A111Q3 067065

mm

NBS SPECIAL PUBLICATION 400

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Semiconductor Measurement Technology:

Sf ^^)sium

STP 572
NATIONAL BUREAU OF STANDARDS

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|:b V 1974

"

'^lOO

Semiconductor Measurement Technology:

;7 Spreading Resistance Symposium

.>

Proceedings of a Symposium

Held at the National Bureau of Standards

Gaithersburg, Maryland

June 13-14, 1974

James R. Ehrstein, Editor

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

> ' » Washington, D.C. 20234

Under the Sponsorship of Committee F-l of the American Society for Testing and Materials

The National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued December 1974
National Bureau of Standards Special Publication 400-10

Nat. Bur. Stand. (U.S.), Spec. Publ. 400-10, 293 pages (Dec. 1974)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1974

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13.10:400-10). Price 13.55. Stock Number 0303-01358
PREFACE

' This Symposium on Spreading Resistance measurements was held on June 13-14, 1974 at the

iJational Bureau of Standards under the cosponsorship of this Bureau and Committee F-1 of the

\inerican Society for Testing and Materials. It consisted of three sessions as detailed in

the Contents on pp. vi to viii.

j The objective of the Symposium was to expose the state of the art with respect to the

pheory, practice and applications of the electrical spreading resistance measurement techlique. This technique which has seen rapidly increasing interest and use over the last 10

)r more years, has noteworthy versatility for profiling dopant concentrations over many

jrders of magnitude in multiple layer semiconductor structures. Nevertheless, the ever in-

:reasing demand on all measurement methods, caused by device fabrication utilizing active

regions often less than 1 ym in thickness, taxes the theory, practice and successful applization of all techniques, including the electrical spreading resistance.

It is hoped that this symposium, by illustrating the successful applications which

lave been made of the technique, and by indicating some of the areas where limitations

iiave been found to exist, will encourage further effort by interested parties, to find

solutions to those limitations.

' Finally, by compiling a store of well documented measurement practice in one volume,

]lt is hoped that the beginner in this technique will find rapid solutions to possible

lasic problems, so that he too may make rapid and successful use of this technique.

James R. Ehrstein

Editor

I

ill
SPREADING RESISTANCE SiruruSIUM

ABSTRACT

This Proceedings contains the information presented at the Spreading Resistance

Symposium held at the National Bureau of Standards on June 13-14, 1974.

This Symposium covered the state of the art of the theory, practice and applications

of the electrical spreading resistance measurement technique as applied to characterization

of dopant density in semiconductor starting materials and semiconductor device structures.

In addition to the presented papers, the transcripts of the discussion sessions which were

held directly after the Theory, Practice and Applications sessions are also included.

These transcripts, which were reviewed by the respective respondents for clarity, are essentially as presented at the symposium.

Key words: Dopant concentration, dopant profiles, metal-semiconductor contacts,

resistivity, semiconductor surface preparation, silicon, spreading resistance.

±v
SYMPOSIUM COMMITTEE

P. LANGER, Symposium Chairman

Bell Telephone Laboratories

Allentown , Pennsylvania

K. E. BENSON, Cochairman - Theory Session

Bell Telephone Laboratories

Allentown, Pennsylvania

F. VIEWEG-GUTBERLET, Cochairman - Theory Session

Wacker Chemitronic

Burghausen, West Germany

B. MORRIS, Cochairman - Practice Session

Bell Telephone Laboratories

Allentown, Pennsylvania

P. LANGER, Cochairman - Practice Session

Bell Telephone Laboratories

Allentown, Pennsylvania'

A. MAYER, Cochairman - Application Session

RCA Corporation

Somerville, New Jersey

F. PADOVANI, Cochairman - Application Session

Texas Instruments, Inc. Dallas, Texas

J. R. EHRSTEIN, Chairman - Publicity, Arrangements, Publication

National Bureau of Standards

Washington, D. C. 20234

V
CONTENTS

Paper No.

I-l.

1-2,

1-3.

Page No.

Welcome from NBS

Judson C. French, Chief, Electronic Technology Division

National Bureau of Standards, Gaithersburg , Maryland

Welcome from ASTM

Robert I. Scace, Chairman, ASTM Committee F-1

General Electric Company, Syracuse, New York

Keynote Address

Robert G. Mazur

Solid State Measurements, Monroeville, Pennsylvania

SESSION I - THEORY

T-1. The Physics of Spreading Resistance Measurements

S. J. Fonash, Engineering Science Department

Pennsylvania State University

University Park, Pennsylvania

T-2. Formal Comparison of Correction Formulae for Spreading Resistance

Measurements on Layered Structures

P. J. Severin, Philips Research Laboratories

Eindhoven, The Netherlands

T-3. Two-Point Probe Correction Factors

D. H. Dickey, Bell and Howell Research Laboratory

Pasadena, California

T-4. On the Validity of Correction Factors Applied to Spreading

Resistance Measurements on Bevelled Structures

P. M. Pinchon, R. T. C. La Radiotechnique Compelec

14 Caen, France

T-5. SRPROF, A Fast and Simple Program for Analyzing Spreading Resistance

Profile Data

B. L. Morris and P. H. Langer, Bell Telephone Laboratories

Allentown, Pennsylvania

T-6. Multilayer Analysis of Spreading Resistance Measurements

Gregg A. Lee, Texas Instruments Incorporated

Dallas, Texas

17

27

45

51

63

75

SESSION II - PRACTICE

P-1. An Automated Spreading Resistance Test Facility

J. C. White, Western Electric Company

Allentown, Pennsylvania 95

P-2. Angle Bevelling Silicon Epitaxial Layers, Technique and Evaluation

P. J. Severin, Philips Research Laboratories

Eindhoven, The Netherlands 99

P-3. Spreading Resistance Measurements on Silicon with Non-blocking

Aluminum-Silicon Contacts

J. Krausse, Siemens AG

Munich, F. R. Germany

vi
Paper No. Page No.

P-4. The Preparation of Bevelled Surfaces for Spreading Resistance Probing

by Diamond Grinding and Laser Measurement of Bevel Angles

A. Mayer and S. Shwartzman, RCA, Solid State Division

Somerville, New Jersey 123

P-5. Spreading Resistance Correction Factors for (111) and (100) Samples

H. Murrmann and F. Sedlak, Siemens AG

Munich, F. R. Germany 137

P-6. On the Calibration and Performance of a Spreading Resistance Probe

H. J. Ruiz and F. W. Voltmer, Texas Instruments Incorporated

Dallas, Texas 145

P-7. Comparison of the Spreading Resistance Probe with Other Silicon

Characterization Techniques

W. J. Schroen, G. A. Lee, and F. W. Voltmer, Texas Instruments, In- corporated, Dallas, Texas 155

P-8. Preparation of Lightly Loaded, Closely Spaced Spreading Resistance

Probe and Its Application to the Measurement of Doping Profiles in

Silicon

J. L. Deines, E. F. Gorey, A. E. Michel, and M. R. Poponiak

IBM, Systems Products Division, East Fishkill Facility

Hopewell Junction, New York 169

SESSION III - APPLICATIONS

A-1. A Direct Comparison of Spreading Resistance and MOS C-V Measurements

of Radial Resistivity Inhomogeneities on PICTUREPHONE ^ Wafers

J. R. Edwards and H. E. Nigh, Bell Telephone Laboratories

Allentown, Pennsylvania 179

A-2. Investigation of Local Oxygen Distribution in Silicon Single Crystals

by Means of the Spreading Resistance Technique

F. Vieweg-Gutberlet , Wacker Chemitronic

Burghausen, F. R. Germany 185

A-3. Use of the Spreading Resistance Probe for the Characterization of

Microsegregation in Silicon Crystals

F. W. Voltmer and H. J. Ruiz, Texas Instruments Incorporated

Dallas, Texas 191

A-4. Effects of Oxygen and Gold in Silicon Power Devices

J. Assour, RCA, Solid State Division

Somerville, New Jersey 201

A-5. The Evaluation of Thin Silicon Layers by Spreading Resistance

Measurements

G. Gruber and R. Pfeiffer, Solid State Measurements, Incorporated

Monroeville, Pennsylvania 209

A-6. Evaluation of Effective Epilayer Thickness by Spreading Resistance

Measurement

H. Murrmann and F. Sedlak, Siemens AG

Munich, F. R. Germany 217

vii
Paper No. Page No.

A-7. The Experimental Investigation of Two-Point Spreading Resistance

Correction Factors for Diffused Layers

N. Goldsmith, R. V. D'Aiello, and R. A. Sunshine, RCA Laboratories

Princeton, New Jersey 223

A-8. Applications of the Spreading Resistance Technique to Silicon

Characterization for Process and Device Modeling

W. H. Schroen, Texas Instruments Incorporated

Dallas, Texas 235

LATE NEWS PAPER

Improved Surface Preparation for Spreading Resistance Measurements

on p—Type Silicon

J. R. Ehrstein, National Bureau of Standards

Gaithersburg, Maryland 249

DISCUSSION SESSION

List of Participants 257

Discussion - Theory 259

Discussion - Practice 262

Discussion - Applications 268

Concluding Remarks

P. H. Langer - Symposium Chairman 278

Appendix - Bibliography 279

Certain commercial materials and equipment are identified in this paper in order to adequately specify the experimental procedure. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards, nor does it imply

that the material or equipment identified is necessarily the best available for the

purpose.

viii
AUTHOR INDEX

Author Page No

Assour, J. 201

Deines, J. L. 169

Dickey, D. H. 45

Ehrstein, J. R. 249

Edwards, J. R. 179

Fonaah , S • J

.

17

Goldsmith, N. 223

Gruber, G. 209

Krausse, J. 109

Lee, G. A. 75

Mayer, A. 123

Morris, B. L. 63

Murrmann, H. 137

Murrmann , H

.

217

Pinchon, P. M. 51

Ruiz, H. J. 145

Schroen, W. J. 155

Schroen, W. J. 235

Severin, P. J. 27

Severin, P. J. 99

Vieweg-Gutberlet , F. 185

Voltmer, F. W. 191

White, J. C. 95

ix
p

1/

I! J
WELCOMING REMARKS

AT THE

ASTM/NBS SYMPOSIUM ON SPREADING RESISTANCE MEASUREMENTS

GAITHERSBURG , MARYLAND

JUNE 13, 1974

BY JUDSON C. FRENCH, CHIEF

ELECTRONIC TECHNOLOGY DIVISION

NATIONAL BUREAU OF STANDARDS

Good morning. It is a real pleasure for me to bid you welcome to the ASTM/NBS Symposium

on Spreading Resistance Measurements on behalf of the National Bureau of Standards and, in

particular, on behalf of the Bureau's Electronic Technology Division. I welcome also your

co-host Bob Scace, Chairman of Committee F-1 on Electronics of the American Society for

Testing and Materials.

Sharing this period of welcome with Bob is, I believe, representative of the long continuing cooperation between NBS and ASTM in many fields, always with the common interests of

improvements in technology, in methods of measurement and specifications, and in the proI motion of sound and effective voluntary standards.

I Many of you are old friends of NBS and our Division but some are becoming acquainted

'; with us for the first time at this Symposium. I would like to address my first few remarks

I to these new visitors. I am sure you are aware of the NBS role in maintaining and disseminating the primary standards of measurement for this Nation. But the Bureau carries on an

, amazingly wide variety of activities in other fields as diverse as pollution control and

building research, dental materials and cryogenics, standard reference data and computer

research, all stemming from the broad charter established by Congress nearly three quarters

of a century ago. Here again in its breadth and subject matter the Bureau's interests parjallel those of ASTM to a surprising degree,

i Closest to the interests of this audience and of much of ASTM's Committee on Electronics

: is the work of our Electronic Technology Division. This Division focuses its resources on

solving critical measurement and standardization problems associated with the manufacture,

procurement, and application of essential electronic components.

( Most of the work of this Division is devoted to semiconductor electronics. This comes

as a surprise to many who ask: Why does the Bureau need to work in a field which so sophisticated, so technologically advanced, and so innovative? The answer is that the sophistication and innovative abilities of the semiconductor industry have led to the development

^ of new processes and new devices much faster than the measurement techniques for their conij trol and characterization have been developed.

I In the fifteen years or more that our staff has worked with the semiconductor industry

and its customers we have seen increasing need for improvements in practical methods of

imeasurement for analysis, control, and specifications in this field. And we have learned

jithat the Bureau can be especially helpful in this field because of its neutrality in evaluating measurement methods, and associated technology, and because its charter encourages it

jto work in the area of generic measurement for industry-wide use and market-place application.

Ilhis is an area where individual companies understandably find less incentive for extensive

research than in areas leading to new and proprietary processes and designs.

i|

I As a result, the NBS Semiconductor Technology Program has been established, having as

lits goal the development and standardization of improved methods of measurement for use in

ispecifying materials and devices and in control of device fabrication processes: methods

that have been well documented and tested for technical adequacy, are of demonstrated precision of an industrially acceptable level, and are acceptable to both users and suppliers.

1
If such methods are used by the electronics industry, they are expected to provide a more consistent set of measured results and interpretations and, hence, lead to improved

quality control and yield in the manufacturer's plant, and to improved reliability and

economy in the customer's applications.

But even when NBS is successful in providing such methods how does it assure the industry will use them? Only by working closely with the industry and its customers in the

first place to ascertain for what measurements improvements are needed, then to carry on interlaboratory , or round robin, evaluation of the improved methods to show their practical

value and precision, and finally to inform the electronics community of the resulting methods and to encourage their adoption as voluntary standards. This last step is important

because NBS has no enforcement or regulatory authority in this field.

And here again we find ourselves working closely with ASTM which can so effectively

provide an avenue to accomplishing these NBS aims, aims which are, of course, common to thos

of ASTM's Committee on Electronics.

Our Program now encompasses work on selected measurements, ranging from those needed to characterize silicon and oxides and interface states, through those for photolithography,

process control using test structures, bonding and die attachment, and hermeticity; on to thermal and electrical properties of finished devices. And we report our output not only

through ASTM but through many other channels including a special series of NBS publications

with which many of you are familiar.

But I would like to reminisce for a moment, back to 1960 when our program was not so extensive and when our first project in the semiconductor materials measurement field was

undertaken.

It was undertaken at the request of ASTM's Committee F-1 and the subject was measurement of resistivity. I have a very personal interest in this subject because I learned of

the need in my first day of attendance at an F-1 meeting. And ASTM and NBS have done a lot

together on this subject in the intervening years. We developed an improved four-probe

method, improved in precision by an order of magnitude as a matter of fact, and the method

and its various correction factors and other aspects now play a part in five ASTM standards.

Later a scanning photovoltaic technique for convenient, essentially non-contacting, radial

profiling was developed. Most recently we have issued a Standard Reference Material, com- prising two boron doped silicon wafers with certified resistivity values for checking measurements; and their stability is now being tested in a long term cooperative experiment

with the industry. These are the first Standard Reference Materials issued for the semiconductor industry's use.

But sophistication in the industrial development of devices has raised new problems

which can only be solved by new techniques for resistivity measurements yielding resolution

far beyond the capability of the currently standard four-probe technique. Where the fourprobe method is limited to resolution of the order of millimeters, resolution of the order

of micrometers and better is needed now for determination of crystal uniformity and for control of junction profiles.

The spreading resistance measurement method you will be discussing today and tomorrow

is a leading contender in this field. We are working, as are many of you, to develop this

method to a level of repeatability and understanding, both in and between laboratories, to meet the industry's needs. We are anxious to learn of the new developments to be reported

here today and tomorrow.

So I will say no more now, except that it is a pleasure to be able to provide the

facilities of the Bureau for this Symposium and to join with ASTM in encouraging the ex- change of information in this rather new and very important field.

2
WELCOMING REMARKS FROM ASTM

Robert I. Scace

General Electric Company

Syracuse, New York

Good morning. On behalf of ASTM Committee F-1, the other sponsor of this meeting, I want to welcome you all. Spreading resistance measurements are only one of many measurement techniques with which Committee F-1 is concerned. To give some perspective, let me

describe a little of ASTM's background in electronics for you.

ASTM is a large association of professional people who are engaged in developing standards on subjects ranging from railroad rails to surgical implants, and electronics is just

one of over 120 such topics. Committee F-1 was established in 1955, developing out of work

on electron tube materials which had previously been in a committee on copper. One of our major efforts has been in the development of ways to measure the properties of semiconductor

silicon.

As Judson French has mentioned, NBS and ASTM have collaborated closely in this work,

especially in resistivity measurements. Fifteen years ago we were lucky if two different

people could measure the resistivity of a piece of silicon to within a factor of two, but

now with the use of ASTM "methods it is possible to do this measurement to an accuracy of a couple of percent. Similar progress could be cited for many other measurements essential

to good process control in our industry.

Achievements such as these are one of the professional satisfactions of work in ASTM.

We can all do our jobs better with better measurement tools and techniques. Another more

personal reward is in the relationships established over the years with the people in ASTM.

Committee F-1 meets three times a year to do its work, and this frequent contact on common

technical problems results in close friendships with fellow professionals.

