-Choudhury, P. G. McMullin 

nad J. R. McCormick, J. Solid State Electronics, Vol. 22, p. 415 (1980). 

7. A. Neugroshel, F. Lindholm and C. T. Sah, IEEE Trans. on Electron Device, 

Vol. ED-24, p. 662 (1974). 

8. H. J. Hovel, "Semiconductor and Semimetals," Solar Cells, Vol. II, 

Academic Press (1975). 

9. J. G. Fossum, F. A. Lindholm ,and M. S. Shibib, IEEE Trans. on Electron 

Devices, Vol. ED-26, p. 1294 (1979). 

10. A. Rohatgi et al' J Second Monthly Report on "Research on the Basic 

Understanding of High Efficiency in Silicon Solar Cells," SERI Contract 

No. XB-3-02090-4. 

441 
11. J. G. Fossum and D. S. Lee, Solid State Electronics, Vol. 25 (8), p. 741 

(1982). 

12. C. T. Sah, "Study of Relationships of Material Properties and HighEfficiency Solar Cell Performance on Material Composition," First 

Technical Report, DOE/JPL Contract No. 956289-83/1, July 1983. 

ACKNOWLEDGEMENTS 

The authors would like to acknowledge the invaluable contribution of 

the late J. R. Davis for device modelling and guidance. They would also like 

to thank T. W. O'Keeffe, D. L. Meier, and D. N. Schmidt for special response 

measurements; T. W. O'Keeffe, B. Yoldas, and N. J. Rooney for double-layer AR 

coating; J. B. McNally, F. S. Youngk, and G. Machika for cell processing; S. 

Karako for help in cell testing, computer programming, and model calculations; 

and G. S. Law for reading and preparing the manuscript. This work was 

supported by SERI Contract No. XB-3-02090-4 and by the U.S. Department of 

Energy under prime Contract No. DE-AC02-83CHI0093. 

( 

442 
DISCUSSION 

CISZEK: Ajeet, could you comment whether there is any influence on the 

process or the temperature of the oxidation that you use to create your 

passivation -- on the effectiveness of it? 

ROHATGI: Yes, that's a very good question. That passivating oxide is not so 

easy to grow, because first of all you are growing it on a highly doped 

surface. It is not like growing an oxide on a silicon wedge, as you do 

in MOS. So the quality is ver'y critical and the thickness control becomes 

difficult, especially when yot! are making such types of cells, because 

the oxidation rates on n+ and p+ are very different. On n+ the 

oxidation rate is about three times faster than on the p+. So it is 

very critical that you proceSll your device under well-controlled conditions for the oxidation step. You almost have to tailor the oxidation 

in-house, because it is very uensitive to the processing condition. The 

thickness there is very crith~al. If you are off by 30 to 40 seconds you 

find out that y(")u have exceedE~d the oxide thickness that is optimum for 

the passivation and the advant.age that you are gOi11g to get from antireflection coating. But if it is very thick you are going to get hurt in 

reflection losses. 

MILSTEIN: Basically, what I want bo do is to confirm some of the hydrogen 

passivation work tha:t Steve and Ajeet have talked about. We also have 

passivated a string of cells. These were provided by Bob Campbell; they 

are made on web. I presented most of this at the IEEE meeting, but we 

have some further data. The po:int that Ajeet made on improving efficiency, I think is very important. All of this is published, and will be 

out in the IEEE Proceedings. But basically. if you look at some of the 

not-evcn-so-good cells, you see a 1.5 efficiency. The numbers are hard 

to read. You will see full one point efficiency improvements on some of 

the others, again, on cells that were not all AR-coated. We have also 

looked at the spectral-response data. When Ajeet mentioned his results 

we took a look at some of ours, and I'll show you two unpassivated cells 

that we did. Here is cell 10, which was passivated, and here is cell 3, 

which was not passivated, and if I can line them up we find that for one 

of the cells the response, in fact, improved; for the other, it did not 

change very much from virgin cells that had not been passivated in any 

way. The upper curve is cellS and the lower curve is a ain cell 10, 

passivated, and you can see that there has been virtuall¥ no change 

there. So the hydrogen passivation clearly is doing things and it is not 

a one-shot result, it's been seen by more groups than one. The question 

is, what's going on, and are we going to work on that problem? I might 

point out that we have an experiment in progress too. We took two pieces 

of web, one as-received, and after about a 30-minute implant, pumping as 

much hydrogen as we could, we sent. it off to NBS to have them look at it 

with neutron activation to trr to locate hydrogen in the sample. 

QUESTION: Just to follow up on what you said, we also have attempted to find 

out where the hydrogen is located by neutron resonance reaction technique, 

where we come with nitrogen 15, which reacts very strongly with hydrogen 

gas. This ~easurement was done at the University of Western Ontario, by 

443 
Professor Tong, and what we found ,was that 5 ppm hydrogen is present 

right at the surface, and this concentration goes down to about 1 ppm 

when you are 1,000 A deep. Unfortunately, the detection limit is only 

1 ppm, so we were not sure whether we had hydrogen b,~yond 1,000 A, 

which is well within the emitter depth that we have. So we have been 

able to detect hydrogen at least as deep as 1,000 A, and it could be 

beyond that. 

RAO: Ajeet, in all of your data on that material with the hydrogen passivation 

and all the other data that othe~ people have presented, I tbink you have 

one piece of data where you show the efficiency before'AR coating and 

then after AR coating. I think, if I'm not wrong, the rest of the data 

including the one Joe presented just now don't show what happens after 

the AR coating. Looking at your data, the AR coating only improves by 

about 36~ in your hydrogen-passivated cell, which is much lower than the 43~ that you are talking about. 

ROHATGl: There is a very good reason for that, because this AR coating was 

applied after the cell wa.s finished, and when you try to spin the AR 

coating with the grid lines you never get the kind of improvement that 

you get when you put on the AR coating without the grids because when 

you are spinning it, you don't get the same thickness of AR coating near 

the grid lines. 

RAO: So you anticipate that you will be able to ·get the 4Q~" to 43~ improvement 

with AR coating on the hydrogenated cells? 

ROHATGI: No, this experiment was not done for that. I think we will have to 

modify our process sequence a little bit. We will have to do hydrogen-ion 

implantation at a different stage; we will not do it at this stage. It 

may be even more interesting to find out that hydrogen-ion implantation 

really works from the back, and this is another reason for looking into 

that. That way we don't have to do anything to the front. You finish 

the whole cell and before you put on the back metal you hit the cell with 

hydrogen-ion implantation and then put on the back metal. So you have to 

play some clever games with cell processing when you get to this stage. 

TURNER: Your optical optimization calculation implied that you were using an 

oxide 1aye~ that was only 100 A thick. Was that really what you used? 

ROHATGI: For the oxide passivation, that's the lowest layer, which is the 

passivating oxide. Then on top of that we put 475 A of Ti02 and then 

on top of that we have 986 A of Si02.· 

TURNER: But you got good passivation out of 100 A of oxide, and that's very 

good. 

ROHATGI: You don't want to go thicker than that -- otherwise it's going to 

hurt you in the reflection losses. 

SAKIOTIS: I don't know if I missed it or not: did you mention the area of 

these cells you discussed? 

444 
ROHATGI: Most of the cells are 1 x 1 cm; we are now making cells that are 

4 cm square. 

SAKIOTIS: Do you have any results on the larger ones? 

ROHATGI: Yes, larger ones are not quite as good. The lS.l~ cell that you saw 

is 1 x 1 but the larger one is about 17.S. So we have some difficulty. 

But they are not more th~n 4 cm square in any case. 

LESK: The nuclear people at W~~tlnghouse have reported that above a few times 

of 1019 hydrogen, there is :i.OSs of hydrogen at the surface, and you are 

doping at 101S I'm wondering if anybody has looked at the possibility 

that hydrogen implant at these levels may be removing something from the 

surface area that may have been hurting us in improving the characteristics. 

ROHATGI: Okay, if we did the reflectivity measurement to see if we have modified the surface in any sense and -- in at least reflective measurement 

within what we have -- done anything drastic to the surface, the reflectivity we did before ~nd after the implantation was identical. But we 

are not sure if we are removing anything, and that's a very good point. 

We should really do the spreading with this measurement to see if we have 

actually taken something off and our surface dopant concentration has 

changed. 

QUESTION: May I make just a short comment? I have worked with h{drOgen 

implantation years ago using high energy and pumped in at 10 8. It is 

my experience if you go that high that hydrogen forms bubbles in silicon, 

so if you go to lower energy then it's most likely that you remove some 

from the surface. 

ROHATGI: That's a good comment. I don't think we know the answer to what we 

have inside our cell at this point. We don't know where the hydrogen is 

located or if it has formed any bubbles. We are just trying to do more 

measurements to find out more about it. 

YOO: What is your oxide passivation temperature and time, roughly? 

ROHATGI: It's a low-temperature oxide, it's about SOOOC, and the time you 

have to set depending on what kind of dopant surface concentration you 

have, because oxidation rate, as I mentioned, is a function of how heavy 

doping you have. So there is no real fixed time. If you are working 

with low surface doping concentration, you have to go t,o longer times. 

445 
'.' .', 

"\, ! 

.J 

.. 

, 

'I~ .. ·'101 

j 

'J\ i \Ii 

,. ,If . ,~ 

') h 

~ 

.~ 

I 

N85-31S42 

PROCESSING TECHNOLOGY FOR HIGH EFFICIENCY SILICON SOLAR CELLS 

M. B. Spitzer and C. J. Keavney 

Spire Corporation 

Bedford, Massachusetts 01730 

ABSTRACT 

Recent advances in silicon solar cell processing have led to attainment of 

conversion efficiency approaching 20%. In this paper we review the basic cell design 

investigated at Spire and indicate features of greatest importance to achievement of 20% 

efficiency. We discuss in detail experiments to separately optimize high efficiency design 

features in test structures and discuss the integration of these features in a high 

efficiency cell. In this work, ion implantation has been used to achieve optimal 

concentrations of emitter dopant and junction depth. The optimization reflects the 

trade-off between high sheet conductivity, necessary for high fill factor, and heavy doping 

effects, which must be minimized for high open circuit voltage. A second important 

aspect of our design experiments is the development of a passivation process to minimize 

front surface recombination velocity. We indicate the manner in which a thin Si02 

layer may be used for this purpose, without increasing reflection losses, if the 

antireflection coating is properly designed. We also present details of processing intended 

to reduce recombination at the contact/Si interface. Data on cell performance (including 

CZ and ribbon) and analysis of loss mechanisms are presented. We conclude with a 

discussion of the ultimate performance that may be achievable with this type of 

processing. 

INTRODUCTION 

The attainment of 20% conversion efficiency in flat-plate Si solar cells is presently 

the goal of the National Photovoltaics Program (1). To this end, we have been conducting 

research on the ion implanted Si cell. This work recently led to the achievement of 

conversion efficiency of 18 %, and efficiency approaching 20% appears possible in the near 

future (2,3). In this paper, we review the results to date with emphasis on cell processing 

aspects, and we indicate the device design and cell processing techniques that appear 

necessary for achievement of the national goal. 

The high efficiency ceU process to be discussed is based on the use of high lifetime 

float zone Si. This material was selected owing to superior minority carrier lifetime over 

a broad resistivity range. One promising alternative is the use of Czochralski silicon, 

which will be feasible if modest diffusion length (",,200p.m) can be achieved in low 

resistivity wafers. Many aspects of the techniques to be presented are applicable to 

polycrystalline material as well, with conversion efficiency commensurate with the 

diffusion length in such material. We will report in this paper on the application of some 

of our processing techniques to sheet materials. 

PRECEDING PAGE BLANK NOT FILMED 

447 
"" '. >jf-. ",..,,) <If!~; . ,,' Uf.- ~ "'t !J;".' '* "r~ ~, t~ ~ . ..;.:. ~ Ii J' "n ~~' ~"'~ X: , = 

,~ The junction f~r~ation technique to be discussed is based on ion implantation and 

thermal annealing. As was shown in a recent paper, the ion implantation process allows 

one to reproducibily adjust the emitter dopant concentration to near optimal values (4). 

In addition, the thermal anneal process can provide a passivating surface oxide if oxygen 

is admitted to the gas stream. The versatility of this junction formation technique has 

made possible rapid progress in emitter design. . 

In order to gain a better understanding of the loss mechanisms operating in our 

developmental cells, we have used a solar cell modelling code developed at Brown 

University by one of the authors (5). The results of the modelling will be provided where 

appropriate throughout this discussion. The one-dimensional model is described in detail 

in reference 5, and will only briefly be described here. 

The modelling code evaluates the analytic solution of the inhomogeneous diffusion 

equation which we assume governs minority carrier transport in the quasi-neutral emitter 

and base of the solar cell. The quasi-neutral regions are assumed to terminate at the 

space-charge region on one side, and at a minority carrier mirror (characterized by a 

surface recombination velocity) at the other side. The analytic solution for the sum of 

the diffusion current and a space-charge region light-generated current is integrated over 

the solar spectrum to obtain short circuit current (Jsc), open circuit voltage (V oc) and 

efficiency. In addition, provisions have been made for front surface reflection loss, 

shadow loss, reflection from a back surface mirror, and light-trapping (6). 

