DRL No. 198 

DRD Line Item No. SE-8 

T- --__ __- 

 

DOE/JPL-956525-85/05 

9950-1181 

77 ~ -~ 

DOE/JPL-956525-85/8 

Di st ri buti on Category UC-63 

PAr L 4u 

HEAVY DOPING EFFECTS IN HIGH EFFICIENCY SILICON SOLAR CELLS Q07 

Annual Report 

For Period Covering 

June 24, 1984 - June 23, 1985 

By: 

F. A. Lindholm and A. Neugroschel 

UNIVERSITY OF FLORIDA 

Department of Electrical Engineering 

Gainesville, FL 32611 

JPL Contract No. 956525 

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

energy and forms part of the Solar Photovoltaic Conversion Program to initiate 

a major effort toward the development of low-cost solar arrays. This work was 

performed for the Jet Propulsion Laboratory, California Institute of 

Techno1 ogy , by agreement between NASA and DOE. 

(NASA-CH-173954) HEAVY DOFING EFFECTS IN Ne7-13853 HIGH EFFICIENCY SILICCB SCLA6 CELLIS Annual 

Report, 24 Jun 19E4 - 23 Jun, 15E5 [Florida 

uaiv,) 109 F CSCL ?OA Unclas 

G3/44 43631 
This work was performed for the Jet Propulsion 

Laboratory, California Institute of Techno1 ogy, and was 

sponsored by the U. S. Department of Energy through an 

agreement with the National Aeronautic and Space 

Administration. 

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 speci f ic commerci a1 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. 
TABLE OF CONTENTS 

SUMMARY (EXTENDED ABSTRACT) .................................... .i v 

CHAPTER 

ONE INTRODUCTION .....,...,,,................~0~..~~........~.......1-1 

TWO HEAVILY DOPED POLYSILICON-CONTACT SOLAR CELLS..................2-1 

THREE EXPERIMENTAL STUDY OF THE MINORITY CARRIER TRANSPORT AT THE 

POLYSILICON-MONOSILICON INTERFACE ........ ......................3-1 

FOUR SOLUTION OF THE CONTINUITY EQUATION IN PLANAR SYMMETRY CASES 

AND ASSESSMENT OF PHOTOLUMINESCENCE DECAY......................4-1 

FIVE TRAP CONTROLLED MINORITY-CARRIER MOBILITY IN HEAVILY DOPED 

SILICON .....e.00..0.0..0.0...0...e...00..~~~0..0~0.e0.0e~000e~05-1 

SIX DETAILED INTERPRETATION OF PHOTOCONDUCTIVITY DECAY 

RESPONSE FOR LIFETIME OETERMINATION............................6-1 

GENERALIZED RECIPROCITY THEOREM FOR SEMICONDUCTOR DEVICES......7-1 

MINORITY-CARRIER DIFFUSION COEFFICIENTS AND MOBILITIES 

IN SILICON ........,........oo......o...8-1 

SEVEN 

EIGHT 

NINE DISCUSSION AND RECOMMENDATION ................~~.~~..~.~~.~~..~~9-1 

iii 
SUMMARY (EXTENDED ABSTRACT) 

We report the first use of a (silicon)/(heavily doped polysilicon)/ 

(metal) structure to replace the conventional high-low junction (or backsurface-field, BSF) structure of silicon solar cells. 

back-ohmic-contact control samples, the polysil icon-back solar cells show 

improvements in red spectral response and open-circuit voltage. Measurement 

reveals that a decrease in effective surface recombination velocity S is 

responsible for this improvement. Decreased S results for n-type (Si :As) 

polysilicon, consistent with past findings for bipolar transistors, and for 

p-type (Si:B) polysilicon, reported here for the first time. 

present polysilicon-back solar cells are far from optimal, the results suggest 

a new class of designs for high efficiency silicon solar cells. 

technical reasons are advanced to support this view. 

Compared with RSF and 

. 

Though the 

Detailed 

We present the results of an experimental study designed to explore both 

qual i tatively and quantitatively the mechani sm of the improved current gain in 

bipolar transistors with polysil icon emitter contact. 

were deposited and annealed at di fferent condi ti qns . 

Polysilicon contacts 

The electrical 

properties were measured using p/n junction test structures that are much more 

sensitive to the contact properties than are bipolar transistors. A simple 

phenomenological model was used to correlate the structural properties with 

electrical measurements. Possible transport mechanisms are examined and 

conjectures are made about'-upper bounds on transport parameters in the 

principle regions of the devices. The main conclusion of this study is that 

the minority carrier transport in the polycrystalline silicon is dominated by 

a highly disordered layer at the Polysil icon-monosi 1 icon interface 

characterized by very low minority-carrier mobility. 

recombination velocity at the n+ polysilicon - n+ monosilicon interface was 

The effective 

iv 
found to be a strong function of fabrication conditions. 

that the recombination velocity can be much smaller than lo4 cm/sec. 

The results indicate 

The decay of excess carriers induced in a semiconductor sample by a laser 

pulse is studied. 

dependence of the hole-electron generation rate provoked by the laser beam. 

The effect of surface recombination can be minimized by waiting until the 

response drops to about one-percent of its initial value. The accuracy of 

photoluminescence decay measurements of Auger lifetime is examined in view of 

this and other criteria developed here. 

The decay rate is proved to be independent of the spatial 

The activation behavior of the minority-carrier mobility and diffusivity 

in heavily doped (- lo2' c13'~) Si (Si:As) is investigated in the temperature 

range, 20 K to 350 K. Experimental results indicate that hole transitions 

between the valence band and localized shallow states give rise to the 

observed behavior. The activation energy is about 10 meV, which suggests that 

the localized states originate from band tails but does not rule out trapping 

at boron atoms in the compensated n+ region. 

Photoconductive decay provides a method for estimating recombination 

lifetime in semiconductors. It often exhibits a single characteristic time. 

For samples having 1 arge recombination-center densities, previous experiments 

indicate that this characteristic time can considerably exceed the steadystate lifetime. 

results. The explanation involves the effect on the overall photoconductive 

decay of the multiple characteristic times that describe trapping and 

We present apparently the first explanation of these 

recombination through <- bound states for variations of the electrochemical 

potentials that are small relative to the thermal voltage. 

A reciprocity theorem is presented that relates the short circuit current 

of a device, induced by a carrier generation source, to the minority carrier 

V 
Fermi level in the dark. The basic relation is general under low injection. 

It holds for three dimensional devices with position dependent parameters 

(energy gap, electron affinity, mobility, etc.), and for transient or steadystate conditions. This theorem allows calculation of the internal quantum 

efficiency of a solar cell by using the analysis of the device in the dark. 

Other applications could involve measurements of various device parameters, 

interfacial surface recombination velocity at a polycrystal 1 ine si1 icon 

emitter contact, for example, by using steady-state or transient photon or 

mass- pa rt i cl e rad i at i on. 

A new method for accurate measurement of minori ty-carrier diffusion 

coefficients in silicon is described. The method is based on a direct 

measurement of the minority-carrier transit time through a narrow region of 

the p-n junction diode. The minority-carrier mobility is obtained from the 

diffusion coefficient using the Einstein relation. The method is demonstrated 

on low-doped n- and -p-type Si (dopings - ~m'~) and is compared with the 

literature data for the majority-carrier mobilities. The results show that in 

low-doped Si the electron minority- and -majority-carrier mobilities are 

comparable, but the hole minority-carrier mobility is significantly higher 

(- 30%) than the corresponding majority-carrier value. 

earl i er data of Dzi ewior and Si 1 ber . The results confirm 
I 

CHAPTER ONE 

INTRODUCTION 

This annual report descri bes techni cal f i ndi ngs resul ti ng from JPL 

contract 956525 for the period June 24, 1984 to June 23, 1985. 

The purpose of this contract is to assess the status of critical 

parameters describing heavily doped si 1 icon , to integrate this assessment into 

an effort aiming toward determination of these parameters and their 

incorporation in silicon solar cell design, and to develop associated 

measurement methods. 

doped polysilicon, particularly to its use as a quasi-blocking contact at 

The interest in heavily doped silicon extends to heavily 

surf aces. 

doped silicon, which typically adjoins heavily doped layers in silicon solar 

cells. 

It extends a1 so to measurement methods designed to explore di 1 utely 

Professors Fred A. Lindholm and Arnost Neugroschel of the Electrical 

Engineering Department of the University of F1 orida serve as principal 

investigators for this contract. Several graduate students have participated 

significantly in the conduct of the research: 

K. Misiakos, and 3. S. Park. 

M. Arienzo, B. Y. Hwang, Y. Komen, R. Issacson, M. Spitzer and Professors P. 

T. Landsberg and C. T. Sah. 

T. W. Jung, 3. J. Liou, 

Other collaborators have included Peter Iles, 

In the brief description to follow presently concerning the content of 

the chapters of this report, some of these people named above are indicated, 

through the appearance of their initials, as principal contributors to the 

chapter bei ng descri bed . Prior to outlining the content of each chapter, we list immediately below 

the journal papers (two invited) and the conference papers (including one 

invited plenary lecture) that have resulted from this contract research. 

those papers for the present reporting period, June 1984 to June 1985, are 

Only 

1-1 
1 isted. 

period. 

We include both papers pub1 i shed and papers accepted during thi s 

PAPERS SUPPORTED BY CONTRACT e56525 

F. .A. Lindholm and 3. J. Liou, "Improved determination of lifetime and surface 

recombination velocity by observing transient voltages ,'I 18th IEEE 

Photovoltaic Speci a1 i sts Conference, October 1985 (invited plenary 1 ecture to 

be presented). 

F. A. Lindholm, A. Neugroschel, M. Arienzo, and P. A. Iles, "Front and back 

polysil icon-contacted solar cell s ,'I 18th IEEE Photovoltaic Special i sts 

Conference, October 1985 . K. Misiakos and F. A. Lindholm, "Generalized reciprocity theorem for 

semiconductor devices," J. Appl . Phys ., tentativeiy scheduled for October 1, 

1985. 

K. Misiakos and F. A. Lindholm, "Toward a systematic design theory for silicon 

sol ar cell s using optimization techni ques'l,- Sol ar Cell s, Oct . 1985 (invited 

paper) 

A. Neugroschel, F. A. Lindholm, and C. T. Sah, "Trap controlled minoritycarrier mobility in heavily doped silicon," Solar Cells, to appear in 

Sept. 1985. 

- 

A. Neugroschel , "Minority-carrier diffusion coefficients and mobilities in 

silicon," IEEE Electron Device Letters, vol. EDL-6, pp. 425-427, August 1985. 

K. Misiakos, F. A. Lindholm, and A. Neugroschel, "Solution of the continuity 

equation in planar symetry cases and assessment of photo1 uminescence decay," 

J. Applied Physics, vol . 58, pp. 1647-1650, August 1985. 

F. A. Lindholm, A. Neugroschel, M. Arienzo, and P. A. Iles, "Heavily doped 

polysi 1 icon contact sol ar cell s ,'I IEEE €1 ectron Device Letters, vol . EDL-6, 

pp. 363-365, July 1985. 

P. T. Landsberg, A. Neugroschel, F. A. Lindholm, and C. T. Sah, "A model for 

band-gap shrinkage in semiconductors with application to silicon," Physica 

Status Solidi (a), to be published July 1985. 

F. A. Lindholm, "Uncertainties about the physical electronics of n+ and D+ 

silicon, with applications for solar cells", Solar Cells, vol. 12, pp. 131- 

140, June-July 1984 (invited paper). 

B. Y. hang and F. A. Lindholm, "Detailed interpretation of photoconductivity 

decay response for lifetime determination," Solar Cells, vol. 14, No. 2, 

pp. 187-190, May 1985. 

1-2 
A. Neugroschel , M. Arienzo, Y. Komen, and R. D. Isaac, "Experimental study of 

the minority carrier transport at the polysilicon monosilicon interface," IEEE 

Trans. Electron Devices , vol . ED-32, pp. 807-816, Apri 1 . 

0. von Roos and F. A. Lindholm, "Steady state currents in semiconductor 

filaments or grains in case of large surface recombination velocity on lateral 

surfaces," J. Appl. Phys., vol. 57, pp. 415-417, January 1985. 

- 

This report proceeds as follows. Chapter Two (FL, AN, MA, PI) describes 

the first use of polycrystalline silicon as a passivant for the surfaces of 

silicon solar cells. Chapter Three (AN, MA, YK, RI) reports experimental 

findings about the mechanisms underlying this passivation--that is, this 

reduction of surface recombinati-on- velocity. 

about 10%m3, we inferred that the value of this velocity could be as small 

For doping concentrations of 

as 15 cm/s for small-area devices. Chapter Four (KM, FL, AN) provides a 

detailed mathematical assessment of the Auger-impact rate coefficients 

determined by the photo1 umi nescent decay method (Dzi ewi or and Schmi d , 1977). 

We conclude that in principle the method can yield accurate values despite the 

presence of large surface recombination velocity and despite areal 

inhomogeneity of the incident laser beam. 

experimental ly the credi bi 1 i ty of the model for Val ues of the mi nori ty-carrier 

mobility and diffusivity that are much smaller than the values of the majority 

carrier counterparts, at least for doping concentrations substantively above 

1018/cm3. 

other shallow bound states associated with the minority-carrier band 

(Neugroschel and Lindholm, 1993). The results support this model. 

Chapter Six (BH, FL) provides a detailed interpretation of the photoconductive 

decay method for examining volume or bulk lifetime in silicon wafers. 

Chapter Seven (KM, FL) puts forward a generalized reciprocity theorem for 

semi conductor devices. This theorem a1 1 ows cal cul ati on of the i nternal 

Chapter Five (AN, FL, CS) examines 

This model involved trapping of minority carrier at bandtail or 

1-3 
quantum efficiency of a solar cell by using the analysis of the device in the 

dark. Chapter Eight (AN) sets forth experimental findings concerning the 

measurements of minority-carrier mobility and diffusion coefficient in 

dilutely doped silicon (about 1015/cm3). The results show that the hole 

minority-carrier mobility is 30% higher than the majority-carrier value. 

Design considerations immediately follow from these findings. 

briefly discusses the results of this annual report. 

Chapter Nine 

1-4 
CHAPTER TU0 

HEAVILY DOPED WLYSILICON-CONTACT SOLAR CELLS 

INTRODUCTION 

Highly conducting polysil icon contacts to crystal1 ine si1 icon are widely 

used in bipolar integrated circuits [I]. Among other properties, these 

heterojunctions reduce recombination current by forming quasi-blocking 

contacts C23. 

Our purpose is to describe experimental results and their implications 

deriving from the first use of such contacts in silicon solar cells. 

Specifically, in this paper we report the results of introducing such contacts 

at the back surface. The resulting solar cells show large improvements in red 

spectral response RSR and moderate improvements in open-circuit voltage Voc 

when compared with control cells made with the conventional back-surface-field 

(RSF) structure or with back-ohmic contact (BOC) structures. To assess the 

origin of these improvements, we measure the effective recombination velocity 

S of minority carriers in the monocrystalline silicon as they enter the 

polysilicon layer. This determines that S(polysi1icon back) < S(RSF 

controls), and we interpret this lowering of the recombination velocity to be 

the mechanism responsible for the improvement in Voc and RSR. 

and controls described here have n-type and p-type base regions; the decrease 

The solar cells 

in S resulting from p-type polysilicon (Si:B) is reported here for the first 

time. 

FABRICATION 

i- The substrate resistivity was 2 - 0.5 n-cm for both the p-type and n-type 

samples. The p-type substrates were chemically polished on the back side; the 

n-type substrates were polished chemically-mechanically. About 2000 A thick 

layers of n+ and p+ polysilicon was deposited (in-situ doped) at 670°C in an 
atomospheric pressure CVD reactor. 

875°C for about 12 min., and the p+-emitter (Si:B) was diffused at 9W0C for 

30 min. 

protected the other side of the sample. 

polysilicon into the base occuring during the emitter diffusion creates a 

The n+-emi tter (Si :P) was diffused at 

During the polysilicon deposition and the emitter diffusion, CVU-Si02 

Out-diffusion from the doped 

crystalline low-high junction of thickness (200 A [2]. The thinness of the 

resulting n+ (or p') layer at the back suggests that negligible recombination 

occurs in its volume. 

The conventional Al-paste alloying technique formed the BSF region to a 

depth of about 3 to 5 p for the p-base BSF controls. Phosphorous diffusion 

formed a one-micron thick BSF region for the n-base BSF controls. These 

n-base controls and back-ohmic-contact controls had an ohmic contact (Ti + Pd 

+ Ag) deposited and then annealed on the back surface. The p-base samples had 

a thin layer of A1 under the Ti + Pd + Ay, and the heating was below the 

Al-alloy temperature (- 4UOo C) . 