For the next two days we will be discussing spreading resistance measurements on silicon. This is a very powerful technique for analysis of structures and control of processes

which is now mature enough to discuss at length. I hope you all find these sessions valuable, and I also encourage you to come to future Committee F-1 meetings to participate and

to contribute further to the development of spreading resistance techniques.
I!

'iiI1

4i
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS , Gaithersburg, Md. , June 13-14, 1974.

Keynote Address

Symposium on Spreading Resistance

Gaithersburg, Maryland

June 13-14, 1974

Robert G, Mazur

Solid State Measurements, Inc. 600 Seco Road

Monroeville, Pennsylvania 15146

1. Introduction

This is the first symposium ever to be held on the subject of spreading resistance

I measurements. As I see it, the purpose in having this meeting is to gather together those

" who are currently using the spreading resistance measurement technique in their work on semiconductor processing problems along with others who would like to be able to do something about the same or similar problems, in the hope that, by sharing our knowledge and exi perience, we may all be better able to use the spreading resistance technique to our own advantage. I hope and believe that we will achieve this particular goal and that therefore in

I the future this meeting will be referred to as "The First Symposium on Spreading Resistance

Measurements .

In deciding what I should talk about in a keynote speech for such an occasion, two related subjects came to mind. First, a number of individuals who haven '

t

worked in the semiconductor industry from its earliest days have expressed an interest in the questions of

where the technique came from as well as why and how it came about. Therefore, in the first

|, part of my talk today I would like to relate the background of the spreading resistance technique as I know it

.

The second subject that came to mind is also in response to certain people that I've

met over the years. These are the people who, when first exposed to the spreading resis-

,j tance technique, rapidly developed a "hang-up" with respect to the mechanics of the contacts

used. In an attempt to shed some light in this area, I will devote the second part of this

morning's talk to what I know about the achievement of reproducible, known-geometry, metalsemiconductor, small-area pressure contacts. These contacts are what I have often referred

to in past discussions as "conditioned" contacts.

2. The Spreading Resistance Technique: Who, What, Why, Where and When.

The Spreading Resistance Technique is a method used to obtain quantitative measurement

of the local resistivity of certain semiconductor materials. Currently, the technique is

ijused most extensively on silicon. An essential feature of the technique is the achievement

I' of sufficiently high spatial resolution so as to allow detailed evaluation of those variations in dopant concentration which are important to the manufacture of semiconductor devices. The technique is based on measurement of the "spreading resistance" or "constriction

resistance" of small-area metal-semiconductor pressure contacts. It is currently in wide

use in mapping inhomogeneities in silicon crystals and in obtaining thickness profiles of

many of the diffused, epitaxial and ion-implanted layers produced during semiconductor device processing.

Small area metal-semiconductor pressure contacts are historically somewhat loosely

called "point" contacts. The spreading resistance effect associated with such contacts has

a distinguished place in the history of semiconductor technology. Certainly one of the

earliest practical applications of a semiconductor device was the use of a point-contact

rectifier in "crystal" radios during the early days of the radio age (1)^. Later, the

^ Figures in brackets refer to literature citations at the end of this paper.

5
desire to understand and thus to improve point-contact diode detectors used in early World

War II radar equipment sparked the efforts of a number of research groups in work on germanium and silicon. This work eventually led to the discovery of the transistor effect in

late 1947 by Bardeen, Brattain and Shockley at the Bell Telephone Laboratories in Murray

Hill, New Jersey (2)

.

However, there is an even closer relationship between spreading resistance measurements

and the invention of the transistor. From the beginning of my work with the spreading re- sistance technique, I have been impressed by the fact that a key step in the Bardeen,

Brattain and Shockley transistor invention involved a spreading resistance measurement (3)

.

The experiment is detailed in the Physical Review for 1948 immediately following the note

describing the transistor effect. This crucial experiment established the existence of additional charge carriers produced by injection from a metal-germanium point-contact identical to the emitter used in the first point-contact transistor. Brattain and Bardeen showed

that the potential associated with a current flow through a metal-semiconductor point contact did not fall off with increasing distance from the point in accordance with a standard

spreading resistance calculation but rather exhibited an anomalous decrease in the rate-ofchange of potential in the immediate vicinity of the contact. This behavior was explained

as being due in part to the injection of additional charge carriers into the semiconductor

with a consequent lowering of the resistivity near the contact.

At this time, I'd like to call your attention to an interesting aspect of this

Brattain-Bardeen injecting point-contact experiment, specifically that, to the best of my

knowledge, the experiment has never been repeated. Not that I am suggesting that their work

needs corroboration but I consider it surprising that such an elegant experiment which so nicely illustrates a basic phenomenon in semiconductor physics should not have been repeated

many times over if for no other reason than for its educational effect.

This situation stands out even more in contrast with the often-repeated Haynes-Shockley

experiment (4) which provides a measurement of the drift mobility of charge carriers in a semiconductor by timing the arrival of a pulse of injected carriers at a point down the

electric field relative to the original point of injection into the bar. Because of Its fundamental nature and its simplicity, the Haynes-Shockley experiment has been repeated many

times over in a number of university and industrial laboratories since the description of

the experiment was first published. Now, the question is: why has the equally fundamental

and simple Brattain-Bardeen spreading resistance experiment not been repeated as many times?

I would like to suggest that the main reason is the experimental difficulty of the BrattainBardeen measurement; it is no easy job to do a potential probe within micrometers of a metal-semiconductor point contact. I believe that the significance to us of the familiarity

of the Haynes-Shockley experiment and the relative obscurity of the Brattain-Bardeen experiment is that our experimental problems with spreading resistance contacts are not trivial

ones

.

Before leaving this subject, I'd also like to point out that Brattain and Bardeen

credit W. L. Bond with construction of their micromanipulator. If we should ever need to produce a name for an award of the like in conjunction with spreading resistance measurements, I think that the name of Bond should be a front-runner.

Returning to the history of spreading resistance after Bardeen, Brattain and Shockley,

I must admit that I have no firsthand knowledge of developments during the 1950's. However,

the relationship between semiconductor resistivity and point-contact spreading resistance

must have been used off and on in semiconductor materials evaluation, at least sufficiently

so as to warrant inclusion in several publications, including volume 6, Part B of the book

"Methods of Experimental Physics", edited by K. Lark-Horovitz and V. A. Johnson (5). The

basic spreading resistance measurement method is described under the heading "Spreading

Resistance Measurements" in the chapter entitled "Conductivity Measurements on Solids".

The treatment, while brief, is complete in that it indicates both the high spatial resolution of the technique as well as its primary problem—that of determining true contact

dimensions

.

My personal experience with the spreading resistance technique dates to the first job

I was assigned on beginning work at the Westinghouse R&D Center in June of 1959. At that

time, Westinghouse was in the middle of an extensive program to make use of germanium and

6
silicon dendrites, produced by growth from a supercooled melt. The end product of the dendritic growth process was a ribbon or strip of semiconductor single crystal, having a width

of about 1 mm and a thickness of about 0.1 mm. The dendritic ribbon could be grown at a rate of several feet per minute and produced in lengths of up to several hundred feet with

the dendrite being rolled up on a reel located above the crystal puller for storage and

later use. The plan was to make use of the nearly perfect surfaces of this material for

automatic device fabrication with no lapping, etching or other surface treatment of chips

needed. My job was to measure the resistivity of as-grown dendrites using a traveling onepoint potential probe.

Very soon after I began work (or perhaps even before that time) someone began to suspect that the dendrite material being grown was too inhomogeneous in resistivity to be of use in practical device manufacture. This later turned out to be the case and, unfortunately for the dendrite program, the inhomogeneities turned out to be inescapably associated

with the fundamental growth habit of dendrites.

However, before the demise of the dendrite program became certain, I was given the

i additional task of developing some way of quantitatively evaluating dendrite crosssectional resistivity variations. I began with the point-contact voltage breakdown techInique which had already come into use for evaluating N on epitaxial silicon (6). Figure

1 shows some raw data obtained on a dendrite cross-section which was grown from a melt containing both P-type and N-type impurities. The conductivity type and the point-contact

breakdown voltages measured at various points on the cross-section are shown. The data show

jthat the central part of the dendrite (which grows first) is P-type of relatively lower resistivity as compared to the "arms" of the H-structure pattern in which such dendrites grow.

(The material between the "arms" of the H-structure solidifies last and is N-type. Although

the point-contact breakdown technique did work more or less, I eventually abandoned it because of inadequate reproducibility as well as the fact that it was difficult to obtain

absolute resistivity values over the wide range of both P- and N-type resistivities found

in the dendritic material.

I next tried to use free-carrier infrared absorption with a small diameter lightbeam

ibut soon found that, at least for me, this approach yielded a better thickness gauge than

ijit did a dopant-level monitor.

Meanwhile, the reproducibility of I-V characteristics observed during point-contact

Ipreakdown voltage measurements as well as during low voltage point-contact rectification

type testing was so good that I was led to consider the possibility of making spreading

resistance measurements as described in the Lark-Horovitz book (5). I tried the technique,

asing the same traveling one-point probe apparatus that I had inherited on coming to

I iJestinghouse , along with a Keithley 610A Electrometer. The 610A had an ohmmeter function

ijDuilt in via a constant current generator and an electrometer measurement of the total voltage across the current output terminals. The key feature for me was that this instrument

lad a useful sensitivity extending down to below one millivolt so that I was able to use low

I'jnough currents for a given resistivity sample such that the spreading resistance measurepent could always be done with a total applied voltage in the vicinity of 10 millivolts.

With such a low bias level, significant change in sample resistivity due to injection of

fexcess carriers was avoided along with several other undesirable effects normally associated

Iwith voltages much greater than kT/q (e.g., high-field mobility modification and contact

, Ideating).

I Figure 2 shows the probe and the 610A Electrometer as well as the stack of brass washters used to load the probe to 25 grams. This loading was used for germanium — I later

jjised 45 grams for silicon measurements. These load values were dictated by the desire to

iHave the load large with respect to frictional force in the distorted ball bearings used to

pivot the probe arm and yet not so large as to crack samples during probing. The probes

|ised were standard (at the time) phonograph needles.

Early results were encouraging. The spreading resistance values measured on a given

iample were reproducible to within a few percent and furthermore, the size of the micropracked region left on the sample after a spreading resistance measurement agreed rather

t Ifsll with the circular contact size expected on the basis of a Hertz formula calculation

for the case of a spherical surface having the radius of curvature of the phonograph needle

' 7

ill 565-448 0 - 75 -2

f
mating with a plane surface (7). For the case of a silicon to osmium contact with a loading

of 45 grams, I calculated just under 4 micrometers for the value of "a" where "a" is the

radius of the contact spot.

The fact that the Hertz formula used in calculating contact size is based on the

assumption of elastic stress in the materials involved while the micro-cracking in itself

clearly indicated the existence of an inelastic situation didn't bother me much. A lot of

physical situations behave even when the underlying assumptions are violated somewhat.

What did cause me to pause for a long while in the early development of the technique was the inability to fit a single value of "a" into the classical spreading resistance formula for both P-type and N-type material. According to my understanding of the situation,

the simple formula Rg = p/4a should have applied (7). Thus, the calculated and observed

value for "a" should have been verified by a spreading resistance measurement on a single

sample of known resistivity. However, and unfortunately, things were not so simple. Measurements on samples of different resistivities or of opposite conductivity types with the same resistivity led to inconsistent results when compared to the values expected from the

simple Rg = p/4a relationship. At first, it appeared that the calculated value for "a" would fit the experimental data if a proportionality constant "k" = about 3 were to be inserted for N-type material; i.e.

for P-type, Rg = fand for N-type, R„ = ~-

s 4a = 4a

However, with more careful measurements over a wider range of P- and N-type resistivities,

I found that, in fact, k was not a constant at all but rather a complicated function of p and that, furthermore, the k(p) function for P-type material differed from the k(p) for Ntype samples.

This situation led others then and later involved in spreading resistance measurements

to talk in terms of an "effective contact radius". I rejected the effective radius concept

from the beginning for two reasons: 1) it didn't make sense physically—I just couldn't

believe that impurity levels of one part per million or less could radically alter the hardness of silicon and germanium; 2) a much simpler explanation was available in that osmium

has a larger work-function than silicon and should therefore make a rectifying contact on N-type silicon and an ohmic contact on P-type. Thus, even at zero bias, an additional re- sistance should be observed for the osmium, N-type contact as compared to the osmium, P-type

contact. The measured resistances for N-type and P-type samples were in the right direction—with the measured spreading resistance on 1 ohm-cm N-type silicon, for instance, being

about a factor of three larger than that measured on P-type 1 ohm-cm silicon. FurtHermore

,

a work-function barrier effect would cause a variation in measured spreading resistance with

change in sample resistivity in qualitative agreement with the shape of the k(p) function.

The work function-determined zero-bias barrier model even fitted the fact that I subsequently found that "k" was not only a function of semiconductor material, conductivity

type and resistivity but that it also depended on the mechanical finish of a sample surface

and even the time elapsed between surface preparation and measurement. This behavior would

be consistent with a model based on a property such as the work function which would be ex- pected to have some dependence on the physical and chemical nature of the surface.

Despite the magnitude of the problem involved in understanding the contacts used in

these early spreading resistance measurements, the high degree of reproducibility which was experimentally observed suggested that I could get on with the job that needed doing by

generating a calibration curve of spreading resistance vs^. resistivity through making mea- surements on known resistivity samples. With this approach, the complications posed by the j complex dependence of the k-function on conductivity type and surface finish could be handled by generating separate calibration curves for P- and N-silicon with a particular surface finishing procedure that could be kept constant for both known-resistivity samples and

the unknown test samples.

8
With calibration curves so generated, measurement results were at least good enough to successfully establish that germanium and silicon dendrites were extremely inhomogeneous in

dopant concentrations.

Another result of generating the calibration curves was the fact that I became convinced that nothing other than a strongly empirical approach would suffice for further measurements with the spreading resistance technique. This conviction grew out of the discovery

that the calibration curves for lapped and polished N-type silicon samples crossed each

other in the vicinity of 1 ohm-cm. This result (and the surface "aging" effects) clearly

indicated that spreading resistance measurements were affected by the electrical properties

of the silicon surface and that therefore, a satisfactory theoretical understanding was

beyond reach for some time to come.

Thus, my development work on the technique subsequent to this time was concentrated on making the contacts as reproducibly as possible and on achieving the highest degree of re- producibility possible in sample surface preparation.

I Development work on the spreading resistance technique continued despite the close-out

of the dendrite programs because new programs arose in which high spatial resolution measurements were needed, especially in research and development into the growth of multilayer

I homo-epitaxial silicon structures for use in high-power devices. This work was primarily

j under the direction of T. L. Chu who then headed the epitaxial growth work at the

j Westinghouse R&D Center. Without his early support, the spreading resistance work at

I Westinghouse might easily have ended in its infancy.

j The state of development achieved during this part of the work at Westinghouse is

; illustrated by the data and remarks presented as oral papers by myself and by Dave Dickey

at the ECS Meeting in Pittsburgh in 1963 (8).

i

j The 1963 "state-of-the-art" is also well illustrated by the 1966 paper, co-authored by

iDave Dickey and me (9). This is so because this paper was my first and it took a couple of

lyears to actually get into print.

As is made clear in the 1966 paper, by the middle of the 1960's we had a useful and

jjpractical technique. We knew that it involved three basic requirements:

1) Reproducible contacts : these had to be mechanically generated in such a way

that they were reproducible over periods of months or longer. They had to be

produced without even microscopic sliding or other motion during contact-make

and had to be capable of positioning within ±1 micrometer of a given standard

placement

.

2) Low applied voltage : the voltage across spreading resistance contacts had to be small enough so as to avoid significant amounts of carrier injection, contact heating or the like.

3) Calibration : the spreading resistance technique is a comparison technique.

Unknown resistivity samples must be evaluated through the use of calibration

curves produced by making spreading resistance measurements on samples of known

resistivity (these calibration samples are generally measured with a 4-point

probe and are prepared so as to have the same surface finish as the unknown

resistivity material to be measured).

N. B. Because of this dependence on calibration, the results obtainable with

the spreading resistance technique are limited in accuracy only by the quality and the quantity of the calibration work done.

While the technique practiced up until 1966 was a manual one, it was useful and prac-

|:ical. This is illustrated by Figure 3 which is a resistivity profile produced by the manual spreading resistance technique as of about 1962. Figures 4 and 5 illustrate early use

t>f the automatic spreading resistance probe at Westinghouse in profiling thick epitaxial

structures then under development for power device use. A typical process-control problem

9
which illustrates the need for spreading resistance data is shown by the defective profile

of Figure 5. Figure 6 illustrates a typical N on epitaxial structure.

The main drawback to our measurements at the time involved the need to correct the raw data in order to obtain true resistivity /impurity concentration values in thin layers of

interest. This need arose because of the existence of two basic assumptions in the derivation of the equation Rg = p/4a, i.e.:

1) all sample boundaries are at "infinity", i.e., far away from the contact as compared to the size of the contact (see Holm (7)).