The equilibrium mi.nority carrier concentrations are calculated using Fermi 

statistics. The rigid band approximation is used to calculate the effects of band gap 

narrowing. Position dependence of doping, mobility, and lifetime are not included in this 

model and this limits the agreement between calculated and measured spectral response 

for short wavelengths. Nevertheless, we are able to achieve reasonable agreement with 

most other measurement data. 

In the next section, we discuss the selection and characterization of the silicon 

used in our work. We follow this with a discussion of emitter design and fabrication, 

including the importance of surface passivation and ohmic contact design. The results of 

this work indicate the significance of high base minority carrier lifetime, and we report 

on new results from an investigation of the effects of cell processing on diffusion length. 

We conclude with a description of the cell design that we are pursuing for attainment of 

20% conversion efficiency. 

SELECTION OF SILICON 

It is well known that fabrication of superior silicon cells based on conventional pin 

junction designs requires silicon of the highest minority carrier lifetime (7). Development 

of a particular design and process sequence requires knowledge of the post-process 

lifetime; such data are of particular importance to the selection of base resistivity. For 

this reason, we investigated post-process lifetime of a variety of float zone slices. 

448 
Back surface field (BSF) cells were fabricated using a simple baseline process (<", 

from float zone slices obtained from Wacker and elsewhere. No antireflection (AR) 

coatings were used. Figure ! replicates diffusion length data obtained by the method of 

Stokes and Chu (9) from quantum efficiency (QE) measurements of completed cells. The 

triangular data points indicate Wacker W ASO-S slices. The square· data points are 

Czochralski slices. Cell data is indicated in Table 1. It can be seen that AM 1 conversion 

efficiency is about 10-11?'; for the W ASO-S material of each resistivity. In order to 

determine how efficiency might be improved, we examined loss mechanisms in detail. In 

this way we were able to make significant improvements to the baseline process. 

1000 

.... 

-E --_.-- =4 _ .... - - -- .... J: 

t- .... -.... -• ~ 100 • 

Z 

W 

-I 

Z 

0 

en 

:::> • • 

u. • u. 

C 10 .... :::> WASO - S 

0.01 0.1 1.0 10 

RESISTIVITY (n-cm) 

FIGURE 1. DIFFUSION LENGTH AS A FUNCTION OF RESISTIVITY. The dotted line 

indicates the functional dependence of LD upon NA that is assumed in 

our theoretical ca1cula tions. 

449 
TABLE 1. CELL PERFORMANCE DATA FOR Si EVALUATION EXPERIMENT 

RES. LD V J FF EFF 

GROUP GRADE (Ocm) (Ilm) (m~ (mAsrcm2) , (%) (%) 

A CZ 0.17 18 585 18.5 77.7 8.4 

(003) (0.6) (2.7) (0.5) 

B FZ 0.26 109 598 22.3 79.0 10.5 

001) (0.1) (0.7). (0.1) 

c WASO-S 0.18 139 597 22.3 77.3 10.4 

(FZ) (002) (0.1) (1.4) (0.2) 

0 WASO-S 0.33 154 599 22.8 78.2 10.7 

(FZ) (001) (0.1) (1.0) (0.1) 

E WASO·,S 2.1 212 583 23.4 78.9 10.8 

(FZ) (001) (0.1) (0.3) (0.1) 

F WASO-S 10 462 571 24.4 77.4 10.8 

(FZ) (001) (0.1) (0.3) (O.l) 

G WASO-S 10 227 563 24.1 77 .1 10.5 

(FZ) (004) (0.2) (0.4) (0.2) 

H FZ 0.32 129 597 22.8 78.9 10.7 

(001) (0.1) (0.5) (0.1) 

I CZ 0.027 530 12.0 54.6 3.8 

(036) (0.1) (16.8) (0.7) 

J CZ 0.012 364 7.6 53.2 1.5 

(079) (.02) (1.8) (0.4) 

NOTES: Area = 4 cm2, T = 28°C, Lo. derived from quantum efficiency curves (9). 

Standard deviation shown in parenthesis. 

Careful inspection of Table 1 indicates a large variation in fill factor (FF) for" 

lower resistivities; this variation increases with decreasing resistivity. An examination of 

the dark I-V curves for representative cells, shown in Figure 2, indicates that leakage 

current increases as resistivity decreases. Through experimentation, we determined that 

this leakage current arises at the edges 9f the solar cells, which in our process are cut 

from the original wafers with a diamond wheel dicing saw. Etching of the edges to 

remove the saw damage removes this leakage path but also removes some active junction 

area. The deleterious effects on Jsc that edge etching causes can be minimized by 

either use of mesa etching defined by photolithography, or by using an ion implantation 

mask similarly defined so as to restrict the junction from kerf areas. Both methods were 

. found to reduce the leakage current to negligible levels. For large-area cells .in which 

edge leakage current is small compared to the diode forward current, this type of 

processing will probably be unnecessary. 

450 
IZ 

W 

a: 

a: 

::J 

() 

! 

ORIGINAL PAGE' IS 

OF POOR QUALITY 

IA~--------------------------------~ 

O.IA 

10mA 

ImA 

O.lmA 

LOT 4357 

T· 2S'C 

AREA'4 em 2 

-----.IS .Gem 

- -'- -.3 .Gem 

-.-----.- 2 .Gem 

---IO.Gem 

0.1 02 03 0.4 

BIAS (volts) 

/ 

0.5 1,)6 07 

FIGURE 2. DARK I-V FOR REPRESENTATIVE CELLS OF VARIOUS RESISTIVITIES. 

451 
Figure 3 illustrates a comparison of measured external quantum efficiency (QE) 

data to the results of cell modelling, for a representative cell from group G in Table 1. 

Good qualitative agreement is obtained. Exact fitting was not attempted for two 

reasons: first, the absolute error in the QE data is not precisely known and second, the 

code cannot model position dependent parameters that are believed to be important in ~he 

emitter. Integration of the model QE data, however, yields good agreement with 

measured Jso and this is shown as a function of resistivity in Figure 4 with front 

surface recombination velocity as a parameter. In Figure 5 we present a comparison of 

the measured Voc data to the calculated values, with band gap narrowing ~Eg) as a 

parameter. The modelling suggests that for low resistivity Si, band gap narrowing and 

surface recombination velocity dominate V oc. 

1.0 

NO AR COATING 

P = 10.acm 

> 

0 0.8 

z 

w 

(3 

u:: 

LL 

W • ~ 0.6 

::::» 

Iz 

« 

::::» 

0 0.4 ..J 

« 

Z 

a: 

w 

lX 

w 0.2 

• 

~I O· 400 600 800 1000 

WAVELENGTH (nm) 

FIGURE 3. COMPARISON OF QUANTUM EFFICIENCY DATA TO MODEL 

CALCULATIONS FOR A CELL FROM GROUP G, TABLE 1. 

452 .. ' 
25 iC\I 

-

E 

u 

..... 

< 24 E 

-tz 

W 

a: 

a: 

::> 23 - 0 

!:: 

::> 

0 

a: 

0 22 

ta: 

0 

J: 

(/) 

21 -

T a2S-C 

NO AR COATINGS 

,.",. 

", 

,.",. 

/" 

", 

/" 

/' /' 

/' ... / & -," ",-'-

,.",. /" / 

SaO em/sec /" ", ~/' /" /" ,. /1 / .... Sa 2. lOS emlsee /' 

/"" 

/' 

S. 107 em/sec 

J 

0.1 

/' 

/' 

/' 

• 

1.0 

RESISTIVITY (.oem) 

.,.... / 

.". 

T", 

",& 

/' 1 

." ..... "., 

"., 

10 

FIGURE 4. COMPARISON OF MEASURED AND CALCULATED Jsc AS A 

FUNCTION OF BASE ACCEPTOR CON CENTRA TON •. 

We elected to work with cells of conventional thickness, even though calculations 

have shown that thin cells have theoretical advantages if minority carrier mirrors and 

.light-trapping can be achieved (10). Our choice avoided the extraordinary care that 

handling thin (rv.50,.,.m) cells requires. The modelling of cells with conventional thickness 

(rv400llm) indicated that best efficiency would be obtained from low resistivity Si, 

provided that the emitter saturation current could be reduced, thus indicating the 

importance of pursuing research on emitter design. 

453 
T-2S-C 

700 NO AR COATINGS 

-> E 

-

w 650 

CJ 

:.oJ ~ 

0 

> 

lS 600 .. 0 S. 2 x I OS emllee a:: 

(3 .dEg-125 meV 

Z 

W 

a.. 

0 550 

500L-__ ~ ______________ ~ ______________ ~~ __ -J~ 

0.1 1.0 10.0 

RESISTIVITY (.oem) / 

FIGURE 5. COMPARISON OF MEASURED Voc DATA TO MODEL CALCULATIONS. 

EMITTER EFFECTS 

In a recent paper, we analyzed the importance of reduction of peak ~mitter dopant 

concentration, and it was shown that a very wide range of doping concentrations can be 

achieved with ion implantation (4). In Figure 6, we reproduce data that indicate that 

optimal QE at 350 nm is obtained for either arsenic or phosphorus emitter dopant 

concentrations of about 2xlO l9 cm-3• Voc appears to have a peak in this range as 

well, as shown in Figure 7. Unfortunately, the actual emitter concentration for which the 

maximum Voc is obtained is obscured by low base diffusion length; i.e. in the 

neighborhood of the optimal donor concentration, the Voc is base-limited. We will 

return to this point in a later section. . 

Figures 6 and 7 indicate that there is an advantage to passivating the front surface 

when shallow (""'O.2~m) junctions are employed. Our experience indicates that as the 

junction is made de~per, the beneficial effects of passivation diminish; however, we have 

not conducted controlled experiments on this aspect. 

454 
WITH 5i02 

~ 0.5 DAI 

g AP 

'" OP 

~ 0.4 

> o 

z 

w 

U 

u: 0.3 u.. 

w 

::iE 

i= 

~ 0.2 ,:) 

a 

..J 

< 

~ 0.1 

I!! 

ORfGfNAL PAGE' fS 

OF POOR QUALIT't 

B 

• " a ,,_. • • 

~ NO AR COATINGS EMPLOYED 

1020 

PEAK EMITTER DONOR CONCENTRATION (em-3) 

o 

FIGURE 6. QUANTUM EFFICIENCY AT 350 n:n. (A) Passivated As and P implanted 

emitters in' 0.2 ohm-em Si, (b) Non-passivated As and P implanted emitters 

in 0.2 ohm-em Si, and (C) Passivated P implanted eTlitters in 0.3 ohm-em Si. 

o.65.__----------------------, 

PHOSPHORUS IMPLANTATION 

WITH 5102 

0.60 

--0-0- - - - -0 _..0-

---- --- '> ..s 0.55 

w 

C!' 

~ 5 0.50,L-----... 10~18-------I..J.O:-:::19-------10.&.:2:-:::0-.. 

> 

I- 0.65.....------------------------, 

5 ARSENIC IMPLANTATION 

U 

a: 

C3 

z 

w 

a. 

o 

0.60 

0.55 

WITH 510z __ -0- -00---0 

_.0--

uO-~-__ ----------~.~-------~2 -- 0.50'------1.J.0;;18-------~10~19;;-------::10~ZiiO ~ 

PEAK EMITTER DONOR CONCENTRATION (cm-3) 

FIGURE 7. Voe AS A FUNCTION OF NO, WITH AND WITHOUT Si02 

PASSIVA TION. 

~ 455 

/ - L 
Surface preparation can often affect the attributes of the ion-implanted emitter. 

In a later section, we describe the use of texture-etching to reduce reflectivity and 

enhance absorption. This etching, however, increases the front surface area, which 

necessitates a change in the ion implantation dose. To identify the optimal ion 

implantation dose for such an etched surface, we fabricated texture-etched solar, cells 

with a range of doses. Detaiis of this experiment are reported in reference 2. Figure 8 

replicates the Voc data for cells having Si02 passivation and for the same cells with 

Si02 removed. It can be seen from Figure 8 that the removal of the Si02 h:"1.s a 

strong effect on V oc. 

There would seem to be three factors that control minority-carrier transport in th,;~ 

emitters of both the textured and polished devices: deleterious surface recombination, 

deleterious recombination and/or energy gap narrowing resulting from heavy doping 

effects, and advantageous minority-carrier reflection by the field resulting from the 

gradient of the doping. When Si02 surface passivation is present, the optimal ion 

implantation dose is approximately 5x 1015 ions/cm2 for a textured surface. Use of 

higher doses would seem to introduce deleterious heavy doping effects in the emitter 

which cause an increase in the saturation current. The existence of enhanced 

recombination in the near surface region is suggested by spectral response measurements 

that show that blue response decreases as the doping is increased (Figure 6). For lighter 

implantation doses, a loss in minority-carrier reflection occurs, owing to the reduction in 

the gradient of the doping near the surface. This reduction in doping perhaps allows an 

increase in carrier recombination at the front contact, and so V oc. decreases as the 

concentration is decreas~d. For the case in which the Si02 passivation is removed, the 

recombination at the surface exerts a strong inffuence on Voc. In such a case, an 

increase in the peak dopant concentration that results from increase of dose increases 

the reflection of minority carriers, but the improvement is limited. 

-

> 

E 620 -

W 

<!:J 

ct: 

i- 610 

..J 

0 

> 

i- 600 

5 REMOVED 

(.) 

a: 590 

(.) 