MEASUREMENTS AHD EXPERIMENTAL DATA 

We made measurements to compare the merit of the polysi 1 icon-back-contact 

structure to that of the BSF and BOC controls. Our main object was to explore 

the influence of the back surface recombination velocity, which enters the 

boundary-Val ue problem descri bi ng the solar cell s . To obtain the boundary-value problem, we follow Shockley in thinking of 

the device as comprising two quasi-neutral regions separated by a junction 

space-charge region [3]. 

surface of tne quasi-neutral base. If we define the surface as the interface 

between the silicon and the polysilicon Contact, characterized by S, we get a 

simple model in which the polysi \icon recombination and transport mechanisms 

We focus on recombination in the volume and at the 

2-2 
are imbedded in S. 

the 1 ow-hi gh (p/p+ or n/n+) crystal 1 i ne junction begi ns. Then S characteri zes 

recombination occuring in the transition and heavily doped regions. 

usual carrier density and voltage re1 ati ons together with the continuity 

equation for minority carriers, completes the boundary-value problem.) 

For a BSF cell, we define the surface as that plane where 

(The 

Using an AM0 spectrum, we measured the solar-cell parameters. 

the one most closely linked to S is the red spectral response KSK, 

(A > 6000 A). 

having a polysilicon contact show significant increases in Voc and RSR over 

those having an ohmic back contact or an aluminum-alloy back surface field. 

Note, however, that the alloy BSF controls showed no improvement compared with 

the BOC controls in Voc and only a slight increase in RSR. 

that the alloy process failed to yield an effective back-surface field. It is 

common experience that the alloy process does not consistently yield good BSF 

regions for p as low as 2 8-cm, although it is reliable for higher base, 

resistivities. For the cells having an n-type base, both the polysilicon 

devices and the BSF controls, formed by P diffusion, showed significant and 

similar increases in RSR when compared with the response of the BOC 

control s . 

Of these 

The data appear in Table 1. For a p-type base, the cells 

This indicates 

To assess whether one can attribute these results to smaller S, we 

measured S and diffusion lenyth L using an MUS-switch version of the method of 

Ref. [4]. 

blocking contact that is markedly superior to the low-high junction of the 8SF 

controls (Table 1). 

In these experiments, the si licon-polysilicon junction provides a 

2-3 

~- 

. 
UISCUSSION AN0 EXTENSIONS 

The most important columns in Table 1 pertain to the red spectral 

response and to S, which emphasize the improvements deriving from the 

polysilicon/silicon back contact. The improvement in Voc is less strikiny, 

partly because Voc depends not only on S but also on the collective effects of 

L, shunt conductance and recombination current in the junction space-charge 

region and in the quasi -neutral eini tter. 

The polysilicon/silicon junction is also superior in other respects. 

Process control for BSF devices is critical for good performance. This is 

particularly true for the A1 alloy process commonly used to fabricate a p-type 

BSF region. As noted, this process does not reliably form good BSF regions 

< for p - 2 h2-cm. 

temperatures required may degrade lifetime and the low-high junction may be 

shifted by subsequent thermal processing such as that used to form the p/n 

junction. Both diffusion and alloy processing consumes part of the substrate, 

which may pose difficulties for thin solar cells. 

polysi 1 i con-back structure derives f roin a non-cri ti cal deposition process at 

low temperature [Z]; the post-deposition heat treatment also is not 

critical [2] . substrate. It can be controlled precisely and is reliable, as employment in 

bi pol ar i ntegrated-ci rcui t techno1 oyy has shown . 

For BSF regions formed by solid-state diffusion, the hiyh 

In contrast the 

Polysi 1 icon back processing consumes essenti a1 ly none of the 

Consider now extensi0n.s of the present design. First, consider low-p 

substrates (0.5 8-cm < p < 0.1 8-cm, corresponding to doping concentrations 

- 1017 cm-3), which reduce base-region volume recombination, thus tending to 

increase Voc and efficiency T). 

substrates have never been made. 

injection conditions (5) and for p > 0.5 G-cm approximately. 

However, effective USF regions on low-p 

In BSF solar cells, Sp = p-' for lowFor 

2-4 
p < 0.5 Q-cm,the potential barrier V(BSF) between the lowhigh-doped sides of the BSF junction becomes ineffective: V(BSF) = 

(kT/e)l~g[N(l~~)/N~ff] < 2.3(kT/e) where N(1ow) is the doping concentration on 

the low-doped side and Neff - 10l8 cm-3 is the effective doping concentration 

on the high-doped side, corrected for band-gap shrinkage AEG. 

Ref. 5, 

carrier diffusivity D and diffusion length L pertain to the highly doped 

side. 

that Smax(poly junction) << Smax(BSF) . relatively low value of SmaX(poly junction) are still debated in the 

literature. The polysilicon of Ref. 2 and that for our devices of Table 1 was 

~m-~) and 

Thus from 

S = (D/L) [N(low)/Neff(high)] + D/L = S(max), where the minorityFor a polysi 1 icon-contacted solar cell, recent experiments [2] show 

The mechanisms underlying the 

deposited without an intentional interfacial oxide, and Ref. 2 advances the 

view that the low value of S(max) derives from extremely low values of D in 

the highly disordered interfacial region. 

Thus we anticipate that polysilicon deposition can give low-S contacts on 

base regions having low resistivities (- 0.1 n-cm). From the results of 

Ref. 2, we anticipate S < 1000 cm/s. 

Attaining high efficiency (TI) depends on reducing S at the front surface 

as well. Thermal oxides have proved effective over the surface, exclusive of 

that portion where ohmic contacts exist. Even though ohmic contacts 

constitute only 5% or less of the front surface, one should note that the 

increase in emitter recombination current caused by areal inhomogeneity 

greatly exceeds that calculated by consideration of the areal ratio of low-S 

to high-S regions [6,7]. To avoid the resultant drop in TI, Green et al. [8] 

have used thin tunneling oxides between the silicon and the metal. 

Substitution of heavi ly doped polysi 1 icon for the tunneling oxides may provide 

a better contacting structure with higher yield and longer life. 

2-5 
Sah has recently proposed detailed practical designs for control ling the 

recombination losses at the front, or emitter, surface [9]-[10]. 

proposed using thin and doped polysilicon layers between the metal and the 

heavily doped silicon surface of the emitter while using a thermal oxide over 

the emitter area not shadowed by metal. Employing the data of Ref. 2, he has 

calculated a practical maximum efficiency of above 23% provided by the low 

recombination losses at the front and back surfaces and assumed volume 

recombination only by Auger and radiative processes. 

He has 

Thus, we suggest elements of the following new class of silicon solar 

cell designs: 1) Use thin (= 150 pin) base regions of resistivity - 0.1 62-cm 

contacted on the back by heavily doped polysilicon; 2) Interleave the front 

surface with oxide and a polysiliconlmetal system; 3) Use either an n-type or 

p-type silicon for the base region. 

As suggested by the work of Sah quoted above, we expect that these solar 

cells could have very high conversion efficiencies. 

together with the somewhat related efforts using SIPOS junctions to reduce 

surface recombination [ll], constitute recent significant departures from 

conventional silicon solar cell designs. 

The present work, 

ACK NOM LEDGEME NTS 

The portion of this work done at the University of Florida was supported 

by the Jet Propulsion Laboratory (Contract 956525) and the National Science 

Foundation (Grant ECS-8203091). We thank T. W. Jung for performing the SCCO 

measurements. 

2-6 
REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

T. H. Ning and R. I>. Isaac, "Effect of emitter contact on current gain 

of si 1 icon bi pol ar devi ces ,'I IEEE Trans. Electron Devi ces , ED-27 -' pp. 2051-2055, NOVO 1980. 

A. Neugroschel, M. Arienzo, Y. Komen, and R. 0. Isaac, "Experimental 

study of the mi nori ty-carrier transport at the polysi 1 i con-monosi 1 i con 

interface," IEEE Trans. Electron Devices, ED-32, pp. 807-816. 

W. Shockley, "The theory of p-n junctions in semiconductors and p-n 

junction transistors," Bell Syst. Techn, J., vol. 28, pp. 435-489, 

July 1949. 

T. W. Jung, F. A. Lindholm, and A. Neugroschel , "Unifying view of 

transient responses for determining 1 ifetime and surface recombination 

velocity in silicon BSF cells, with application to experimental shortcircuit current decay," Special Issue on Photovoltaics of the IEEE 

Trans. Electron Devices, E, 0-31 pp. 588-595, May 1984. 

J. R. Hauser and P. M. Dunbar, "Minority carriers reflecting properties 

of semi conductor hi gh-1 ow junctions ,I' Sol i d-State El ectron., vol . 18, 

I>P. 715-716, July, 1975. 

F. A. Lindholm, J. A. Mayer, 3. H. Davis, and J. I. Arreola, 

"Degradation of solar cell performance by areal i nhomogenei ly ," Sol idState Electronics, - 23, pp. 967-973, Sept. 1981. 

R. J. Schwartz, J. L. Gray, G. 6. Turner, 0. Kanani, and H. Ullal, 

"Numerical modeling of p-i-n hydrogenated thin film silicon solar 

cells," Proc. of 17th Photovoltaic Specialists Conf., pp. 369-373, 

May 1984. 

M. A. Green, A. W. Blakers, J. Shi, E. M. Keller, and S. R. Wenham, 

"High efficiency silicon solar cells," IEE Trans. Electron Devices, 

ED-31, pp. 679-683, May 1984. 

C. Tang Sah, "Barriers to achieving high efficiency," Proceedings of the 

23rd Project Integration Meeting, March 14-15, 1984, Progress Report 23, 

Jet Propu'l sion Laboratory, pp. 123-130, JPL Pub1 i cation 84-47. 

C. Tang Sah, "High efficiency crystalline silicon solar cells," Second 

technical report, DOE/JPL-056289-84-1. 

E. Yablonovitch, R. M. Swanson and Y. H. Kwark, ''An n-SIPOS: p-SIPOS 

homojunction and a SIPUS-Si-SIPOS double heterostructure," 17th IEEE 

Photovol tai c Speci a1 i sts Conf . , pp. 1146-1 148, flay 1984 [ 84CH2019-8) . 

2-7 
TABLE 1 

Summary of measured parameters at 28" C, (no AR coating). The cells have 

area A = 4 cm2 and thickness of about 210 f 10 pm except for cell 2N which was 

330 thick. The results are the average values from 10-20 cells. 

1P P ohmic 513 63 310-350 

2P P BSF 51 4 64 310-350 4 .2x104-5x104 

5P P poly-Si 583 

BSF 

67 .7 310-350 1100-1500 

2-8 
CHAPTER THREE 

EXPERIMENTAL STUDY OF THE MINORITY CARRIER TRANSPORT AT 

THE POLYSILICON-MONOSILICON INTERFACE 

I. INTRODUCTION 

It was demonstrated [l-31 that the common-emitter current gain of bipolar 

transistors can be improved by replacing the emitter metal contact by a highly 

doped polysilicon layer. A number of works, both theoretical and 

experimental, investigating this effect, were published [l-81. In all these 

studies, the analysis was done on the actual emitter structure of the bipolar 

transistor consisting of a thin (- 2000 A) heavily-doped monocrystalline 

emi tter region contacted by a heavi ly-doped polysi 1 icon 1 ayer about 2000 A 

thick. The analysis of such a structure is difficult due to uncertainties in 

the parameters of both the monosilicon and polysilicon bulks and a poor 

understanding of the interface between the polysi licon and the single crystal 

silicon layer. These uncertainties are further augmented by the presence of 

the grain boundaries in the polysil i con. Thus , numerous assumptions are 

requi red to establish a mi nority-carrier transport model in the above system 

[ 4-81. 

The region which is most difficult to characterize is the polysiliconmonosilicon interface. This region is very sensitive to the fabrication 

conditions and to the surface treatment before the CVD process of the 

polysilicon deposition [2,7]. 

concentration was observed [7,91 as a result of the donor dopant seyreyat on 

at the interface. The interface may also act as a natural sink for deep- eve1 

impurities and cause precipitation of interstitial oxyyen froin the bulk. The 

properties of the interface are very Strongly influenced by a presence of a 

very thin insulating interfacial layer created by oxidizing silicon before the 

polysilicion deposition. This can be achieved by thermal oxidation [Z] or by 

a cherni cal treatment [7]. 

A peak in the arsenic and phosphorus 

3-1 
These and other variables make the evaluation of the relative importance 

of the polysilicon bulk and the interface very difficult, both theoretically 

and experimentally. De Graaf and de Groot [Z] investigated the current gain 

of the n'/p/n transistors with an intentionally grown oxide layer at the 

polysi licon-monosilicon interface. They suyyested that the current gain 

enhancement is controlled by the tunneling mechanism through the oxide 

layer. Ning and Isaac [3] have shown that, for the n+/p/n transistors with a 

polysilicon emitter contact with no intentional oxide layer at the 

polysilicon-monosilicon interface, the minority hole base current becomes a 

function of polysilicon thickness if the film thickness is less than about 

500 A. 

hole transport in the polysilcon film within about 500 A of the interface. 

The devices used in [3] with different thicknesses of the polysilicon film had 

identical polysilicon-monosilicon interfaces. 

This indicates that the current gain enhancement is determined by the 

In the present work we have examined the roles of the polysiliconmonosilicon interface and of the polysi licon bulk in much more detail than has 

been done previously. 

with identical interface properties, while varying drastically the polysilicon 

bulk properties. This is achieved by usiny a bilayer Structure of polysilicon 

films [9J, described in detail in the next section. 

different from that taken by other researchers C2,7J who varied the interface 

treatment while depositing the same polysil icon layer. 

The microstructure of the polysilicon film and of the interface was 

We intentionally emphasize the interface using devices 

Uur approach is, thus, 

examined by transmission electron microscopy (TEM) and the distribution of 

arsenic in the polysilicon film and at the polysilicon-monosilicon interface 

was studied by means of secondary ion inass spectrometry (SIMS) [9]. These 

structural properties of the polysilicon film and the interface are 

correlated, for the first time, with the electrical measurements. 

3-2 
To study the polysilicon-monosilicon interface we use a p/n junction test 

structure, rather than a bipolar transistor. The test structure and its 

fabrication are described in Section 11. 

structure has a number of important advantages in comparison with the bipolar 

transistor and wi 11 be instrumental in developing the phenomenol o y i c a l 

transport model and revealing the domi nant recombi nation mechanisms in the 

polysilicon, Sections 111 and IV. 

As is discussed later, this 

11. DESCRIPTION OF DEVICES AND FABRICATION 

The test structure, shown in Fig. 1, consists of a 0.06 Qcm p-type 

substrate with a thin (- 0.8 pm) n-type epitaxial layer with doping density 

NDD = 10l6 grown on top. One kind of devices had an n+ contact ring 

implanted; the second kind of devices on the same wafer does not have the 

ring. The purpose of the ni ring, which covers less than about 5% of the 

device area, is to assure a good ohmic contact with the relatively low-doped 

epitaxial layer. One half of each wafer was contacted by a 1500 A or 2500 A 

thick polysilicon film, Fig. l(a). The deposition and the heat treatment 

after the deposition were done very carefully and were specifically designed 

for the purpose of enabling the separation of the role of the interface and 

the bulk on the current transport. Wafers were etched in a buffered HF 

solution prior to polysilicon deposition. It is very important to emphasize 

here that each kind of polysilicon device had a reference device with a metal 

A1 contact (both with and without the n+ ring), Fig. l(b), made on the other 

half of each wafer. The A1 contact was also deposited on top of thz 

polysilicon film. The devices are separated from each other by an oxide layer 

around the periphery 

the measured current 

from 6 x cm2 to 

that minimizes the surface leakage, thus assuring that 

originates mostly from the bulk. 

1.2 x cm 

The device areas ranged 

2 

3-3 
The polysi 1 icon films, deposited using an atmospheric pressure CVD 

reactor at 670°C, were one of the following: 

(a) 1500 A undoped polysilicon deposited without any external arsenic 

source (grain size about 100 A). 

1500 A in-situ arsenic doped (grain size larger than about 400 A). 

Bilayer: 1500 A of undoped film followed by deposition of 1000 A 

in-situ doped film (grain size larger than about 300 A). 

(b) 

(c) 

Each of these three groups of devices was subjected to various post-deposition 

treatments. The deposition and annealing conditions are summarized in 

Table I. - - 

The arseni c-concent rat i on profi les measured by SIMS [9] are shown i n 

Fiy. 2 for some of the devices from Table I. These profiles depict the 

average concentration of the cross section consisting of the yrain-boundary 

region and the bulk. There is evidence [lo] that in the in-situ doped films, 

about 30-50% of the arsenic dopant resides in the grain boundaries. 

grain boundaries have smaller cross-sectional area than the adjoining grains, 

the arsenic concentration in the grain boundaries is larger than in the 

bulk. Based on the diffusion coefficients of arsenic in the polysilicon [9], 

we infer from the SIMS profiles of the in-situ doped films (Fig. 2.(a)), that 

Since the 

the arsenic concentration is about 5 x 1OZo CITI'~ in the grains and about 10 21 

in the grain boundaries. The dopant in the as-deposited polysi licon film 

is largely inactive and is subsequently activated duriny the heat treatment 

step. 

depends strongly on the annealing temperature and time [ll,lZ]. 

in-situ doped sample 2BE annealed at 1000°C, 15 min, for example, the 

activation ratio is about 0.1 [ll]. The activation ratio for the devices 

annealed at 900°C (devices 1C,10) and at 800°C (device 16) is not exactly 

known, but it can be expected to be about 0.01 [11,12]. 