2) the resistivity in the semiconductor sample is uniform throughout.

The paper by Dickey (8) gives a theoretical solution to the boundary condition imposed

by the presence of an (insulating) p-n junction within several contact diameters or less of

the probe. The results and limitations of this and several other correction schemes will

be the subject of several papers to be presented here in the next two days. Suffice it to say that the correction factors are probably the greatest problem in the use of spreading

resistance measurements today.

3. The Nature of the "Conditioned" Probe

Rather than getting into any discussion at all of correction factors, I'd like to use my remaining time to get into the second part of this talk. This involves abandoning the

historical approach in order to present a contact model and some remarks which will reflect

my best current understanding of the mechanical and physical aspects of what I call

"conditioned" probes.

I believe that this aspect of the spreading resistance technique is worth taking the

time for now for three reasons:

1) "conditioned" contacts are the primary requirement for a practical spreading

resistance measurement technique;

2) the mechanical aspects of spreading resistance contacts have not been discussed in detail in the published literature;

3) I believe that a realistic picture of the contacts used for spreading resistance measurements is fundamental to proper understanding and use of measurement results.

In my early attempts to get around the problem posed by not being certain of the true dimensions of the spreading resistance contacts, I elected to proceed by first assuming that

the Hertzian value for "a" as calculated was correct. This then suggested that 1 Q*cm P- type silicon involved a barrier free contact and led to the selection of 1 Q'cvci P-type

samples for use in checking probes. On such samples, measurements should depend only on geometrical spreading resistance. These standard samples eventually became our "QTA"

samples, with "QTA" being an abbreviation for "Qualification, Test and Alignment".

During subsequent checking of probes on these samples, I founJ that, despite the fact

that new probes would have a variable and relatively high measured spreading resistance when

first run, they would subsequently show a lower and quite uniform value after being used in

making spreading resistance measurements on lapped (bevelled) samples. Typically, new

probes would give values of up to three or four thousand ohms on the QTA sample, but, after

running on lapped samples for one or two thousand measurement points, the probes would con- sistently show a decrease of measured QTA resistance to about 600 Q.

This behavior, when viewed in the light of the known inability of simple cleaning pro- cesses to remove all residual abrasive from lapped silicon samples, led me to begin thinking

of the probes as undergoing some kind of "conditioning" process. This process was not at al]

well understood but the results were so reproducible from one probe to another that I felt

justified in using probes so "conditioned" for routine measurements—depending, of course,

on calibration curves for absolute results.

10
My understanding of the conditioning process has increased only slowly over the years

mostly as a result of using hundreds of probes on many individual pieces of spreading re- sistance apparatus over a long period of time. While I still cannot claim complete understanding of the process, the attainment of stabilized measured spreading resistance values

on a standard (QTA) sample for many different probe tips strongly suggests the achievement

of a mechanically reproducible contact situation subsequently involving only elastic deformation of the metal probe.

Furthermore, while it is well known that the true electrical contact area between contact members is small as compared to the size of the apparent contact region (7) , experimental evidence shows that even the apparent area of the spreading resistance contacts being

used for measurements is very small — for the 45 gm probes used in my early work, the overall contact area was 5 x 10~^ cm^. It seemed obvious that there had to be some limit to the

"normal" orders-of-magnitude difference between apparent contact size and the actual

electrically-conducting contact size; i.e., given a conducting region small enough and with

sufficiently high pressures, the electrically-conducting contact size should approximate the

apparent contact size. This idea eventually became embodied in a definition of a useable

and practical "conditioned" spreading resistance contact.

Basically, by a "conditioned" probe, I mean one which is so contoured and chemically

treated that, despite the fact that the surface of the probe is rough on a micro-scale, the

micro-contacts made by it when it is set down on a silicon surface are sufficient in number

and grouped closely enough so that the overall effect is as if there is a single circular

contact of specific, reproducible radius "a". A corollary idea is that, under these conditions, "a" is large enough relative to the load applied that the pressure at the metal semiconductor interface will be within the elastic range of the metal involved and the contact

will therefore be mechanically reproducible .

A rather complete treatment of the geometrical concept behind this definition of a "conditioned" contact is contained in the work of J. A. Greenwood (10)

.

I can also offer a few further remarks relative to the details of spreading resistance

contacts and probes which may aid you in becoming comfortable with the idea of a "conditioned" probe.

The probes used for spreading resistance measurements are initially imperfectly

contoured—they are nominally of a one mil (25 ym) radius of curvature at the tip and are otherwise contoured as shown in Figure 7. The probe tips are rough on the micro-scale,

having a surface roughness of approximately 1 ym. Thus, when set down on a smooth silicon

surface, they initially contact the silicon at several randomly-scattered points corresponding to high-spots in the tip-contact region. As the load on the probe increases, the con-

|tact area increases, both by enlargement of the first contact spots and contact-make at new

Ispots.

j The initial contact points are the regions under which the applied pressure first exijceeds the fracture stress of the silicon material and are therefore the points from which

micro-cracks will radiate upon lifting the probe. Note that it may be possible for the

festress at some of the later contact points to be large enough to crack and displace the

prittle silicon oxide layer while not becoming great enough to cause cracking in the silicon.

Irhis would result in no micro-cracks radiating from these points and hence no way to visually

;itell afterwards that electrical contact was made at such a point,

i]

li Furthermore, current density is quite non-uniform in a flat circular contact—very

||Little current flows through the center of the contact. Therefore, lack of true electrical

iContact in the central region of a contact pattern will in general not appreciably affect

the measured spreading resistance. One way of looking at this is to observe that in using

pontacts for spreading resistance measurements, we are primarily concerned with the

erimeter of the contact.

The model as described here also suggests that the individualized patterns of microallipracks observed for a particular probe are primarily indicative of the detailed microfopography of that probe tip and are not necessarily directly related to the electrical

i

I 11
properties of the final contact. Therefore, detailed study of contact-spot micro-crack

patterns may well turn out to be a study of the micro-metallurgy of osmium-tungsten (or

whatever other material the probe is fabricated from) rather than anything else.

Thus, I now see the "conditioning" process as one wherein the probe tip is so con- toured and roughened (on a micro-scale) that, when properly placed on a silicon surface,

it produces a contact which may well be a cluster of micro-contacts but, if so, the cluster

is so grouped that the result is the same as if the electrically-conducting area was a single spot with the radius "a" given by the Hertz relationship for the probe radius of

curvature and the load and materials involved.

Given acceptance of this "conditioned" probe concept and definition and the equipment

capable of producing such contacts without sliding or other mechanical problems, the practical problem becomes one of knowing when the "conditioned" contact situation is reached.

I believe that the primary criterion for assessing contact quality must be a reproducibility check on a standard sample . In line with this approach, we use slices taken

from a common batch of 1 ohm-cm, p-type silicon wafers which were "chem-mechanically"

polished years ago. Through direct experience, we have been able to establish practical

limits for spreading resistance values obtained on these standard samples for conditioned

probes under normal conditions.

The criteria and limits that we now suggest are the following:

Table 1

a) Probe Load 45 gms 20 gms

b) Measured resistance per probe on UNREFINISHED QTA sample 300-700 ohm 600-1000 ohm

c) Diameter of Circumscribed Circle

around contact spot pattern 8-9 ym 5-6 pm

In addition to these criteria there are several other "characteristics" of conditioned

probes that may be useful in your evaluation of the suitability of particular probes for

spreading resistance measurements. These are:

1) conditioned probes make contacts whose measured spreading resistance on QTA

samples is relatively stable in time. Where vibration is not unusually severe, measurement values on QTA samples will remain stable within several percent or less after a typical initial increase of approximately 5%.

2) conditioned probes yield measured values on QTA samples which are much more

uniform from one point to the next than are the values obtained with uncon- ditioned probes.

3) conditioned probes are more .easily seen in the microscope than are unconditioned probes, probably because of a larger number of micro-contacts with a resultant increase in light scattered from the (111) plane facets produced

by fracture.

The remarks that I offer here are based on my own attempts to rationalize the behavior

of spreading resistance probe contacts during measurements over a period of some 13-14 years.

I hope that these comments will assist others in increasing their understanding of the

physics and mechanics of the "point" contact used in the spreading resistance measurement

technique.

1 2
References

H. C. Torrey and C. A. Whitmer "Crystal Rectifiers", 1st ed. , McGraw-Hill Book Co

New York (1948) .

'

J. Bardeen and W. H. Brattain, Phys. Rev. 74' 230 (1948).

W. H. Brattain and J. Bardeen, Phys. Rev. 74, 231 (1948).

J. R. Haynes and W. Shockley, Phys. Rev. 7_5, 691 (1949).

"Methods of Experimental Physics" V. 6, Part B, Solid State Physics, ed. by K. LarkHorovitz and V. A. Johnson, Academic Press (1959).

J. Brownson, J. Electrochem. Soc. Ill , 919 (1964).

R. Holm, "Electric Contacts Handbook", 3rd ed. Springer, Berlin (1958).

R. G. Mazur, Abs. No. 56 and D. H. Dickey, Abs. No. 57, Papers presented at the

Pittsburgh Meeting of the Electrochemical Society, Spring, 1963. See Extended

Abstracts of the Electronics Div. Vol. 12, No. 1.

R. G. Mazur and D. H. Dickey, J. Electrochem. Soc. 113, No. 3 (255-259) March 1966.

J. A. Greenwood, Brit. J. Appl. Phys., 17, 1621-1631 (1966).

N20 \P25 P45 P40

N40

N30

N50

/

N20 y ^ P30

N25\P30 P35

N47 N

N45 CC^MP P25

N40 Cq|hp P37

P40

co'mp

)

' N20

N45

N45

COMP

i

NI8

N25

N50

N50

N20

Figure 1 - Map of a three-zone dendrite cross-section, showing the experimentallydetermined conductivity type and point contact breakdown voltage as a function

of position on the cross-sectional surface. Vertical: approximately 0.25 mm; Horizontal: approximately 0.9 mm.
Figure 2. The first Westinghouse spreading re- sistance probe apparatus.

10' -

^10

Eo

Figure 3. Spreading resistance - derived resis- t -t tivity profile of a defective epitaxial thyristor^^^

structure: manual probe data, circa 1962. ^

10'"

Figure 4. Early automatic spreading resistance

profile of a P"^ NN+ epitaxial power device

structure.

10'-16 -12 -8 -4 -2 0 2 4 8

POSITION COORDINATE NORMAL TO

THE BASE- COLLECTOR JUNCTION

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s

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DEPTH BELOW TOP SURFACE POINT TO POINT

SPACING ISlO/im

14
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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

The Physics of Spreading Resistance Measurements

Stephen J. Fonash

Engineering Science Department

Pennsylvania State University, University Park, Pennsylvania 16802

The spreading resistance method is uniquely suitable for the determination of electrical resistivities in a number of situations. However

the technique does not simply measure the resistivity beneath the contacts. Considering the two probe configuration, what is actually measured is the ratio AV/l. Here AV is the difference between the Fermi

levels of the probes necessary to maintain the sampling current I. This

difference in the Fermi levels of the probes depends on the zero bias re- sistance of the probe - semiconductor contacts, the effective resistivity

of the layers in a multilayer structure, and the configuration of the

structure. The zero bias resistance depends on temperature and details

of the metal-semiconductor contact including surface history. Effective

resistivities enter into the measurement - and not the actual resistivities - because of the fact that the use of pressure probes creates a stress field under the contacts. This field falls off with a characteristic length of the order of the contact radius. Thus piezoreslstivity

effects - well known for Si - can be operative under the contacts. As a consequence of these various effects the interpretation of what AV/I is

actually measuring is not straightforward. Practical application of the

spreading resistance technique necessitates making certain simplifying

assumptions. In light of the various phenomena involved in a spreading

resistance measurement it is imperative that the implications of these

assumptions to the accuracy of the measurement be understood.

Keywords: Correction factor; crystallographic orientations; effective

contact radius; interfaces; metal-semiconductor contacts; multilayered

structure; piezoreslstivity; resistivity; spreading resistance; stress;

zero bias resistance.

1. Introduction

The use of the spreading resistance technique 11-5]"'" for resistivity measurements in

|l(iomogeneous and inhomogeneous semiconductor materials is finding increasing popularity,

ilostensibly this method is quite simple and straightforward. However, due to geometrical

Figures in brackets indicate the literature references at the end of this paper

17
effects, the presence of material interfaces, the presence of space charge regions, and the

presence of stress fields, there are a number of physical phenomena which come into play

when this measurement is made. An understanding and appreciation of these various phenomena

involved in a spreading resistance measurement is necessary for a meaningful application of

this technique.

To determine what physical phenomena are playing a role in spreading resistance measurements and to determine how they influence the measurement a simple two probe configuration

\J2 will be assumed for this discussion. (See figure 1) Obviously the conclusions that will

be reached can be applied to other configurations used in spreading resistance measurements.

As is shown in this figure, it is also assumed that this measurement is 'being made on a layered structure for generality.

In the configuration depicted, a current I is flowing into probe contact one and flowing out of probe contact two. These metal probe-semiconductor contacts are, ideally, flat

circular areas whose radii are determined by the force on the probe and the Young's moduli

of the metal and the semiconductor . The electrostatic potential which is set up by

this current flow must be such that

Z = h

= 0 (all r) (1)

and

dZ (all r not under the contacts) (2)

Under the contacts, since there is a current flowing.

dZ

i 0 (3)

Z = 0

In addition, since no current flows out the sides of the structure.

8X

(4)

lateral

surfaces

where X is a coordinate normal to any lateral surface under consideration,

n These four statements constitute very general constraints on the electrostatic

potential. However ^ as a function of position in the structure must actually be found

since the potential difference AV between the probes, necessary to drive I, is to be com- puted. Really it is the ratio AV/l which is to be found since this is the quantity measured

by the spreading resistance technique

2. The Physical Phenomena Involved

To be more specific, the quantity to be measured AV/I can be written as

18
AV/I = -AV

(5)

JJo o

eff 8Z

ridrj

Z = 0

where the subscripts refer to a polar (r ,6) coordinate system situated, for convenience in

discussing this integral, at the center of circular contact one. This expression assumes

that, just beneath the metal probe-semiconductor contact, the current is carried by drift

in the semiconductor. The need for an effective resistivity - instead of the actual re- sistivity p - will become apparent; p reduces to p in the absence of a mechanical stress

field. The fundamental question, what does AV/I measure, can be answered by a study of

eq. (5)

It is clear that eq. (5) underscores the necessity of finding the electrostatic

potential ^ = ijj(r ,9 ,Z) in the semiconductor. At first glance this is straightforward since

ijj should satisfy Laplace's equation in the semiconductor and it is known to be subject to the boundary conditions given by eq. (1) - (4). However, the potential difference measured

between proba one and probe two, the quantity AV, is the difference between the Fermi levels

(electrochemical potentials) of the two metal probes. Thus, if ip is to be written in terms

of AV as it must be to obtain an answer from eq. (5) which depends only on the structure, it

is necessary to relate the Fermi level in metal one to \p in the semiconductor beneath contact one. Correspondingly it is necessary to relate the Fermi level in metal two to ^ in

the semiconductor beneath contact two.

With a layered structure such as that shown in figure 1, a second problem becomes

apparent: i/j does not satisfy Laplace's equation in the interface regions. In these interface regions (1 - between layers I and II, 2 - between layers II and III, and 3 - between

III and IV) there is an assumed abrupt change in resistivity. That is, in the interface

regions, a transition occurs from one value of doping density to another. Figure 2 shows,

in cross-section, some region of interface 1, for example; figure 3 shows the band diagram

for this cross-section. In general these transition layers are of width w. where j = 1,2,3.

From figure 3 it is seen that a charge density a. exLsts in these interfac^ regions.

Consequently

V^ii = 0 (6)

may be assumed valid for layers I, II, III, and IV; it can not be assumed valid for the

interface regions

.

Considering the first problem, it is apparent that a boundary condition at the contacts

relating the Fermi levels of the metals and \p is needed t''] • the electrostatic potential^

in the semiconductor is measured (see figure 4) henceforth with respect to the Fermi level

2The electrostatic potential in the semiconductor is measured positively down, from the

Fermi level of probe two, to the position of the Fermi level in the semiconductor in this

analysis. See figure 4.

I

19

I
of metal probe two, then it follows that the current density normal to the contact at some point (r2,92) in the metal-semiconductor boundary two is continuous at the boimdary and that

Here 4^2 is the value of \p under this contact (ie, Z = 0) at some general (t2%Qz) ; this polar

coordinate system at contact two is defined analogously to (ri,9i). A similar condition may

be developed for contact one; ie, [7,^

liH = - AV)

dz_]

Z = 0

(8)

where \p], is the value of i) under contact one (ie, Z = 0) at some general (ri,^). Of course AV is the difference between the Fermi levels of the probes, as stated previously.