Z 

W 

A.. 580 

0 

2 4 6 8 10 

ION IMPLANT'ATION DOSE (x 1015 ions/cm2) 

FIGURE 8. OPEN-CIRCUIT VOLTAGE AS A FUNCTION OF ION-IMPLANTATION 

DOSE FOR TEXTURE-ETCHED CELLS. The dose shown is the total dose 

measured by the implanter and is not corrected for the texture present on 

the target. 

456 
The optimization and theoretical analysis of our junction formation process applied 

to a textured surface requires knowledge of the resultant doping profile formed by the 

above iroplantation parameters on the {Ill} surfaces of the pyramids. For diffused 

junctions, one may perhaps assume that the junction profile replicates that which is 

formed on a standard {II Ii surface. It is not clear, however, that the depth distribution 

of implanted ions is equivalent to that obtained in an ordinary polished wafer, oWing'to 

scattering effects that may differ in the two cases. A further difference between 

diffusion and ion implantation is the increase in surface area mentioned above that 

obtains when texture is present. This increase requires a corresponding increase in ion 

dose. 

F or the above reasons, measurement of the dopant profile would be desirable. 

Unfortunately, the textured surface is not easily profiled using conventional techniques 

such as secondary ion mass spectroscopy, owing to obvious difficulties with depth 

calibration. For this reason, we conducted an experiment based upon ion implantation of 

a polished (lll) wafer, suitably oriented with respect to the ion beam, to simulate the 

implantation of the {Ill} facets of the pyramids. This experiment is described in greater 

detail in reference 12. 

A polished control (l00) wafer was first implanted with 31 P+ using the 

convent~onal geometry. The implantation energy was 5 keY and the dose was 

2.5 x 10 15 ions/cm2r, An experimental (l11) wafer was then implanted with 3lp+ at 

5 keY to a dose of 5.2 x 10 15 ions/cm2, with the (111) surface oriented at an angle of 

54.7° with respect to the ,ion beam to replicate the orientation of the facets of the 

textured surface. The specific dose, which includes 'an area correction related to the 

implantation angle, was 3 x 10 15 ions/cm2• Both wafers were then annealed in 

flowing dry N2 using a three step process: 550°C-2hr., 850°C-15 min., 550°C-2hr. with 

ramping between steps. Dry oxygen was admitted to the gas stream during the 850°C step 

to grow the thin oxide neCl~ssary for passivation. 

Spreading resistance analysis was obtained for both wafers, and is shown in 

Figure 9. The analysis indicates that the profiles are without detectable difference. This 

is not surprising, since the implantation parameters for polished and textured wafers were 

separately optimized for high cell performance. The value of the peak dopant 

concentration obtained in this experiment has been used in the modelling which follows in 

the next section. 

To further refine our solar cell emitters, we have been inve~tigating the role of 

recombination at the front ohmic contact. To this end, we have been experimenting with 

the reduction of ohmic contact area, while keeping the shadow loss constant, as has been 

done elsewhere (13). Figure 10 illustrates two methods of implementing this technique. 

In method A, the opening in the passivating oxide through which contact is made is 

reduced in width so that the opening is more narrow than the grid line. In method B, the 

openings are small separate squares. Both techniques require photolithography and 

alignment; however, one method of producing type A contacts would be to make the grid 

lines as narrow as the desired openings in the oxide. The width of the lines might then be 

increased to the desired width by electroplating, thus obViating alignment. 

457 
1020 

?>:, 

~.~ .. ~ ... PHOSPHORUS o POLISHED 

1019 

~~ • TEXTURED ,... 

(I) .'0 

Ie "0 

U 

.... "'0 

Z 10lB ea 

0 0 

fi ·0 

a: 0 tZ 1017 BORON 

W 0 

0 ~~~~ ....•.•.... 

0 

Z ~~ 0 • 

a: 1016 

UJ 

0: 

a: 

c( 

0 lOiS 

1014 L-_~,.-_~_--::-,:::-_-:::-~_-::-,::~--:~ 

o 0.1 0.2 0.3 0.4 0.5 0.6 

DEPTH (microns) 

FIGURE 9. SPREADING RESISTANCE ANALYSIS OF A SIMULATED TEXTURED (I 11) 

WAFER AND A (100) CONTROL. 

GRID LINE 

(A) 

OPENING 

IN Si02 

GRID 

CUT-AWAY 

GRID LINE 

(B) 

OPENING 

IN Si02 

GRID 

CUT-AWAY 

FIGURE 10. TWO METHODS OF REDUCING OHMIC ~ONTACT AREA. 

458 
Results with this type of processing are thus far inconclusive. In Figure 11 we 

replicate data from an experiment in which the ohmic contact area was varied a.s 

described above (4). Best results were achieved for reduced area, but the saturation 

current in these devices may arise mainly in the base, and so the optimal value of ohmic 

contact area may be obscurred. Further experiments are in progress and will be reported 

at a later time. 

630 

--> E 

...... 

w 

(!) 620 

« 

I-

...J 

0 

> 610 

!::: 

::> 

0 

a: 

0 600 

Z 

w 

a. 

0 

590 

!~I------I \T ---1/1 

r I 

. /\''-1 

/1 

I 

80 

78 

~ 

a: 

76 0 

I0 

~ 

74 ...J 

~ 

72 

! 

.01 .1 10 

CONTACT INTERACTION AREA (mm2) 

FIGURE 11. Voc AND FF AS A FUNCTION OF OHMIC CONTACT AREA. 

(Base resistivity is 0.3 ohm-em.) 

100r-------------------------------------------------------~ 

~ w 

(.) 

z 

~ 

~ 50 

it 

w 

a: 

oJ 

oJ 

W 

(.) 

O~ 400 600 800 900 1000 1100 

WAVELENGTH (nm) 

FIGURE 12. REFLECTION LOSS FOR A TEXTURED PASSIVATED SOLAR CELL. 

459 
~~,.:",~. 

'<\':.'i-

" ~.' ", .\,,~ ~ ,~ \ 

~ .:'~1. \' 

\ . " , .. ' . 

.. 

Our results thus far on emitter design indicate the importance of both reduction of 

emitter dopant concentration and use of passivating oxide. This passivating oxide exerts a 

negligible influence on the reflection loss. To emphasize this point, we show in Figure 12 

the measured reflectivity (courtesy 'Of Dr. D. Arvizu, Sandia) from a textured solar cell. 

It can be seen that the reflection loss is indeed very small. The passivation can also ,be 

applied to sheet materials without severely affecting the AR coating. Recently we 

applied our emitter formation process to nonagon EFG ribbon. AM 1 efficiency prior to 

AR coating was 9.7 %. After evaporation of a single Ti02 layer, efficiency increased to 

13.2%, indicating a gain of 36%; higher gain would be possible with a more suitable AR 

coating (such as Ta205). 

HIGH EFFICIENCY CELL DESIGN 

Figure 13 illustrates the details of the solar cell structure yielding the highest 

efficiency to date. The texture-etched front surface is ion-implanted to form the 

emitter, as discussed in the previous section. The surface is provided with a thin layer of 

Si02 to reduce the front surface recombination velocity. An AR coating of Ta205 

is applied on top of the Si02; the thickness of this layer is optimized to minimize the 

reflection resulting from the presence of the Si02. We have not reduced the ohmic 

conta<:=t area in this design. 

n+ 

ION-IMPLANTED 

EMITTER ----t~_...JI+'~ 

Ti-Pd-Ag 

\ 

BORON-IMPLANTED BSF \ 

Ti-Pd-Ag 

Si02 

PASSIVATION 

FIGURE 13. ILLUSTRATION OF THE SOLAR CELL STRUCTURE INVESTIGATED 

IN THIS WORK (not to scale). 

460 
I 

I 

Table 2 indicates the fabrication process for this cell design. The back surface is 

first implanted with llB+ and annealed to form a p+ region. During the anneal, a 

thick surface oxide is grown to be used later for masking purposes. The resulting p+ 

layer is ab.out 1 m deep and has a peak concentration o~ 1020 cm-3( 14). Because the 

diffusion length is much less than the cell thickness, the p-p+ junction is probably' not 

effective as a back surface field (15); however, the p+ region does aid the formation of 

a low resistance back contact. 

TABLE 2. CELL FABRICATION PROCESS 

Implant back 

Anneal/oxide 

Pattern oxide 

Texture 

Implant front 

Anneal/ oxidize 

Apply contacts 

Saw to size 

Plate contacts 

Apply AR coating 

Test 

11B+ 50 keY, x 10 15 ions/cm2 

550°C -- 2 hrs. 

950°C -- 2 hrs. 

Acid etch 

Hydroxide etch 

dry N2 

wet 02 

31 P+ 5 ke V, dose-variable 

550°C -- 2 hrs. 

850°C -- 15 min. 

550°C -- 2 hrs. 

Evaporated Ti-Pd-Ag 

2 cm x 2 cm 

Ag 

Evaporated Ta205 

AMI, 100 mW/cm2, 28°C 

As discussed earlier, the surface oxide on the front was patterned to form an 

emitter ion implantation mask. The oxide mask defined the edges of the front phosphorus 

implant and so formed a planar emitter structure on each solar cell. 

After patterning of the front oxide, the fronts of the wafers were texture-etched 

in a potassium hydroxide solution. Oxide on the back protected the boron implant from 

the etch. The fronts were then implanted with 31 P+ and annealed as described in the 

previous section. Evaporated Ti-Pd-Ag contacts were applied to both sides of the wafers 

and were patterned on the fronts using the photolithographic lift-off process. 

Electroplating was used to decrease the contact line resistance. The final step consisted 

of electron-beam evaporation of a Ta205 AR coating. 

461 
The resulting cells have been described in several recent publications (2, 16). 

Efficiency of up to 18% has been obtained, and the devices have been well characterized. 

We report here that an abbreviated form of the above process has been applied to 

Czochralski wafers supplied by Arco Solar Crystal Production. Efficiency of 16.8% was 

achieved (AM 1, 28°C) and higher efficiency may be possible if the complete process is 

applied. 

In Ta.ble 3, we summarize calculations of theoretical efficiency that indicate 

aspects of cell design that limit efficiency in the 18%-efficient FZ cells. The first entry 

in the table indicates the limit efficiency for a cell with width of 381 Ilm, made from 0.3 

ohm-cm silicon. The only loss mechanism included in this calculation is Auger 

recombination (17); perfect light trapping and minority carrier mirrors are assumed (10). 

It is interesting that the upper limit to Jsc is 43.8 mA/cm2, considerably higher than 

has been obtained in actual cells. Thus, considerable improvement is possible in J sc' If 

neither light-trapping nor a back surface reflector (BSR) is present, the limit to Jsc is 

42.2 mA/cm2. Incorporation of actual reflection loss measured on a high efficiency cell 

(see Figure 12) indicates that Jsc can be as high as 40.6 mA/cm2. 

The diffusion length measured on our best cells is about 150 p.m. Replacement of 

the Auger-limited diffusion length ("'900pm) with the actual value reduces the Jsc to 

36.9 mA/cm2. Thus, a considerable amount of current is lost in our cells owing to bulk 

recombination. This loss can be overcome by increasing the diffusion length through more 

careful processing or by gettering. An alternative would comprise thinning the cell and 

adding a BSR. 

The Voc indicated for a 150p.m diffusion length is 649 mV. The calculation of 

Voc is extremely sensitive to the value of the effective masses, or in another 

formalism, to the value of the intrinsic concentn~tion assumed. In our calculation, we 

used Fermi statistics with an effective density of states given by the average effective 

masses for electrons and holes (18). Owing to uncertainties in the effective masses, the 

effective density of states, and to heavy··doping effects in general, this calculation can be 

considered only as a rough estimate of the Voc. 

Inclusion of front surface recombination and bandgap narrowing reduces V oc to 

values as low as 6! 8 m V, if the data from reference 11 is used. By using a value for ~Eg 

of 70 meV, we find good agreement with experiment. This may reflect the fact that our 

model assumes uniform doping, so 70 meV is perhaps an average value characterizing the 

heavily doped region near the surface and the lightly doped region beneath it. The shadow 

loss in our cells is approximately 3.5%; however, the reflection loss (already subtracted) 

includes reflection from the contact. Therefore, we only include a. shadow loss of 2 % in 

our calculation. Inclusion of the measured series resistance of 0.32 ohm-cm2 (2) drops 

the FF to 81.6%. It can be seen that reasonable agreement with an experimental cell is 

attained. 

The results in Table 3 reveal that a large amount of carriers are lost to bulk 

recombination. To quantify the effects of LO on Jsc, we modelled the cell described 

above with LO as a parameter. The result is shown in Figure 14. It can be seen that. for 

the case of no BSR, increase in. L'O to 200J,Lm yields nearly ImA/cm2 gain. The 

addition of a BSR with reflectivity of 90% would increa.se Jsc to 36.6 mA/cm2; 

increasing LO to 200 pm in that case would yield Jsc of over 37 mA/cm2. In the 

next section we will describe experiments intended to raise LO to over 200 1-'01. 