The activation ratio (carrier concentration/dopant concentration) 

For the 

3-4 
For the wafers with the bilayer polysilicon film we have employed arsenic 

diffusion at low temperatures to obtain a preferential grain boundary 

diffusion from the top in-situ doped layer towards the interface, while 

minimizing the bulk diffusion [SI. The diffusivity of arsenic in the grain 

boundaries at T = 800 - 850°C is about three orders of maynitude greater than 

the diffusivity in the bulk. The SIMS profiles for some of the bilayer 

samples, before and after the heat treatments, are shown in Fig. 2( b) . The 

arsenic concentration in the originally undoped layer depends upon the heat 

treatment. 

treatment at 800°C for 64 hours, arsenic diffused through the grain boundaries 

and reached the interface c91. From the SIMS profile, the average arsenic 

concentration in the grain boundaries is estimated to be about 5 x 

lo2" ~m'~. 

8 hours the arsenic does not reach the polysi 1 i con-monosil icon interface and 

the arsenic concentration drops from about loz1 

of the film to the background concentration of about ld7 

[9]. This background level is due to the residual impurities in the 

deposition system and was detected in the undoped film. 

As an example, in the bilayer film of the sample 1J after heat 

However, in the sample 2BA with a heat treatment at 750°C for 

in the in-situ doped part 

- 

AI though during the heat treatment arsenic diffuses mainly through the 

grain boundaries, some diffusion occurs from the grain boundaries to the bulk 

of the grains. To minimize this outdiffusion, the annealing conditions were 

tailored in such a way as to allow arsenic to just reach the interface. The 

outdiffused region is very narrow especially at the interface, where arsenic 

outdiffuses only during a fraction of the total heat treatment time. For 

exainple, for 800"C, 10 hrs, the arsenic concentration should drop from 2 x 

lozo to lOI7 in about Only 100 8. During a fraction of the heat 

treatment time, arsenic will also diffuse into the epitaxial layer. The width 

of this diffusion should also be in the order of - 1OU A. As a result of the 

3-5 
preferential grain boundary diffusion, a heavily doped thin interfacial region 

AN is created at the metallurgical polysilicon-monosilicon interface. 

Figure 3 illustrates schematically the expected arsenic concentration profiles 

at the interface corresponding to the SIMS data data for the sample 1J from 

Fiy. 2(b). 

Comparison of the SIMS profiles, Figs. 2(a) and 2( b) , clearly shows that 

the in-situ doped and the bilayer devices have similar arsenic, and thus 

electron, concentrations within about 100-300 A thick interfacial layer AW, 

but their bulk concentrations are different (see Fig. 3). Due to the 

activation ratio, the in-situ doped devices nave a bulk electron concentration 

of about N = 5 x lo1* - 5 x 10'' ~rn'~ in comparison with N << 10l8 

-- . 

for 

the bilayer samples in the originally undoped layer adjacent to the interface. 

As will be discussed in detail later, separation of the interfacial layer from 

the rest of the polysilicon film is also necessitated by very different 

microstructures in these two regions. 

Based on this simi I ari ty of the polysi 1 i con-monosi 1 i con i nterf aci a1 

layer, if the interfacial layer dominates the minority carrier transport, we 

expect the in-situ and the bilayer samples exhibit similar electrical 

properties. 

carrier transport, then we would expect the in-situ doped and the bilayer 

devices to have different electrical properties. 

If, however, the bulk properties of the polysilicon determine the 

I I I. MOUEL DEVELOPMENT 

In this section we develop a simple phenomenological model for the 

mi n o r i t y - c a r r i er transport with the aim of identi fyi ny the domi nant 

recombination mechanism in the polysilicon-monosilicon structure. 

3-6 
Figure 4(a) shows the test structure under forward bias. For the present 

purpose we consider the polysilicon-monosilicon interface (Fig. 3) to be a 

thin layer of width AW - 100 A that includes the high-low junction in the 

epitaxial 1 ayer, grai n-boundary space-charge-region (SCR) at the metalluryi cal 

interface and the highly doped reyion adjacent to the metallurgical interface 

in the polysilicon. 

single effective time constant z (int). 

analysis and will yield useful results. 

We assume that this region can be characterized by a 

This assumption simplifies the P 

Using a charge-control representation for the hole current J and the P 

electron current Jn at x=O, we write 

J = Jp(0) + Jn(0) (3) 

where Q (epi), Q (int) , Q (poly) and Qn(sub) are the excess charges in the 

epitaxial layer, the interfacial layer, the polysilicon bulk, and the 

substrate, respectively with corresponding time constants T (epi) , zp(int), 

T (poly) and zn(sub), and J (W ) is the recombination current density at the 

ohmic contact, x = WE. 

the p/n junction space-charge region which can be evaluated separately [ 131 , 

i f necessary. 

P P P 

P 

P PE 

In (1) - (3) we have neglected the recombination in 

Having described the cross-sectional microstructure and composition of 

our devices, Figs. 2 and 3, and defined the current components, (1) - (3), we 

will in the next Section analyze the data in order to: (i) separate the 

3-7 
measured current into components and (i i) identify the parameters that 

determine the minority carrier transport in the interfacial layer and in the 

polysi 1 icon film. 

IV. EXPERIMENTAL RESULTS AND DISCUSSION 

A. Summary of Results 

Figure 5 shows the measured current-vol tage (I-V) characteristics for 

some representative devices from Table I. The hole saturation current 

densities Jpo for all devices used in this study are listed in column IV of 

Table I. The values for Jpu were obtained by determining the electron 

saturation current Jno < 2 x A/cm2 from the doping density and from the 

measured diffusion length in the p-type substrate (Ln i 9 prn) obtained by the 

X-ray method C141 and then subtracting it from the measured saturation current 

Jo. I-V characteristics were measured both on devices with and without the n+ 

contact rings; the values for Jpo were identical, but the devices without the 

n+ rings had a larger series resistance RS (see discussion below). 

curves exhibited an ideal J=exp(qV/kT) dependence for at least 3-4 decades of 

current. Thus no corrections for the non-ideal space-charge-region and 

surface recornbi nati on currents were requi red. 

measured on devices with an area of 62 x 23 mil2 in which the perimeter 

effects are neyligible. 

at least 20 devices. 

-. -- 

N 

N 

The I-V 

The results reported here were 

Each JPo value in Table I is the average value over 

The following important observations can be made from Fig. 5: 

(a) The current density for the in-situ doped polysilicon devices is 

about 3 orders of maynitude smaller in co!nparison with that of the 

metal contact. This demonstrates the sensitivity of our test 

structure to the interface conditions and the usefulness of the 

polysi 1 icon contact in suppressi ny the current. 

3-8 
The heat treatment after the deposition of the in-situ doped 

polysilicon film causes almost no changes in the measured 

current. This is evident from the comparison of the device 1A 

without any heat treatment with the device 1B heat treated at 

800°C, 64 hrs. 

The undoped polysilicon film, device lE, behaves as a surface with 

large recombination velocity with no improvement in comparison with 

the reference metal contact . The bilayer device 1I without heat treatment is identical to the 

undoped device 1E without heat treatment. 

The bilayer device 1J after 800°C, 64 hrs heat treatment, exhibits 

about the same current density as the in-sitil doped device 1B with 

the same heat treatment, 

Devices, without the n+ contact ring, with undoped film (1E) and 

bilayer film without heat treatment (11) have a large series 

resistance RS, which is demonstrated by the deviation from the 

J = exp(qV/kT) dependence at V > 0.3 volts. The series resistance 

RS is greatly reduced for these devices if the measurement is taken 

on the device with the n+ contact ring, as illustrated in Fig. 5 

for the device 1E. 

._ 

- 

The above observations (a) - (f) and the results in Table I lead us to 

the following conclusions: 

(1) Large currents measured in all devices with the undoped polysilicon 

1 ayer contacting the monosi 1 icon 1 ayer precl ude the possi bi 1 i ty of 

an effective thin interfacial oxide layer [2,7] between the 

polysilicon and the monosilicon in our devices. 

de Graaf and de Groot [Z] that a 20 - 30 A thick interfacial oxide 

It was proposed by 

3-9 
1 ayer represents a tunnel i ny barrier for the mi nori ty holes, which 

suppresses the mi n o r i t y - c a r r i e r current in the polysi 1 icon. If 

such a layer was present in our devices, the hole current would be 

limited by the tunneling mechanism [2,5,8] through this layer in 

both the doped and undoped samples. 

intentionally grow an interfacial oxide prior to the polysilicon 

I n t h i s work, we did not 

deposition that may produce such a tunneling barrier (2,7]. 

(2) The polysilicon-monosilicon interface is very sensitive to the 

arsenic concentration, rather than to the electron concentration. 

This conclusion is based on the observed insensitivity, discussed 

in (b) above, of the hole current to the heat treatments of the in- 

---_ 

situ doped devices. The electron carrier concentration in the CVD 

deposited polysi 1 icon is a function of the postdeposi tion heat 

treatment [11,12) and increases with the heat treatment 

temperature. Thus, large differences in the carrier concentrations 

can be expected before and after the heat treatments [11,12].~ On 

the other hand, the arsenic dopant concentration is almost 

independent of the heat treatment in the in-situ doped films [SI. 

The correlation between the arsenic concentration at the 

interface on the one hand, and the current density and RS on the 

other hand, is further demonstrated in Fig. 6 for the devices with 

bilayer polysilicon films. The comparison of device 11 with no 

heat treatment with two devices after heat treatment (devices 

lJ,lL) shows a drastic reduction in the current density. The 

arsenic concentration at the interface before the heat treatment is 

the residual < 10 cm , while after the heat treatment the 18 -3 N 

20 -3 concentration is -1U cm (see Fig. 2). Uevice 1K heat treated 

3 - 10 
at 900°C for 15 min still gives Jpo equal to that of the device 

11. Apparently, the arsenic does not reach the polysiliconrnonosi 1 icon interface after the 901)"C, 15 mi n thermal treatment. 

This is consistent with the recently published values for arsenic 

diffusivity in the grain boundaries [9]. From Fig. 3 in [9] we can 

deduce that the product which is a measure of arsenic 

penetration through the grain boundaries, has to be much laryer 

than about 500 A for arsenic to penetrate through the - 1500 A of 

the originally undoped layer of the bilayer film. For 900°C, 15 

min heat treatment, the value of (Dt)1/2 is only about 550 A, but 

is about 2000 A for the'devices 13 and lL, where arsenic did reach 

the interface, as Fig. 2(b) illustrates. The device 2BA, for which 

(Dt)l/' = 280 A, behaves similarly to device 1K (see Table I). The 

RS is large for the non heat treated case and decreases with 

increasing (Dt)1/2, thus directly reflecting the penetration of the 

highly doped and conductive arsenic front through the grain - 

boundries towards the interface (91. A large RS in all undoped 

devices (< As/cm ) and in the bilayer device 11 suygests 

that the residual arsenic in the undoped films is present mostly in 

the nonactivatiny lattice Sites, or more probably, that most of the 

free electrons are trapped at the grain boundaries leaving the 

grains essentially depleted [15,161, which results in a large 

resistivity of the polySi1icon film. 

heat treatment can also be attributed to the lowering of the grain 

boundary barriers in the pOlySiliCOn film because of the increased 

doping in the vicinity of the grain boundaries [16,17]. 

3 

The reduction in RS after the 

3 - 11 
B. Separation of Current Components 

In the previous discussion we described the electric behavior of devices 

with various polysilicon films and their correlation with the microstructural 

composition. Below, we analyze the data and attempt to identify the possible 

domi nant physi cal mechani sms governi ng the mi nori ty carrier transport in the 

polysilicon film. In order to do that, we have t o f i r s t separate the measured 

currents into components defined in (1) and (2) and, thus, extract the desired 

values of the recombination currents in the polysilicon. Then we correlate 

the phenomenological model with experimental results for polysilicon films 

with different microstructures. 

The five current components--in (1) - (2) can be divided into two groups, 

based on the criteria of the doping density in the particular region. Regions 

with doping densities smaller than about 

activation energy corresponding to the energy gap of intrinsic Si, while 

regions with doping much larger than 

energies (bandgaps) because of the bandgap narrowing AE~ C181. 

the above criteria, we can write 

~m'~ are expected to exhibit 

cm'3, wi 11 have smal ler activation 

Considering 

- 

where EGI is the intrinsic Si bandgap, AE~ is the average bandgap narrowiny 

for the entire heavily-doped region, Up, and uno are the preexponential 

constants in Q =' Qoexp(qV/kT), and J 

density. 

discussed earlier, the precise value of the Qno(sub)/zn( sub) component was 

(W ) is the saturation current 

The activation energy in (5) is thus EG = EI;I - A€. < 'EtiI. 

PO E 

As G 
a1 ready determined independently, thus, only the hole current wi 11 be 

discussed henceforth. 

Figure 7 shows the activation plots [lS] for representative devices, with 

undoped, bilayer and in-situ doped polysil icon films. The activation curve 

for the reference device with metal contact is also shown. 

To construct the activation plot, we have to properly account for all 

telnperature dependent parameters in (4) and (5). This is done by plotting 

versus 1/T. Here, EGI(0) = 1.206 eV is the linearly extrapolated energy gap 

of intrinsic Si at 0 K, C is a temperature independent constant that involves 

device parameters (such as geometry, doping, mi nori ty-carrier mobi 1 i ty , and 

minority-carrier lifetime), qc = (EFg - EC)/kT (see Fig. 4(b)), and FlI2(ncr] 

is the Fermi-Dirac integral of the order of 1/2. 

for a transparent region bounded by a surface with very large surface 

recoinbination velocity, e.g. metal contact or undoped polysil icon contact, 

In the above expression, m=4 

2 4 

P where Jpo a[ni(kT/q)pp] = T , provided that the minority-carrier mobili,ty p 

is temperature independent C181. On the other hand, if the metal contact is 

replaced by a contact with low surface recombination velocity, then 

Jpo =(niW/.c 2 ) a T3 [19], i.e, m=3, provided that the minority-carrier P 

1 i fetime is temperature independent. 

In Fig. 7, we show the activation plot for the in-situ doped device 18 

and the bilayer device 13 for which Jpo (polysilicon) << Jpo (metal); thus, 

m=3. 

assumption of 'I; 

300 K < T < 370 K used in Fig. 7. The slope of the activation plot is 

This yields EG = 1.206 f 0.03 eV (i.e. hEti = 0 f 30 meV). The 

f f(T) is very reasonable in the narrow temperature range, P 

relatively insensitive to small variations in In. For example, the activation 

energy for the device 1J for 1~3.5 is larger by only about 10 meV compared to 

3 - 13 
that for m=3. Thus, only a negligible error is caused if T~ varies slightly 

with T. 

In the case of the devices with metal contact and undoped polysilicon 

contact films, setting m=4 neglects the temperature variation of the minoritycarrier mobility p 

= 60 * 20 meV. 

carrier hole mobility in the low-doped (-lO''~in-~) epitaxial layer is the same 

as the temperature dependence of the majority-carrier hole mobility, which 

The result for m=4 is EG = 1.146 f 0.020 eV, i.e. AEG P' 

Assuming now that the temperature dependence of the minorityT-lo8 for 300 K < T < 400 K [ZO], then a correction to the above NN 

follows p a P 

result is required. This is done in Fig. 7 using flT-1*8 = T2*2 instead of 

T 4 , yielding EG = 1.206 f 0.025 eV, I .e. AE~ = 0 k 25 meV. 

The activation energies for the other devices from Table I, not displayed 

in Fig. 7, are equal to the values of the representative devices discussed 

above. 

In contrast, Fig. 7 also illustrates the activation curve corresponding 

to the hole recombination in the n' monosilicon layer obtained from the n+/p 

monosilicon junction with uniformly doped transparent 0.15 pm n+ layer with 

electron concentration N = 2 x lo1' ~m'~. The activation energy for this 

n+-monosilicon layer (using m=4) is smaller by about 0.135 eV, EG = 1.071 f 

0.025 eV, in comparison with the value for the epitaxial n-monosilicon 

obtained from the device with the metal contact. This difference can be 

interpreted as bandgap narrowing in the n+-monosi 1 icon region of 

hEG = 135 meV [18]. 