The quantity C is the reciprocal of the zero bias resistance of the contacts per unit

area. They have been assumed to be identical. Equations (7) and (8) - as well as the re- maining analysis - assume that the bias AV is small compared to kT so that the J-V

characteristics of the metal- semiconductor contacts may be linearized.-^ Equations (7) and

(8) may be written in integral form as

a 2n

I = J

j" CiJ;2r2dr2d62 (9)

and

a zn

I = / J C (AV - r:drid9i (10)

These constraints are placed on the solution to eq. (6).

Having related to the metal Fermi levels through eq (7) and (8) - a necessity since

it is the difference between these Fermi levels which is actually measured - it is now

possible to turn to the problem posed by the interfacial regions between layers. Rather

than finding the electrostatic potential in these space charge regions [JQ , an alternative

approach is to relate the solutions for \p in two adjacent layers. If these interfaces are sufficiently thin, the current normal to these transitions regions is constant through the

regions (9,10). Thus it follows that (see fig. 2 and 3)

eff

8Z

h.

J

eff 3Z

(11)

h .+w.

J J

As is discussed in ref. QS] , the current density depends on the difference in the Fermi

levels between the metal and the semiconductor. If the general expression for this current

density given in ref. QSQ is linearized about zero bias, (7) and (8) result. That is, the

right hand sides of (7) and (8) are just Taylor series expansions of the J-V characteristics.

20
is one such relation joining solutions in adjacent layers. Since eq. (6) is second order,

another joining relation is needed C^.lOj. Following reasoning similar to that which led to

eq. (7) and (8) , it is seen that this relation is provided by

eff 3Z

= C. h. + w, I

(12)

where all of these quantities in eq. (12) can depend on position in the boundary planes Z =h

.

and Z = h. + w. of interface region j.

2 2 Of course, rather than using eq. (11) and (12), one could determine the electrostatic

potential in the interface regions by solving Poisson's equation |^] . Boundary conditions

would then be imposed on the electrostatic potential and its normal derivative (the electric

field) at h. and h. + w., if this approach were selected. Such an approach is, of course,

an exact on^ as opposed"' to the approximations (eq. (11) and (12)) involved in the alternative.

From a practical point of ^view, one is forced to select eq. (11) and (12) in dealing with

these interface regions C?J •

With either approach ^ is completely specified in the semiconductor. Further, it must

obey eq. (l)-(4) as well as conditions (9) and (10) . Thus in principle 4^ can be completely

determined and the resistance measured experimentally (ie, eq. (5)) can be evaluated in terms

of the material parameters of the semiconductor structure. That is, it is possible to establish what is being measured by the ratio AV/I. Unfortunately, examination of the

conditions on ijj as developed above demonstrates that the ratio AV/I can not just depend on

the resistivity beneath the contacts since i|j does not. From this development presented it

is clear that AV/I will depend on C, the parameter characterizing the probe-semiconductor

contacts, on the geometry, the interfacial regions and the effective resistivity p j.^. eit

At this point it is necessary to establish why it is an effective resistivity that

enters into i^J and, therefore, into AV/I. This effective resistivity that appears in the

conditions imposed on ^ (see eq. (7), (8), (11) and (12)) arises from the presence of stress

fields in the material. As is well known, in the presence of a stress field the resistivity

must be expressed as a second rank tensor p [11,1^; thus

P = P

1 + All Ai3

A21 1 + A22 A23

A31 A32 1 + A33

(13)

where p is the scalar resistivity (in the absence of any stress). The second rank tensor^

is related to the stress tensor JI. by the fourth rank piezoresistance tensor _II_^1 ,1^ Of

course A vanishes if there is no stress field. Obviously there is a stress field under the

probes [3,13J. This could even extend down (see figure 1) to at least the first interfacial

region.

So it is an effective resistivity - determined from eq. (13) - which enters into \p. If

the probe has a pressure p applied to it, then for a {100} plane on Si (n or p type) p under the contacts is given, after some manipulation, by

Pgf£ = P (l-pHii) (lA)

21
For contacts on a {ill} plane, the corresponding expression is

for n or p type Si. Here the II are components of a collapsed JI_.

Using data for the II.. in the literature [11, 1^ and p = 10'"' dynes /cm^ results in the

determination that, for """-^ {100} planes, under the contacts

p^^^~ 2 p for n-type Si (16)

and

•^eff ^ ^^'^ P ~ ^-^^^

For {ill} planes, under the contacts

P^ff"^ P f n - type Si (18)

and

Pg^^~ .lOp for p - type Si (19)

Unfortunately these are just estimates since data at high stress levels are not available for the n. . and the H. . depend on doping. However, the point has been made that an effective resistivity - due-' to stress - enters into ii. Whether or not P^^^ differs significantly from p depends on the stress and the crys tallographic orientation. On the basis of

eq. (18) and (19) alone one would estimate that the measured resistance AV/l, for a given

resistivity, would be lower for p-type material than for n-type if both had a {ill}

orientation and identical contacts and geometry. This piezoresistance effect may also be

at least partially responsible for correction factors of less than unity which are seen on p-type Si. •

The zero bias resistance per area of the probe - semiconductor contacts, which enters

into ijj and, therefore, into AV/I, also depends on stress. In fact C is a function of the

stress, temperature, doping, and crystallographic orientation fl4-lQ . The quantity C depends, in addition, on surface history. C^^jl^J Thus, in a spreading resistance measurement, AV/I depends on considerably more than just the resistivity of the material beneath

the contact, as this above development has indicated.

3. Practical Considerations

The measured quantity AV/I depends on the contacts, mechanical stress, temperature, and

the geometrical configuration of the layers as well as their resistivity and transition

regions. Therefore, it is not surprising that, to employ the spreading resistance technique

it is necessary to assume that the resistivity of layer I (see figure 1) is related to the

2 2
ijneasured AV/I by

AV— = K

I

(20)

where K is a correction factor and the remaining terms are the ideal spreading resistance

for a semi-infinite slab using the two probe configuration flT} . The quantity a ^ should

be the radius of the contacts - a quantity depending only on the mechanical properties of

the probe - semiconductor system. In actual fact, if K is used to correct for structure

(that is, used in some manner to account for eq. (11) and (12) as is done in ref, D-73)> it

is found that ^^^f is an effective radius not a geometrical radius. It can vary by a factor

of more than 2 with resistivity D-^ and in practical applications is determined from a calibration curve obtained from a body of uniform resistivity. Obviously the effective

radius is attempting to account for the various other phenomena involved in a spreading

resistance measurement which were discussed in section 2.

It is interesting to establish how eq. (2) may be obtained from eq. (5), a statement

'hich is fundamentally correct. If eq. (5), (7), and (8) are manipulated, it follows from

ome straightforward algebra that eq. (5) can be written as

a 2n

2 +1 i i

^^^^-'^^^ r,Ar,dQ, AV = 2 ^^1)

I a 211^ , ,Q la 2n^ , f

rCridridGi f

ridridS^

oh o o

Itfhere the probes have been assumed identical. In the term involving and ip2 , it is

(necessary to evaluate these quantities at equivalent points under the contacts in integrating

bbviously the first term on the right may be interpreted as a resistance arising from the

[contacts only. The second term involves (through the conditionson ijj) the contacts, the

geometry of the layered configuration, the interfacial regions, and the piezoresistivity

effects

.

If C is assumed constant and very large (ie, ohmic contacts between the probes and the

semiconductor) the metal Fermi levels line up with the Fermi level of the semiconductor just

iaeneath the contact. Thus in this case, i|^2 = 0 and = AV replace eq. (7) and (8) and eq.

|jC21) reduces to

a 2Jl AV. 1 r r (^1 - ^2) n dn dBi (22)

I'ma^J J

Jsing an approximation in eq. (22) for proposed by Schumann and Gardner f93 allows eq. (21)

jjjto be finally reduced to

AV ^eff I • (23) _ = K

2=** I 2a

phere K is a function of the various layer resistivities (which may actually depend on stress

t least for the first layer), the radius a, and the geometry [SQ . Of course, here a is the

icadius of the contacts.

2 3

565-448 0-75-3
The approximation for ij; used to obtain eq. (23) assumes the C. of eq. (12) are infinite

Further it does not obey the conditions = AV and ijj2 = 0 applicable in the assumed case of

ohmic contacts but rather fits a postulated current distribution under the contacts - an expediency used to avoid mixed boundary conditions [9] . Thus if the K of Schumann and

Gardner is used in eq. (2) , a is attempting to account for piezoresistivity and the zero bias resistance of the contacts. It can not account for the C. quantities of the inter- ' face layers since it is usually obtained from a calibration cu'Jve for uniform material.

Thus using eq. (21) and a K developed as indicated is beset with assumptions and

simplifications. This fact has led Hu [l/Q , in commenting on the limits of accuracy one could expect from eq. (21) , to note that this "mathematical model of the multilayer

spreading resistance rests on a number of simplifying assumptions, most of which are not

accurate .

4. Conclusions

From eq. (21), it can be seen that the quantity being measured for the structure shown

in fig. 1 is

AV = 2R + R (24)

where R is a measure of the contact resistance only and R depends on the contacts, the

resistivities, and the geometry of the structure. If eq. (20) is used for R, the accuracy

of the measurement is limited obviously by the choice of K and a that is,

is limited by the approximation used for in the term

^ the accuracy

2Jl 1 X Z c (^1 - ^2) ridnde

I a 211 / /c ndr iQDl

In practice the term involving R^ in eq. (24) is frequently neglected.

References

(1

(2

(3

(4

(5

(6

(7

(8

(9

Holm, R. , Electric Contacts Handbook , Springer, Berlin (1967).

Gardner, E.E., Hallenback, J.F., and

Schumann, P.A. , Solid-St. Electron, 6_, 311 (1963).

Mazur, R.G. and Dickey, D.H., J. Electrochem. Soc. 113 , 255(1966).

Gupta, D.C. and Chan, J.Y., Rev. Sci. Instr. 41, 176 (1970)

Schumann, P.A., Gorey, E.F., and

Schneider, CP., Solid St. Tech. 15,

50 (1972)

Kramer, P. and Van Ruyven, L. , Solid

St. Electron, 15, 757 (1972).

Foxhall, G.F. and Lewis, J.A. , Bell

System Tech. Journal. 43, 1609 (1964).

Fonash, S.J. 783 (1972)

Schumann, P.A. and Gardner, E.E. Electrochem. Soc: Solid St. Sci.

87 (1969).

Solid St. Electron, 15,

, J. 116.

(10) Brook, P. and Smith, J.G., Electronics

Lett. , 9, 253 (1973)

(11) Smith, C.S., Phys. Rev. 94, 42 (1954).

(12) Smith, C.S., Solid St . Physics (F.

Seitz and D. Turnbull, Eds.) 6_, 175.

Academic Press, Inc. N.Y. (1958).

(13) Severin, P.J., Solid St. Electron.

14, 247 (1971)

(14) Kramer, P. and Van Ruyven, L. J. , Solid

St. Electron. 15, 757 (1972).

(15) Kramer, P. and Van Ruyven, L.J., Appl.

Phys. Lett. 20, 420 (1972)

(16) Fonash, S.J., J. Appl. Phys., 45, 496

(1974)

(17) Hu, S.M. , Solid-St. Electron. 15, 809

(1972)

24
i 1

Figure 1. Configuration for Spreading Resistance Measurements on a Layered Structure. The Two-probe setup is shown.

REGION I

Figure 2. The Transition -or Interface- Region Between Two Ideally Uniform Layers.

25
CHOSEN AS REFERENCE

FOR ELECTROSTATIC POTENTIAL

OF SEMICONDUCTOR

Figure 3. An Energy Band Diagram Through an Interface Region Such as That

Shown in Figure 2. Bias Drop Across this Region is Indicated.

z

REGION I

Figure 4. Diagram Showing the Energy Band Bending Under the Contacts. Also

indicated is the reference electrostatic Potential.

26
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposi

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

FORMAL COMPARISON OF CORRECTION

FORMULAE FOR SPREADING RESISTANCE

MEASUREMENTS ON LAYERED STRUCTURES

P.J. Severin

Philips Research Laboratories

Eindhoven, The Netherlands

The spj^eading- resistance of a metal contact on a semiconductor sample is analysed for infinite geometry, with

three different boundary conditions: a specified potential

' of the contact, a uniform contact current density and a current density dependent on contact resistance. The cases

! of a thin layer on a perfectly conducting substrate and on

a non-conducting substrate are analysed each for the

boundary conditions of uniform current density and of the

i current density distribution valid for the infinite

1 geometry. With a perfectly conducting substrate the two

boundary conditions yield about ^0fo difference. With a non-conducting substrate calculations based on both

i current density distributions produce in the thin layer

' approximation the same In r dependence required. The

j constant terms in both approaches are different by 5%

I and the constant current density result in addition agrees

with the result obtained with a totally different transmission-line approach. The actual three-point-probe

measurement situation is discussed. The danger of correcting

the precise spreading resistance measurement results with

an error of ^'fo, with formulae derived on the basis of a formal model which is sensitive to the choice of the

boundary conditions by up to 10^, is stressed. The effects

of undefined thickness, bevel edge and transition layer

curving upwards are mentioned as further complications.

Key words: Contact resistance, correction formulae,

sheet resistance, silicon, spreading resistance.

1 . Introduction

Spreading resistance measured on a structure of infinite lateral extent, but finite layer thickness d is different from the spreading

resistance measured on an infinite geometry. Their ratio is generally

jreferred to as a correction formula for a finite thickness measurement

jresult. Such formulae have been derived by Schumann and Gardner [l ], initial-

"ly for a two-layer system and extended later (2]to g. graded sjbructure. This

theory has been used in computer solutions by Yeh [3j, Kokhani [^J Hu [5]

ISome preliminary studies are available in the form of reports [6 , 7 j • In the standard solution for infinite geometry a constant potential

j|V of the contact of radius A is specified and the potential V(r,z) and

itlie current density distribution J (r,o) over the contact are calculated,

iln the approach followed by Schumann et al . ] to solve the potential for

Ifinite layer thickness d the same current density distribution J (r,o) is

z

^ ^Figures in brackets indicate the literature references at the end of this paper.

27
used to calculate V(r,o). The potential V of the probe is obtained byaveraging v(r,o) over the contact area. tEis problem is solved for any

ratio of the resistivities of the layer and of the substrate. In

order to check the validity of this approach we have studied the sensitivity of the solutions for the two limiting cases = 0 and ^^=00 to the

choice of the boundary conditions. In particular we studied the cases

d /a « 1 and d/A >^ 1, which have well known solutions.

In the next section the case of infinite geometry is investigated

using the conventional approach (2.1 ) and assuming a uniform current

density over the contact (2.3 )• The effect of the boundary condition

resulting from contact resistance which modifies the current density

distribution over the contact, is also examined (2.2). In the iikird section

devoted to the case = 0, the approach of Brooks and Mattes [8]is shown

to be incorrect (3«1 ) and the approach with uniform current density over

the contact (3^2) is compared to the results obtained by Schumann et al.[l]

(3«3)» In the fourth section, devoted to the''case J)^ =00 , the same two

approached are again compared ,( 4 . 1 ) and f 4. 2), and both approximations are found to yield divergent integrals for v(r,z). When the difference between

the potential V of the contact and the potential V(r,o) is introduced

the malignant terms cancel. With both approaches in the thin layer approximation the satisfying result is found that the potential depends on r as In r ,(4.1) and (4.2). This is also the experimentally verified result of an elementary consideration (4.3)- A transmission-line approach, valid for

thin layers with a contact resistance which influences the current distribution at the contact, described earlier [9^ is compared with the present

results (4.3)' In the approximation of dominant contact resistance this

transmission-line approach produces exactly the same expression as did the

uniform currrent density approach (4.1 ). Schumann's approach yields a slightly different result. Spreading resistance measurements are essentially three-point-probe measurements. Two different probe configurations are currently in use with different but related formulae. The difference in

particular for thin layers is discussed in the fifth section.

The experimental results of spreading resistance measurements are extremely precise fio], about ^'fo. The conversion to the local resistivity,

let alone to the local dope atom concentration, is hindered by the uncertainties originating from the choice of a not sufficiently realistic model

for a thin layer structure. In addition to this, the effective contact

resistance due to micro-contacts, deeper damage or barrier-resistance,

should be taken into account. Furthermore, the effects of the bevel edge,

of the finite transition layer at the interface and of the modification of

the transition layer due to the exposure at the bevel are mentioned in

the summary.

2. Infinite geometry

The potential distribution due to a circular metal disk of radius A

at potential V on a semi-infinite medium of resistivity j> has been

discussed by various authors. Formulated in this way or as the problem of

a charged disk on top of an isolating medium it is a classical text book

example of the application of mixed boundary conditions l^ ^ , 1 2j 2.1. Mixed boundary conditions solution

In cylindrical coordinates , shown in figure 1 , the potential V(r,z) is

a solution of Laplace's equation, which reads for circular symmetry

J + = o

28
?he solution can be easily obtained with separation of variables to

^iven in terms of a Bessel function J^(kr)

be

in this solution as a first boundary condition has been used

'(r, «o ) = 0, and the second boundary condition at z = 0 is of

t mixed nature [12], for the potential of the contact

o nd for the electric field strength

o

0 this set of dual integral equations

s known to be the solution because

for a < ft <

for > a

Oo

2.