462 
TABLE 3. ANALYSIS OF LOSS MECHANISMS OF SPIRE'S HIGH 

EFFICIENCY SOLAR CELLS 

Limit Efficiency 

of 0.3 !2cm cell 

(Auger recomb. only) 

No Light-Trapping 

No BSR 

Finite Reflection Loss 

SRH Recombination 

(LD=150~m) 

Front Surface Recombination 

(S=2x 1 04 cm/ sec) 

Bandgap Narrowing 

~Eg 

(lOO meV 

(80 meV 

70 meV 

Joe Penalty for 

Front Texture 

Shadow Loss (2%) 

Series R (0.32 ohm-cm2) 

Actual Data, Cell 22B 

Voc 

(mV) 

713 

713 

712 

711 

649 

646 

618 

629 

633 

625 

624 

624 

627 

43.8 

43.0 

42.2 

40.6 

36.9 

36.3 

36.3 

36.3 

36.3 

36.3 

35.6 

35.6 

35.9 

FF 

(%) 

84.7 

84.7 

84.7 

84.7 

83.6 

83.6 

83.0 

83.2 

83.3 

83.3 

83.3 

81.6 

80.0 

EFF 

(%) 

26.5 

26.0 

25.5 

24.5 

20.0 

19.6 

18.6) 

19.0) 

19.2 

18.9 

18.5 

18.1 

18.0 

Notes: Calculations assume base width is 381 I-Lm, T=28°C, Intensity = 100mW/cm2, 

AMI. 

In the event that efforts to raise LD beyond 200 I-Lm fail, one can consider thinning 

the base of the cell. A calculation of Jsc as a function of base width is shown in Figure 

15, for the case of back surface reflectivit~ of 90%. For a cell with base width of 200~m, 

an increase in Jsc of about 0.5 mA/Cm is ~ained. If the cell is thinned and LO is 

raised to 200 IJ.m, Jsc of greater than 37 mA/cm will be attained. 

463 
~ - 38 P"O.3Dem 

~ T"2S"C 

! sa"Oem/lie 

WS"3SllIm 

ffi FRONT SURFACE TEXTURED 

a: 

~ 0 37 

~ 0 

5 

Ia: 

0 

:z: 

CI) 36 

C 

~ => 

~ 

<3 35~~~ ________ ~~ ________ ~~ ______ ~~ __ ~ 

150 200 250 300 

BASE DIFFUSION LENGTH (j.Jm) 

FIGURE 14. SHORT CIRCUIT CURRENT AS A FUNCTION OF DIFFUSION LENGTH. 

C\I 

-

E 

o 

.... 

< .s 

39 

~ 38 

w 

0: 

a:: 

:::;) 

o 37 

lS 

o 

a:: 

o 36 

~ o 

~ 35 

T=28°C 

R"0.9 

P=0.3.Qcm 

58=0 em/sec 

FRONT SURFACE TEXTURED 

LO= 200pm 

200 300 

BASE WIDTH (J,lm) 

400 

FIGURE 15. SHORT CIRCUIT CURRENT AS A FUNCTION OF CELL THICKNESS. 

464 
, .... 

" 

'\, : 

. I .. 

Improvements to LD will also affect V 00 although the gain is harder to 

quantify, owing to the large number of assumptions needed for calculation of Voc. 

Nevertheless, Voc as high as 660 m V is consistent with base resistivity of 0.3 ohm-cm 

and diffusion length of 200 II. m, and experiments to reduce the ohmic contact area may 

reduce the emitter saturation current to negligible levels, thus enabling us to realize the 

base-limited Voc. Similar results have already been demonstrated elsewhere (3). 

EXPERIMENTS TO INCREASE Jsc 

The preceding discussion has assumed that a BSR with reflectivity of 90% can be 

achieved. In fact we have developed such a BSR and in Figure 16 replicate experimental 

reflectance data from a polished AR-coated sample with Al evaporated on the back. The 

reflectivity of photons having energy less than the band gap, for which silicon is largely 

transparent, is greater than 90%. It is our assumption that the reflectivity of the BSR is 

as high for shorter wavelengths but the reflectance of photons with energy greater than 

the band gap has not been measured. However, the wavelengths that penetrate to the 

BSR are in general near the band edge, so the assumption is probably a good one. 

100 

90 

80 

70 

'" 

~ 60 '"' Z 

0 

i= 50 

0 

UJ 

....I 

tL 40 

UJ 

a: 

30 

20 

10 

OL-~ ___ ~~ __ ~~~~~~~~~~~~~~~~~~~ 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 

WAVELENGTH (rwn) 

FIGURE 16. BSR REFLECTIVITY FOR AN AR-COATED CELL. 

465 
We have also examined the effect of our processing on cell lifetime. This was 

motivated by the anomalously low values of LO that were obtained in a number of 

experiments, such as those reported in reference 4 and in earlier sections of this paper. In 

many of our emitter experiments, it was found that the base diffusion length had been 

degraded by the processing. We therefore devoted most of our attention to this pr091em. 

After a detailed examination of our furnace and gas lines, cleaning processes, annealing 

gases, and ramping, we identified our wet oxidation process to be a step that degrades 

lifetime. We have now eliminated wet oxidation from our sequence. 

Recently we began experiments to increase" diffusion length by gettering. The 

exact gettering processes that we are pursuing were taken from the literature and will be 

reported upon in a later publication. Owing to reservations about conducting an unusual 

process in our annealing tube, we used a sintering tube for the first gettering experiment. 

Since this tube is used for sintering solar cell contacts, it might be contaminated by Ti, 

Pd, or Ag. After a high temperature procedure in the sintering tube, the wafers were 

fabricated into cells. It was found that LO in control cells had degraded to about 100 

Ilm, but LO in the gettered cells increased to 170 Ilm. It is our conjecture that 

annealing in a clean tube may yield much higher values of LO, and this is presently 

being tested. 

CONCLUSIONS 

Processing experiments have shown the importance of surface passivation, not only 

to V 00 but also to Jsc• Analysis of loss mechanisrns indicates that considerable 

improvement to Jsc may be obtained if diffusion length is increased. Improvement to 

V oc is also possible by reducing emitter recombination. Many of these techniques can 

be applied with advantage to sheet materials. Certainly all of the above processing can 

be applied to CZ, with efficiency approaching that of FZ if gettering is successful in 

improving LO. High efficiency can also be achieved vlith other sheet materials such as 

ribbon by using our junction formation and passivation techniques. 

This work has indicated the manner in which the goal of 20% conversion efficiency 

may be achieved. Through process improvements such as gettering, thinning of the base, 

and addition of a BSR, Jsc of FZ cells may be increased to 38 mA/cm2. 

Improvements to the emitter", including reduction of ohmic contact area, may increase 

Voc to 660 mV. We have already achieved FF of greater than 0.8. If these features can 

be integrated in one cell, efficiency of 20% will be achieved. The application of this 

processing to present~day sheet Si will be an important step toward the OOE goal of 15% 

efficiency at $90/m2. 

ACKNOWLEDGMENTS 

The authors are grateful to a number of contributors at Spire Corporation, and in 

particular acknowledge the assistance of H. Orake and L. Geoffroy with cell fabrication. 

The authors also wish to thank Dr. J. Milstein of SERI for help throughout this work. The 

authors thank Arco Solar Crystal Production and Mobil Solar Energy Corporation for 

supplying some of the materials used in this work. This research was supported by the 

U.S. Department of Energy through contracts with SERI, JPL and the DOE Small Business 

Innovative Research Office. 

466 
REFERENCES 

1. "Five Year Research Plan 1984-i 98811 of the U.S. Department of Energy National 

Photovoltaics Program Photovoltaic Energy Technology Division, Office of Solar 

Electric Technologies, U.S. DOE, (May 1983). 

2. M.B. Spitzer, S.P. Tobin and C.J. Keavney, IIHigh Efficiency Ion-Implanted Silicon 

Solar Celis," IEEE Trans. Electron Devices ED-31, No.4 (1984). 

3. M.A. Green, A. W. Blakers, J. Shi, E.M. Keller, and S.R. Wenham, 1119.1 % Efficient 

Silicon Solar Cell," Appl. Phys. Lett. 44, 1163 (1984). 

4. M.B. Spitzer, C.J. Keavney, S.P. Tobin, F.A. Lindholm, and A. Neugroschel, 

IIMechanisms Limiting Open Circuit Voltage in Silicon Solar Cells,1I Record of the 

17th IEEE Photovoltaic Specialists Conference, Orlando (1984). 

5. M.B. Spitzer, liThe Upper Limit to the Theoretical Efficiency of P-N Homojunction 

and Interfacial Layer Heterojunction Solar Celis,1I Ph.D. Thesis, Brown University 

(1981). 

6. D. Redfield, IIMultiple-pass thin-film silicon solar cell~" Appl. Phys. Lett. 25, 647 

(1974). 

7. M. Wolf, IIUpdating. the Limit Efficiency of Silicon Solar Cells,1I IEEE Trans~ 

Electron Devices ED-27, 751 (1980); see also; D.L. Bowler and M. Wolf IIInteractions 

of Efficiency and Material Requirements for Terrestrial Silicon Solar Cells,1I IEEE 

Trans. Components, Hybrids, and Manufacturing Technology, CHMT-3, 464 (980). 

8. M.B. Spitzer, "Basic Understanding of High Efficiency in Silicon Solar Celis," 

Annual Report for SERI Contract 2B-3-02090-3 (1984). 

9. E.D. Stokes and T.L. Chu, IIDiffusion Length in Silicon Solar Cells from 

Short-Circuit Current Measurements," Appl. Phys. Lett. 30, 425 (1977). 

10. M. Spitzer, J" Shewchum, E.S. Vera and J.J. Loferski, "Ultra High Efficiency Thin 

Silicon P.N. Junction Solar Cells Using Reflecting Surfaces,1I Rec. of the 14th IEEE 

Photovoltaic Specialists Conference, San Diego, 1980, p. 375. 

11. J.W. Slotboom and H.C. de Graaff, IIMeasurements of Bandgap Narrowing in Si 

Bipolar Transistors," Solid-State Electronics 19, 857 (1976). 

12. C.J. Keavney and M.B. Spitzer, "Solar Cell Junction Profiles in Ion-Implanted 

Texture-etched Surfaces," accepted for publication in J. Appl. Phys. (1984). 

13. A Meulenberg and R.A. Arndt, "Surface Effects in High Voltage Silicon Solar 

Celis," Rec of the 16th IEEE Photovoltaics Specialists Conference (1982) p. 348. 

467 
14. M.B. Spitzer, M.M. Sanfacon, and R.G. Wolfson, "Ion Implanted Junctions for 

Silicon Space Solar Cells," Rec. of the 18th Intersociety Energy Conversion 

Engineering Conference, Orlando, 1983, p. 1213. 

15. H. T. Weaver, "Ineffectiveness of Low-High Junctions in Optimized Solar Cell 

Designs," Solar Celis, 5, 275 (1982). 

16. M.B. Spitzer, CoJ. Keavney, S.P. Tobin, and J.B. Milstein, "Ion Implanted Cells with 

18% Conversion Efficiency," Record of the 17th IEEE. Photovoltaic Specialists 

Conference, Orlando (1984). . 

17. J. Dziewior and W. Schmid, "Auger coefficients for highly doped and highly excited 

silicon," Appl. Phys. Lett. 31, 346 (1977). 

18. S.M. Sze, Physics of Semiconductor Devices, John Wiley & Sons, 1981. 

468 
DISCUSSION 

CISZEK: Mark, do you have any thoughts on how you might be able to get reduced 

area contact to a wafer through an oxide? 

SPITZER: I'll have to draw a slide of that. What's the Green secret? I don't 

have to draw that, I can explain it. What you do is you make a very fineline grid. It would not be suitable for carrying the currents that you 

want~ but it has the area of the opening in the oxide that I showed. And 

then you overplay it, you let the electroplating balloon the grid lines 

in their proper proportions; then you are left with grid lines that just 

touch a very small area along the surface. There is no alignment involved. The problem with that, I think, is the grid lines falloff; you 

have to be careful. I don't like it. 

QUESTION: You can cross the lines, you make your slot and then cross your grid 

lines, you'll get a dot contact. 

SPITZER: I was worried in doing that technique. I was worried about depositing the AR and having stripes on the wafer. 

QUESTION: Mark, in your l8~ efficient cell the surface dopant concentration 

was 3 x 1018 , or what? 

SPITZER! In the 18~ cell we think it was 3 x 1019 . So we used the same 

implant parameters for that experiment, where we measured the profile, as 

had been used on the l8~ cells. 

OLSON: Both in your work and Ajeet's you applied some of the things you 

learned to sheet materials, and! really think with some neat results. I 

think one interesting point to make is that your work on the good floatzone material is really a leading edge, and I think it is really important 

to have the high-efficiency work on this high-quality material lead the 

way. And it's clear that now you are beginning to apply it to work on 

low-cost sheet material. 

SPITZER: I agree with that. And there is one other thing that we are working 

on, and that is to scale up the area of the cell. I think it also has to 

be applied to a fairly large-area device. 

OLSON: It's there we are going to really learn what·s really limiting the 

performance, and ultimately that might payoff. 

SPITZER: I agree. I think we should stay with float-zone for a while. 

JOHNSON: Mark, what was the sheet resistance of your emitter? 

SPITZER: The baseline emitter that we started out was about 80 ohms per square 

and the one that is 3 x 1019 is about 200 ohms per square. 

DAUD: Mark, could you tell me what the resistivity of the Czochralski silicon 

was that you got from ARCO? 

469 
SPITZER: Actually, I know what it is, but I don't have permission to disclose 

any thing 'about the material, so you can ask one of the AReo guys. But 

there is nothing crazy about it, its just ordinary stuff. 