The activation energy of the reference device with the metal contact is 

described exactly by (4) (polysilicon is absent here) and the current is due 

completely to the low-doped epitaxial layer (Jpo >> Jno) where AEG = 0. The 

fact that the result obtained from the activation plot of this device gives 

3 - 14 

, 
EG = EGI(0) = 1.206 eV within the experimental accuracy of about 2 0.025 eV 

establishes a credibility for the activation plots and also provides a value 

for comparison with the devices with polysi 1 icon contacts. 

The hole saturation current density for the devices with polysilicon 

contact in which Jpo(polysilicon) << Jpo(metal) , assuming Lp >> Wepi and Sp << 

Dp/Wepi 9 can be written as [19,21] 

Here S is the effective surface recombination velocity at x = Wepi, resulting 

from the recombination losses in the polysilicon. The observed activation 

energy and the fact that J (polysilicon) << J (metal) imply S << 

Wepi/zp(epi). The hole distribution corresponding to this case is 

schematically depicted in Fig. 4(c). 

Lp = 26 pm. 

P 

PO PO P 

From (6) we then find 7; = 0.6 psec and P 

To corroborate the fact that Sp is negligibly small in our devices ,and to 

avoid the uncertainties in the interpretation of the activation plots, we have 

fabricated the test structures by depositing an i n-si tu doped polysi 1 icon 

films on epitaxial layers with different values of Wepi: 0.8 pm (p = 0.6 Qcrn), 

8 p.m (p = 1.2 Qcm) , and 12.8 pm (p = 0.6 Qcm) . treatment conditions were identical for all three devices. The heat treatment 

was done at 900°C for 15 min, and corresponds to that of the device 10 from 

Table I. 

The deposition and the heat 

Usiny (6), we can calculate the values of S + Wepi/tp(epi) from the P 

measured J and from the known doping densities. Then a plot of S + 

Wepi/t (epi) versus Wepi is expected to yield a straight line, with a slope P 

proportional to z (epi) = 0.6 psec, assuming that z 

PO P 

in the 8 pn and 12.8 p P P 

3 - 15 
epi taxi a1 1 ayers s about equa to that in the 0.8 pm layer deduced above. 

Since Sp is identical for all devices, an extrapolation to Wepi + 0 yields 

Sp. This plot is shown in Fig. 8, yielding Sp - 1s cm/sec << Wepi/Tp(epi) for 

all three devices. 

The exact value Of sp is of importance, since it represents the des 

recombination losses in the polysilicon, includiny the losses in the 

red 

interfacial layer. The approximate value of S - 15 cm/sec deduced above 

indicates that the recombination losses in the polysilicon film are only about 

10% of the measured hole current. The polysilicon-monosil icon interface thus 

acts as a very efficient barrier for the minority carriers. 

P 

- Hence 

where we have neglected Jpo(WE) because it was found experimentally [3] that 

Lp(poly) < 500 A, which is much less than the thickness of the polysilicon 

films used in this work. 

N 

C. Discussion 

The TEM study revealed that the grains in the in-situ doped polysilicon 

films after heat treatment at 900°C - 1000°C are essentially columnar and the 

grain diameter is at least 400 A and as large as about 1000 A [22]. 

effective hole diffusion length in the heavily-doped polysilicon is L 

[33, i.e., L c grain diameter. Such polysilicon film thus has only a few or 

no grain boundaries in the direction of the current flow and can be considered 

to be almost a single crystal n+ layer separated froin the monocrystalline 

epitaxial layer by only grain boundaries (or an interfacial layer) at the 

The 

P- < 500 A 

P3 - 16 
metallurgical interface. Thus, if the very thin (-200 A) interfacial layer 

(Figs. 3, 4) is transparent for the minority holes, then the diffusion hole 

current in the bulk of the polysilicon film with N - lo1' cmm3 is expected to 

be about equal to the hole current of the single crystal nt/p junction of 

Fig. 7 with N = 2 x 10 cm which is Jpo = 4 x A/cm at 25OC. This 19 -3 2 

e measured J for the devices with 

at least a factor of 40 larger than 

PO 

recombination losses in the 

in tne 

d have to 

value is about one decade larger than t 

the in-situ doped polysilicon films and 

the value estimated in (7) for the tota 

polysilicon film. To explain the discrepancy of about two 

current, the effective transport parameters in the polysil 

be markedly different from their-monosilicon values. 

decades 

con wou 

Modeling of the transport in the polysilicon is complicated by the grain 

boundaries. As a first approximation, we will treat the polysilicon 

analogously to the transport in the single crystal Si, as justified above, but 

with an effective value for the parameters, such as bandgap, mobility, and 

lifetime, to account for the influence of the grain boundaries. The effective 

parameters are average parameters for the polysilicon film corresponding to 

the average grain size. This approach was used before [3,4]. We can then 

write 

where Ne(poly) = 10l8 cK3 is the effective doping [18,23] in the heavily 

doped polysi 1 icon. 

an almost flat hole quasi-fermi level in the epitaxial layer up to the 

metallurgical interface, Fig. 4(b). This is justified by the fact that 

J (polysilicon) << 3 (metal) and by noting that the recombination losses in 

In (8), we have used the quasi -equi 1 i bri uin assumpti on of 

PO PO 

3 - 17 
the very thin (< 200 A) diffused region in the epitaxial layer can be 

neglected [19,241. 

have to be at least 40 times smaller than the single crystal value. This is 

not a likely possibility in the large grains with L N grain diameter. To 

explain the results by lower value of hEG in the polysilicon requires a 

difference of about 100 meV between the single crystal and polysilicon 

N 

Note here that, to remove the discrepancy , Up(poly) would 

P 

~ values. However, the measured activation energies in our devices and in the 

bipolar transistors [3] do not support this assumpti on. 

For the bilayer devices, we have a more complicated situation. The 

interfacial region is heavily doped, followed by a 1500 A thick undoped layer 

and again a heavily doped 1000 A-wide in-situ doped layer (Fig. 3). The 

heavily doped grain boundaries (N - 10'" crnm3) within the lightly doped grains 

create a high-low junction with low effective recombination velocity [25], 

thus only slightly affecting the current flow. 

If the minority holes were to diffuse across the about 200-300 A thick 

interfacial layer into the low-doped region, the expected current from (8) 

would be much larger than for the in-situ doped devices, because N,(poly) << 

1018 cm'3 in the low-doped grains. The measured hole currents for the in-situ 

doped and bilayer devices are, however, almost equal. The exceptions are the 

bilayer devices where the heat treatment was not sufficient to obtain high 

arsenic concentration at the interface. The differences in the values of 3 

of less than about a factor of two between the bilayer devices 13, 1L and the 

in-situ doped devices, can be attributed to small variations in Wepi, zp(epi), 

and mainly NDD. The average doping density in the epitaxial layers was 

measured by the C-V technique and varied frorn about 9 x 1015 

2 x 10l6 ~m'~. This fact is also reflected in the spread of the Jpo values 

for the devices with the metal contact which was in the range from about 

4 x 10-l" A/cin2 to about 6 x 

PO 

to about 

A/cmz. 

3 - 18 
The preliminary conclusions (1) and (2) in Section IV-A and the 

discussion in this section lead to the following: 

(i ) The mi nori ty carrier transport at the polysil i con-monosil i con 

interface with no intentional insulating layer at the interface is 

determined by the carrier transport within the polysil icon, rather 

than by a tunneling through an insulating layer. 

(ii) The similarity of the electrical properties of the devices with the 

in-situ doped and the bilayer polysilicon films suggests a 

correlation between the electrical properties and the 

microstructure of the very thin interfacial layer within about 

200 - 300 A of the metallurgical interface in the polysilicon 

film. 

the x = Wepi plane (Fig. 4) recombine within 200 - 300 A of the 

metal 1 urgi cal interface. 

It also suggests that most of the minority carriers crossing 

(iii)In order to explain J (polysilicon contact) << J (n' monosilicon), P P 

the heavily-doped interfacial layer must have properties 

significantly different from the properties of the monosilicon. 

(iv) The dominant mechanism responsible for low J (polysi 1 icon contact) 

is much more sensitive to the arsenic dopant concentration at the 

interface than to the carrier electron concentration at the 

i nterf ace. 

P 

The polysilicon-monosilicon interface can be regarded as a region with a 

high degree of disorder. This is due largely to the very sudden transition 

from the orderly epitaxial single crystal ldyer to the CVU-deposited 

polysilicon with the randomly oriented (without prefered orientation) grains 

of a few hundred Angstroms in size. It was recently observed by means of 

cross-sectional TEM that the arsenic doped polysil i con-monosi 1 icon interface 

3 - 19 
consists in some cases of a crystalline phase with about 40 A averaye grain 

size, compared to - 400 A in the bulk of the polysilicon film, while in some 

other cases this interface is amorphous [22,26). It is well known that the 

di sordered reyi ons of semi conductors are associated with l ow carrier 

mobilities (and diffusivities) As an example, the drift majority-carrier 

mobilities in amorphous Si are p = (2-5) x 10 cm /Vs and p = 5 x 

-2 2 

n P 

cm2/VS [27]. Even smaller values are expected for minority carriers. 

The disorder contributes to the random component in the atomic potential 

which results in band tails [28]. Trapping by band tails was identified as 

one of the possible mechanisms causing very 1 ow mobil ity in amorphous Si 

[27]. Band tails can be responsible for low minority-carrier nobility by a 

process of trapping also in heavily doped sinyle crystal Si, as was recently 

suggested [29]. 

-_ 

The microstructure at the interface and the electrical measurements lead 

us to a proposal for a possible mechanism of current suppression by the 

polysilicon contact: very 'low minority carrier mobility (and diffusivity)' in 

the very highly doped and disordered interfacial region. Note that both 

ainorphous structure and very small grains at the interface predict low 

mobi 1 i ty. 

Because of the large sensitivity of our test structure to the interface, 

we can make a better estimate of the minority-carrier mobil i ty in the 

polysilicon than made before in [3]. 

reasonable model for the recombination current Q (int)/.r: (int) in the 

interfacial layer. 

current can be described as a diffusion current 

In order to do that we have to have a 

P P 

We assume again that, as a first approximation, this 

3 - 20 
The quantity on the right-hand side of (9) results from (7). 

the parameters in (9) by a single crystal Si values, we have 

Approximating 

l8 -3 Ne - 10 cm 

Auger lifetime. 

[18], and T (int) - T~ = 2 x 10-losec c301, where TA is the P 

Equation (9) then implies the upper limits for 

Dp(int) - 5 x loe3 cm2/s 

and 

Thus, Op(int) from (9) and (loa) is about 3 orders of magnitude smaller than 

the single crystal value. 

The rough approximations of (loa), (lob) do not take into account the 

consequences of the detailed microstructure of the interface, but they do, 

nevertheless, lend support to the interpretation based on the possibil ity of 

large gradient in the minority-carrier diffusivity at the polysiliconmonosilicon interface. This mechanism will greatly suppress the current. The 

minority carriers will then recombine very close to the metallurgical 

polysilicon-monosilicon junction without the possibility to diffuse deep into 

the polysilicon. 

An alternative explanation can be offered by an interface in a 

heterojunction form with a very large barrier for holes. 

can be created because of a position-dependent chemical cornposi tion giving 

rise to spatial variations of the bandyap, electron affinity and the band 

edges of the conduction and valence bands [31]. As an example, if a thin 

The heterojunction 

3 - 21 
(- 20 A) amorphous layer exists at the interface [22,26], a discontinuity of 

the bandgap and electron affinity may result. 

structure would, however, require much more detailed information about the 

To further analyse such a 

chemical and electronic structure of the interface than presently available. 

Even though the heterojunction model or the tunneliny model c21 cannot be 

excluded as a possibility, there are however two findings that point 

particularly in the direction of the low mobility model. 

of the correlation between the recoinbination current and the dopant arsenic 

First, the finding 

density agrees with studies which show that at the microscopic level the 

atomic potential has a random component because of the random distribution of 

impurities whether impurities are ionized or not [32]. 

observation by Ning and Isaac C31 of the dependence of the base current in the 

-- .. 

Second, the 

bipolar transistor on the polysilicon thickness. 

base current was observed for transistors with the polysi 1 icon film thickness 

of 300 A or less. This observation agrees with our model of carrier 

A noticeable increase in the 

recombination within the interfacial region, such as illustrated in Fiy. 3 for 

the bilayer film structure. 

The undoped polysilicon contacts in devices 1E - 1G behave as interfaces 

with very 1 arge recombination velocity with current densities about equal to 

the current densities for the reference metal contacts (see Table I). This is 

expected because the potenti a1 profile at the interface between the epi taxi a1 

layer with N = N cm-3 and the polysilicon with N < 1U16 cK3 creates 

an electric field in the direction of the hole flow, thus aiding holes across 

the interface. The recombination current inside of the undoped contacts is 

expected to be large because of low electron density and small grain size 

(- 100 A), as (9) implies. The above arguments apply also to the bilayer 

devices 11 and 1K. 

DO = 

3 - 22 
It is very convenient to characterize the polysi 1 icon-monosi 1 icon 

interface by the effective surface recombination velocity S 

junction in the epitaxial layer at x = Wepi (Fig. 4), which is defined as E331 

at the high-low P 

S = J (W )/qAP(W .) P P epi epi 

where nP(Wepi) is the excess hole density and 3 (W ) is the cu P epi rent de i ty 

at x = Wepi The value of S cannot be deduced exactly without a precise 

knowledge of z (epi), since the bulk recombination in the epitaxial layer is P 

not negligible in our devices, but is in fact dominant. An approximate value 

of Sp - 15 cm/sec was deduced before. 

limit of S 

by neglecting the bulk losses (i.e. by setting Wepi/Tp(epi) = 0), or from 

P 

For many purposes, however, an upper 

is sufficient. This upper limit can be obtained exactly from (5) P 

- 'p/'ep i 

P) (3 (Q)/J P 'pmax 

where 3 (a) = [(qn.D z )/(NDDWepi)] exp(qV/kT) is the current for the reference 

P 1P 

device with the metal contact. The upper limit values for S calculated from 

(12) are listed in Table I. 

From the upper limit of S given by (12) we can also estimate the upper 

P 

P 

limit of the effective surface recombination velocity at the n+ polysilicon-n+ 

monosilicon metallurgical interface. Assuming that the thin n+ outdiffused 

monosil icon layer is essentially transparent we obtain from Jp(Wepi) = 

J (n+ poly-n+) P 

3 - 23 
where Ne(int)/NDD(epi) = 10l8 ~m-~/lOl~ 

approximate value of S - 15 cm/sec in (13) yields S (n'poly-n+) = 

1500 cm/sec. 

= 100 [lS]. Using the 

P P 

The n+ polysilicon contact on the top of the n+ diffused or implanted 

monosilicon emitter in the bipolar transistor can be also characterized by 

(13), since (13) reflects the recombination in the polysilicon independently 

of the doping in the monosilicon. The low value for Sp(n+poly-n+) in 

comparison with S N lo6 cm/sec for the Ohmic metal contact explains, 

qualitatively, the improved current yain in bipolar transistors with 

polysi 1 icon contacts to thin emitters. 

P 

IV. SUMMARY 

In this work, we have presented the results of a detailed experimental 

study of a polysilicon-monosilicon contact. 

explain both qualitatively and quantitatively the mechanism of improved 

current gain in bipolar transistors with polysilicon contacts. The study 

correlates the microstructure of the polysil icon-monosil icon junction with the 

electrical properties. The electrical properties were measured usiny p/n 

junction test structures (Fig. 1) that are much more sensitive to the contact 

properties than are bi polar transistors. 

Correlation of the electrical results with the microstructure yielded the 

The purpose of this study was to 

conclusion that the minority-carrier transport in the polysi 1 icon-monosilicon 

junction is controlled by a highly disordered layer within N 100 R of the 

interface characterized by very low minority-carrier diffusivity. 

conclusion confirms the model of Niny and Isaac that explained the improved 

current gain by D (n' polysilicon)/ D (n+ monosilicon) = 0.3. 

results indicate, however, that the effective 0 

This 

The present P P 

in the n+ polysilicon has to P 

3 - 24 
be substantially smaller than the corresponding value in the n' monosilicon to 

obtain the quantitative agreement with the data: 

monosilicon) - 5 x 

minority holes at the n' polysi 1 icon-n'monosi 1 icon interface was found to be 

much smaller (s lo4 cm/s) than the kinetic limit value for ohmic contact 

(- 5 x 106 cm/sec). 

D (n' polysilicon)/D (n' P P 

The effective surface recombination ve ocity for 

We did not study the effects of surface treatments prior to polysilicon 

deposition, namely the effects of thin interfacial oxide layer [2,7]. 