<2A.C vTt^

V. A. /e

,nd

that the potential becomes

lie current i flowing into the metal contact is given by

for o < ^ < ^

for A. ^ ^

for o < ^ < >^

for A. •> ^

(2)

(3)

(4a)

(4b)

(5)

(5a)

(5b)

(6)

ilich with eqs (6) and (Sb) becomes

(7)

(8)

(8a)

le well known spreading resistance formula for infinite geometry. It is

kteresting to note that the electric field has infinite strength at

1= A, which is physically unrealistic.

29
2.2. The influence of contact resistance

on the current density distribution.

In practice the ideal spreading resistance as given by eq. (8a) is

seldom or never measured. The contact to the semi-conductor is not as perfect as it is supposed to be in formulating the problem: usually- an extra voltage c3rop is noted due to zero-bias-barrier resistance [13,1^], a multitipped [TO ^ 15 3 l6 ] or otherwise incomplete contact. This effect is

usually taken into account by calibrating the probe so that the effective

spreading resistance

= Ms) ^ , or introducing a series contact resistance to ^/k-A

(9)

(9a)

However, it is not self evident that the extra voltage drop can be

considered as being due to a series resistance which does not influence

the current density distribution over the contact area. This problem can

be analysed as follows. The boundary condition which incorporates the

specific contact resistance R' ( SL cm )_, is

which with A = R'/p

(10a)

and

gxves

3X '^^

''4 = 0

(10b)

The contact resistance makes the mixed boundary conditions quite

complicated, but by choosing an oblate spheroidal coordinate system the same boundary conditions can be formulated conventionally [17 ] . With the

coordinates shown in figure 2,

Laplace's equation can be separated by putting

into

(11)

(12a)

(I2b)

(12c)

The solution to eqs (I2b) and ( 1 2c ) in terms of Legendre polynomials

P (x) and Q (x) reads

30
y C'^) = ^^07) < 9- C;/^;- (13)

From the boundary conditions it follows that some coefficients are zero,

because with r, z oo likewise ti^-^oo , and P (z) —> oo as z , the

coefficients c =0 to satisfy V O, for r,z —> oo , Because at ^ = 0

the electric fieldj

the solution snould be even inj. Finally Q^^ (5) has a singular point at ^

= 1 so that the coefficient b^^ must be zero. Hence the solution is

Oo

Ok)

When this solution is subj ected to the newly formulated boundary condition,

eq. (

1 0b ), the condition to be satisfied reads

= i

n=^ 1^1 -h^^i ^ -i=<^ J (13)

This condition can be converted into an infinite system of linear equations

for the unknowns a , which upon proper truncation can be numerically

solved to the requxred precision. The total current i^ can then be easily

calculated from

(16)

The calculation of a has been done and the surprising result is that

for the parameter J\. / assuming the values 0, 0.1, 1 and 10 the resistance is, by at most a few percent larger than the resistance obtained by

simply adding R'^lirf)^ and ^I'-ffi in series. The parameter A /A,

apart from a factor '^/v j is equal to the ratio of these two resistances

and the range investigated covers any practical situation. Hence in the

infinite geometry the separation implied in eqs (9) and (9a) turns out to

be allowed. However, the effect of contact resistance R on spreading

resistance is more complicated in a finite geometry. An example is treated

in sec. 4.4

2.3. Solution with uniform contact current density distribution

An alternative way to avoid the mixed boundary conditions and the

infinite field strength at r 1=; A is to specify the electric field, instead

of the potential at the contact. The electric field corresponding to a uniform current density distribution at the contact is given by

= for 0 < r < A (-,7a)

31
and, as before,

= ^ for r > A.

The potential of eq. (2) then yields

(17b)

and f (k) follows from comparison with

/ (< ^) (^-) -

SO that the potential reads

for o < < /9

for

for

for

Q <. \ < f)

(17c)

(I7d)

(18)

77-/? (19)

According to this equation the potential at z=0 of the contact depends

on r. This is a direct consequence of the choice of the uniform current

density boundary condition. By averaging the potential V(r,o) over the

contact area V , expressed in R = Y /± . o o is found to be

8_

(20)

It is to be concluded that at least for the infinite geometry this

approximation of an uniform current density at the contact is a fairly

good one, differing by only S'fo from the result in eq. (8a).

It is worth noting here that R has never yet been verified with

sufficient precision to be able to decide unequivocally between eqs (8a)

and (20). Generally, spreading resistance measurements are hampered by a large contact resistance, which has not been determined separately with

sufficient precision and accuracy. An experimental determination of R , within a few percent error, was done recently with a mercury probe [18]

Because the mercury probe has a much lar-ger contact diameter 2A=1 mm than

any conventional probe and should be applied on a carefully prepared

surface, the contact resistance does not play a role. The spreading

resistance on bulk material has been found to satisfy eq. (8a) or (20) over

a range of four decades of resistivity on N-type Si, as shown in figure 3-

3. Thin layer on infinitely conducting substrate

3.1. The Brooks and Mattes approach

A structure to which a spreading resistance measurement is frequently

applied, consists of a thin layer of thickness d ^ A on a much better

conducting substrate. Considering the substrate as a perfect conductor

this problem has been treated by Brooks and Mattesf8j. Unfortunately, they

made an error and the problem should be formulated as follows.

32
The potential again is a solution of Laplace's equation

y(^,*) = Jell ^""^ e.C-^;^"^*-) ^ (21)

which, because V(r,d)=0 and hence

can be simplified to

(22)

o

The mixed boundary conditions corresponding to eqs (4a) and (4b) now

read as

(23)

K ' \d.i 0X<) (^1. e ) jZ'.C^^)

o

and

oo 4o(

for o<^<^ (2^^)

(>i,o) ^-JoL^ (t,(<) -I (^^ + ^ ^^(AA)^, for^>^. (24b)

There is no known analytical solution to these dual integral equations and

this line of reasoning cannot be pursued.

Brookes and Mattes arrive at the mixed boundary conditions on the

surface in the form

o for o < < (25a)

and, with the correction of an obvious misprint,

for A >/9 , (25b)

o to which

(25c)

„ would be a solution were it not that and are functions of k, which

they derive later, and not constants as they appear to suggest. Their

final result, which has been computed and is plotted in figure 4, is however

remarkably close to the results obtained otherwise.

3.2. Solution with uniform contact current density distribution

As discussed in sec. 3-1» the potential cannot be solved analytically

assuming a constant potential of the contact V . However, an analytic

solution can be obtained if it is assumed that the electric field is

3 3
uniform over the contact area, as done for the infinite geometry in sec

2.3.

Application of the boundary condition eq. (l?) and the relation

eq. (18) to the non-zero field strength of eq. (2^b) yields

and hence

(27)

Now the average value of v(r,o) over the contact area, the applied

potential , with ^

- cL j and 9C = -4 ^ , expressed in R^=V^/i^, is

^ - ^ vfl J ^.^^ ^^^^ The validity of this equation can be checked by considering the two extreme

cases of a very thick and a very thin layer. With a very thick layer,

y «>, oo > and R approximates the expression for infinite geometry eq. (20

)

For a very thin Sayer the integral eq. (28) yields as expected

Oo

(29)

Eq. (28) has been computed and is presented as a plot of R ( dI )/R

( 00 ) vs d/A in figure h.

3.3. Solution with infinite geometry contact current density distribution

The choice of a uniform electric field is one of several possibilities

to avoid the mixed boundary conditions by specifying the electric field

at the top side of the structure. Schumann et. al . [I ] have based their

analysis on the choice of the field strength at the contact that exists

with an infinite geometry

iTr a (/?^- ^^y^"^ 0 < r < A (30a)

and, as before,

(^,0) =0 for r > A. (30b)

The potential, subjected to the boundary condition V(r,d)=0, as before, is

given by eq. (23)« Now applying to the non-zero field strength of eq.(24b)

the boundary conditions eq. (30), it can be seen fromeq. (5b) that

' ~ xTTf) ^ zm^^^ ' (31)

3 4
Hence the potential reads

o -f- ^

(32)

The average value of V(r,o) over the contact area, V , expressed in

R =V /i , yields

s o^ o'

(33)

Making the approximation for a thick layer directly from the potential

eq. (32) at the surface 5C =0, it is found tlrat the potential equals the

potential for the infinite geometry eq. (6). The spreading resistance

(33) > in the same approximation correctly yields R as in eq. (8a).

For a thin layer the spreading resistance is found to 'Be given as expected by eq. (29). Eq. (33) has also been computed and plotted in figure 4.

3.4. An experimental approach

An experimental approach has been followed by Cox and Strack[l9] who

studied the resistance in the case in point as a function of contact

radius A. They assumed that the resistance is composed of the contributions due to contact resistance, spreading resistance corrected for

finite thickness and residual resistance:

TT L/f)''^^^

^^^^ By plotting the total resistance R vs 1/A the three different components

can be separated. From electrolytic tank experiments they concluded that

I the function f obeys the empirical relation

(35)

which has the correct value in the extremes d -»> o and d 00

Eq, (35) has also been plotted in figure k.

h. Thin layer on zero-conductivity substrate

^.1. Solution with uniform contact current density distribution

Another structure for which it is of interest to know the spreading

(resistance as a function of the thickness d A is a thin layer on a

jnon- conducting substrate or separated from a conducting substrate by an isolating layer.

The potential is again given by eq. (21 ) and the electric field at

iz=d equals

00

(36)

35

1^
Because (jt^cL^ rr o should be valid for all r

-ioL (37)

and hence the electric field at z=0 is

(38)

Applying the boundary condition eq. (l7) and eq. (l8), eq. (38) yields

V -9 ^

(39)

The average value of V(r,o) over the contact area, V , with

y = d/A and x = kA is found to be

Vo

-e. -f- ^ 7

7 - (40)

For a very thick layer the potential and the spreading resistance

approximate the expressions for infinite geometry eqs (l9) and (20). For

any other layer, and mathematically for any layer, the integral eqs. (39)

and (4o) do not exist. However, when the potential at the distance r at

the surface z=0 is referred to the averaged potential V of the contact, a non-divergent integral is found because the malignant terms cancel

7r ft X

For a very thin layer, y —> o, the integral in eq. (4l ) can be solved

exactly. Then for z=0 eq. (39) can be approximated as

o and invoking the expression fsoj

(42)

(^3)

it follows that

(44)

36
This is a satisfying result because this dependence on r is exactly the

dependence which follows from an irrefutable elementary consideration,

eqs (49) and (50), which, moreover, has been verified experimentally with

high precision by us. Using eq. (kk) the non-divergent integral eq. ( 1 ) can be written as

Because the integral equals I/8, eq. (45) can be written a£

(45)

J><< (45a)

In this way it has been shown that by considering the potential

difference the divergency of the integral is removed, that the correct

dependence of the thin layer resistance on the distance r is obtained and

that the resistance between the contact and r=A equals _p /8 ir d. In

sec. 4.3 it will be recapitulated that this value has also been obtained

earlier f 9J f~rom a very different transmission-line model. In the absence

of a zero-voltage reference at infinity, R should be defined from a three

point-probe system to be discussed in sec.S*

4.. 2. Solution with infinite geometry contact current density distribution

Applying" the Schumann et al . [I ^ approximation to this structure, by

imposing the boundary condition eq. (30 ) and the relation eq. (5a) to eq.

(38) it is found that

Co

ol^ — L^'^)

(46)

Hence the average value of V(r,o) over the contact area, , yields

o ji ^ JL <r (2+7)

For a very thick layer this expression approximates the expression

for infinite geometry eq. (6). For any other, and mathematically for any

layer, the integrals eqs (46) and (47) are divergent. Again referring the

potential at the distance r at the surface z=0 to the averaged potential

, a non-divergent integral is found

For a very thin layer, y -?> o, eq. (48) reads

^» - ^^^) - ^ {'-^ - U^'t)} '

(48a)

37
which can be solved exactly to yield

Vo - V(^A) = -111

^

A ± .

(48b)

This result cannot experimentally be distinguished from eq. (45a) obtained

with the constant current density approach.

4.3. Solution with transmission-line approach

From elementary considerations it is clear, that at a distance r from the centre E (r,z)=0, that the total current i is related to

E r , z j a s

(^9)

and that hence for a thin layer the potential difference between points

at r=A and r equals

V//)) - = -1^1— A ± .

(50)

The difference between the potential V of the contact and the

potential at r=A should be added to the potential eq. (50). However, this

potential is only independent of z when the layer is very thin with

respect to the probe radius. For this geometry a transmission-line model

has been worked out [9]jwhere the current is assumed to flow in the z- direction only through the contact resistance R at the metal-silicon

interface and radially anywhere else. The resistance R between the

contact and the cylinder wall at r=A has been calculated to be

X-nd (3^)

with u^ = ^^5>/'?c'<^ . The function F(u) = (u)/ul^(u), where I and

are modified Bessel functions of the first°kind, is plotted in ?igure

5. An essentially similar approach with a linear geometry has been

followed fox' many years to derive the contact potential based on an expression [9]given by Shockley. Eq. (51 ) can be used for the same purpose.

This approach can be compared to that followed in sec. 4.1 only when

R is dominant, so that the contact resistance can be considered as a

c series resistance which does not affect the current density distribution.

Under these conditions

'YK — —— •+ »

exactly and almost the same result as obtained in eqs (45a) and (48b),

respectively, along totally different lines.

38
! 5- Three-point-probe configurations

For spreading resistance measurements two different three-pointprobe configurations are currently in use each with different, but

related correction formulae. They are presented in figure 6, as parts of

an in-line four-point- probe arrangement with three equal probe distances s, because the two configurations can be easily related in this way.

It will be shown that the two configurations yield very different

measurement results with thin layers in particular. The three probes are referred to as voltage, current and common probe. The spreading resistance

jis measured below the common probe.

From superposition of the potentials due to the input and output

Icurrents the potential differences measured in configurations A and B can

easily be shown to be

i (53)

land

jwhere V is the potential drop of the common probe due to spreading

jresistance. Reversing the current in B and superimposing this configurajtion onto A the normal four-point—probe arrangement is obtained, that is

(55)

IThe four-point-probe measured potential for a thin layer on an isolating

substrate is given by

(56)

id for bulk material by

TTS ' (57)

po^aring the voltage drop due to the spreadi^^xresistance i ^ /kA to

tVgo » it is evident that the contribution is negligib£e for bulk

'material (s ^ A). For a thin layer the sheet resistance generally

seriously reduces the precision of the desired information which is in

|;he spreading resistance term.

I The next problem to be treated is whether the voltage or the current

)robes can be replaced by a bottom contact.

When the structure to be investigated is such that the support is

"-hick or highly doped so that it can be considered as an equipotential

j^urface, a voltage or current contact can be connected to it. Calling the

(pottom potential the potential difference reads in configuration A^ of

figure 6 as L <:>».) = V{S) _ (58)

39

565-443 0-75-4
and in configuration as

(59)

which is identic5il to eq. {^k) of configuration B. The difference

between eqs (53) and (58) amounts to half the four-point-probe value.

When in configurations and B^ the voltage probe is displaced towards

infinity^ the measurement result is evidently the same as with a bottom

Voltage contact.

In figure 6D the configurations A and B are presented with bottom

current contacts. When the configurations C and -C are superimposed on

D the voltages read

(60)

and

(61)

Hence in configuration D

^ ^ ^ (62)

(a ) which is equal to ' ,and in configuration C

(63)

which is half the four-point-probe value. Upon applying a bottom current

contact the potential is reduced in configuration A and is increased in

configuration B by half the normal four-point-probe value.

6. Siiiranary and conclusions

The resistance between a metal contact of radius A at uniform

potential and an electrode at infinity to material of resistivity J> of

infinite extent is the spreading resistance ^ /k-A. An extremely thin

top layer representing a contact resistance is generally considered as a series resistance. It turns out to influence the potential distribution

itself and to increase the resistance by h'fo over the series combination.

Imposing the boundary condition of a uniform current density distribution

over the contact area instead of a uniform potential yields a spreading

resistance higher by at most 8'fo over the series combination.

The potential problem for a layer of finite thickness d is solved fo; a perfectly conducting arid a non-conducting substrate. For both problems

the boundary conditions of uniform current density aind of the current

density distribution found with infinite thickness are tried.