470 
TEXTURE ETCHING OF (100) SILICON FOR SOLAR CELLS 

Lawrence D. Dyer 1\18 5 " 31 6- 4- .-

Texas Instruments, Incorporated~ - !t 

Sherman, Texas 75090 

INTRODUCTION 

In a solar cel I it is desirable for the light-absorbing surface to consist of facets such that incident. rays must undergo at 

least two reflections prior to escape. This can be accomplished 

by mechanical means (1) or by photolithographic protection of 

1 ines or arrays, but the former results in deeply damaged material 

and the latter requires polished surfaces and expensive processing. In 1974 Haynos, et al (2), reported an unspecified chemical 

means of creating the proper kind of 1 ight-col lection texture on 

(100) silicon 51 ices. This procedure converted the (100) silicon 

surfaces to random arrays of microscopic pyramids. Only 50 days 

later, Baraona and Brandhorst (3) reported nearly identical texturing with aqueous solutions of hydrazine hydrate, and showed 

that such behavior could be deduced from device fabrication etching experiments and observations of Lee (4). Soon thereafter 

similar texturing was accomplished by safer and less expensive 

sodium and potassium hydroxide solutions (5-7). In the meantime 

other benefits of this texturing had been realized: improved 

collection from l~teral refraction (2) and internal reflection in 

the case of thin cells (3). 

Various workers have reported studies, optimizations, and improvements of texturing using basic solutions (3-13). In 1977 

Fissore, et al (7) proposed that the pyramid texture was generated 

in the case of KOH etching by nucleation sites covered by sil icate 

salts precipitated at random. In 1977 Scott-Monck, et aI, (9) 

proposed a similar situation for 2% NaOH etching with and without 

isopropyl alcohol (IPA). In 1978 Dyer (10, 11) proposed a similar 

model except that most protective sites were thought to be 

growths, not precipitates. An attempt was made to quantify the 

various promotional effects. The purpose of the present paper' is 

first to explain in detail the attempt at understanding and quantifying texturing; second, to give an experimental description 

with observations on the proximity effect (8) and the effect of 

additions of water glass that were discovered during this work; 

and third, to show 1;hat the precipitate or growth models account 

for almost all of the known promotional effects . 

. PROCEDURE 

QUALITATIVE.--Qualitative. test runs were made in which concentration, temperature, pretreatments, ultrasonics, alcohol additions, 

containers, etc. were varied. Since similar procedures have been 

described in many texturing reports to date, they will not be 

repeated here. 

471 
..... .'- ~" . " 

,;-.. ~~~~rfT~rA"fI~E'~~:In order to quantiFy texturing it was First tried ~ to measure the Fraction of light reFlected back From the textured 

surFace. A simple apparatus consisting of a light source~ a stereomicroscope, and an exposure meter was constructed and used to 

get relative numbers of merit For various treatments. This approach was abandoned when it was realized that the measurement 

lacked sensitivity in the Final stages or texturing,' as well as in 

the early stages where specular reFlection swamps the readings. 

In addition this approach reveals nothing about the microscopic 

details or texturing. 

The approach taken to quantiFy texturing was to measure the 

Fraction of area covered by pyramids, as seen under the microscope, realizing that, For all practical purposes on (100) sil icon, texturing is the degree to which the surFace is converted to 

pyramids. Exceptions are 1) anomalous reFlection when the pyramids have sizes comparable with the wavelength or light, 2) extra 

reFlection when the large pyramids Formed have lost, their protective tops and begin dissolving From the apexes or the pyramids. The 

measurement or rractional area coverage has several advantages: it 

is versatile over a wide range of pyramid-producing capabilities 

because th~ etching time selected can be varied to produce convenient densities of pyranlids, and the measurement is independent 

or pyramid size or'magnirication. 

DETAILS OF QUANTITATIVE TESTS.--Texturing was done at 90 deg. C. 

at two concentrations, 1 and 4 wt. % NaOH. Isopropyl alcohol 

(IPA) was semiconductor grade, and water glass (Na2Si03.xH20) was 

reagent grade 40-42 deg. Be'. The proximity or the test surFace 

to another surFace was established by either or two methods. In 

the r·i rst, simp 1 e jigs were xonstructed, each cons i st i ng or a 

stainless paddle and Terlon \eJ or Delrin @ screws. The screws protruded through the paddles at three positions around the slice and 

were located radially such that slices with rlats could be wedged 

into place by rotating the slice until the Flat was out of alignment with the screw. Proximities were controlled by choice of 

screw thread For a given thickness of slice. In the second method 

the slices were placed between glass slides with 'suitable spacers. 

Ordinary rubber bands were used to hold each pack together, and 

the angle of the slice From the horizontal was measured. Threeinch silicon waFers, p-type, 1 ohm-cm, (100) were used. Polished 

waFers were used For the Fractional coverage studies to eliminate 

the enhancement of pyramid Formation by rough surraces (3, 10). 

Pyrex and stainless steel containers were used and each waFer was 

etched 3 min. in 301. aqueous NaOH at 100 deg.C. prior to texture 

etching. 

MEASUREMENT. METHOD.-- A compound incident-light microscope with 

IOxl0 counting reticle was used. A convenient method or assessing 

the area covered by pyramids was to count the pyramids in each row 

of the grid in size groups: 0.1-0.2, 0.2-0.3, etc. (Fractional 

sizes of a unit square on the grid.) This assessment of pyramid 

size can be done surprisingly rapidly and accurately. The numbers 

472 
ror the ten rows in the grid were totaled in each size group and 

converted to relative areas by the appropriate size ractors. The 

rractional coverages were summed to obtain the total pyramid coverage. These va lues were measured a't two or more places on the 

slice and averaged. 

RESULTS 

qUALITATIVE OBSERVATIONS.--Results or previous workers will be 

listed as well as those or the present study. 

POSITIVE INFLUENCES.--The rollowing chemical additions to 

KOH or NaOH solutions enhance texturing or (100) silicon: 

o Alcohols (5-9) 

o Methyl ethyl ketone (MEK) (9) 

o Films or long-chain carboxylic acids (9) 

o Fingerprints (11) 

o Water Glass. (10) 

The rollowing physical conditions promote texturing: 

o As-cut or lapped surraces (3) 

o Terraces in NaOH-etched as-cut surraces (10) 

o Proximity to another surrace (8). This efrect was discovered by noticing that the places where the slices were 

wedged into holders were often textured better than the remainder or the slices. Optimum proximity ror developing 

pyramids was round to be 0.4-1.0 mm. The controlling factor appears to be the entrapment or hydrogen bubbles between the two surraces, and thus viscosity, rlow, and angle 

or the surraces rrom the horizontal are all ractors. The 

observation or the beneficial errect or the bubbles is in 

contrast to previously-reported ideas about the errect or 

bubb 1 es (9, 13) • 

o Repeated use or texturing solution (11) 

o Adherent growths or particles lert arter NaOH or KOH pretreatment. In ract, some growths or precipitates remain 

attached to the tops of the pyramids arter texturing, even 

arter rinsing with 0.1. water. Figure 1 shows such a 

growth as seen by the scanning electron microscope (11). 

NEGATIVE INFLUENCES.--In the present work it was noted that 

texturing was inhibited by polyvinyl chloride cement and by cer473 
tain plastic slice holders. In addition, the Following observation was made by Baraona and Brandhorst (3): 

"For a given etch composition and temperature, there appears 

to be an optimum etch time to achieve maximum structural 

perFection and uniFormity. IF etching continues beyond this 

time the pyramids begin to disappear, and Flat, shiny regions begin to emerge." 

NEUTRAL FACTORS.--IF a texturing bath was used repeatedly, 

visible precipitates accumulated in it, but had no apparent 

eFFect on texturing. 

RESULTS OF QUANTITATIVE TESTS.--Figure 2 compares the results of 

various treatments in 1% NaOH on percentage of surFace coverage by 

pyramids. The result was that each additive or promoting condition (proximate surFace) caused a 2 to 20-Fold increase in pyramid 

coverage. Also a threshold concentration exists For Na2Si03.xH20. 

Figure 3 compares the results of various treatments in 41. NaOH. 

Similar results to those at 1% were seen. The proximity eFFect 

exerted a strong inFluence at both concentrations. 

INTERPRETATION OF RESULTS 

Several authors have reached the conclusion that texturing of 

(100) silicon occurs by the Formation of protected spots on the 

surFace (7,9). This conclusion could, in Fact, be reached From 

the knowledge in device Fabrication on (100) sil icon that any masking material will generate pyramidal mesas. The Following is a 

line of reasoning From the atomic model that allows the same conclusion. AFter that, the protective mechanism will be discussed. 

ATOMiC MODEL.--In order to more clearly appreciate the surFace orientation aspect of the texturing problem, atomic models are 

shown. Figure 4 shows a Fisher- HirschFelder-Taylor model or 

"sphere" model of a perFect (100) surFace of silicon. The surFace 

consists of an array of pyramid tips having <111> sides. Each 

surFace atom has an equal chance to become the tip of' a pyramid. 

ThereFore, some external inFluence selects the preFerred sites of 

pyramid Formation. Figure 5 shows a model of a pyramid on the 

(100) Face. The selectivity of etchants, including sodium and 

potassium hydroxides, can be explained by considering the two ways 

in which atoms are held into the illustrated sUl~Faces: One type is 

bonded only twice and is typiFied by the perFect (100) surFace and 

by the tip of a pyramid, the other kind is bonded three times and 

is typ iF i ed by the perFect (1 11) surFace and by the sides and 

edges of the pyramids. Th~ perFect (Ill) surFace etches very 

slowly compared with the (100) surFace in preFerential etchants 

(14). Clearly, iF a means can be Found to protect small areas of 

the (100) surFace, each area will become the tip of a pyramid as 

the (100) surFace is progressively dissolved. 

474 
~. 

, , 

MECHANISM OF FORMING PROTECTED SITES ON (100) SILICON IN SODIUM OR 

POTASSIUM HYDROXIDES. 

The chemical reaction ror texturing in NaOH or KOH solutions is as rollows: 

2MOH + Sf + H20 --) M2Si03 + H2 t, 

where M represents sodium or potassium. Since pyramid rormation 

is enhanced in dilute (1/2-41.) and not in concentrated (30-401.) 

aqueous NaOH solutions, the protective ractor is related either to 

product insolubility in the etchant or to its low dissolution 

rate. Third, since addition or small amounts or Na2Si03.xH20 to 

NaOH solutions enhances pyramid rormation; and the Na2Si03 produced in the reaction has limited. solubility in aqueous NaOH and 

even lower solubility in NaOH-H20~IPA mixtures, some reaction 

product 1 ike M2Si03 must be the protective ractor and it must be 

grown or precipitated at random sites. Figure 6 shows a schematic 

diagram or the stages in the process ror" texturing with NaOH. with 

and without enhancement errects. 

The reasons ror ravoring the idea that the protective products are growths rather than precipitates are: rirst, it is dirricult to see why precipitates would occur prererential lyon the 

terraces or pitted surraces. Second, precipitates have only a 

slight tendency to. bond to the sil icon under a liquid. particularly one under agitation rrom gas develo~ment. Third. the neutral 

errect or the precipitates that accumulate rrom extended use or 

the texturing bath ravors the growth hypothesis. 

The positive inrluences can now be explained as rollows: 

Alcohols and MEK decrease the solubility or the reaction product. 

Water glass suppresses dissolution or growths or reaction products by the mass-action principle. Fingerprints and rilms or 

long-chain carboxylic acids slow the vertical dlrrusion or reaction product; proximity (intermittent bubble-entrapment) acts the 

same way by providing a gas barrier to product dirrusion. As-cut 

or rough surraces texture better because they are already closer 

to the textured state. Repeated use or the texturing solution 

works progressively better because or build-up o~ reaction 

product. 

The negative inrluences are explained as rollows: PVC cement 

stops the reaction instead or slowing it. Too long texturing 

eventually removes the protective growths rrom tops or the pyramids, which leaves them rree to dissolve down to base level. 

PRACTICAL USES OF RESULTS.--The variety or agents that promote 

texturing make it possible to select a wide variety or texturing 

solutions. The synergistic errect or combined additives or physical conditions broadens the possibilities rurther. By more rapid 

pyramidization, a smaller range or sizes ror pyramids is possible. 

lr a texturing process has stopped producing adequate absorption 

or light. one can look ror inhibiting agents such as PVC cement 

475 
residues, or examine the pyramid tops to see iF they are dissolving away either From some contaminant like a Fluoride, or From 

over-etching. 

CONCLUSIONS 

o Texturing of (100) silicon surFaces in sodium or potassium 

hydroxides occurs by the growth of a reaction product in a random 

array of surFace sites, which leads to pyramids remaining at the 

~ites aFter other parts of the surFace dissolve away. 

o Various additives and conditions promote texturing by increasing the probability of localized growth of reaction product. 

o A new texture-promoting inFluence--a proximity eFFect--was 

discovered in this work. This eFFect was Found to Further enhance 

texturing in the presence of promotional additives. 

o A method of quantiFytng the pyramid-producing capabilities 

of each texturing solution was developed. 

o Combined eFFects of additives or physical conditions are 

synergistic with respect to pyramid density. 

ACKNOWLEDGMENTS 

The support of this work by JPL contracts 954405 and 954881 

is grateFully acknowledged. Discussions with R. Roques, D. Coldwell, and B. Carbajal are greatly appreciated. 