The saturation current density in the polysilicon contact was found to be 

less than about 

collector current density in the bipolar transistor with basewidth of about 

0.1 pn, base sheet resistance of about 8 kQ/square and current gain p = 100 is 

about 10-l' A/cm2 [3]. This implies that current gains > 1000 are possible, 

provided that the recombination losses in the n+ monosilicon emitter can be 

suppressed, for example by reducing the width of the n' monosilicon reyion 

A/cmz at 25T. The typical value of the saturation 

C2,341* 

The sensitivity of the test structures used in this study to the 

polysilicon contact and the accuracy of the method used to separate the 

current components was limited mainly by the minority-carrier lifetime in the 

epitaxial layer. More conclusive experiments [2'1] using devices with varyiny 

widths and dopings of the epitaxial layer would be desirable to improve the 

accuracy of the analysi s. 

A very low effective surface recombination velocity for the minority 

carriers at the polysi 1 i con-monosi 1 icon interface suggests appl i cations of 

polysilicon contacts in devices other than bipolar transistors. 

could be a back-surface-field solar cell in which the recomb nation losses at 

the back hiyh-low monosilicon contact can limit the cell eff ciency. 

An example 

3 - 25 
ACKNWLEDGME NTS 

The authors wish to express their appreciation to 8. Ginsberg, R. Shultz, 

M. Smyth and all other members of the silicon facility for their technical 

assistance. We also wish to thank T. H. Niny, D. D. Tang, and H. Stork for 

helpful discussions. 

One of the authors (A.N.) would like to thank Professor F. A. Lindholm 

for many valuable discussions related to this work. One of the authors (A.N.) 

also wishes to acknowledge the support of the National Science Foundation 

under Grant No. ECS-8203091 and the support of the Jet Propulsion Laboratory 

under Contract No. 956525. -- . 
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A theory 

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J. G. Fossum and M. A. Shibib,"A minority carrier transport model for 

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6. Soerowirdjo and P. Ashburn, "Effects of surface treatments on the 

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May 1981. 

J. Murota and T. Sawai, "Electrical characteristics of heavily arsenic 

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Devices, vol ED-24, pp. 662-671, June 1977. 

3 - 27 
14. W. Rosenzweig, "Diffusion length measurement by means of ioniziny 

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15. J. Y. W. Seto, "Electrical properties of polycrystal line silicon fi'lms", 

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16 . 

17. 

G. Baccarani and B. Ricco, "Transport properties of polycrystal 1 ine 

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A. Neugroschel, S. C. Pao, and F. A. Lindholm, "A method for determining 

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Electron Devices, vol. ED-29, pp. 894-902, May 1982. 

18. 

19. M. A. Shibib, F. A. Lindholm, and F. Therez, "Heavily doped transparentemitter regions in junction solar cells, diodes, and transistors" 

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IEEE '- 

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22. C. Y. Wong, A. E. Michel, and R. D. Isaac, "The poly-sinyle crystalline 

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- 

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25. A. Neugroschel and J. A. Mazer, "Effects of grain boundaries on the 

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3 - 28 
29 . 

30 . 

31 . 

32 . 

33. 

34 . 

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See for example J. R. 

reflecting properties 

Electronics, vol. 18, 

M. A. Green and R. 8. 

emitter transi stors", 

227, July 1983. 

- - 

P. Tunstall, Auyust 1978. 

Hauser and P. t4 . Dunbar, "Minority carrier 

of semiconductor hiyh-low junctions", Solid-state 

pp. -715-716, July 1975. 

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IEEE Electron Device Lett., vol. EDL-4, pp. 225- 

3 - 29 
TABLE I 

Summary of heat treatments and electrical measurements. Heat treatments for 

poly-si1 icon contacts were performed in argon. Electrical measurements were 

done at 25OC. 

JPO 'pmax CONTACT DEVICE HEAT 

TREATMENT (10-13~/~~2) (cm/sec ) 

Undoped 1E none (5.8 f 0.4) x lo3 - lo6 

Polysi 1 icon 1F 800°C, 64 hrs (5.5 f 0.5) x lo3 - lo6 

(1500 a) 1G 900°C, - 5 min (5.5 * 0.5) 103 - 106 

In-si tu 1A none 7 f 0.3 175 

Doped 1B 8OO0C, 64 hrs 10 f 1.5 250 

Polysi I i con 1c 900°C, 5 min 6.6 f 0.5 175 

(1500 a) 1D 900°C, 15 min 6.5 f 0.3 165 

2BE 1000°C, 15 min 6 f 0.5 165 

Bi 1 ayer : 11 none (4.2 * 0.2) 103 - 106 

1500 A undoped + 1J 8OO0C, 64 hrs 4.9 f 0.6 175 

1000 A in-situ 1K 900°C, 15 min (4.2 f 0.2) x lo3 - lo6 

doped 1L 850°C, 14 hrs 5.2 f 0.6 180 

2 BA 750°C, 8 hrs (4.0 f 0.3) x lo3 - lo6 

Met a1 

Ref e rence 

- 

450°C, 20 min (5 t 1) 103 - 106 

3 - 30 
FIGURE CAPTIONS 

Fig. 1 Cross-sectional view of devices used in this study. 

(a) Device with polysilicon contact film; 

(b) Reference device with metal contact only. The broken lines in (a), 

(b) show the implanted n'-contact ring in the epitaxial layer. 

Devices with and without the contact rings were fabricated on the same 

wafer . Fig. 2 SIMS profiles of the arsenic distributions [8] for: 

(a) The in-situ doped polysilicon with no heat treatment; 

(b) The bilayer film before heat treatment (11) and after 75OoC, 8 hrs 

-_ 

(ZBA) and 85OoC, 64 hrs (13) heat treatments. The extent of the As 

profile into the monosilicon is not larger than the resoiution of the 

SIMS equipment which is about 1 decade per 100 A [9]. 

Fig. 3 Schematic illustration of the arsenic concentration profile in the 

vicinity of the polysilicon-monosilicon metallurgical interface for the 

bilayer film after heat treatment. The shaded areas show the 

preferentially doped regions around the grain boundaries and the arsenic 

diffusion into the monosilicon. The broken lines depict the width of 

the arsenic diffusion from the grain boundary monolayer to the bulk of 

the yrai ns. The screened ar2a wi thi n the i nterfaci a1 layer symbol i zes 

the fact that the microstructure of the polysilicon film in this area is 

very different from the microstructure in the rest of the polysilicon 

film. 

Fig. 4 (a) Schematic illustration of a forward biased test structure with 

heavily-doped n'polysil icon contact showing the separation of the 

polysilicon film into two layers: the interfacial layer and tne 

polysilicon bulk. 

Band diayram for the forward bias. (b) 

3 - 31 
(c) Profile of the minority hole concentration for the case of low 

effective recombination velocity at x = Wepi. The broken line depicts 

the approximate decay of tne minority holes in the polysilicon. 

Fig. 5 Current-vol tage dependencies for several devices with polysi 1 icon 

contact and for the reference device with metal contact. 

Fig. 6 Current-voltage characteristics for devices with bilayer polysilicon 

contact. 

Fig. 7 Activation plots C18.I of C(I /T")C~X~(~,)/F~/~(~~)] = exp[-(EGI/(0) - PO 

AEG)/~T] = exp( -E6/kT) versus 1000/T for devices with undoped, in-situ 

doped, and bilayer polysilicon contacts. Activation plots for the 

device with reference metal contact and for the reference n+/p 

monosilicon junction are also shown. The slopes yield EG = 1.206 f 0.03 

eV for the metal reference device and for the polysilicon devices 16, 

13, and 1F. The slope for the n+/p monosilicon device yields EG = 1.071 

f 0.025 eV. 

-- . 

Fig. 8 The dependence of S + Wepi/zp(epi) on the thickness of the epitaxial P 

layer Wepi. The extrapolation to Wepi+O yields S - 15 cin/sec. P 

3 - 32 
- LJ 

11 

sio2 I 

LJ polysilicon 

film 

11 

n - epi \ sio2 

p - substrate 

1 AP n+- contact ring 

I Si02 

n - epi 

Si02 \ 

p - substrate 

FIG. 1 

Neugroschel et. al. 

3 - 33 

, 
_- 

mn 

'E 

z 

0 

0 

1O2lF: 

a 

a 1O2OU 

Iz 

W 

0 

z 

0 

v) 

o 10~~- 

1 0l8 

monocrystal 

I 1 1 i 

in - situ 

doped layer 

I - I 

I 

- - 

- 

- 

1 I f I I i * 

DEPTH (nm) 

(a) 

mn 

'E 

U 

0 

z 

0 

F= 

W 

0 

z 

0 

0 

I I I 

100 

I I 

I I 

200 300 

3 - 34 
.. . 1 

I' 

i 

i 

i I 

I 

! 

I 

I 

I 

b 

monosilicon It- polysilicon ~ 

bulk 

metallurgical 

polysilicon - 

monosilicon 

interface 

/- 

M= interfacial 

layer 

FIG. 3 

3 - 35 
_- 

I 

I 

1 

I 

I n - epi p - substrate I 

\ - ,E[N I;--- '. ---A------ - 

E2p- - - - 

EC \ 

----- ------ 

4 1 

X x=o Wepi 

FIG. 4 .. 

3 - 36 
2 1E-04 W 

n 

Iz 

W 

2 1E-06 

0 

a 

1E-08 

I 

1 I I 1 1 T=25 "C 1 

I 1 I I I I 

06 .2 04 

VOLTAGE (V) 

FIG. 5 

3 - 37 

, 
1E+OC 

1 E-02 

1 E-04 

1E-06 

1 E-08 

I 1 1 I 

I I 1 I I I 

-- . / A 1J, 1L ’ \/ 

VOLTAGE (V) 

FIG. 6 
Y 

\ 

W 

n 

(3 

I 

1 0-1 

- 1 0-1 IO-1 

1 0-1 

(3 

ws 

Y 

L 

I 

FIG. 7 

3 - 39 

? 
. -- ---- 

.- 

I 

240C 

200c 

1600 

1200 

800 

400 

I 1 1 1 1 1 

FIG. 8 

3 - 40 
CHAPTER FOUR 

SOLUTION OF THE CONTINUITY EQUATION 

IN PLANAR SYMHETRY CASES AND ASSESSMENT 

OF PHOTOLUMINESCENCE DECAY 

I. INTRODUCTION 

Photolum nescence decay is one of the methods used in determining the 

minority carr er lifetime in heavily doped silicon [l]. 

of exciting a silicon sample by a laser pulse and thus generating excess 

electron-hole pairs. The lifetime is derived from the decay rate of the 

excess charge. This decay as a function of time is obtained by monitoring the 

radiation emitted by the few electron-hole pairs that recombine throuyh 

radiative recombination. 

other methods because it involves no assumptions reyardiny the band structure 

The method consists 

In principle, this method is more reliable than many 

and the transport parameters in heavily doped silicon. On the other hand, the 

method has the drawback that surface recombination prohibits the decay from 

being purely expoential. 

and shape of the laser beam was not clarified previously. 

Moreover, the effect on the decay rate of the size 

Recent papers [2,3] have investigated the time dependence of the 

luminescence decay, and in particular the influence of surface recomb nation 

on the decay rate for special types of excitation. 

equation is solved analytically for the total excess charge in the case of a 

finely focused beam, while in [3] the problem is simplified to one dimension 

by considering uniform excitation. In both cases it is found that the effect 

of the surface recombination can be minimized by waiting several lifetimes, 

after the laser is turned off, before medsuriny the decay rate. 

In [2] the contin ity 

In this work we extend the analysis of [2,3J for the yenerdl case of 

arbitrary excitation, and prove that the beam size, shape and uniforinity does 

not affect the decay rate. An upper bound for the error due to surface 

recombination is derived. In agreement with c1,2,31 the effect of surface 

4-1 
recombination is found significant only in the initial part of the 

transient. 

for the continuity equation when planar symetry exists. 

In addition, as a preliminary result, a simplified form is given 

11. SOLUTION OF THE CONTINUITY EQUATION IN PLANAR SYWETRY CASES 

Figure 1 i 11 ust rates an infinitely extending semi conductor sample 

terminating at the z=O and z=W planes. The laser beam shown is meant as an 

example of excitation. The following analysis is, in general, valid for any 

other type of excitation, for example, thermal generation, and mi nori tycarrier injection over a potential barrier. 

to p-type is straightforward). 

The sample is n-type (extension 

The continuity equation for holes is 

where 3 is the hole flux and G and U are generation and recombination rates 

in excess of their thermal equilibrium values. Integration of Eq. (1) over 

the z = Z'(0 < Z' < W) plane yields 

P 

4-2 
ww 

Here Q(Z',t) = I I P(x,y,Z',t)dxdy is the number of holes per unit 

distance on the z=Z' plane, and Jpx, Jpy, Jpz are the components 

of Jp = Jpx x + Jpy y + Jpz z. All of the integrals above are assumed to be 

finite. 

w -OD 

+ -+ + 

By Gauss' theorem, 

where rw is the infinite circle on the z=Z' plane, and dc is the 

infinitesimal vector normal to r,. The integral 

the hole flux crossing the infinite circle, and is zero under restrictions on 

G(x,y,z,t) that are nearly always obeyed. Therefore, Eq. (2) becomes: 

+ I (Jpx x + J $)-df is rW PY 

aj - aQ = - I dxdy + Gdxdy - I I Udxdy at (3) 

where from now on we omit the (infinite) limits of integration for brevity. 

Expressing J in terms of drift and diffusion and assuming that the 

P 

PZ 

electric field, diffusivity, and mobility (Ez, Op, p j are functions only of z 

and that the recombination rate is linear (U = (P-PO)/~ with T = ~(z)), we 

rewrite Eq. (3) as 

QO 

at P az p z az az T T 

2 ao (lJ E ) 

- aQ=o -?-!$+[$-,E]-- [% + L] Q + - + !! Gdxdy . (4) 

Here Qo = 

the z=Z' plane. 

usual one-dimensional continuity equation results. 

I POdxdy is the equilibrium number of holes per unit distance on 

If, in Eq. (4), P replaces Q and G replaces IIGdxdy, the 

4-3 
Equation (4) is a differential equation for the total charge on the z=Z' 

are independent of the i njecti on DP' pP plane. 

level (independent of P). Assuming this, we can rewrite Eq. (4) in terms of 

the number (per unit distance) of excess holes in the z=Z' plane, 

It is linear provided E,, 

Q' = 1 1 APdXdy = Q - Q,: 

Equation (5) results from Eq. (4) because -0 aPo/az + p E P = 0 . P PZO 

The recombination velocities S1, S2 of the front (z=O) and back (z=W) 

surface of the sample enter to determine the boundary conditions of Eq. (5): 

aQ' (t ,w) 

P aZ 

S1 Q'(t,O) = D g'(t,O) , S2 Q'(t, W) = -D P az 

Under such boundary conditions the solution of Eq. (5) depends only on 

the total generation rate on the z=Z' plane (IJGdxdy) and not on G as a 

function of x and y. Knowledge of Q'(z,t) does not, of course, provide 

~P(x,y,z,t). However, it does provide the total minority current in the z 

direction, I = -e 0 aQ'/az + e p E Q' , and the total number of excess 

holes, 

Z P PZ 

0 

W 111 APdv = Q'dz 

Therefore, when one seeks to determine either the total 

or the number of excess holes, Eq. (5) suff 

minority current 

ces, provided on y that the 

transport parameters of the semiconductor do not depend on the injection level 

and are functions only of z. Equation (5) is much more convenient to use in 

the determination of (measurable) current than is the standard continuity 

equation. 

4-4 
I I I PHOTOLUMINESCE DECAY RESPONSE 

We now apply Eq. (5) to the study of the decay of the excess charge 

induced by a laser pulse in a semi-infinite (W==) sample having constant 

doping concentration. 

and for D independent of z Eq. (5) simplifies to 

For low injection minority carriers flow by diffusion 

2 

2!L=Daq'Q' + Gt(t)(l-K)a e-'' 27 az at 

where Gt(t) is the total photon flux of the laser beam, R is the reflection 

coefficient, and a is the absorption coefficient. 

dropped for simp1 ici ty. 

In (6) the subscript p is 

- -. 

The boundary conditions are 

where S is the surface recombination velocity. 

If Gt(t) is the unit impulse function, Gt(t) = 6(t), then Laplace 

transformation of Eq. (6) with time yields 

where s is the Laplace transfonn operator. The boundary conditions for 

Eq. (8) are the Laplace transformation of Eqs. (7). The solution is 

where r = S/D. 

4-5 
If Q',(t) the total number of excess carriers and QIt(s) its Laplace 

transformation, then 

Q) Q) 

Q',(t) = I Q'(t,z)dz => Q',(s) = 1 Q'(s,z)dz = 

0 0 

. (10) 

1-R - (1-R) (r+a)aD[Jm - Jp rl 

2 -Da +s+( l/~) 4-m [-Da2+s+( l/t) Xs+( 1/-r)-Dr2] 

Taking the inverse Laplace transform of Eq. (lo), we obtain 

where L = a is the hole diffusion lenyth. This result holds independently 

of the beam shape and is the same as Eq. (8) of Ioannou et a1 [2] derived in 

the case of a finely focused beam. 