For the first problem a difference of about 10^ is found with both

40
)Oiuid.ary conditions. Another published solution is found to be

lathematically incorrect. For the second problem both boundary conditions

ield divergent integrals for the potential. However, the difference

letween the potential of the contact and the potential at some point r

"ields a finite integral. With the boundary condition of uniform current

ensity at the contact the In r-dependence of the. voltage is found which

"ollows from elementary considerations and which has been verified expeimentally. Moreover, the other voltage term representing the geometricaly constrained spreading resistance for a thin layer turns out to be

qual to the value obtained from a completely different approach based on transmission-line model. The other boundary condition of the same

.ensity distribution as found for infinite geometry also yields the In r-

.ependence and a constant term smaller by ^fo. The latter approach has been followed by Schumann et al.[l]in their

alculation of the spreading resistance not only as a function of d/A, as

one here, but also as a function of the ratio of layer to substrate

esistivity $i I Sx ' which only the two extremes have been studied

ere. It is evident that all results are only valid as far as the model

s valid ajnd it is the pertinent conclusion of this contribution that

qually reasonable boundary conditions yield results which are different

y about lO^o. Agreement with experimental results of this precision

xists only for the In r-dependence, which is found with both approaches.

he infinite geometry expression J> /4a has been verified with about this

recision with a Hg probe fl8] and experiments in which probes with small

ontact area are used, are troubled by contact resistance. Schumann*

hoice of the boundary conditions is a logical one because the infinite

eometry with $1 1 Sx, ~ ^ can be used as a reference in this way.

evertheless, in view of the results obtained above it appears worth

iepeating Schumann* s computer exercise with various conditions. It is

jrobably safe to say that in interpreting thin layer spreading resistance

(easurements , which may be precise with in 1^, the precision drops to

Ijbout 10^.

:h| It would, moreover, also be better to include from the very beginning

She influence of the contact resistance, which influences the current

Jensity distribution at the contact, particularly for a thin layer on a

ess conducting substrate. When all this preliminary mathematical work

or spreading resistance on a non-bevelled structure has been done

orrectly, the influence of the edge on a bevelled surface should be

ncluded, as with four-point-probe correction formulae for finite geometry.

Furthermore, it should be realized that on any layered structure the

ijransition is not abrupt but extends over a finite length, due to dope

)tom gradient, space charge or both. Therefore in spreading resistance

ijiorrection formulae the thickness obtained with the infrared multiple

j'jnterf erence method should be used with caution [21 , 22

J

. Finally on a bevelled structure the complication arises that the

jitiarge carrier distribution is perturbed by the exposure of the transijion on the bevel. In a PN-junction the zero-bias depletion layer

iLxtends so far to both sides of the junction that the net charge

jianishes. In a bevelled PN-junction therefore the lower^ide boundary of

iliie depletion layer curves upwards where the top- side boundary would

i||itersect the bevel surface. The top-side boundary then must also curve

jNpwards and a modified space charge pattern results suggesting a smaller

IjiBpth of the interface. These effects are well known to give rise to

Ijipwer surface break-down voltages, as discussed by Davies and Gentry f23j . fliLmilar effects occur, on a smaller scale, with an NN junction where

Miarge spills over a few Debye lengths into the lowly doped layer, but

:||{ay show a different space charge distribution near the bevelled surface,

i It is the author *s opinion that sufficiently reproducible and precise

preading resistance measurements can be done, but that for the interpreition of the data to extract explicit and accurate information on the

tesistivity of layered or bevelled structures theory is seriously deficient.

41
Acknowledgement

The assistance of Prof. Dr. C.J. Bouwkamp in some analytical

problems, of Ir. V. Fontein in some numerical problems and of

Dr. J.D. Wasscher in carefully reveiwing the manuscript is gratefully

acknowledged

Refer

1 P. A. Schumann and E.E. Gardner,

J.Electrochem.Soc. 1 1

(1969)

87.

2 P. A. Schumann ajid E.E. Gardner,

SolSt.Electr._l_2 (1969) 371.

3 T.H. Yeh, Silicon Device

Processing, NBS Spec.Publ.

337 (1970) 111.

k T.H. Yeh and K.H. Kokhani , J.

Electrochem. Soc

1 1

(1969)

1461 . 5 S.M. Hu, Sol. St.Electr. _L5

(1972) 809.

6 E.E. Gardner and P. A. Schumann

IBMTR 22191, July I965.

7 E.E. Gardner, P. A. Schuunann

and E.F. Gorey, IBMTR 2239^,

May 1967.

8 R.D. Brooks .and H.G. Mattes,

BSTJ ^ ( 1 971 ) 775.

9 P.J. Severin, Philips Res.

Repts 26 ( 1 971 ) 359.

10 P.J. Severin, Symposixim on spreading resistance measurements, NBS (197^).

1 1 R. Holm, Electrical contacts

handbook. Springer Verlag,

Berlin, 1958.

12 J.N. Sneddon, Mixed boundary

value problems in potential

theory, North-Holland Publ.

Co. Amsterdam ,1 966 .

es

13 R.G. Mazur and D.H. Dickey,

J.Electrochem.Soc. 113

(.1966) 255.

^k ¥.A. Keenan, P. A. Schiimann,

R.P.Phillips and A.H. Tong,

Ohmic contacts to semiconductors, ed. B. Schwartz, Electrochem. Soc. (1969) 263.

15 P.J. Severin, Silicon Device

Processing, NBS Spec.Publ.

337 (1970) 224.

16 P.J. Severin, Sol . St . Electr

^h ( 1971 ) 247.

17 C.J. Bouwkamp, IEEE Transact.

Antennas and Propagation, APIS (1970) 152.

18 P.J. Severin, Paper 75 presented

at the Chicago, Illinois, Meeting

of the Electrochemical Society,

May 13-18, 1973.

19 R.H. Cox and H. Strack,Sol.

St.Electr. _!_0 (1969) 1213.

20 I.S. Gradshteyn and I.M. Ryzhik,

Table of integrals, series and

products, Acad. Press, 1965>

6. 533.

21 P.J. Severin, Appl.Opt.

(1970) 238I; J_1_ (1972) 691.

22 P.J. Severin, J.Electrochem.Soc.

121 (1974) 150.

23 R.L. Davies and F.E. Gentry,

IEEE Transact. Electron Devices

ED _!_!_( 1 96k) 313.

1 V//////7y77T/7777\

ft ,

id

r

ft

•3z

Figure 1. The geometry of the contact and the two-layer structure.

42
Figure 3. The spreading resistance R2113 = V2i/ii3

(fig. 6B) plotted vs the four-point-probe resistance R23m> both measured with mercury probes,

on bulk samples. The solid line represents

Rg = p/4A, where 1 Q corresponds to p = 0.2 Qcm.

Figure 2. The oblate spheroidal

coordinate system schematically

drawn.

10-'

/

Figure 4. The spreading resistance R, normalized by the spreading resistance on infinite geometry

Roo =p/4A, plotted vs the normalized thickness d/A, as calculated by Brooks and Mattes (sec. 3.1), by

Schumann (sec. 3.3), by Severin (sec. 3.2) and measured by Cox and Strack (sec. 3.4). The two ranges

are noted on the horizontal axis.

t 1.2

1

0.8

0.6

0.4

0.2

0

0

0

5

0.5

7 8

_d_

A

0 Brooks & Mattes

X Cox 8 Strack

• Schumann

0 Severin

1

1 1

0°'

0 , 0 j-ffr

< c

c ^^^^

(

r

10 (upper curves)

1 (lower „ )

43
F(u)

1 20

16

12

1

;

1

i

0

aJ OA 0.6 0.8 1.0 1.2 —^ u

Figure 5. The, function F(u)

with u2 = a2 p/R'd.

1 2 3 U. tl 1

^1

^ 1 +C

1 ^

it

-c

1 it jjtti^i B

1 1 D

1

ZZZZZZZZZ2Z

\

Figure 6. The two alternative three-point-probe arrangements for spreading resistance measurements (A and B) , modified with bottom voltage probe (A^ and Bi), and

modified for bottom current probe (D) , with two arrangements used in the text (C and

44
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10. Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Two-Point Probe Correction Factors

D. H. Dickey

Bell and Howell Research Laboratory

Pasadena, California

The effects of sample boundaries on resistivity measurements made

with a two-point spreading resistance probe are calculated for various

boundary conditions. The results are presented in the form of dimensionless correction factors. The problem of depth-dependent resistivity

in a thin layer is considered, and a method for correcting measurements

on such layers is described.

Key words: Boundary correction; calculations; electrostatic analogue;

resistivity; semiconductor; spreading resistance.

1. Introduction

The two-point spreading resistance probe as originally developed [1]' was characterized

by a sampling volume substantially smaller than then-current resistivity probes. The accurf acy available with the technique did not justify correction for sample boundaries when it was used for bulk samples of even moderately small size. Improvements in the accuracy of

' the technique in recent years, coupled with the desire for probing smaller and smaller

j samples has made correction for sample boundaries a necessity. The purpose of this paper

I is to present correction factors for a variety of boundary conditions, including conducting

I and non-conducting edge, end and subsurface boundaries. A simplified approach to the problem of a depth-dependent variation in resistivity in a thin layer will also be presented.

2. Method of Calculation

The resistivity of a sample is assumed to be related to the resistance measured between

the two probes according to

p = 2aR/F ohn-cm (1)

where a^ is the contact radius and F is a dimensionless factor that contains the correction

for sample boundaries.

The following development is similar in many respects to that used by Uhlir [2] for the

conventional four-point resistivity probe, and makes use of his results for those cases

Vigures in brackets indicate the literature references at the end of this paper.

45
involving image sources. The basic approach is to invoke the electrostatic analogue of the

current flow problem, in which equipotential contacts are replaced by capacitor plates and

current sources are replaced by electrostatic charges.

A point charge in free space establishes the same potential distribution as that of a current I flowing from a point into an infinite medium of homogeneous resistivity if the

charge has magnitude

Ip/4ir esu (2)

In practicality, current flows from a surface contact into a half-space of resistive

.medium, so the current required to establish a certain potential distribution is one-half

that implied by equation 2. Rewriting equation 1 for F in terms of the potential difference

between the two probes, we find

I

2a AV/Ip (3)

Combining equations 2 and 3, the correction factor we seek for two probes on the surface of

a half-space can be written in terms of the electrostatic analogue as

(a/^)AV/q (4)

where q is the charge on one contact, -q is on the other and aV is the potential difference

between them.

To illustrate, we take the simple case of a semi-infinite solid with the probes separated by a distance s^. We replace the contacts with two capacitor plates having charges +q

and -q and calculate the potential difference between them. The potential on the first

plate is

V-] = qTT/2a - q/s (5)

where the first term is owing to the charge on the first plate (the capacitance of a disc is

2a/TT esu) and the second term is the contribution from the negative charge on the other

plate; assumed to be concentrated in a point. The potential on the second plate is equal to that on the first, but opposite in sign, so the potential difference is

AV = q(w/a - 2/s)

and the correction factor, from equation 4, is

F = 1 - 2a/Trs

(6)

(7)

This expression represents a negligible correction for very large values of s/a, and

should be valid for any practically attainable smaller probe separations.

46
3. Calculations for Abrupt Boundaries

3.1. The Infinite Slab

The method of images may be used to calculate the correction factor for the case in which

the probes are on one surface of a thin slab. The arrangement of the image plates in the

electrostatic analogue is illustrated in figure 1. Each plate has associated with it an infinite array of images, which ensure that the normal derivative of the potential will

vanish in the planes corresponding to the upper and lower boundaries of the slab. As before,

we write the potential on the first plate as a sum of contributions from each of the real

and image charges. Fortunately, the contribution from exactly such an array of image

charges has been conveniently summed by Uhlir. Using his result, we find

Vi = qir/Za - q/s + (q/2t)M(s/2t) (8)

where the first two terms are the potentials owing to the charges on the two real plates, t

is the slab thickness and M(a) is a function tabulated by Uhlir. The M-function has the

limiting form for large s/t:

M(a) = 1/A + ZlnX - 0.2318 (X > 1.5) (9)

The potential on the second plate is again equal but opposite in sign to that on the first,

so from equation 4 we obtain

F = 1 - 2a/Trs + (a/Trt)M(s/2t) (10)

This result is valid for slab thickness greater than the contact radius, but breaks down

somewhat for smaller thicknesses because the image charges can no longer be assumed to be

concentrated in a point.

For very small sample thicknesses, the resistance model is equivalent to one in which

the equipotential contacts extend through the entire thickness of the sample. The problem

therei^ore becomes two-dimensional and can be solved in many ways. An electrostatic analogue

is the two-parallel-wire transmission line, for which the capacitance per length t is

C = t/4£n{2s/a) esu (11)

The capacitance is just q/AV, and since this problem is not confined to a half-space the

correction factor is one-half that given by equation 4. The result is

F = 2a£n(2s/a)/7rt (12)

jl Equations 10 and 12, valid for large and small sample thicknesses, respectively, are graphed

1 versus t/a for s/a = 100 in figure 2. The two formulas are in excellent agreement for

^ t = a.

I In the case where the lower surface of the slab is a conducting boundary, the electroI static analogue consists of the same array of images as shown in figure 1 but with different

I signs. The lower set of signs indicated in figure 1 apply in this case. These images can

i be considered to be made up of two superimposed sets: those about being a set with

r charge -q and spacing 2t superimposed on a set with charge +2q and spacing 4t. This

arrangement satisfies the requirement that the tangential component of the field must

vanish in the plane corresponding to the lower boundary. Again using the results of Uhlir

47
for the potential owing to the image charges, assuming they can be represented by point

sources, the potential on P] is

= q^/2a - q/s + (q/2t)M(s/4t) - (q/2t)M(s/2t) (13)

V2 is the same, but with opposite sign, so

, F = 1 - 2a/Trs + (a/TTt)[M(s/4t) - M(s/2t)] (14)

This formula is useful for sample thickness greater than the contact radius.

For very thin layers on a conducting substrate the measured spreading resistance should

be independent of probe separation s^. The electrostatic analogue is the parallel disc

capacitor with plate separation 2t. The capacitance in electrostatic units, including the

effects of fringing, is

C = (l/8t)[a + (2t/Tr)£n2]2 esu (15)

Again, this model is not confined to a half-space, so the correction factor is one-half

that given by equation 4:

F = (4t/Tra)/[l + (2t/^a)£n2]2 (16)

Equations 14 and 16 are graphed as a function of t/a in figure 3. The agreement at

t = a is not exact, but close enough that we can assume the validity of equation 16 for

t < a> and equation 14 for t > a.

3.2. The Quarter-Infinite Solid

The case in which the probes are near and parallel to the edge of a thick sample

requires only two image contacts instead of the infinite arrays encountered with a thin

sample. The potential on each plate is therefore the sum of four terms, and the potential

difference is

aV = 2q[w/2a - 1/s t l/2w ; l//4w2 + s2' ] (17)

where w is the distance from the line between the probes and the sample edge. The upper

set of signs apply when the edge is insulated, and the lower set applies when the edge is

a conducting boundary. The correction factor is:

F = 1 - 2a/TTS t a/TTW + 2a/Tr/4w2 +

$2' (18)

If the line between the probes is perpendicular to a sample boundary, the potentials on the two contacts are not equal and opposite since there is no longer a symmetry plane midway between them. The potentials can however be immediately written, and the resulting

correction factor is

F = 1 - 2a/^s + a/2TT£ ; (2a/TT)/(2£ + s) + (a/2^)/(£ + s) (19)

48
jij where I is the distance from the boundary to the nearest probe. Again, the upper set of

1 signs apply if the edge is insulated, and the lower set applies for a conducting boundary.

3.3. The Semi-Infinite Slab

For the case in which the probes are parallel to the edge of a thin slice, four infinite

arrays of images are required. The potential on one of the contacts can be obtained from the

j superposition of three pairs of arrays of the type shown in figure 1. If the probes are

il parallel to the edge, the potential on the positive contact is

= qu/2a - q/s + (q/2t)M(s/2t) + q/2w + (q/2t)M(2w/2t)

- q//4w^ + s^ + (q/2t)M(>/4w^ + sV2t)

where w is the distance from the edge and the upper signs are used if the edge is insulated.

The potential oh the negative contact has the same magnitude so the correction factor is

F = 1 - (a/TT)[2/s + 1/w t 2//4w2 + s2]

+ {a/^t)[M(s/2t) - M(w/t) + M(/4w^ + s^ /2t)] (21)

This result is valid only for sample thickness greater than the contact radius. For

thinner samples, a model similar to that used to obtain equation 12 is useful. Other

correction factors for more complicated boundary conditions can be obtained by using the

process outlined in the preceding cases.

4. Inhomogeneous Resistivity

The final case to be considered is the one in which resistivity varies with distance

, from the surface of an infinite slab. If the resistivity is a monotonical ly increasing

' function of depth, the profile can be approximated by dividing the sample into a number of

superimposed electrically parallel bodies, each with a different thickness. For illustration, consider the rectilinear resistivity profile shown in figure 4. This profile is the

result of superimposing three bodies of thickness tg, t] and t2, each having uniform

j resistivity 3p. The relation between p, the surface resistivity, and the spreading

' resistance measured at the surface is in this example:

p = 2a Rd/Fg + l/F^ + l/F2)/3 (22)

where F^ is the correction factor calculated from the thickness tp. In practice, one must

1 estimate the thicknesses t] and t2, these being the depth at which the resistivity is 3p

and 3p/2, respectively. If measurements are made at various depths on an angle-lapped

j sample, the t^'s can be estimated with increasing accuracy by considering first the

|| deepest measurements and working out to the original surface.

In general, the surface resistivity obtained by this method from a division of the

sample into N superimposed parts each with resistivity Np is

N-1

P = 2a R I 1/NF^ (23)

n=0

"

j where Fq is calculated from the total sample thickness, F^ from the depth at which the

' resistivity is approximately Np/n, and R is the spreading resistance measured at the

surface.