REFERENCES 

1. B. Dale and H. G. Rudenberg, "Photovoltaic Conversion, 1. 

High EFFiciency Silicon Solar Cells", Proceedings of the 

14th annual Power Sources ConFerence, U.S. Army Signal Research and Deve 1 opment Lab. Ft. Monmouth, N. J

O

., May ( 1960) 22. 

2. J. Haynos, J. Allison, R. Arndtt and A. Meulenberg," Proc. 

Int. ConF. Photovoltaic Power Generation", Hamburg, Germany, 

COMSAT Report 74-35-CLR,(1974)487. 

3. C. R. Baraona and H. W. Brandhorst, NASA Technical Memorandum TMX 3326, Record of Meeting at Lewis Res. Center, 14-15 

Nov 1974. 

4. D. B. Lee, J. Appl. Phys. 40(1969)4569. 

476 
5. W. E. Taylor and F. M. Schwartz, "Demonstratfon of the Feasibility of Automated Silicon Solar Cel 1 Fabrication", NASA 

Lewis Contract NAS3- 18566. Rept. TR3. Oct. 1975. 

6. P. Stella and J. Scott-Monck, JPL Contract 954600, First 

Quarterly Rept., Dec. 1976. 

7. A. Fissore, B. Waldman, and G. M. Oleszek, J. Electrochem. 

Soc. 124(1977)216C. 

8. L. D. Dyer, see B. G. Carbajal, JPL Contract 954405, Second 

Quarterly Rept., Apr. 1977. 

9. J. Scott-Monck, C. Gay, P. Stella and F. Uno, Tech. Rept., 

AFAPL-TR77-36(1977). 

10. L. D. Dyer, see B. G. Carbajal, JPL Contract 954881, Second 

Quarterly Rept., Apr. 1978. 

11. L. D. Dyer, J. Electrochem. Soc. 125(1978)256C. 

12. G. T. Jones, S. Chftre and S. S. Rhee, ERDA/JPL-954605-78/5; 

Final Rept.; Apr. 1978. 

13. S. R. Chitre, Conference Record of the Thirteenth IEEE Photovoltaic Specia'lists Conference, IEEE Press, (1978)152. 

14. D. L. Kendall, Appl. Phys. Lett. 26(1975)195. 

15. A. I. Stoller, RCA Rev., Jun(1970)271. 

16. A. D. Morrison, prfv~te communication, (1984). 

APPENDIX 

VERTICAL METALIZATION IN SOLAR CELLS 

AND OTHER SEMICONDUCTOR DEVICES 

One of the factors that reduces solar cell e~ficiency (and, 

device packing density) is that a fraction of the active area (about 10%) must be metalized to collect current from the remainder 

of the device area. This metal ization is in the form of "fingers" 

and "bus bars" that are much thinner than their breadth. and is 

placed parallel to the sl ice surface. The metal is at least 2 

microns thick so that light is prevented from entering and generating carriers in the underlying volume beneath the metal. The 

present proposal is to place the metallization vertically so that 

much of the area formerly beneath metal can generate carriers. A 

gain in efficiency of almost all that lost to metallized area can 

be expected, i.e. perhaps 9.5% if 10~ was metal. 

The proposed method consists essentially of metalizing deep, 

narrow grooves in silicon that have been introduced by the orien-

,477 
tation-dependent etching of (110) surFaces (15). In a solar cell, 

the collection junction would be Formed aFter the grooves were 

installed, and metalization would then be carried out. 

The metal ization could be accomplished by various techniques: 

ion plat i ng, electro 1 ess depos it ion, low temper'ature chem i ca 1 

vapor deposition, or sputtering. It would preFerably coat both 

sides of a groove; Filling up the groove might give problems with 

mismatched thermal expansion coeFFicients. Connection of the 

several collection Fingers could either be accomplished by metal ization of the solar cel 1 edges or by introducing a second set of 

groove directions that lie 70.53 deg. From the First set. Contacts could be made to the edges or to small horizontal patches 

of metal ization. The Foregoing idea may also be used in device 

manuFacture in which the goal is to conserve area that is presently used in horizontal metalization. 

IF this method is successful, the beneFit to earth-based 

solar cells will be oFFset by the inability to texture-etch the 

required (110) silicon surFaces; on the other hand. space-based 

solar cells may still beneFit because of diFFiculties with the 

textured cells in this application (16). 

/ 478 
Ffgure 1. Reaction P oduct Growth at Top of 

Texturing Pyramid on (100) Sfl icon 

479 
w 

~ II: 

w 

> 8 

w 

~ I&. 

II: 

;:, 

en 

'fI!. 

15 

10 

5 

• 

NaOH 

ALONE 

1% IPA 

ADDED 

0.5 mm 

PROXIMITY, 

Sa FROM HORIZONTAL 

F1gure 2. EFFects of Various Enhancement Conditions 

on 1. Coverage by Pyramids Arter Texturing 

in 11. NaOH ror 5 m~n. at 90 deg. C. 

480 

li , 

\ 

i 

, • 

i' 

~ 

I 

I 

I 

! 

i 

i 
20 

15 

UJ 10 

<.!J 

~ UJ 

> 

o 

u 

UJ 

u 

~ ac 

~ 

lit 5 

~ 

Figure 3. 

NaOH 

LO 

-

--

-

%f ~ 

ADO 0 

--

-----

-

--

-

Na 2Si 03 

SOL ' 

ADD EO 

--

--

-

-----

-

--------

--

-

--

--

------

--

--

-------

-

--

-

0. 5 

PROX I 

6- 0 

HOR I ZO T. 

---

-

--

--

-

--

-

---

-----

---

-

--

-----

--

-

--

-

--

-----

---

--

---

--

EFFect s o f Various Enha ncement Co nditions 

on 1. Coverage by Pyrami d s AFter Texturing 

in 4~ NaOH For 10 min. at 9 0 deg. C. 

481 
Figure 4. Atomic Mode l or (1 00) Face or Silicon 

Figure 5. Atomi c Model or Texturing Pyram i d 

on (100) Face or Sf! icon 

ON AL P 

OF. 'OOR QUALITY. 

482 
, " 

.~ 

. " 

,. .. 

{ 100 } SURFACES 

------------~,,- ~-~------------ PROTECTIVE NUCLEI 

b I ! 

PYRAMID EMERGENCE 

---A--------

FURTHER DISSOLUTION 

SURFACE LARGELY REFLECTIVE . TEXTURING COMPLETE 

(.1 N.OH ONLY. (bl TEXTURING ENHANCEMENT BY 

ADDITIONS OR PROXIMITY. 

Figure 6. Schematic Diagram or Stages in Texturing Process with and without 

Enhancement Errects 

-. 

483 

R 
DISCUSSION 

QUESTION: Is there any difference between that structure and the DKVJ cell? 

with Sandia's support, the development of that kind of metallization, we 

are probably six or seven years . . . 

DYER: I was on one of the DKVJ contracts so I know something about the structure. The making of the grooves is the same idea, you have to do masking, 

and you have to use a substrate with [110] orientation. It has disadvantages: you can't texture it then if it's [110] unless someone discovers 

some new way of texturing a non-[110] orientation. That may be, then, 

only an advantage for space, where you can't use the texturing. 

ROSE: We supported it from a concentrator point of view, because you can etch 

those grooves deep, and the way you extract the current out of it at very 

high concentrations is no different from dragging out through a thin 

layer. The reason we gave it up -- it's still a good operating cell, 

even up in SOO-sun concentration -- the reason we gave it up, is it is a 

large-emitter-area cell and there's limitations on Voc involved in it. 

All I do is bring it up becQuse it doesn't seem to me like it is a new 

idea, it's something we have supported and given up. 

DYER: Except that here you are putting the metallization down here. In other 

words, there'S no metal contact on the top; there is no shadowing. 

ROSE: That's right. That is the DKVJ cell. 

DYER: Well, you still had to have bus-bars come across and collect from that. 

ROSE: No, you run them out the ends. 

DYER: Well, I was involved with the VKJ concept, and it had this idea in about 

1976 after a contract like that and there are some differences, which I 

guess we can talk about. Of course you don't have shadowing and 

shingling. 

RAI-CHOUDHURY: If this texturizing takes place by these reaction products, 

masking the reaction, why does it not work on [Ill]? Can· you CODmlent? 

People always have difficulty texturizing. 

DYER: We already have the low-energy face there; you are stuck. 

MARTIN WOLF: I have been requested to prepare a summary of this meeting, not 

here, at some later time, and I would like to ask the presenters of all 

the sessions, not just this one here, to be so good as to supply me with 

perhaps four to six of their slides or viewgraphs, namely those that they 

think are either the most instructive or the most impressive-looking, 

which might help me then to perhaps select one or two from among them to 

use in the summary. So it doesn't have to be here that you get me the 

slides or viewgraphs, but if you could send them to me, the address is in 

the attendees list. I would appreciate this very much. Thank you. 

484 

I 

I 

~ • 

" ~ 

~ 

1 

I 

1 

, 

1 

1 

I 

I 
SUMMARY AND DISCUSSION 

SESSION 

R. Kachare, Moderator 

1

~ 

~ 

I 

, 

i 

I 
SUMMARY AND DISCUSSION SESSION 

PRINCE: Anything you want to say? The major problem we have in the Department 

of Energy, as I mentioned the other day, is that we are being squeezed 

again. We will not have as much money to spend on each of the areas as 

we originally thought we were going to have. So the question is, what ' 

should we be doing in the Department of Energy to improve the efficiency 

of solar cells? We have heard all sorts of different approaches to 

things: modeling of various types, general theoretical analyses, some 

experimental work that has resulted in moderately high-efficiency cells, 

and so on. We heard also about measurements of various types that will 

enable us to evaluate what we are getting out of these devices. So, I 

thought we ~'fcdld just start off by -- well, actually, I don't, know where 

to start off. Perhaps by explaining what I think I heard during the 

session that I headed. I think that's what we all were asked to do, but 

I think I'm g,oing to forego that. I'll tell you one thing that did 

bother me: I heard several conwents about the importance of the emitter 

region -- and in one talk, that the emitter region has very little effect 

on the efficiency of solar cells. On the other hand, I heard in other 

talks that unless you have very low surface recombination velocity on the 

emitter surface, you're never going to get 20~ cells. That's inconsistent. I've heard a lot of other inconsistencies during the last three 

days. I'd like to clarify these inconsistencies. 

QUESTION: Hay I comment'on that? That·s not inconsistent at all. I think 

what you're seeing is, it depends on what the limiting mechanism is in 

the cell that you're looking at, and it's clear that if you're base 

limited, it really doesn't make any difference whether you passivate the 

surface. If you are emitter-limited, and Auger isn't large, and band-gap 

narrowing isn't killing, you then emitter is very important. I thought 

it was very healthy, this conference, because I think that realization is 

now getting to a lot of people that simply running an experiment --

passivation, not passivation -- and observing that it did not make any 

difference, doesn't tell you anything. As a number of people have said, 

you really have to optimize the entire cell and that is what really is 

important. I don't think any of those things are inconsistent. 

SCHWUTTKE: I'm challenging. I'd like to see if I can say something without 

getting into trouble. I think the question, as I see it; is: where do we 

go from here? In that sense, I think the problem has a couple of different facets. From my point of view, certainly; I think I have already 

expressed the idea that we need to have a complete understanding of what 

it takes to get to a specified level of efficiency in terms of the bestfirst-principles kinds of things we can do. I think there are people who 

are working on that problem, and I think they are going to give us some 

pretty impressive results in the near future. I think the other thing 

that really matters is the industrial participants in the program doing 

those things that allow their product to be a better product. Because 

that's really what this entire program is all about. From that point of 

view, I have tried to make available to DOE participants, and to people 

who are not participating in DOE programs at this stage of the game, that 

information that we have. I would hope that kind of thing would continue; I would hope that the information that we are finding will be 

485 
used. In terms of the critical issues. I would totally agree that the 

material issue is one that needs to be resolved: how do you get a realworld material that is good enough to be able to make cells consistently 

that are worthy of the processing we are finding out about? If ther,~ has 

to be something done in that area. then maybe it behooves us to think 

about that kind of a question. I think materials questions in general •. 

in all photovoltaics, are a major issue. 

SIRTL: Do you expect me to say something as a part of the wrapup of we have 

been listening to for several days? It may be a kind of egotistical wish. 

I already mentioned that to make gettering or gettering systems a science. 

he situation now, and the situation in other areas that have nothing to 

do with solar technology, is that so many different companies have their 

"black boxes" of what they call gettering processes. They never would 

like to disclose anything on that. On the other hand, we need to make it 

a more consistent technology in later years. We need a kind of wellunderstood buffering system that prevents the outbreak of blaming each 

other for being the culprit. The manufacturer of the material. or the 

device maker; if we would have reached some kind of gettering science, we 

would be much better off. and that of course includes a better knowledge 

of what direct combinations that predominate what recombination centers 

may' look like. We really are at the vet·y beginning of any understanding, 

and my feeling is, that is included in the science of gettering. 

KOLIWAD: I have three observations. One is in the same line that you talked 

about. emitter importance. I have this concern about the work in the 

process-related area. process research area, as an example: do we have 

optimum emitter profile? It concerns me especially because of the heavy 

doping effects. and the field, as a result of the band gap or the bandgap tailing. Dick commented this morning that in a static field they 

distribute in ways that are complementary to each other, so we are not 

doing any research at all in tailoring the profiles. The second observation I have. I would again emphasize what Fred mentioned this morning. 

on the contacts -- the importance of contacts for high efficiency. There 

are a couple of areas that I think are in the area of process research. 

if you will, or process technology research, and I think some emphasis 

should be given to those areas. 