If the laser pulse has a flux N(t) that lasts for a finite time T, then 

the response Q",(t) will be the convolution of N(t) with Q't(t): 

t 

0 

Qi(t) = I N(T') Qi(t-t')dt' 

If N(T) is a square pulse of amplitude N and width T then, Eq. (12) 

yields for t > T 

22 

-t/z L a t/z - 

Qi(t) = OraNTe r- [( LV- 1 ) - 'a-l e erfc( LaJt/z) - 

22 L a (t-T)/z 

-e TIT e e r f c ( L a J ( t - T ) l r ) + L( ( L2a2-1)-l - ( L2r2-1)'l) 

4-6 
If S = r = 0, Eq. (13) reduces to 

Q",(t) = N T (l-R)[eT/Z-l] t > T 

which is a purely exponential function with time constant 2. 

As a more general statement, if S=O, the decay of the excess charge will 

be exponential independently of the shape of the surface at which the sample 

terminates and independently of the presence of internal fields. This can be 

proved by integrating the continuity equation, 

over the volume of the sample and applying the divergence theorem: 

- w' = - Sp'df - - 1Q' . z S at 

Here Q' is the excess minority-carrier charge and the integral above is the 

hole flux at the surface. This vanishes for S=O. Therefore, 

- 3Q' = - - 1 Q' and Q' = Q'(0) e -t/z , t>O . at z 

When SfO, eq. (13) implies that Q",(t) is not exponential. A measure of 

the deviation of Q", froin the exponential function (Constant exp( -t/T) follows 

froin considering the function: 

4-7 
- 1 db(t)/dt -dC1 nQttt (t) I du;/dt 

-- dt Q", =t+T 

where b(t) is the negative of the expression in the square bracket of 

Eq. (13). The smaller that [db(t)/dt)/b(t)] is the more accurate is the 

estimation of z by the slope of 1nQ1lt. 

One can prove that [db(t)/dtl/b(t) is an increasing function of S and 

1/T. 

excitation. Then Q", becomes: 

As a worst case, we consider infinite recombination velocity and impulse 

where N' is the strength of the pulse. In such a case: 

This is an increasing function of La and when La + =, then 

[db(t)/dt]/b(t)+l/Zt. Therefore, in the worst case, by measuring the slope 

1nQ1lt at time t, the time constant derived will be z/[l+(t/Zt)] instead of 

Z. Thus T/2t is an upper bound for the percentage error in determining Z. 

This bound is much lower than the one, 2.47 z/t, considered by Tyayi et a1 

[Z]. Consequently, the maximum error of Dziewior and Schmid [I] due to 

surface recombination is approximately ~/[2(5z)] = 10%. 

If an accuracy of 20% in the recombination lifetime is required, then 

0.8 = l/[l+(T/Zt)] which implies t=2t. Now the question arises: 

know when t is equal or greater than 2~? If Lad- > 2 Eq. (14) can be 

simp1 i f i ed : 

how can one 

4-a 
This implies that Q1'+,(2z)=0.05 Q1It(O) 1/La. 

estimate its range, then a can be chosen so that La<5, implying Q", (2~)>0.01 

Q1It(0). Therefore, by waiting until the response drops to 1% of its initial 

value, t will be greater than 27; and the error less than 20% 

If L is not known but one can 

IV. SUMMARY 

The excess charge stored in a sample after laser pulse excitation depends 

only on the flux of photons of the laser beam. 

charge is higher than the reciprocal of the bulk lifetime by, at most, a 

factor .t/2t. This is a result of surface recombination, the associated error 

of which can be suppressed below 20% by waiting until the response drops to 1% 

of its initial value when Lac5. Thus, in so far as the effects of surface 

recombination and of uniformity of the incident beam are concerned, 

photoluminescence decay is a reliable method for determining bulk lifetimes. 

The decay rate of the excess 

ACKNOWLEDGMENTS 

This work was supported by the Jet Propulsion Laboratory under Contract 

No. 956525 and by the National Science Foundation under Grant No. ECS-8203091. 

4-9 
REFERENCES 

[l] J. Dziewior, W. Schmid, "Auger coefficient for highly doped and highly 

excited silicon," Applied Physics Letters, vol. 31, No. 5, 1 Sept. 1977. 

[2] D. E. Ioannou, R. J. Gledhill, "Effect of surface recombination on the 

decay of excess minority carriers in semi conductors induced by finely 

focused picosecond pulsed laser beam," J. Appl . Phys., 56, (6), 

15 Sept. 1984. 

- 

[3] M. S. Tyayi, J. F. Nijs, and R. J. Van Overstraeten, "Effect of surface 

recombination on the transient decay of excess carriers produced by 

short wavelength laser pulses," Solid State Electronics, 5, pp. 411-415, 

1982. 

- 

4 - 10 

, 
FIGURE CAPTIONS 

Figure 1 Schematic i 11 ustrati on of an i nf i ni te semi conductor sample bounded 

by planes z=O, t=W, and excited by a laser beam. 

4 - 11 
I 

I 

I 

I 

I 

i 

I 

I 

I 

I 

I 

I 

I 

4 3' 

II 

N 

4 - 12 
CHAPTER FIVE 

IN HEAVILY DOPED SILICON 

I. INTRODUCTION 

TRAP CONTROLLED MINORITY-CARRIER MOBILITY 

Recently [l], we presented experimental evidence for low diffusivity and 

mobility of minority holes in hiyhly arsenic doped (concentrations 

lozo ~m'~) n-type Si. This evidence suggests that the minority-carrier 

- diffusivity (and mobility) is about an order of magnitude smaller than the 

majority-carrier diffusivity in comparably doped p-type Si. As an 

explanation, we suggested a simple transport model that emphasized trapping by 

localized tail states in the minority band. The commonly used assumption of 

an equal minority and majority-carrier mobilities and the neglect of the tailstates effects on the minority-carrier mobility was also questioned in a 

review article by Abrams et a1 . [E]. 

minority-carrier diffusion in n+ Si may be trap limited. 

Here we report qualitative evidence that 

Figure 1 illustrates the band structure, including the tail states, for 

n+ Si. As was already discussed in [l], for low-level injection, the minority 

holes occupy energy levels near the mobility edge E". In the model proposed, 

the holes from the extended states in the valence band can be captured by the 

localized tail-states for some mean time ttrapping, andthen released back 

into the valence band. This process, shown by arrows in the Fig. 1, will 

decrease the hole mobility. If the scattering rate of holes inside the band 

is comparable with the hole trapping rate, Sah and Lindholm [3] derive that 

is the characteristic co~~is~on free time dependent on the mean of 

the scatterin3 mean free time, tSc,tt, and the mean trapping time, ttrapPinJ, 

Here tcoll 

5-1 
of a minority hole trapped at a bound state energy level ET, and m* 

P 

effective mass for holes. 

is the 

P We investigate the temperature dependence of IJ. by 

estimating ttrapping c31: 

'Ittrappi ng e p = ATm exp [-(ET - Ev)/kT] (2) 

where A is a temperature independent constant. 

simplicity, trapping at one shallow level (close to EV) in the tail band or at 

an acceptor level in the n+ region. 

dopant acceptor (boron in our case) in the p-type substrate of a diffused or 

ion implanted n+/p diode. 

rn = 2 [3]. However, for band-tail distorted band, the value of m is not known 

and must be determined experimentally, as is attempted below. At low and high 

temperatures, respectively, (2) reduces to 

In (2) we have assumed, for 

Such an acceptor level can come from the 

For a parabolic valence band and no degeneracy, 

'/tcoll I low T = l/tscatt ' '/tcoll I high T = '/ttrapping (3) 

Combi ni ng (1) and (3), we obtai n the trap control 1 ed mi nori ty-carri er mobi 1 i ty 

where EA = ET - Ey > 0 is the activation energy of the bound-state level ET. 

11. EXPERIMENT AND ANALYSIS 

Our experiments provide qualitative support for the hole-trapping 

model . of the photocurrent response of both n+/p and p+/n photodiodes. 

The experiments involved a measurement of the temperature dependence 

The 

5-2 
wavelenyths of the incident light used create electron-hole pairs almost 

entirely in the heavily doped nt or pt region. 

minority carriers to the collecting p/n junction and the consequent shortcircuit current Isc depends on the minority-carrier mobility p and diffusivity 

0 [43. Hence Isc and its temperature dependence supplied a vehicle for 

Transport of photogenerated 

studyiny p nd 0. 

The devices for which we report findings here were fabricated by arsenic 

implantation into 5 Q-cm p-type Si substrates followed by 1200°C anneal for 

30 minutes. The resulting n+ layer was 1.5 pm deep and the sheet resistance 

was 10 B/square. The As concentration was - 1020cm-3 and nearly independent 

of position x over about 0.6 ptn below the surface (x = 0); for x > 0.6 pm it 

slowly decreases becoming about 3 x 1019cm-3 at 1 pm. The surface was 

unpassivated, covered only by a thin (- 10 A) native oxide layer. 

devices with both unpassi vated and SiOz passivated surfaces were a1 so 

studied. The results are similar to those to be presented here. 

Other 

The metal 

contacts covered less than 10% of the area of the front surface. 

The IsC(T) dependence was measured in the wavelength range h = 0.38 to 

0.4 pm for which the electron-hole generation rate follows G(x) = G(O)exp(-ax) 

[4], where a > lo5 cm" [SI. Hence contributions of G(x) to Isc oriyinating 

in the p/n junction space-charge region and in the p-type substrate are 

negl i gi bl e. Thus [41 

AqF(1 - K) aDp + Sp 

- 

P sinh (r) W + cosh (TT) W 'SL 

D 

ISC - a0 

P P P 

Here A is the device area, F is the illumination flux density, K'is the 

reflection coefficient, S is the effective hole surface recombination 

velocity, W = 1.3 pn is the thickness of the quasi-neutral n+ layer, 

P 

- 

L? - 

5-3 
(Dpp'p)1/2 is the hole diffusion length, T~ is the hole lifetime, and Dp is the 

hol e di f f usi vi ty . The analysis of (5) is complicated if one wishes to obtain the magnitude 

of the diffusivity 0 or mobility p = D (kT/q) from the measured Isc. In 

this note we are interested, however, only in a qualitative trends and try to 

present a simple picture consistent with the data. 

consider now the temperature dependence of Isc. The temperature dependences 

of a and R [63 and z = T~ (Auger lifetime) [7] are very small This leaves 

S and D as the only temperature dependent parameters in (5). We neglect the 

temperature dependence of S 

based on experimental results and on theoretical predictions. 

P PP 

For this purpose we 

P 

P P 

for a moment, later justifyiny this assumption P' 

Recent measurements indicate that L = 1 pm in the nt silicon doped at P 

about lo2' [8]. Using W/L = 1 we expand the hyperbolic functions in (5) 

and set sinh x = cosh x: 

P 

1 

ISC as 

B - [aDP + Sp] 

P 

where B = AqF(1-R)/W is a temperature independent constant. 

two special cases. First, if S >> aDp, Isc = B/a. In this case Isc f f(T) . This contradicts our experimental result that Isc increases with T (Fig. 2). 

Thus the second case prevails: a0 >> S (note that a > 10 cm ). P P 

Consider (6) for 

P 

5 -1 

To obtain the simple picture, we try the assumption, m=O, and find from 

(4) and (6) that 

IsC/T = C exp(EA/kT) (7) 

5-4 
where C is also nearly temperature independent. 

is predicted to yield the activation energy EA = ET - E". 

From (7), log (IsC/T) vs. 1/T 

On the other hand, if we make the more common assumption of equal 

majority-and minority-carrier mobilities (and diffusivities) , we would then 

observe 

IsC/T LI: C' 

where in deriving (8) we have used the consistent assumption of near 

temperature independence of the majori ty-carri er mobi 1 i ty (hole mobi 1 i ty = 

45 cm2/Vs at T = 20 K; 42 crn2/Vs at T = 300 K [SI). 

The experimental data to follow will decide in favor of (7) rather than 

(8) , implying trap-controlled minority-carrier mobility as opposed to equal 

minority-and-majority-carrier mobilities. 

Figure 2 shows the activation plot of Isc/T versus 1/T for two values 

of F. 

the inferred mobility depends weakly on T because (in our model) the bound 

states in the minority band tail have a negligible emission rate and tScatt is 

a weak function of T. 

in agreement with (1). For T > 160 K, pp levels off as predicted by (2) for 

shallow traps. From Fig. 2 we can distinguish two temperature ranges EA:' 

10 meV, 70 K < T < 160 K, and EA 

At low temperature, consistent with our simple model summarized in (7) 

Mobility drops at T N > 70 K (where tscatt - ttrapping 1 

N 

2 meV, T < 70 K. 

These activation energies do not have a simp1 e interpretation because of 

the many levels in the tail. Nevertheless, the value E = 10 meV and the 

decrease of p with increasing T are consistent with (2) and (4) of our model 

for shallow traps with (ET - EV) < kT. 

9 meV to about 8.5 meV as F is increased by a factor of five. 

A 

P 

Moreover, EA decreases from about w 

Increasing F 

5-5 
moves EFp closer to EV (Fig. 1) which increases the occupation of the tail 

states closer to EV and EA= 

observed. 

mobility activation behavior is observed, the variation of the energy yap with 

T is very small [lo], which justifies our assumption of nearly temperature 

independent a and R [SI. 

(ET - EV)/kT is expected to decrease, as 

In the temperature range froin about 70 K to about 160 K, where the 

The effect of the temperature variation of the effective surface 

recombination velocity S (T) on ISC(T), which was neglected, is now made 

credible by the following considerations. 

expected to be about EG/E = 0.55 eV in a Shockely-Read-Hall model even though 

the surface has distributed states in the energy yap [ll]. Second, S at the 

heavi ly-doped n+ surface is 1 i kely domi nated by temperature insensitive Auger 

effects [ll]. Third, results similar to those shown in Fig. 2 were also 

obtained from the devices for which passivation by SiOz sharply decreased S 

P 

First, if S (T) is important, EA is P 

P 

P' 

The fact that Isc is not negligible below - 100 K indicates that most of 

< the minority holes are in the extended band states at T - 100 K with only a 

small fraction trapped at the tail states and immobilized. For the 

excitations used to measure IsC(T) and also for low-level hole injection in 

the dark used in [l], the hole concentration in the n+ region is very small. 

We can then conjecture that the penetration of the localized tail states into 

the energy gap is only a very small fraction of the energy gap. This 

supposition, based on our data, agrees with recent theoretical calculations of 

the band structure of heavily doped Si L-121. 

It follows directly from our trapping model that p(minority) < 

p(inajority) could apply also in the absence of the tail states because shallow 

impurity levels can act as traps near the minority-band edge (Fig. 1). This 

suggests that p(minority) may strongly depend on Compensation. A lack of 

5-6 
compensation in their epitaxial p/n diodes may be responsible for the 

experimental observation by Oziewior and Si 1 ber [13] that p(mi nority) = 

p(majority) for concentration in si < 1019 cm-3. 

Although the assumptions needed to derive (7) from (5) introduce some 

inaccuracy in the model for the activation energy of minority-carrier mobility 

(diffusivity), the general conclusions derived by comparing (7) with the 

experimental trends exhibited in Fig. 2 are anticipated to remain valid. The 

exact value of the activation energy in a single-trap model remains in 

question. When more detailed knowledge concerning the values and the 

temperature dependencies of parameters in (5) become available, one can then 

use data presented here to explore aspects of the minority-carrier band tail. 

The purpose here is less ambitious. We have demonstrated activation 

behavior of the minority-carrier mobility and diffusivity, exhibiting thereby 

an activation energy of the order of kT (for 300 K) as one expects for the 

prominently active tail states. Moreover, our data in Fig. 2, as interpreted 

here, supports the inadequacy of the commonly used assumption of equal 

majority- and-minority-carrier mobilities; in turn, this supports 

interpretations, such as that in [l], of larger values of energy-gap narrowing 

than is common in the literature. 

Lastly, we point out that the assumed value, m = 0, and values in < 0 in 

(4) are self-consistent with the experimental results of Fig. 2, but values 

m > 0 are not. 

shows an activation behavior, thus the assumption of p(majority) = p(mi nori ty) 

is always wrong (see Eq. 8). 

This work was supported in part by National Science Foundation Grant 

ECS-8203091 (A.N.), Solar Energy Research Institute Contract No. XB-3-02090-2 

(F.A.L., A.N.), and Jet Propulsion Laboratory (C.T.S.). We acknowledge useful 

discussions with Peter T. Landsberg. 