49
5 . References

[1] R.G. Mazur and D.H. Dickey, Electro-Chem. [2] A. Uhlir, Bell Syst. Tech. J., 3±, 105 (1955)

Soc. Abstracts, 12, N. 148 (1963)

±q +q

RELATIVE THICKNESS

_^ J ^ Figure 2. Correction factor, F, versus the

ratio of sample thickness to contact radius

for insulated boundaries and probe separFigure 1. Arrangement of image contacts ation s = 100 a. for an infinite slab. Upper and lower signs

are for insulated and conducting lower

boundary, respectively.

I I I I I 1 1—I I I 1 1 1

1

1 1—I I I 1 1

RELATIVE THICKNESS

Figure 3. Correction factor, F, (formed by

splicing equations 14 and 16) versus the ratio of sample thickness to contact radius for a slab with

conducting lower boundary. Probe separation s = 100 a. The dotted lines are the continuation of the individual equations beyond the point of joining.

S P

2 DEPTH

Figure 4, Resistivity profile re- sulting from the superposition of three layers of different thickness

but uniform resistivity 3p

50
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

On the Validity of Correction Factors

applied to Spreading Resistance Measurements

on Bevelled Structures

P. M. PINCHON

R.T.C La Radiotechnique Compelec

Route de la Delivrande

B.P. 6025 - 14 Caen France

I The correction factors in spreading resistance measurements

are generally determined by using a plan-parallel model of a

! single or multi-layer structure. This paper will discuss the

I applicability of these factors to the profiling measurements on a

'I bevel, and call attention to possible systematic errors which can

'! appear in the case of an insulated layer or a low/high type of

1 structure.

After a short discussion on the spacial resolution of the

spreading resistance probe, the case of a homogeneous isolated

j layer is examined in more detail. A simplified expression for the

value of spreading resistance was calibrated against published

data using fitting coefficients.

It is then easy to show that the use of a correction derived

I for parallel structures is not correct for the case of a thin,

isolated layer, when the measurement is made on a bevel.

Indications are also given on the parameters which could

minimise the problem

The experimental part of this paper shows a series of profiles made with P-type epitaxial layers.

After the application of the usual corrections, the various

I electrical boundaries or geometrical conditions are seen to affect

' the results in accordance with the discussion. An edge effect which

is significant even at great distance from the edge, is also described.

In the absence of a three dimensional theor}/ for correction,

the use of small spacing is recommended in conjunction with a small

radius of contact and a shallow bevelling angle.

Key words: Accuracy; bevelled structures; correction application;

{ correction factors; edge effect; profiles; resistivity profiling;

small spacing; spreading resistance.

I 1 . Introduction

According to Mazur CO, the spreading resistance technique has been increasingly popular

in the last years for resistivity measurements mainly due to its high spacial resolution

Jl compared to other methods. But in the case of measurements on thin layers, the measurement

I values must be corrected to give the actual resistivity depending on geometrical factors

|i and on the nature of the layer boundary.

51
Theoretical models have been used to derive these correction factors in the simple case of a two-layer system C2»33 and later, extended to a graded structure, [4I using a multilayered approach. Up to now these calculations of corrections have always been based

on a plan-parallel structure having infinitely wide lateral dimensions.

The aim of the present paper is to e.Tamine in which conditions these correction factors can be applied to measurements made on bevelled structures where the lateral homogeneity is

evidently not maintained at large scale (compared to the contact radius) and what kind of errors are involved in doing so.

2. Qualitative background

We shall assiime that the probe has a plain, circular contact with the material, of no contact resistance.

The figure 1 shows qualitatively what shape of ciirrent streams and equipotential lines are involved in three distinct cases, under a spreading resistance probe : a) thin layer on shorting substrate, b) infinitely thick sample, c) thin layer on insulating substrate.

In all cases the current sink is considered located at infinity, and the layers or the bulk

supposed to be homogeneous in resistivity.

In the case of thick samples, figure lb the equipotential surfaces tend rapidly to be

hemispherical as the distance increases from the probe. Using this approximation it can easily be shown that 95^ of the voltage drop is obtained at a distance x related to the

radius of contact, ro by :

In the case of a highly conducting boundary, figure 1ao it is evident that the voltage drop is confined in a very small space, smaller than that of the thick sample. On the

contrary, the case of the insulating boiuidary, figure 1c, indicates that the voltage drop is

practically in the lateral direction, and closely related to the sheet resistance of the

layer. It will be seen later how this lateral voltage drop can still be of importance at distances greater than 20 Tq.

Let us take as reference, the spacial resolution of the thick homogeneous sample. Thus,

the fact of the non homogeneity at large scale in the lateral direction in the case of a bevelled layer becomes important in structures of the low/high type and very pronounced for

an insulated layer.

3. Semiquantitative model

Let us restrict our discussion to the case of homogeneous thin layer, of thickness : t,

resistivity : ^ , limited by an insulating boundary.

Elementary theory shows that the lateral resistance of a disc, having an inner contact

of radius : , an outer contact of raidus : r^ , figure 2, is given by

(2)

Figures in brackets indicate the literature references at the end of this paper.

52
With an arbitrary geometry of 5 point contacts, as shown in figure 3» the circumference of the contact of radius : r^ being the common electrode, it is easy to obtain the

voltage drop between the circumferential contact and the voltage probe : (V-Vo), assuming

that the distances : a, b and c are large compared to r^ :

- ( c

For thin layers, the graph in figure 1 suggests that the spreading resistance is dominated by the lateral sheet resistance. Thus, by comparison with the spreading resistance of

the infinitely thick material it becomes :

(3)

If we relate to Tq, introducing a fitting parameter such as r^ =o(,Tq, a linear relation of the correction factor (C.P) is found versus (t/rg)"^ this being confirmed by the

published data of Gardner ^3} obtained by more accurate derivation, for the range of

t/ro < 1

Using the in-line geometry, with a spacing : s, the common electrode on one side, the

fitting parameter is obtained by comparison with Gardner's curve and found ; (<xO,8,

The value of the spreading resistance for thin layer is then approximated, for t/rQ<1 by :

(4)

This indicates that the spreading resistance is mainly equivalent to the resistance of

a sheet having a side injection contact of 0,8 radius.

/" For thicker layers, using again approximate models including fitting parameters we may

decompose the spreading resistance into

(5)

where R„p = total spreading resistance

SR

r1 : R "local" resistance

"lateral" resistance

Jl .( 1 - lIL ) An ^ 7r/3t/

where ^ and IT are fitting parameters;

and,

R

2 =

(6)

(7)

^ t represents the radius of a; hemisphere in which the "local"resistance is expressed,

!i and

yt represents the radius of a ring from which the "lateral" sheet resistance starts to become of importance.

By fitting with Gardner's curve, an agreement of<±10^ is obtained for t/r^yO,'^,

making ;

S = 0.7 andK= 0.8

' 53
Using these semi-empirical relations the correction factor (C.P.)» for a variety of

2s/Tq and t/r^ values can be derived.

Table 1 gives a set of (C.P.) values ranging from large spacing {2s/t^ = 2000) to relatively small spacing {2s/t^ = 20) and for three relative thicknesses : t/rg = 0.5, 2 and 5.

The values in table 1 agree reasonably well with those reported by Sch\imann, Gorey and

Schneider [5^ taking into account of the appropriate probe geometry.

These values are rewritten in the form (20) in table 2, in order to illustrate

the relative importance of the lateral (20) resistance outside a radius of 20r , where CF^^Q^is the correction factor for 2s = 20.

Table 1 . Evaluated correction factors in the case of an insulated, homogeneous layer : 2s/tq relative probe spacing ;. t/r^ = relative thickness ; probe geometry : 3 pt. in-line, common probe on one side

2000 500 100 20

0.5 9.9 8.2 6.1 4.1

(t/ro) 2 2.8 2.4 1.9 1 .35

5 1.6 1.4 1.2 1,024

Table 2. Ratio of the resistance outside a distance of 20 r_ to the resistance

at 20r^: CF - CF (20)

CF(20)

2000

(2s/ro)

SOO 100

0.5 1.4 1.0 0.5

(t/r^) 2 1 .1 0.8 0.4

5 0.55 0.37 0.17

From table 2 it is obvious that it is not correct to apply the standard correction

factors as determined for laterally homogeneous models in the case of a bevelled layer.

Let us take a numerical example, as may be found in practice :

r = 4\m.

3° = lOOOijjn (2s/r = 500)

t = lOijm ° tangent of the bevel angle : I/50

The length of the bevelled part of the layer is only 500pm, length over which the sheet resistance varies from nominal to infinity. But from table 2 it is seen that a very significant part of the spreading resistance comes from the lateral part included from 80(im (=20rQ)

to 1000|jjii (=s) outside the measuring probe.

Thus in general, a three dimensional model is needed for correction factor calculation

in the case of an insulating limit or more generally in the case of low/high resistivity

structures. In view of the complexity of this task it seems more practical to look at the

conditions for which the error involved in the application of classical correction would

be minimised.

54
Obviously a small spacing arrangement is favourable in conjunction with a low bevel

angle in such a way that the sheet resistance variation in the direction of the slope may

be small compared to the probe spacing distance.

However the very last portion of the bevel can never fulfill the right conditions even

with a small probe spacing . Of course the error is confined to a thinner portion of the

layer in this case.

4. Experimental procedure

Experiments have been done using an automatic S.R prober of our construction which

prints on a semi-log paper, the uncorrected resistance values versus distance. The system

works in the constant voltage mode (lOmV) with a dual polarity print ^t each point ; it

has a 3 pt. in-line probe made with tungsten carbide needles , having a tip radius of » 20^un. The applied contact force is 20 - 25 grams.

I For the experimental part shown hereafter, P type silicon layers have been selected.

We found, as others have, that the contact resistance is lower for P-type material. Thus

the measurements are more sensitive to bulk properties (i.e. proximity of an interface).

I When measuring a bevel, we always apply a metallic shorting strip on which the two accessory probes make contact directly. This shorting is made of indium-gallium paint

! applied together with a mechanical scratching. Only the common probe is working outside

j the strip at a distance : d which is recorded after the measurement. This arrangement is

depicted in figure 4.

The correction procedure has been done as follows : r is deduced in each series of

experiments from the measurement itself on a thick part o? known resistivity (substrate

or average resistivity of a thick layer) according to ;

!

' Rm = Rc + R„„ = K£

4r^

where : Rm is the measured resistance in opposition to Roj^* "the theoretical one

ij and where Rc is the contact resistance supposed to be independent of the layer thickness.

j A value of K = 1 .2 has been used for all corrections on P type material.

Thus the applied correction : M, is related to the calculated correction : (C.P.),

;. corresponding to the simple one-layer system and a plan-parallel structure as mentioned

ji^ in the previous section, by :

M = K - 1 + (C.F.) (9)

K

Trials with K = 1 .0 or K = 1 .4 instead of 1 .2 gave very minorchanges in the corrected

results and hardly any for the part of the layer thicker than 2 microns.

5. Results

I 5.1. Edge effect

I In order to illustrate a bo\uidary effect which may be observed at large geometrical

1 scales, in accordance with the discussion given in section 3, an edge effect has been

jj tentatively looked for in the case of an insulating boundary. An experimental result of

1 this nature has been already given by Severin C^D at the edge of a heterotype epitaxial

I slice . Here, we used a P layer : 8pm thick, resistivity : 4ncm, on an N-type substrate,

j We first recorded the surface measurements over a length of 1 cm at the center of the

I slice, and found it essentially flat. Then the slice was cleaved in two narts and

55

(8)

565-448 O - 75 - 5
re-measured on one half, in the same region as before and in the direction perpendicular to the broken edge, the probes being parallel to it. The probe spacing was s = 3mm.

The result is shown in figure 5 which illustrates clearly the expected edge effect. It amounts to a 20fo increase at a distance as large as y mm. Also on figure 5 is plotted, for

comparison, the calculated effect using an image method and the approximate relations given

in section 3. (The calculated curve has been drawn arbitrarily at a level of 1 OKn)

5.2 Comparison of Corrected Profiles

Having Different Boundary Conditions

In these series of measurements, the depth profiles of resistivity are compared as a function of the boundary nature. In the same epitaxial run three different substrates

have been coated with a P type layer, in order to compare the effects of boundaries in the case of : F/N, P/P and P/P+ configurations.

In the P/P case the choice of the substrate was such that its resistivity would approach

the one expected for the layer, thus allowing a profile which does not require a correction

(substrate resistivity : 3.95ncm).

The uncorrected measurements are given in figure 6. The corrected P/N and P/P+ profiles

are compared to the P/P, uncorrected, in figure 7. It can been seen that the agreement with

the P/P profile is better for the P/P+ corrected profile than for the P/n profile.

In any case the slope of the P layer on the N substrate is wi'ong according to the two others and the possible autodoping contribution which would have led to the reverse tendency. This is attributed to the use of a correction factor which does not fulfil the conditions of bevel measurements.

5.3 Experiments Using Thickness and Probe Spacing Variations

Here, a rather thick (26.5^aii) P type layer on N substrate has been profiled using three

distinct values of the distance d, between the probe track and the shorting strip (see fig-^

The layer has an average resistivity of 5.8ncm as measured by the 4 pt probe method.

The actual measurements are shown on figure 8 and the corrected profiles, figure 9. Now the measurements are taken at a short distance from each other, on the same bevel, and

thus the differences in profiles are likely to be due to the correction errors. They are smaller for the smaller spacing (d = '\20\m) . Then, on the other half of the same slice the

layer has been thinned down to Q\m by etching, bevelled and measured in the same manner as

the previous portion, again using three different spacings d.

The corrected profiles are shown on figure 10. It can be observed that the profile

slopes differ markedly, and the one obtained with the smaller spacing (d = 120|jm) is considered to be more accurate than the others.

If we admit that there must be an agreement between the profiles of figures 9 and 10,

and that this would be optimiim for the smaller spacing, then a downward shift of 20^ is

necessary for the last experiment. This is attributed to a small change in the experimental conditions between the two experiments (which were not done in the same day). By doing

so, we obtained figure 11, which shows the comparison of the six corrected profiles.

6. Discussion

The errors involved by using the common correction factors in the case of an insulated

layer can be sketched as in figure 12 where the practical situation is represented in dark

lines and the situation for which the usual C.F has been calculated is in dotted lines.

The discussion is also restricted to homogeneous layers, for simplicity.

56
At the starting point (fig 12a) the measurement is higher than it would be for a continuous layer because an edge effect occurs, this being roughly equivalent to that of a vertically cut layer at half the level length. Then the corrected value is too high.

At a point near to the middle of the bevel (fig 12b) the higher conductance (two

times higher) of the left hand part compensates for the absence of layer at the right. Then

the usual CP. is nearly correct for all probe spacings.

At the last position close to the junction (fig 12c), the very high conductance of the

left hand side overcompensates for the absence of the layer at the right. Then the measurement is too low after correction.

This qualitative behaviour is clearly observed in figures 7, 9, 10 and 11.

7. Conclusion

The errors involved by the application of correction factors determined for plan

parallel models in the case of bevel measurements have been discussed in a semi quantitative

manner and the behaviour verified by a few experiments.

A three dimentional model is in principle required to derive the correction factors in

the case of low/high configuration. Using the common CP., the errors after correction can

be minimized using a contact radius, a probe spacing and a bevel angle as small as possible.

The general benefit in using a small probe spacing has already been reported [53

The present work leads to the same conclusion explaining by simple models the physical

nature of the benefit in layer profiling.

8. References

[l] Mazur, R. G., Dickey, D.H. J.Electrochem. Soc. 255 (l966)

[3] Gardner, E. E., Symposium on Manufacturing In-Process Control and Measuring

Techniques for Semiconductors, Vol II,

p 19. Manufacturing Technology Division,

A. P. Materials Lab. (I966)

[5] Schumann, P. A., Gorey, E. P.,

Schneider, C P., Solid-State Technology

50 (March 1972)

[2I Dickey, D. H., Electrochem. Soc. Conf.

Pittsburg, Abstr. No 57, April (1963)

CO Schumann, P. A., Gardner, E. E. Solid-state Electron. 12 371 (1969)

[6] Severin, P. J. Philips Res. Repts. 26 359 (l97l)

57
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cr 00

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ett 1-13

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59
Figure 8. Uncorrected profiles of one P- layer on N-substrate. The distance, d,

from the probe to the strip is the parameter.

Figure 9. Same profiles as in figure 8,

after correction, using k = 1.2, r = 5.2um

and d as indicated for Id/r^.

Figure 10. Corrected profiles for a portion of the same slice as figure 9, but

after thickness reduction of the layer to

8ijm prior to measurements.

60
Figure 12. Qualitative effect of the bevel geometry: the usual correction factor is: too small in a) (edge effect) nearly adequate in b) too large in c)

61

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

SRPROF, A Fast and Simple Program for

Analyzing Spreading Resistance Profile Data

B. L. Morris and P. H. Langer

Bell Telephone Laboratories, Incorporated

Allentown, Pennsylvania

and

J, C. White, Jr.