LOFERSKI: I guess the thing that struck me particularly was Peter's discussion. I have heard him say this before. that the space cells may have 

been 18~, the stuff that they normally make. and of course by changing 

resistivity they would probably have been there. That's a question of 

many different steps and high-quality processing all along the road, I 

guess. Like the gap between what's possible in cells and what exists in 

commercial cells for space, I think, is rather small -- the things that 

are found in the laboratory and up in those space cells. But that is not 

so for terrestrial cells; there is a gap. and I guess what Peter is saying 

is that it's pretty much the same cell, that it's a space-quality cell 

that you are asking for, different resistivity and the higher quality 

material to get beyond the 18~. Like Mark Spitzer was saying: just give 

us better material. and pretty much the same processing that we are using 

to make the 18~ cell will get us to 2~. But the big problem is that gap 

between what's demonstrated as possible and what comes out of the manu486 
facturers. That is an economic problem. Like ',Kartin says, we'll make a 

good cell and then learn how to make it cheap. I have heard someone else 

in the course of the talks say that's not the WilY to go, but that's 

basically it. For space the price is not what people are worrying about 

when they are manufacturing the cells, but for terrestrial application 

it's price -- economics -- that finally get in there. Now you said we 

shouldn't talk economics here, it's high efficiency that we are talking 

about, but there is that gap somehow in cOJmlunication, perhaps not communication so much as the feeling of the terrestrial people that you 

cannot make these high-quality cells cheaply. I don't know how you change 

that. 

QUESTION: I don't feel that way at all, Joe. I thinlc many of us have been in 

the semiconductor industry for many years and we have learned from experience that you do the best you can. And when YOll learn how to do those 

things well, you push your yields up and you get your cost way down, now 

that we have gotten up to this 15~, 16~, 17~ range. 

LOFERSKI: I think we have gone through this cycle of "Well, it can't be that 

it.'s that space cell that will be the terrestrial cell." There was the 

business about .solar-grade silicon that was going to be a lower-grade 

silicon and not the best silicon there is, and now we have come around to 

"It's got to be this solar-grade silicon for high-quality cells, it's the 

best kind of silicon there is, and it's the best for processing all along 

the way. ,t It's a question of doing all those things inexpensively or at 

an acceptable price. 

QUESTION: Just a comment. I think everything is going in the right direction, 

and what we are learning in high efficiency is being applied to making 

the cells for the commercial market today. Their cost is important, as 

it always will be. You have to compete at $6 a watt or whatever it 

happens to be ~t the present time. These things are applicable; we are 

not going to be selling that kind of cell right away. I think there is 

one thing perhaps where DOE is a little off, in my opinion, of dead 

center, and that's in specifying efficiency on a module-sized basis. In 

other words, a 15~ module requires 18~ cells. What is important is the 

efficiency of the cell under glass. You could make 30~ cells and fill up 

half a module and you have a 15~ module. But that's not going to do it. 

It is not very important to a first approximation whether the module is 

20~ bigger or smaller than the average size. It may be for central-power 

systems, where everything has to be squeezed together. We are not going 

to be in that business for many years in this country because there are 

many other technologies that may dominate that market. What is important 

is the world-wide market for small systems. I think that's the real 

mar5et that we are facing today. For that it's ~ot so important, now; 

whether DOE's objective is that or not, perhaps, does not make any 

difference to the world market, but for American industry it may have 

some effect. I think we should be realistic and say what's important. 

We need efficient cells. We want to get the most we can. But what is 

more important is the cell efficiency under glass, cell efficiency in the 

module. We can worry about whether 10~ is more crowded or not but thats 

not important, in my opinion, to the world market today. 

487 
DYER: I want to make a comment on something that someone else brought up in 

this conference about Czochralski vs float-zone. I want to expand on 

that. Czochralski growth is not optimized for solar cells at all and the 

economic question does come into it. Because whoever makes the silicon 

-- and in our case, we make it for our own divisions, our own front ends 

-- has to make it as cheaply as they can, and right now they are asked by 

front ends to make it optimized in several ways. They, or course, want 

to have a very constant resistivity over the whole thing. The segregation laws make it so that you have to, I mean the resistivity changes 

from one end to the other, so they are going to lose something there. It 

would be very nice if you could have one front end want the top part of 

the crystal and another one want another part and so on down to the tail. 

But when one device engineer decides that so-and-so ohm-centimeters is 

right, they all do. So you are putting the manufacturers in that bind. 

Then, in recent years, it has been realized that to have oxygen in the 

crystal is a good thing, and they don't want the oxy'gen to be measured 

just in one place, but both radially and axially along the crystal. So 

there is another restraint put on again, not by the solar-cell industry 

but by the device industt·y. No one has ever at::ked /Omake us some material 

for solar cells." It seems to me that in addition to all of these other 

requests someone has to sit down with people in the growth and selling of 

Czochralski silicon to see if they can't also do something else and provide a material that is good for solar cells, And that could be done, 

but the economic question has to be brought up and addressed. I rest my 

case there, I don't think they have gone as far as they can on it, 

because that isn't the one who is paying the bills. 

QUESTION: I want to take up on Kris Koliwadts comment. Correct me, somebody, 

if I'm wrong. Most of the solar cells that we make, with the exception 

of float-zone silicon, seem to be base-limited. Hence, again the emphasis 

on bulk material is so much more urgent than the process. Tailoring of 

the emitter, if you leave the process in the hands of those who have good 

experience in semiconductor processing, not just solar-cell. Ion implantation diffusion from solid source, liquid dopant, you name it, more than 

one way. More than one way to tailor the emitter profile and I don't 

think we have run out of steam there yet. I think there are problems 

still: in the high-efficiency area is one, of the starting material --

Czochralski, of course, we talked about it; the recombination center in 

Czochralski, especially as a result of heat treatment. One has to address 

it; it is really a materials issue. Hence, how do you get around it so 

that you can apply the knowledge to a cheaper sheet growth process? 

QUESTION: Maybe I should comment a little bit on the same question. It seems 

to me that there are two basic reasons why we live today with this emitter 

profile. The one is that we have not learned really to bring the surface 

recombination velocity to very low values, so that we need what I called, 

in my talk yesterday, the potential step, or in other words a large drift 

field that the profile gives qs. It helps to reduce the effect of the 

high surface recombination velocity. The second is just strictly process 

historical. We have learned how to control diffusions, we have learned 

how to do ion implantations. Both leave us with a steep impurity gradient 

in the layer that we generate by this process, so we automatically end up 

with this type of profile just because of the process we use. Okay, 

488 

,. 

l

~ I 
what's the other alternative? Really, it could be alloying, a liquid 

face regrowth; we don't have those very well under control. We have 

gas-phase CVD epitaxy. We seem to have probler.\s with that. That would 

give us different profiles, then we could live with something else. We 

haven't learned as well to use these processes ror solar-cell fabrication. So to some degree it is historical. Again, if you could make one' 

of these other processes work, we would not necessarily -- probably we . wouldn't at all -- want such a high surface concenb"ation, and we probably 

would have other means available to control the surface recombination 

velocity better, if you don't have such a high surface concentration of 

impurity. So we could move into a quite different technology here, but 

we don't quite know how to do it. So that's my response to Kris's 

question. 

I have two other things I wanted to mention. I think this meeting has 

shown us very clearly that we really ha'lfe moved to a new technology level. 

People have made use of modeling, of the the available analytical measurements, to understand exactly what the devices they are making are 

like, where their limitation are. They have analyzed where the next step 

for improvement has to be. They have moved along and made improvements 

in understanding of device physics, modeling, and the analysis of devices 

through measurements, and they have reached this new level of l8~ to 19~ 

efficiency. And we see that it can be done by quite a few people. It's 

not that just one individual that has this capability, and we also see 

that each one has put emphasis a little bit differently in how he got to 

this l8~ to 19~ level and through the modeling and analysis has seen what 

else, with today's technology, he can do to design this device better, to 

process it a little bit better, so that he probably can get to 2~. So 

we have heard a number of people who felt that 20~ is essentially just 

around the corner. That seems to be the level of ~oday's technology, and 

I think it's a good move ahead from where we were a couple of years ago. 

The question then becomes, what's the next thing? How do we get significantly beyond that point? It looks like, from everything that we have 

been hearing here, that that's not exactly accomplishable with today's 

technology. Again and again we heard that really to get significantly 

beyond, we need better material, and it seems to me, with that, we come 

pretty much to the talks we heard yesterday about what do you do with 

surfaces, what's happening with surfaces. We saw some very impressive 

pictures of what we have learned about how surfaces are reconstructed, 

for instance, and so on. What are the defects in materials, where do 

defects come from in the material? The question then comes, okay, since 

we start to understand what the surfaces are like, we start to understand 

how they. reconstruct themselves, how can we foster it, how can we develop 

processes that will give us this desirable type of surface practically 

all the time? It seems to me we have made considerable research progress 

in understanding but we haven't yet learned really how to apply it. I 

don't know whether my understanding is right or not, but that's the 

impression I got. So I think this might be perhaps a subject we might 

want to discuss a little further here. 

I have an answer for Erhard Sirtl. I didn't like his comments so much; 

let me tell you why. To me, it looks like gettering is something to 

repair what you didn't do well enough before. So, shouldn't we learn 

489 
first to do the things as well as we can or better than we do it now? 

And maybe then still do some gettering, but maybe the first emphasis 

should be to reduce the defects in the material rather than afterwards 

try to repair it; make it right the first time out on the production 

line, and don't send it to the repair shop before you sell it. Those are 

my comments. Let's see whether we can get some good discussion from 

th08~. 

QUESTION: I ~lways used to say gettering is an act born out of desperation but 

at some time it is necessary, but on the other side,it spoils manufacturing to be sloppy. I would really like to pick up on the comment made 

by Larry Dyer and also by Marty. Not too long ago the solar-cell industry 

used silicon that the IC industry was throwing away. Maybe, just over 

the last couple of years, they have become more conscious, and they buy 

Czochralski silicon; and then they heard about float-zone silicon, so 

they all rush out and want the float-zone silicon, because somebody told 

them that it's a lot better. Shortly before that everybody was hot on 

sheet silicon because you didn't have to slice it; now we cast for the 

kilo silicon and nobody asks about slicing any more. So there are a lot 

of contradictions in that particular field. What I believe we have to do 

now is come out aggressively and specify the material we would like to 

have and then go after the vendor to develop it. So far, we just take 

what we get. I would like to say we really don't know what your process 

can do, we don't know what float zone can do and we don't know what sheet 

technology can do for us. We have never taken the time to sit down, and 

we have done a lot of modeling, but the hell with it, I'd like to sit 

down with you guys and draw up the specs of the material for a highefficiency cell. You tell me what you want and then we go and find 

somebody who is going to make it. 

QUESTION: Let me now give the answer to Martin Wolf and maybe dwell on some 

inconsistencies in thinking. Let's comment briefly on Schwuttke's comment. Presently we have to live in microelectronics exclusively with 

gettering. Whether it's oxide gettering, whether it's internal or intrinsic gettering, whatever you may call it, we have to live with it 

until somebody comes up with a better understanding to make good and 

cheap Czochralski materials that don't need all that, including the 

device processing. Let's talk about solar cells now. What has been the 

reason I so strongly would like to see gettering becoming a science? 

What is the situation we are in right now? On the one hand we are 

striving for the highest-efficiency cells possible. That's something 

else, that's special research, and we want to give it all the support 

possible . . . we may learn a lot more about the mechanism of a solar 

cell in general, the mechanism of different device concepts and the 

like. But we must never forget that this type of solar cell nearly 

exclusively is made from a material that I would call exotic. Exotic 

means that I don't see, in the near future, ways to realize a production 

of some sizeable quantity. T~at means it's good to have found out how we 

can make high-efficiency cells, but later on we have to learn to live 

with a material that's economically available, and that we can scale up, 

and it's done best in connection with the device maker in a way where I 

think we need gettering. But that may not be the only solution. And by 

gettering, I mean it in all senses; it means that could include hydrogen 

490 
, 

I 

" 11 . ~ 

\ 

) 

passivation, that may even include some kind of intentional complexing in 

the original material. When we now talk about something that has not 

gotten the share of attention in this meeting that it should have, about 

all the terrestrial approaches to make real cheap solar cells and real 

cheap material, I think we haven't come to a point yet where we can talk 

about the standard final quality of material that may have come out fromany kind of process. Developing some special additional treatment to 

improve things here means just a temporary situation, because we have not 

reached maturity in whatever the process may look like. In my feeling, 

gettering can be an early solution to improve things at least to a point 

where the efficiency that can be seen as possible by the device maker has 

reached a certain attractiveness already. But we still have this gap 

between high efficiency of space types of solar-cell technology and the 

technology we mostly are talking about, namely for terrestrial application. That's where we need help to get into shape early to make solar 

cells attractive and efficient -- but it cannot be the maximum efficiency 

that we may reach during the next five years. 

QUESTION: The question about gettering. I thi.nk that your comparison is not 

a better comparison with microelectronics, where all the action is on the 

surface. One-dimensional, two dimensional·-device. Better compared with 

power devices, where current flows through the thickness of the material. 