However, regardless of the value of m, the ISCTm VS. 1/T plot 

5-7 
REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

A. Neugroschel, S.C. Pao, and F.A. Lindholm, IEEE Trans. Electron 

Devices , ED-29, 894 (1982) . K. A. Abram, G. J. Rees and B. L. H. Wilson, Adv. Phys., - 27, 799 (1978) . C.T. Sah and F.A. Lindholm, Solid-state Electron., - 16, 1447 (1973). 

H.J. Hovel, Solar Cells, (Academic Press, New York, 1975). 

G. Lubberts and B.C. Burkey, J. Appl. Phys. - 55, 760 (1983). 

W.C. Dash and R. Newman, Phys. Rev. 99, 1151 (1955). 

J. Dziewior and W. Schmid, Appl. Phys. Lett., - 31, 346 (1977). 

G. E. Possin, M. S. Adler, B. J. Baliga, IEEE Trans. Electron Devices, 

ED-31, 3 (1984). -. 

C.T. Sah, P.C.H. Chan, C.K. Wang, R.C.Y. Sah, K.A. Yamakawa, and 

R. Lutwak, IEEE Trans. Electron Devices, ED-28, 304 (1981). - 

See, for example, S. M. Sze, Physics of Semiconductor Devices, Wiley 

1969, p. 24. 

P.T. Landsberg and M.S. Abraham, Solid State Electron., 26, 841 (1983). 

A. Selloni and S.T. Pantelides, Phys. Rev. Lett., 49, 586 (1982). 

3. Dziewior and D. Silber, Appl Phys. Lett., 35, 170 (1979). 

- 

- 

- 

5-8 
F XGURE CAPTIONS 

Qualitative illustration of the band edges of heavily doped 

n'-si 1 icon. The broken 1 i nes show the unperturbed parabol i c 

bands. The positions of both the electron and hole quasi-Fermi 

Fig. 1. 

levels is also indicated. The arrows near EV indicate hole capture 

and emission by the tail states and by the acceptor level from the 

p-type substrate. The penetration of the tail states into the 

forbidden gap is assumed to be very small in comparison with the 

bandgap EG = EC - Eve 

Fig. 2. Normalized short-circuit photocurrent versus 1/T for A = 0.4 ~JTI. 

The illumination density for curve 1 is five times larger compared 

to that of curve 2. 

5-9 
-Q------ E, (acceptor level) 

IA 

DENSITY OF STATES -- 

Fig. 1 

5 - 10 

~~ ~ 
I 

\ 

Fig. 2 

5 - 11 
CHAPTER SIX 

DETAILED INTERPRETATION OF PHOTOCONOUCTIVITY 

DECAY RESPONSE FOR LIFETIME OETEKHINATION 

Our purpose here is to clarify the relation between the observed 

transient photoconduct i ve decay and a previ ous devel opment of the detai 1 ed 

physics [l] underlying this transient. 

To make this clarification concrete, we begin with a review of the work 

of Othmer and co-workers, who compared photoconductivity-decay lifetime with 

steady-state lifetime for silicon [Z]. Figure 1 reproduces this comparison. 

The steady-state lifetime was measured by steady-state photoconductivity and 

the transient lifetime was measured by transient photoconductivity. By 

introducing various impurities (Zr, Mn, Mg, Ni, and V) known to produce 

recombination centers in Si and by varying the concentrations of these 

impurities, Othmer and co-workers varied the steady-state lifetime. 

scatter of the data. 

photoconductivity decay 1 ifetiine considerably more than a factor of two 

greater than the steady-state 1 ifetime. 

Note the 

Note also the large number of data points yielding a 

From Othmer's results we see that the photoconductivity decay is 

characteri zed by an apparent single characteristic time; yet this 

characteristic time differs considerably from the steady-state 1 ifetime. 

To suggest an explanation for this apparent anomaly, we review briefly 

some aspects of our prevous theoretical work on fast photoconductive switches, 

which we have called photoconductive circuit elements [l]. In these devices, 

incident light creates hole-electron pairs in very high injection in a nearly 

intrinsic reyion of a p/i/n or n/ih or p/i/p photoconductor. 

combination of a Oernber field and a hiyh surface recombination velocity causes 

a peak in the hole and electron density in the y direction normal to the 

Though a 

surface on which the light shines [31, integration of the continuity equation 

6-1 
in the y direction leads one to analyze a related device having no dependence 

of variables in the y direction in the active region. 

resembles that used in MOSFET theory to reduce the number of space variables 

requi red .) 

(This approach 

Then, provided the injection level is high enough that tne particle 

dielectric relaxation time is much less than the drift transit time in the 

x direction resulting from an applied electric field, the device is in a 

quasi-neutral condition [l]. Thus the turn-off transient becomes a problem in 

quasi-neutral photoconductive decay in the simplest model : that in which the 

x or y coordinates do not enter. 

Despite this reduction to a simple model, some complexities arise from 

recombination through many traps--a prorni nent feature of this class of 

photoconductive device [l]. For example, for incremental variations in the 

particle electrochemical potentials, variations that are much smaller than a 

thermal voltage, a detailed description of decay involves two characteristic 

times for each participating bound state in the forbidden band. This 

contrasts with the single characteristic time, the high-level recombination 

lifetime, that prevails for the time-invariant steady state. Note that these 

multiple characteristic times apply only for incremental times. In Ref. 1, 

apparently the first method is developed for determining large-signal 

transient that incorporates these mu1 tiple time constants. 

For the recombination parameters indicated in Fig. 2, we coinpare the l/e 

fall time calculated by this method with that resulting from the standard 

steady-state 1 i fetime, a si ng1 e-1 eve1 Shock1 ey-Read-Hal1 mechani sm. From this 

comparison we see two key results. First, the single-1 ifetime calculation 

underestimates the l/e fall time by about a factor of 1.5 in this example. 

This effect results from the trap readjustment time [l], which is neylected in 

6-2 
the standard single-lifetime model. Second, the net effect of two 

characteristic times, which exist for incremental times, yields an essentially 

single-exponential decay for the large-signal response. 

The combination of these two results suggest an interpretation of the 

data of Fig. 1 different from that advanced by Othmer and co-workers [e]. We 

suggest that the observation of photoconductive decay exhibiting an apparent 

single characteristic time that differs considerably from the steady-state 

lifetime is not an anomaly. 

physics of photoconductive decay for samples having a large density of 

Rather this results directly from the underlying 

recombination centers . -. . 

This physics has several features. First, for incremental times and 

small-signal responses, as defined above, two characteristic times are needed 

for each recombi nation-center level to describe fully the transient decay. 

This detail of the physics was first advanced by Sandiford [4] and later was 

extended by Sah [SI. 

yield the large-signal decay response. 

Ref. 1. Third, the large-signal response has an apparent single 

characteristic time (which exceeds the steady-state 1 ifetime) that prevails 

over several decades of decay of the excess carrier densities. This third 

feature was overlooked in Ref. 1, and apparently has not appeared previously. 

It provides a key to the detailed interpretation of photoconductive-decay 

experiments. 

Second, the incremental decay response can be used to 

A method for doing this appears in 

We acknowledge the support of the Silicon Solar Array Project of the Jet 

Propulsion Laboratory, California Institute of Technoloyy, in conjunction with 

NASA and DOE. 

aspects of this and related work. 

We thank Bob Haminond and C. Tang Sah for help on technical 

6-3 
REFERENCES 

1. B. Y. Hwang, F. A. Lindholm and R. 6. Hammond, "Methodology for 

calculating turn-off transient of photoconductive circuit elements 

in picosecond optoelectronics ,'I IEEE J. Quantum Electron. , vol . QE-19 , pp. 648-657 , Apr. 1983. 

2. S. Othmer and S. C. Chen, "Characterization of nonideal silicon in 

terms of lifetime and diffusion length," in 14th IEEE Photovoltaic 

Speci a1 ists Conf. , pp. 1238-1243, 1978. 

3. B. Y. Hwang and F. A. Lindholm, "Dember effect in fast 

photoconductive ci rcui t el ernents ,'I IEEE Electron Devices , VO~. ED-31, pp. 101-104, 1984. 

4. D. J. Sandiford, "Carrier lifetime in semiconductors for transient 

conditions," Phys. Rev., vol. 105, p. 524, 1957. 

5. C. T. Sah, "The equivalent circuit model in solid-state electronics, 

Part I: The single energy level defect centers," Proc. IEEE, 

VO~. 55, pp. 654-671, 1967. 

6-4 

, 
FIGURE CAPTIONS 

Fig. 1 Comparison of photoconductivity decay 1 ifetime measured by 

Westinghouse and steady-state 1 ifetime measured by Northrop on 

symbols dsrived from the same ingots [Z]. 

Fig. 2 Comparison of decay times for capture rates (thermal velocity times 

capture cross section) cn = c = cm 3 /s, NTT = 10l8 cm3. P 

Curve (a), calculated by using two transient time constants, 

contrasts with curve (b), calculated using a model based on a 

single steady-state lifetime. The l/e decay time is 1.5 times 

longer than that predicted by a single steady-state lifetime for 

the parameters chosen. This theoretical dependence, for InP, will 

scale properly, for example, for Si, where a capture cross section 

of 

electrons in InP) and a flaw density of ld5 will yield z = 1 ps. 

and a thermal velocity of lo6 cm/s (> lo7 cm/s for 

6-5 
WESTINGHOUSE-MEASURED LIFETIME, )IS 

d 0 d in b 

I I' I I 

e 

6-6 
1 

1 014 

1 ol2 

1 o-’O s 

I 1 1 

1 1 1 

2 4 6 a 10 0 

1 O1O 

-.- 

6- 7 
CHAPTER SEVEN 

GENERALIZED RECIPROCITY THEOREM FOR SEHICONOUCTOR DEVICES 

1 

In a recent paper, Donolato has proven a version of the reciprocity 

theorem for the charge collection by a p-n junction in the presence of a unit 

point generation source. The proof was restricted to a uniform material in 

which only the lifetime was allowed to vary with position. We extend this 

proof to p-n junction devices haviny three-dimensional space dependencies of 

all material parameters. 

for transients and state another form of reciprocity relating quasi-Fermi 

levels and point generation in a quasineutral region under low injection 

condi ti ons. 

In addition, we prove that reciprocity holds also 

The conventional rsci proci ty theorem re1 ati ng input voltages and output 

2 

currents in the base of a transistor was proven by bf. Shockley et al. in one 

of the early papers on p-n junction transistors. 

Shockley's procedure in order to prove reciprocity for charge collection. 

In this letter we generalize 

The principal quasineutral region of the diode, where carrier generation 

and recombination takes place, is bounded by the junction SI] and the rest of 

the surface SL (lateral and back surface) characterized by a position 

dependent surface recombination velocity 5'. 

p-type in low injection. Extension to n-type regions is straightforward. TWO 

different excitation cases are considered. 

biased by a voltage V in the dark. 

and a point generation source of strength G is applied at point r'. 

and J',n' are the minority (electron) current density and excess minority 

carrier concentration for cases 1 and 2 respectively, then the boundary 

conditions for each case are 

The region is assumed to be 

In case 1 the junction is forward 

In case 2 the junction is short circuited 

If 3, n 

7-1 
where fJ is a point on the junction edge SJ and 

carrier concentration. The continuity equation 

- where 6(r - r' ) represents a unit point carrier 

r = r' , and T is the lifetime. Because of low 

no is the equilibrium minority 

for cases 1 and 2 is 

G 6(r - r') 

generation source app 

njection, the electri 

ied at 

field 

E, the mobility p and the lifetime T are independent of the excitation. 

system is linear. 

The 

Let vector A be defined by the equation - .- 

The surface integral J A*ds vanishes since on SL 

sL 

From Eq. (1) this integral on SJ becomes 

Ads = Eexp($) - 11 ,f J'ads = [exp(kT) Lt!. c 

- 11 I' 

where I' is the current due to the point source ex ting the p-type reg 

through the junction. Therefore, if S is the entire surface enclosing 

(5) 

on 

the 

quasineutral region, then from Eqs. (4), (5) the total surface integral of A 

becomes 

7-2 
By using Eq. (2) , the Ei nstei n re1 ationshi p for non-degenerate minority 

carriers, U = (kT/q)p, 

-(kT/q)vln no, the divergence of A can be written as 

and the expression for the electric field E = 

- n 0. J' - - n' [Vn' - n'Vln no]=J - - n n V=J = 

0 0 

- 1[Vn + nEl=[qpn'E + qDVn'] - q fl- n zl n' + G 6(r - r')] n kT 

0 0 

- 1 nn' n pkT[vn + nE]=[& n'E + vn'] t q - - q n G 6(r - r') 

0 n7 

0 0 

By using Guass' theorem and from Eqs. (6) and (7) 

I A=ds = I V=A dv => [exp(-) qv - 131' = S V kT 

n n(r') G 

qn(r'J ' - q I G 6(r - r')dv = - 

vo 0 

7-3 
Equation (8) is similar to Uonolato's final expression. 

because we include position dependencies of p, 0 and no(x) . 

It is more general 

We introduce the minority carrier quasi-Fermi level in dark, F,, 

referenced to the majority carrier Fermi level, which is assumed position 

independent . Then, Eq. (8) becomes 3 

- 

becai 

exp(Fn(t')/kT) - 1 

I' = - q G f f(V) exp(qV/kT) - 1 

se of linearity. Thus we can choose V conveni 

exp(qV/kT) - 1 = 1. Then Eq. (9) becomes 

- 

I' = - q Cexp(Fn(r')/kT) - 11 G 

ntly so that 

Equation (10) expresses that the probablility of collection of a minority 

carrier generated at point r' is exp(Fn(r')/kT) - 1. 

In a similar manner, one could prove another form of the reciprocity 

theorem applying to a quasineutral region in low injection: the minoritycarrier quasi-Fermi level at point 1 due to a point source applied at point 2 

is the same as the minority-carrier quasi-Fermi level at point 2 due to the 

same source applied at point 1. 

These theoreins hold also for transients. This is proved by replacing n,I 

and n' ,I' by their Laplace transforms and by transforming the continuity 

equat i ons for zero i ni t i a1 condi ti ons : 

7-4 
1 1 

4 

- - VaJ(s) = - (s + ;)n(s) , 

- - 1 v=J'(s) = - (s + -)n(s) 1 t G(s)G(r - r') q 7 

Substitution of Eq. (11) into (7) and (8) will give the same result as in the 

steady state. 

Equation (10) could be useful in solar cell theory since it allows the 

calculation of short-circuit current from the analysis of the device under 

dark conditions: 

where 1,2 represent the quasineutral emitter and base of the cell , F, is the 

minority carrier quasi-Fermi level in each region in dark and under bias V 

such that exp(qV/kT) - 1 = 1 and G is the generation rate. Equation (12) 

holds under the same assumptions underlying the proof of the reciprocity 

theorem and ignores generation in the space charge region. 

The major assumption in deriving Eq. (8) was low level injection so that 

the system could be treated as linear. Low injection guarantees linearity of 

the system even in the presence of the effects of heavy doping or graded 

chemical composition. In this case, in the equation -vln n = qE/kT, E will 

be the minority carrier field which includes the quasi-fields arising from the 

position dependent energy gap electron affinity and density of states. 

0 

7-5 
. 

Therefore, the original Shockley's proof of reciprocity can be extended 

to heavily doped three dimensional base regions to obtain re1 ations between 

input voltayes and output currents. In this sense, Shockley's proof is more 

general than the recently pub1 i shed proof of reciprocity i n one- dimensi onal 

transistor base regions which takes into account heavy dopiny effects. 

4 

The practical significance of reciprocity is that it can reduce the 

number of unknowns in a problem and reduce the amount of calculations 

3 needed. As an example, in the recent paper by del Alamo and Swanson , the 

quantum efficiency of an emitter could have been found by integrating 

Eq. (lo), since the minority carrier Fermi level as a function of position was 

a1 ready numerical ly cal cul ated under dark condi ti ons. In addition, thei r 

forward and reverse transport factors and saturation currents are related by 

the relation afJof = arJor. Thus the present reciprocity theorem can find use 

in the measurement of such device parameters as the surface recombination 

vel oci ty at a polycrystal 1 i ne si 1 icon contact. 

- 

A1 though not discussed here, reciprocity re1 ations enter the physics of 

many different phenomena, such as heat conduction or therinoel ect ri c effect . These relations are based on fundamental considerations relating to detailed 

balance under thermal equi 1 i bri um and Onsajer' s principle of microscopic 

reversibility. 

ACKNOWLEDGMENTS 

This work was supported in part, by the Jet Propulsion Laboratory and 

Motorol a, Inc. 

7 -6 
, 

REFERENCES 

1 C. Oonolato, Appl . Phys. Lett. 46, 270 (1985). 

2 W. Shockley, M. Sparks and G. K. Teal, Phys. Rev. 83, 151 (1951) . 3 3. A. del Alamo and R. M. Swanson, IEEE Trans. Electron Devices €0-31, 1878 

(1984) . 4 H. J. De Man, M. Y. Ghannam, and R. P. Mertens, IEEE Trans. Electron Oevices 

ED-31, 1720 (1984) 

7-7 
CHAPTER EIGHT 

AND MOBILITIES IN SILICON 

MINORITY-CARRIER DIFFUSION COEFFICIENTS 

Minority-carrier mobility is one of the principal parameters determining 

the transport properties of minority carriers in p-n junction devices. 

majority-carrier mobility (conductivity mobility) is important for 

determination of the resistance of semiconductor regions. 

theoretical expressions for the conductivity mobility in both the n- and ptype Si are available [l-61. 

for the minority carriers. 

mobilities of electrons and holes l.~ using the Haynes-Shockley pulse 

method. 

ohmic drop of forward-biased p-i-n diodes. 

determined the minority-carrier diffusion coefficients, ll = (kT/q)v ,in the 

doping range from about lOI7 ~rn-~ to about 

diffusion length of the minority carriers generated by 10.7 MHz optical , 

excitation. These recent data show good agreement with the conductivity 

electron mobility, but the hole mobility in n-type Si was up to -30% higher 

than the hole conductivity mobility in p-type Si. 

confirmed the result of [lo] for one value of doping (NDD = 2.6 x 10l8 

The 

Accurate data and 

Only very limited date are presently available 

Prince [-/I measured the minority-carrier drift 

P 

Dannhauser [81 and Krausse [9] measured the sum (11, + p from an P 

Recently, Dziewior and Silber [lo] 

cmm3 by measuring the complex 

Rurk and de la Torre [ll] 

In contrast to the results of [lo], the measurements of Prince [7] 

show that both pn and IJ are smaller than the majority carrier values. 

possible reasons for the discrepancies are discussed in [lo]. 

reasons may be due to the insufficient purity of Si crystals used in 1954 by 

Prince [7]. 

Some P 

Additional 

Recause of the scarcity of the accurate and reliable values for minoritycarrier mobilities and because of discrepancies among the results quoted 

above, modeling of p-n junction devices is based on a convenient assumption of 

8-1 

? 
. 

equal minority and majority carrier mobilities. In addition to [lo], several 

other theoretical [12-141 and experimental [15,161 works suggested that the 

above assumption is not valid, particularly in heavily doped Si. To verify 

this assumption, we present a new and accurate method for measurement of the 

minority-carrier diffusion coefficients in semiconductors. The method is 

applicable for both low and highly doped materials and is demonstrated here 

* for low doped Si. 

The present method is based on a direct measurement of the transit time 

of the minority carriers through a narrow region of a p-n diode. Assume a p+- 

n diode in which the hole diffusion length L 2 W, where W is the width of the 

n-base region terminated by an ohmic contact with recombination velocity S. 

As was shown by Gonzalez and Neugroschel [17], the real part of the smallsignal hole admittance for frequencies w 2 10/~~ follows the ,'/' dependence 

according to 

P 

GHF = K(0 /L )(wP/2) 1 /2 

P PP 

2 where K = (q/kT)(qA ni/NDD) exp [(qV/kT) -11 is a constant depending on device 

area A, base doping density ND~, temperature ni2(T), and applied voltage V, 

and T = (L2/0 ) is the hole lifetime. 

to the low-frequency value for large Sp given by the standard relation 

The extrapolation of this dependence P PP 

GLF = K(D /L ) coth(W/L ) gives an intercept at 

P PP P 

wI = (20p/LE) coth2 (W/Lp) . 

This can be further simplified for (W/Lp) 5 0.3 as 

8-2 
2 wI = 2Dp/W = l/~~ (3) 

where T~ = W2/2D is the transit time across the base. 

P 

Equations (2) and (3) are the basis of the method proposed. The method 

requires the measurement of only one parameter GFF, and is applicable for any 

narrow region with known value W, regardless of doping. 

To demonstrate the method, we show in Fig. 1 the measured and theoretical 

dependencies of G vs frequency f = w/2n for a p+-n device with NDD = 7.25 x 

1014 ~m'~ and W = 310 pm. The intercept frequency is fI = 6.59 kHz. 

obtain Dp we use (2) with accurately measured c17-191 Lp = 500 

obtain Dp = 15.71 f 1 cm2/s and p = 608 2 40 cm2/Vs at T = 300 K. This value 

for the mobility is about 30% higher than the majority-carrier value of 470 

cm2/Vs [2]. 

accuracy which is discussed in more detail below. 

P 

To 

10 vm and 

P 

The error of about f 40 cm2/Vs is an estimated total experimental 

The error in using (2) instead of (3) is very small. For example, a 10% 

error in L for the sample in Fig. 1 yields less than 1% error in Dp. 

error can be eliminated by using thinner samples as shown later. 

the above result from the measured conductance we assumed a negligible 

contribution of the p+-emitter to the conductance. 

noting that the intersect frequency corresponding to the emitter transit time 

ttE is fIE = (1/2n)(l/ttE) = (1/2n)(2nn/~1E) = 109 HZ for wE = 0.2 1~m and D, - 

1 cm2/s, which is much smaller than the observed base fIB = 6 kHz in Fig. 1. 

FIote also a small hump at the knee in Fig. 1, which is characteristic of the 

base' and would disappear if the emitter (or shunt conductance) contributions 

were larger than about 5%. The dominance of the base was in addition 

confirmed by comparing the measured dc current with that calculated from the 

base parameters. 

The 

In obtaining 

P 

This can be justified by 

> For f - 60 kHz, the G vs f dependence for the sample in 

8-3 
Fig. 1 begins to bend upwards and converges to the G a f2 dependence because 

of the effects of the series resistance of the sample. This range is not 

displayed in Fig. 1. 

In the samples where the emitter contribution is small, but not 

negligible, GHF a 

(where the base contribution prevails) it converges to GHF = u1/2. 

then use (1) in the u range to obtain 

tollm, where m < 2 at the knee, but for higher values of w 

We can 

Using (4) for the device from Fig, 1 we obtain p 

very good agreement with the 608 

latter value is more accurate because of large sensitivity of K in (4) to 

677 cm2/Vs which is in 

The 

P 

40 cm*/Vs value obtained from (2). 

ni 2 (DP a l/KZ = l/ni4). The value of np used above was from Putley and 

Mitchell [ZO]: nf = (9.61 x 10 32 )T 3 exp [-1206/(kT/q)]. 

valid regardless of the value of S at the contact. 

Note also that (4) is 

Table I summarizes the results from the devices used in this paper. The 

conductance was measured using a Wayne-Kerf B224 bridge and Hew1 ett-Packard 

4274A and 4275A LCR meters. The device BJT is a bipolar nt-p-nt transistor 

with a uniformly doped base with W = 16.5 vn and Ln = 115 um 1211. 

for pn for this transistor was obtained from (3) by measuring the frequency 

dependence of ic/vBE, which is equivalent to (1) for diode. 

using a bipolar transistor is that the collector current ic always follows the 

ideal exp (qVBE/kT) dependence and that the ic depends on the base properties 

only. The base width W was measured using a precision mechanical indicator 

with a resolution of - 0.5 ~rn on the diode structures and by angle lapping and 

staining for the transistor. The error in W was less than about 3% for diodes 

The value 

The advantage of 

8-4 
, 

(W = 240-310 pm) and was due mostly to the nonuniformity of the large area 

samples used (- 0.5-1 cm2). 

samples. The dopant density was obtained by the junction C-V method. 

estimated overall error of the method for the low-doped devices showing a good 

G = f ''2 dependence is about 5%. The error will be larger for thinner high 

doped devices due to the increased error in determining W. 

Figures 2 and 3 show the results from Table I plotted together with the 

This error can be reduced using smaller size 

The 

results from [lo] and one point from [ll]. For comparison we also show the 

majority-carrier values by Thurber, et al. [1,2]. 

the electron minority-carrier mobility is about the same as the majoritycarrier mobility, but the minority-carrier hole mobility is larger than the 

Our present data show that 

corresponding majority-carrier mobility. 

is about 30%. 

and Silber [lo]. Temperature dependence of p and pn was also studied on 

samples from Table I in the range 300K-360K. The preliminary results are that 

p 

majority- carrier mobilities [5,6]. 

For PIDD - 1015 cmm3 the difference 

Our data are thus consistent with the previous work of Dziewior 

P 

T-" , where m 2 - 2.5, similar to the temperature dependence of the 

In summary, a new method for direct measurement of the minority-carrier 

diffusivity and mobility was presented and demonstrated for low-doped Si . The 

method is accurate and requires only a knowledge of geometry in properly 

prepared test samples. Signi ficant differences (- 30%) between the minority 

and commonly used majority carrier values were obtained for p 

found in good agreement with the majority carrier values, 

while p, was P' 

The measurements'can be extended to higher concentrations up to 

- lozo cf3. 

because W has decrease as concentration increases to asslire L 2 14. 

for the concentration range lo1' - lo2' 

This however requires measurements at higher frequencies, 

Results 

will be reported separately. 

8-5 
ACKNOWLEDGMENTS 

This work was supported by the National Science Foundation under Grant 

ECS-8203091, by Motorola Inc., Mesa, AZ and by JPL Contract 956525. 

8-6 
REFERENCES 

1. W. R. Thurber, R. L. Mattis, Y. M. Liu, and 3. J. Filliben, 

W. R. Thurber, R. L. Mattis, Y. M. Liu, and 3. 3. Filiben, 3. Electrochem. 

J. Electrochem. SOC., vol. 127, no. 8, p. 1807, 1980. 

SOC., vol . 127, no. 10, p. 2291, 1980. 

2. 

3. 6. rlasetti, M. Severi, and S. Solmi, IEEE Trans. Electron Devices, 

VO~ . ED-30, p. 764-769, 1983. 

4. J. A. del Alamo and R. M. Swanson, 3. Appl Phys., vol 56, p. 2250, 1984. 

5. S. S. Li and W. R. Thurber, Solid-state Electron., vol. 20, p. 609, 1977. 

6. 

7, M. R. Prince, Phys. Review, vol. 93, p. 1204, 1954. 

8. Fb Dannhauser, Solid-state Electron., vol. 15, p. 1371, 1972. 

9. J. Krausse, Solid-state Electron., vol. 15, p. 1377, 1972. - 

S. S. Li, Solid-state Electron., vol. 21, p. 1109, 1978. 

- - - 

10. J. Dziewior and 0. Silber, Appl. Phys. Lett., vol. 35, p. 170, 1979. 

11. 0. E. Rurk and V. de la Torre, IEEE Electron Device Letters, vol. EDL-5, 

p. 321, 1984. 

12. H. S. Bennett, Solid-state Electron., vol. 26, p. 1157, 1983. 

13. W. P. Dumke, Solid-state Electron, vol. 28, p. 183, 1985. 

14. E. 0. Kane, Solid-state Electron., vol. 28, p. 3, 1985. 

15. A. Neugroschel and F. A. Lindholm, Appl. Phys. Lett., vol. 42, p. 178, 

1983 . 16. A. Neugroschel, F. A. Lindholm, and C. T. Sah, to be published in Solar 

Cells, 1985. 

17. F. N. Gonzalez and A. Neugroschel , IEEE Trans. Electron Devices, 

VO~. ED-31, p. 413, 1984. 

18. A. Neugroschel, IEEE Trans. Electron Devices, vol. ED-28, p. 108, 1981. 

19. T. W. Jung, F. A. Lindholm, and A. Neugroschel, IEEE Trans. Electron 

Devices, vol . ED-31, p. 588, 1984. 

20. E. H. Putley and W. H. Mitchell, Proc. Phys. SOC. London, vol . A72, 

p. 193, 1958. 

21. M. S. Birrittella, A. Neugroschel , and F. A. Lindholm, IEEE Trans. 

Electron Devices, vol. ED-26, p. 1371, 1979. 

8-7 
c 

TABLE I 

Summary of results at 300 K. 

~ 

Device pP pn Base Rase 

Dopant nopi ng 

(cm-3) (crn2/Vs (crn2/Vs ) 

s2 Phosphorus 7.25 x 1014 608 f 40 

5N Phosphorus 3.32 x 1015 620 f 40 

SP9 Boron 1.34 1015 1288 f 50 

BJT Boron 1.40 1015 1256 f 50 

5P Boron 6.31 1015 1200 f 100 

8-8 
FIGURE CAPTIONS 

Fig. 1. Normalized small-signal conductance versus frequency for the sample 

S2 from Table I. The conductance follows the G 

for f - 25 kHZ. 

Minority-and-majority-carrier hole mobilites versus doping 

concentration at 300 K. The error bars for the present data are also 

shown. 

carrier data given by Thurber et al. [Z]. 

approximate fit to the present and previous minority-carrier results 

f "2 dependence 

> 

Fig. 2. 

The solid line is a computer curve fit of the majorityThe broken line is an 

cm. 

Fig. 3. Minority-and-majority-carrier electron mobilities versus doping 

concentration at 300 K including error bars for the present data. 

computer curve fit for majority electrons by Thurber et al. [l] is 

shown for cornpari son. 

A 

8-9 
CHAPTER NINE 

DISCUSSION AND RECOMMENDATION 

Heavily doped polysil icon (Chapters Two and Three) provides the vehicle 

for a new class of silicon solar cell designs. 

exceed 23%. This view is consistent with the projections of C. T. Sah (see 

Chapter Two) made in his research supported by JPL. 

Ultimate efficiencies may 

Our study described in Chapter Four strongly suggests the validity of the 

Auger-impact rate coefficients for Auger band-band recombination determined by 

Oziewior and Schmid (1977), despite the views of other workers. Chapter Five 

provides support for the model for low minority-carrier mobilities in highly 

doped silicon that was proposed by Neugroschel and Lindholm in 1983, under the 

- -- 

support of JPL. 

All of the issues described in Chapters Two through Five are critical 

both to the design of high efficiency silicon solar cells, with the aid of 

computer programs (such as JPL's SEEMA programs), and to the assessment of the 

maximum obtainable practical conversion efficiency for silicon solar cells. 

Chapter Six may help prevent a misinterpretation of the connection 

between recombination 1 ifetime of starting material and the photoconductivedecay data by which it is measured. 

The generalized reciprocity theorem of Chapter Seven is presented in 

brief mathematical style. 

many useful design results will flow from it. The connection it provides 

between dark current and internal quantum efficiency is outlined as a prelude 

Its applications are wide, and we anticipate that 

to further uses. 

Minority-carrier mobility and diffusivity in dilutely doped silicon has 

received little attention since the work of Prince in the 1950's. 

values have been assumed to be available in the standard tables found in text 

and reference books. 

Appropriate 

Our new results should be incorporated into the 

9-1 
numerical values used in either analytical or computer-aided design of silicon 

solar cell . More important than the results of Chapter Eight is the method by which 

the results are obtained. 

carrier diffusion coefficient and mobility of heavily doped silicon. 

determination is essential for systematic design of silicon solar cells. 

will lead also to a determination of the surface recombination velocity 

adjoining highly doped layers. The work of the Stanford group (del Alamo, 

Swanson, and Swirhun) supported by JPL has clarified the utility of 

considering the minority-carrier equilibrium concentration and the effective 

doping concentration as an inseparable, and experimentally determinable, 

An extension of this method can yield the minorityThis 

It 

\ 

quotient. This utility extends only to devices for which the heavily doped 

layers end at surfaces having very large surface recombination velocity S. 

When the surface is passivated, the minority-carrier diffusivity must be 

determined to yield S, and S and effective doping concentration must 

apparently be separately determined experimentally. 

will have such passivation, this becomes a key issue. 

method of Chapter Eight will be part of our approach toward the solution of 

this design and analysis problem. 

Because most solar cell s 

Furthering of the 

9-2 
In 

0 

I I I I ~ 

FF 0 

r 

r 

0 

0 

r 

> 

0 

FIG. 1 

n 

N 

I 

>. 

0 

z 

W 

3 

0 

W 

u, 

Y 

a 

8 - 10 
/ 

/ + 

I 

I 

I 

/ 

/ 

/ 

0 

t’ 

L 

a 

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v) 

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E 

m 

0 

- .- 

L 

.- 

3 

0 

0 

a 

N 

.- 

a 

0 

Icp 

A 

Q) 

L 

L 

n 

m 

E 

cp 

x 

3 

i 

m 

a 

cp 

Q 

er 

n 

L 

a aL 

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10 

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0 

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er 

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er 

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n 

I 

I 

I 

a 

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0, 

a 

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7 

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c 

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er 

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c) 

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tu 

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r 

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E 

> 

c 

v) 

2 

W 

W 

4 

0 

I 

0 

Y 

- 

n 

FIG. 2 

8 - 11 

~ ~~ 
! 

I I 1 I I I I 

a 

QI 

.cI 

n 

L 

.- a si 

uz 

I I I I I I 

r r 0 (0 cv 

I 

0 0 0 0 

0 0 0 0 

FIG. 3 

8 - 12