A solar cell is essentially such a device. When you have a device such 

as that, you can getter but you have to have a material that does not 

have bulk precipitation, something going on in the bulk as a result of 

gettering, because in my experience, or that of all the people I know in 

the processing area, we never even dream of starting with a bad material 

and getter it and then make a device. The only purpose of gettering is 

to prevent contamination during processing. It's not really an answer. 

Can one take a material that is not so good, and getter-improve it, and 

make solar cells? I think the whole area needs to be examined. 

QUESTION: 'I would like to just follow on what Ajeet made a point about. I 

think it's an excellent point, because if you try to getter something 

within the bulk, it's going to kill you. Now, the other choice is 

to go to the surface, whicb is like back-surface damaging, and that is 

going to kill you again because now you are going to raise your surface 

recombination velocity. So it becomes very difficult. And the third 

point is that generally the best gettering is achieved at high temperatures. All those things stand to hurt solar cells, so how you are going 

to do it and apply it to solar cells is going to bea slightly difficult 

question. 

SCHWARTZ: I'd like to switch topics for a moment and talk about modeling. I 

think Martin Wolf probably said it best, near the end of his session: he 

stood up and said this sounds like a modeling session that we have. The 

one thing that struck me was that there were very few device papers presented that didn't either use.as a guide, or rely upon as an interpretive 

tool, some sort of a model. There are all levels of sophistication. But 

almost everyone had some sort of a model that they were using, and I was 

very pleased to see this because I think that the device is deceptively 

simple-looking and still very sophisticated. The realization that the 

model is a design tool, an interpretive tool, seems to be widespread, and 

491 
I was very pleased to see that. The current status, I think, of the 

device codes is that they ~eally are very good in spite of all the time I 

spent last night talking about the things that need to be done. In fact, 

one can show large numbers of plots of all kinds over wide ranges of 

operating conditions and over wide design ranges for which the predictions fall dead on the measurements, within the experimental accuracy of' 

the measurements. The codes are designed to do it, really do an outstanding job of fitting what's there. In fact, they really do a very 

good job of predicting of what will happen under changes before the 

experiments are made. The status is really very good. So what does it 

need? There were needs: maybe three dimensions, time -- actually, time 

is very easy to do, that's a very small extension from where we really 

are. There are some needs, and they were not very well expressed 

directly, but it W\lts implied by a number of questions, and that was the 

codes are only good, useful and easy to use. Therefore. the output is 

very importl1nt, and good graphical output, where you cab sit dewn and 

look at things very quickly and understand what is going on, is very 

important to the use of modeling. I have one other comment: it seems to 

me that there should be larger, wider access to some of the more sophisticated codes. At the present time they really aren't widely available 

for people to use, and that's probably something JPL has been looking 

into. That in fact would help a great deal if there were wide access to 

some of the existing codes. 

QUESTION: Perhaps we cou'ld resolve the controversy between Martin Wolf and 

sirtl if we made the gettering part of the wafer manufacturing process. 

You know your material the best of anybody. If you feel it can profit 

from gettering, you can make a better wafer, include it in the production 

process and maybe get more money for it. 

QUESTION: I think I have to give a better definition of what I understood 

about gettering. It finally, very clearly, should be a help for the 

device maker to get the best quality of his specific device after having 

done, at a fairly late stage of his process, some kind of gettering. I'm 

just speaking for the material supplier because in general, the device 

maker has not had as good an understanding of materials problems as the 

materials maker in general. So we have to live with a situation that 

there are many device production areas that just have to have a very 

simple recipe available that, of course, needs a lot of e'xploration 

before we get to that point in terms of gettering science, as I call it. 

Later on it should be particularly a help for the device maker to get the 

best device possible. 

SIRTL: If you want to getter wafers downstream in the process it has to be at 

low temperature, unless you know some miraculous way of making the atoms 

move faster at low temperature. The problem then is to make a junction 

device. How do you getter downstream without disturbing the device? 

WOLF: One thing bothered me a little on Schwuttke's comment, which is basically a very desirable one, but it's somewhat a chicken-and-the-egg 

problem. The solar-cell industry is a very small industry in comparison 

with the integrated-circuit industry, and probably even the power-devices 

industry. So can we even move the material manufacturers at this point. 

492 

, 

" 17 

t~ 

l 

1 
QUESTION: I don't think you have to move it at the present point, but what 

does prevent you from Blttlns down and drawlns up the specs you would 

like to see? That's the first step, and if we do we will move the guy 

who is going to make it. If you have the specs, maybe you'll find th~ 

guy who wants to do it. 

SCHMIDT: I would like to agree, and perhaps elaborate a little bit on 

Schwartz's comments. I think it is very encouraging that we have 

computer codes that are in agreement in many cases with the perfor~ance 

from the terminals of existing devices. That's a real plus, and the 

codes have been very useful for a number of years, in lending the kind of 

understanding that has helped more people drive the efficiency up. On 

the other hand, I recall that in 1978 Paul Stella gave a paper at the 

Photovoltaics Conference in which he reported a 16+~ AMO cell, which I'm 

fairly sure was an 18~ AMI cell. That was a very expensive cell. The 

point that I am going to make is that we have also heard some talks, 

particularly earlier in this Research Forum, concerning 25~ cells, which 

is sort of No Man's Land. They are pretty easily designed on paper and 

with computer codes. The problem is that the physical parameters are 

probably not available to enable those designs to be achieved in the 

laboratory. Assuming some good lifetime in the base, there is probably 

something that will creep in when you do some heavy doping things. 

Secondly, I would guess there are probably a large number of ways of 

getting high-efficiency cells. I'm now going to say maybe 20~ in a year 

or two and I think we have to pay a lot of attention to the multitude of 

different ways. because not all of those will be easily manufacturable. 

There the device codes are going to come in very handy as we explore 

different ways, for example, of emitter profiling, of contacting, and 

other things that will lend themselves to cells of high efficiency that 

can be manufactured in large volume as economically as possible. Which 

also brings up the utilization of computer codes for the purposes of 

monitoring the manufacturing process by enabling a very sophisticated and 

detailed interpretation of experiments that are going on in fabrication 

processing, as well as those after the cell has been made. At the same 

time I would agree with Dick that the codes are working very well and 

that we have some physics in there that will predict existing 18~ cells, 

I think that there is an awful lot more work that needs to be done in 

fundamental understanding, particularly at the physics end of the 

spectrum. I'm not speaking as a software person, but I think Dick's 

comment last night was that if we can get the physics understood, then 

the software .,ill probably take care of itself, because there are some 

capable people around doing the software. I'm interested in trying to 

work on some ,of these fundamental problems, but I think that it·s very 

urgent that we think of not just achieving a 20~ cell but of achieving a 

20+~ cell in a multitude of different ways so that we can evolve one or 

two or three di~ferent ways of manufacturing such cells in large volume 

and fairly inexpunslvely, and keeping the production line up with 

appropriate monitorhlg. So this is a much larger view of the computer 

codes than many people think of them. 

DAUD: I guess Fred touched a little bit on what I was going to say of going 

beyond 20~, and I wanted to ask a question: if one wanted to go beyond 

20~, what does the panel or audience thin~ is the prime issue? Like do 

493 
we have to So for different design of contacts or different design of the 

cell itself, go to plasma on cell or whatever? What would be the comments 

of the chairmen, as well as anyone from the audience? 

QUESTION: While everybody is thinking of a good answer, I would like to make 

one remark. Of course, I don't actually make any of these cells, so I am 

just an outsider and therefore don't know quite what's going on. But I 

would like to concentrate on the notion of a defect because that really 

seems to be badly understood. First of all you start with the original 

material. ~hat are the defects in there? You then have processing; 

thermal defects are produced, and then the materials cool down and some 

of these defects are annihilated and others survive and get frozen into 

the material. This whole area seems to be where metallurgists and 

engineers and physicists could really usefully work together. But it is 

an area of considerable ignorance. In one of the talks somebody put up 

energy levels, and how they changed with time. . . • It seems to me 

that if you want to improve these solar cells and get long lifetimes and 

get rid of these defects, one really has to be very scientific and 

extremely careful about each of these steps that introduce new defects or 

get rid of others. I am now including in my remarks what sirtl said 

about gettering, because that's also got defects, and how to get rid of 

them. So it seems to me that there we have an area where I feel we are 

at a very early stage and really surprisingly ignorant. All these 

defects contribute to recombination, and so to understand that, the 

defect really comes first. Then we have to understand the recombination 

mechanisms. There is a lot of work to be done. 

QUESTION: You know that for so-called good cells, that make say 18~, or for 

that matter 15~, l6~ cells, we really don't have any technique of determining what defects are in them. Nothing we have on hand is sensitive 

enough, absolutely nothing electrically. You can detect only 17~, l8~ 

cells. Clean as anything, no deep levels of any kind. With the kind of 

techniques we have on hand, we have to find some methods that can determine defects in those good cells we are producing now. If anybody has 

any ideas or anything they are working on, I would like to hear about it. 

SCHWUTTKE: Obviously I agree lOO~ what was said about the tremendous need of 

such detailed characterization before and after processing, and its final 

correlation with device performance. And I'm in this field now for 20 

years, and all I have learned is that it is tremendously complex and 

extremely expensive. And that the instrumentation that has been d'eveloped 

over the last 20 years is so extremely sophisticated that it is very 

difficult for a smaller laboratory to have access to such instrumentation. And then, the major problem is to get people interested in working 

in this field, because you cannot get very famous by doing this type of 

work. There is no fast reward, only a lot of sweat and long hours, and 

these guys are tough to find. Nevertheless, I think there are dedicated 

people who are working exactly along these lines and there may not be 

enough around, so maybe we can motivate some more to assist us in solving 

these extremely complex problems. You know, material science has always 

bad the short end of the stick, compared with device science. The money 

is made on the device side, not on the material side. 

494 
l 

QUESTION: I think I would say talking about good-quality silicon, float-zone 

and that sort of thing, you cannot specify anything but electrical stuff, 

you can specify oxygen, carbon, and then what do you specify is the diffusion length, the lifetime, the resistivity uniformity, things that we 

can measure. Now, how come this thing has a 100 microsecond lifetime? I 

want a millisecond lifetime. There is no good way of measuring what's 

the cause of it, so a crystal grower does not know what to do. 

QUESTION: Let me respond to that. Usually the crystal grower is not expert 

in those ways to have the ability to guess, out of the periodic table, 

these things that will be likely to be in my puller and would be affecting 

his material that way. Usually he doesn't know that. Do we know what we 

are gettering? If we knew what we were gettering we could watch out for 

it in the reactors, in the pullers, it seems to me somebody ought to pin 

down what element or elements it is we are gettering. 

PRINCE: I'm going to let our chairman close out our session. 

KACHARE: One thing for sure, all of us agree that in the last two and half 

days, we learned a lot. I believe that with this High-Efficiency Research 

Forum we are really entering into a new technology. I think most of us 

also accept the fact that basic material requirements need to be defined. 

When we say that, I believe that gettering became a major issue also, and 

some element of ~esearch is needed there. But if I can summarize that in 

one sentence, basically we need to understand the loss mechanisms -- not 

only in the bulk; we also should know what are the defects, what are the 

chemical impurities, what are the dislocations, and also the loss mechanisms between silicon surface and metal, silicon surface·-passivant interfaces. To understand these loss mechanisms, I believe that we have to 

have reliable measurement techniques. I think Lindholm said "let us use 

the effecti'fe parameters," but I have a lot of reservation about them 

because effective parameters may mislead us. So, basically, I am saying 

that to understand these loss mechanisms we have to have reliable measurement techniques. Cell fabrication research also needs additional efforts, 

whether we should use ion implantation, whether we should use diffusion, 

or whether we should have shallow junctions, whether we have this kind of 

emitter, whether we should have high or low junction -- all these issues 

are again for research. Furthermore, I think modeling is very useful and 

I feel that we just started using it. We have a tool now, I believe. 

It's not yet a perfect tool, but at least gives some kind of information. 

We can use it to refine our processing. refine our device design. As of 

today, float-zone material is a research material and not final material 

for our 15~ module, $90/m2 kind of requirement for DOE goals. But that 

material is still useful because by using it, it is at least possible to 

make a 2~ cell, so we are at least establishing some upper limit or a 

proof-·of-concept. Can we bring low-cost sheet materials or any other 

cast material by gettering or by some other techniques to the level of 

float-zone? I have serious doubts about that, but at least we know that 

if you have some kind of material of excellent quality, it is possible to 

make 20~ cells. I believe that measurement techniques are needed to 

-enhance our basic understanding of, for example, heavy doping effects and 

Auger recombination coefficients. I had a lengthy discussion with Swanson 

from Stanford about the Auger recombination coefficients measurement that 

495 
has been made in Germany. We are using those particular numbers as if 

they are reliable numbers. Many people are now questioning those numbers. 

So to understand the heavy doping effects. to understand device performance. to understand loss mechanisms. we need to have reliable measurement 

techniques. In short. I have tried my best to summarize two areas for 

obtaining high-efficiency cells: one is from the material end. and one 

from the design and device processing end -- and then bringing the 

material end and the device end together to achieve the 20~ solar cell. 

at least in the lab. I think it is possible. 

On behalf of DOE. SERI. FSA and the organizing committee. I want to thank 

all of you. I hope the conference was useful for all of us. 

496