Western Electric Company

Allentown, Pennsylvania

The spreading resistance technique is an excellent

method of measuring epitaxial resistivity profiles. In

many cases it is the only method by which the complete

profile may be measured. However, thin film correction

factors must be used to convert the spreading resistance

into a corrected resistivity. Previous calculations of

these correction factors have emphasized a mathematically complex solution which necessitates the use of a large computer. The correction factors used here are calculated from a relatively simple algorithm which

allows the use of a minicomputer. A documented program

is presented which uses these algorithms. This program,

written in FOCAL for use on the PDP8 series of minicomputers, is fast, accurate, easy to use, and provides

a complete data reduction system. Examples of corrected

spreading resistance profiles are presented, and com- pared with independent results such as diode C-V and

four point probe measurements.

Key words: Resistivity profiles; spreading resistance;

thin film correction factors. II.Introduction

If a flat circular probe of radius a is brought into contact with a jsemi-inf inite material of resistivity p, and a current I is passed through

;this structure, practically all of the potential drop will occur within

11.5 X a of the point of contact. [1]^ This is shown schematically in

iiFigure 1. For a contact in which the surface barrier resistance (Schottky

Jresistance) can be neglected, the resistance of the structure is

Rg = p/4a . (1)

'his is known as the spreading resistance. Since real metal-semiconductor

Figures in brackets indicate the literature references at the end of this

I, paper

1
contacts can have appreciable barrier resistance, an empirical calibration

of R vs. p is necessary. These calibration curves are constructed for silicon^by measuring R and p on a large number of samples, both N and P type,

<100> and <111> orientations, with resistivities from 0.001 ohm-cm to

100 ohm-cm. , The spreading resistance set used in this work is the model ASR-100 ' built by Solid State Measurements, Inc. [2] This unit measures the total ) contact resistance between two probes, each of which have a radius of con- tact of approximately 3 microns. For the two-probe case, eq (1) is modified

to read '

or

Rg - p/2a (2a)

2a Rg . (2b)

The assumption that the material is infinitely thick, i.e., that

t/a >> 1, is not true for most of the structures used in semiconductor devices. In particular, epitaxial films, which are grown on .substrates of

different resistivity, usually have thicknesses which are of the same order

of magnitude as the probe radius. For these thin films, the equipotential

lines shown in figure 1 will be distorted, and the relation between R and p will be subject to a thin film correction factor (CF)

p = 2a Rg/CF . (3)

The CF depends upon the relative resistivities of the film (p-^) ^.nd substrate

(P2) f as well as the film thickness. If P2 > P-^' potential lines will

tend to be pushed out of the substrate. In the limit where P -^/P 2 ~ ^' which

is the effective ratio when the film-substrate boundary is an insulating one

(i.e., a p-n junction), the potential lines are unable to penetrate the

boundary. In this case the measured value of R for a given p will be higher

than predicted by eq (2a), and the CF in eq (3) should be greater than unity.

If the boundary is a conducting one, potential lines will be drawn into the

substrate, making the value of R too low. In this case the CF will be less

than unity. ^

2 . Previous Work

A great deal of effort has gone into the problem of calculating the

exact solution of the potential distribution for a real (i.e., multilayer)

semiconductor material under a charged circular disc. [3-5] For the simple

case of a two probe measurement on a two layer system, with a layer of

resistivity and thickness t, and an infinitely thick substrate of

resistivity the spreading resistance is [3]

^s I = 2¥\j / —=213^) (—2 23r-^ I—. o 1 - Ke X

where R^ is the spreading resistance, H = t/a, K = (p2 - p-^)/{p2 + P j^) r 64
S = 2s/a (s is the spacing between the two probes) , x is an integration

parameter, and J and are Bessel functions. The term within the square

bracket is the These CFs are shown schematically in figure 2.

Unfortunately, the relatively simple calculation of eq (4) is not always

a proper representation of the complex structure of a real epitaxial profile,

a more realistic approach is the multilayer concept .[ 3-4 ] This method involves a numerical solution, in which the determinant of a (2N + 2)

X (2N + 2) matrix must be calculated in order to compute the correction factors of a profile with N points. [4] This calculation takes approximately

10 minutes of CPU time on an IBM Model 360/85 to correct a profile of

25 points, [4-5] although a recent paper by Hu[5] states that it is possible

to reduce this time by a factor of about 30.

3. Calculation of CF Algorithms

If spreading resistance profiles are to be used to evaluate epitaxial

material on a routine basis, the data reduction scheme, which includes calculation of the thin film CF, should have the following properties; accuracy,

ease of utilization, and low cost. In the final analysis, the accuracy of

the calculated CF can only be determined by comparing the corrected spreading

resistance profile with a profile determined by an independent measurement

technique. While this comparison includes all of the other possible sources

of error inherent in a spreading resistance profile measurement, and of course in the "other" technique, it is the ultimate test of the entire system, which is really what is important. The ease of utilization includes

total effort needed to reduce the "raw" data produced by the apparatus into

a final profile. Since our ASR-100 is equipped with a data acquisition system which reproduces the data on punched paper tape, it was advantageous to

use a system which could read this tape as a primary input. This factor,

combined with the need for an easily accessed low cost system, led us to

consider writing a program which could be used on a PDP8 minicomputer currently in our laboratory.

A minicomputer using an interactive language such as FOCAL runs at a much slower speed than a large computer using FORTRAN, therefore it was felt

that the only method by which a reasonable calculating speed could be obtained would be to fit the results of eq (4) to a simple mathematical

expression, and then modify this function until the results agreed with

independent profile measurements.

Initial attempts to fit a simple polynomial function were not successful due to the extreme non-linear behavior of the CF, as seen in figure 2.

For the insulating boundary condition (K = +1) , a function of the type

CF = A + Be was then tried. The limits of this CF, as t/a approaches zero

and infinity, are respectively infinity and unity, suggesting a function of

the form

CF. = 1 + B exp (m • t/a) , (5)

where m = m (t/a) . The best fit of this CF to the values of eq (4) was

found for the case where B = 1.4 and m (t/a) is shown in Table 1.

Equation (5) assumes that the p-n junction is a perfectly insulating

boundary. As the junction is approached, and the resistivity of the layer

rises toward that at the junction, this assumption is no longer true, and

results in over-correction of these last ^(^ints^tS] Experimental data obtained from profiling heavily doped 10 cm ) p-type epi on an n-type

substrate were used to derive an empirical correction eq (5) . The best

solution, one that did not produce over correction was found to be:

65
CF. =1+1.4 exp [m • (t/a) ms ^ (6)

where K (P2 - Pi^/(P2 '^1^

Table 1,

t/a Insulating boundary Conducting boundary "n'

0 1 34.32 -0.0637

0 . 2 13 . 55 -0 . 1174

0 3 7.587 -0.1622

0.4 4.905 -0.1995

0.5 3.426 -0.2303

2.511 -0.2558

n 7 1.899 -0.2767

1.466 -0 . 2943

1.149 -0 . 3091

1 0. 9087 -0.3216

2 0.0248 -0. 3830

3 -0. 1599 -0.4041

4 -0.2169 -0. 4142

5 -0-2355 -0.4199

6 -0. 2399 -0.4239

7 -0.2372 -0. 4277

8 -0.2330 -0. 4306

9 -0.2267 -0.4331

10 -0. 2207 -0.4354

20 -0.1706 -0.4431

50 -0.1381 -0. 4430

100 -0.1842 -0.4789

All of the corrections discussed so far have applied to one-dimensional,

semi-infinite material. In fact there is a two-dimensional effect in the CF,

analogous to that of the four point probe. In this latter measurement, the

sheet resistance of a large wafer is R = (Tr/£n2) • V/I , but if the probes

are on the edge of the wafer, the relation is R = 1/2 (TT/£n2) • V/I. In

spreading resistance measurements, this limit il arrived at as the p-n

junction on the beveled wafer is approached by the probes. This 2-dimension

factor, CF2J-J, must be multiplied by the one-dimensional CF.^ to get the

proper resultant. ^^21^ '^^P^'^*^^ upon the spacing between the two probes, and

the lateral distance or the probes from the junction. This factor was experimentally determined for our probe spacing of 0.6 mm, and is shown in

Table 2.

ties

The conducting boundary condition has a CF^^j^ with the following proper1.

2.

3 . CF

CF^j^ < 1 in all cases

CFj^j^ ^ 1 as t/a ^ °°

CD 1 as K ^ 0

As in the case of the insulating boundary, a simple polynomial could not be

found to fit. Equation (4) was used to generate values of CF as a function of t/a and K. The best fit was found to be

66
0 CF^^ = 2 - exp [n • K/(t/a)] (7)

where n = n (t/a) is given in Table 1.

Table 2.

Two-Dimensional Correction Factor for Finite Sheet Size

(Lateral distance from edge) 2D

0 2 .00

10 1.72

20 1.60

30 1.46

40 1.39

50 1. 33

60 1.29

80 1.22

100 1.17

120 1.14

140 1.10

160 1.08

180 1.06

200 1. 04

1,000 1.00

Equation (7) is strictly valid only for the single layer approximation.

Schumann and Gardiner [3] have shown that the multilayer ^pproach is quite

important for N/N /P structures, where the insulating N /P boundary can have

a large ^ffect on the N/N CF . This effect becomes more pronounced as:

1. the N layer becomes ;^hin, 2. the resistivity of the point on the N layer

approaches that of the N layer. An empirical correction for this double

layer case has been incorporated into our conducting CF , this is:

CF^^j^ = ^^Cd' [1 + 1-4 exp (m . TP • UR/RJ] (8)

where RJ = resistivity of last point in N layer

UR uncorrected resistivity of the point to be corrected

TP = (X + TK (N ' ) /a

X = depth of point to be corrected

TK (N ) = thickness of N layer

and m = m [tp'""^] .

! At the N/N^ boundary where UR = RJ and X =0, this factor reduces to the

I insulating boundary CF . For points on the N layer having relatively ^^9^

resistivity (UR > 100 x RJ) , or for the very thick N layers (TK (N ) > ilO X a), this factor approaches unity.

4. Programming of SRPROF (Spreading Resistance PROFile)

!. The complete program utilizing the correction factor algorithms disicussed in the previous section is shown in Appendix I. Comment "cards" and a

I 67
variable list are shown in Appendix II. The prograiraning language is 8K

FOCAL, an interactive language developed by Digital Equipment Corporation for use on the PDP8 series of minicomputers. It is quite similar to BASIC,

which, in various forms, is used on many large and small computers. A flow

chart of the program is shown in figure 3.

The initial parameters entered on the keyboard are wafer identification,

scale factor, orientation, points on oxide (i.e., not on the beveled surface) , thickness and conductivity type of J layers. This data is terminated

by entering a thickness of zero. The data tape generated by the data acquisition system of the ASR-100 is

then entered into the tape reader, a 9999 entered from the keyboard terminates the data. Any "bad" points can be edited at this step by manually

entering the point number and the "correct" resistance of that point.

Starting with the first layer (J = 1) the program calculates the number

of points in this layer, the uncorrected resistivity of the last point in

this layer, calculates the relevant CF, and prints out all data for this

point. A typical output is shown in Appendix III. The Resistivity is the

corrected value, the Doping is calculated from Irvin's work, [7] SR is the

actual spreading resistance, UR is the uncorrected resistivity, and RC is

the radius of contact, RC = UR (2 x SR) . Layers are separated by a blank

line. The output speed is limited by the Teletype printout rate of 10 characters/sec. The computer has sufficient core storage for approximately 100

data points, in addition to the program itself.

5. Results and Summary

The accuracy of the corrected spreading resistance profile, and thus of

the CF calculations, can only be verified by comparing the results to those

of an independent measurement technique. For the conducting substrate

boundary condition, diode C-V profiling is an ideal method of directly measuring the carrier concentration profile, however, it is limited in depth by

breakdown voltage. Two examples of this comparison are shown in figure 4.

Wafer A988-7 is relatively thin epi with a sharp interface. Wafer RL5-1 has

been heated at 1,200°C for 8 hours to produce a large amount of outdiffusion

In both cases the two methods match well over the limited range of the C-V

profile

For epitaxial layers grown on opposite type substrates, sheet resistance may be easily measured by a four point probe. This sheet resistance can also be calculated by SRPROF using a point by point summation of the calculated resistivity. In most cases that we measured this calculated sheet

resistance matches the measured value within + 10%, and in all cases within

+ 20%.

In conclusion, SRPROF is shown to be a fast, convenient, and accurate

method of reducing spreading resistance profile data, which is applicable to

epitaxial layers with either conducting or insulating substrates.

References

[1] R. Holm, "Electric Contacts Handbook", Springer, Berlin (1967).

[3] P. A. Schumann and E. E. Gardner,

Jr., Solid St. Elec. 12, 371

(1969)

[2] Solid State Measurements, Inc.,

Monroeville, Pennsylvania.

[4] T. H. Yeh and K. H. Khokhani, J.

Electrochem. Soc. 116 , 1461

(1969)

68
[5] S. M. Hu, Solid St. Elec. 15_, 809 [6] F. M. Smits, Bell System Tech. J.

(1972) . 32, 711 (1958) .

[7] J. C. Irvin, Bell System Tech. J.

41, 387 (1962)

Appendix I

20. 10 C SRPROF

20. 11 E

20. 12 T Ii:;A "SLICE"P, "SF"SF, "ORNT"OR, " POINTS ON OXIDE"Z

20. 14 T I1;S J=1;S LT=FLOG (10) ;D 27

20. 16 A THK"TK(J);I (TK ( J) ) 20 . 2 4 , 20 . 24 ; A "TYPE"T(J)

20. 17 S J=J+1;G 20.16

20. 24 T 1 1

, "ENTER TAPE" , I

; S 1=1

20.25 A R(I);I (9000-R(I) ) 20.3;I (R ( I

) - . 1 ) 20 . 28

20. 26 S 1=1+1

20. 28 G 20.25

20. 30 S P=-1;S SP=-2

20. 33 S P=P+1;S SP=SP+1;I (6000-R(P) ) 20. 42

20. 34 I (FITR<R(P) /1000>-2) 20. 36, 20. 37

20. 35 I (FITR<R(P) /1000>-4) 20. 37 , 20. 38

20. 36 S R(P) =FEXP<LT* (R(P) /500+2) > ;G 20. 3 3 20. 37 s R (P) =FEXP<LT* (3000=R(P) )/500>;G 20.33

20. 38 s R(P) =FEXP<LT* (R(P) -1000)/500>;G 20.33

20. 42 s SP=SP-Z;F I=1,SP;S R(I)=R(I+Z)

20. 44 A 11, "HOW MANY BAD POINTS ?"P,:

20. 45 S K=0;I (P-l)20.49

20. 46 T I, "LIST I (FROM TRUE EDGE) AND R(I)",:

20. 47 A "i"i, "R(i) "R(i) ,

20. 48 S K=K+1;I (K-P) 20.47

20. 49 D 24.5

20. 52 S J=1;S NP (J) =FITR (TK ( J) /SF) +1; S S=NP(J);S SH ( J) =0

20. 54 S I=S;D 21; S RJ(J)=UR

20. 56 F I=1,NP(J);D 21;D 22;D 23;D 24

20.62 S J=J+1;T :;S SH(J)=0;I (TK ( J) - . 1) 25 .

20. 63 S NP (J) =FITR< (TK (J) -TK(J-l) ) /SF>

20.64 S M1=S+1;S M2=M1+NP (J) -1; S S=S+NP (J)

20. 65 I (TK(J+1) -. 1) 20. 69;D 20.54

20.67 F I=M1,M2;D 21,-D 22; D 23 ;D 24

20. 68 G 20. 62

20. 69 S RJ(J)=1E20;G 20.67

21. 11 S D=SF*(I-1);I (SP-I)25.8;S K=FLOG (R ( I ) /1000)

21. 13 I (T(J)-14)21.16,21.14,21.16

21. 14 I (OR-111) 21. 22, 21. 32, 21. 22

21. 16 I (OR-111) 21.42,21.51.21.42

21. 22 S UR=-. 56655+1. 0596 *K+.01805*Kf 2-. 33462E-02*K+

21. 23 s UR=UR- . 84064E-04*K't 4 ; G 21.6

21. 32 s UR=-. 7 9246+. 993 6*K+. 024 67 3 *K+2+. 6596 8E-03*Kf

21. 33 s UR=UR-. 173lE-03*K+4- . 393 94E-04 *K+ 5 ; G 21.6

21. 42 s UR=-. 18 87 6+1.038 7*K+.059796*K+2+. 27 823E-02*Kt3

21. 43 s UR=UR-. 1048lE-02*Kf 4- . 14122E-03*K+5 ; G 21.6

21. 51 I (R(I) -850) 21.54

21. 52 s UR=-. 33364+2. 2216*K-. 70895*K+2+.12841*K+3

21. 53 s UR=UR+.91035E-04*K+4-.13896E-02*K+5;G 21.6

21. 54 s UR=-. 57755+.71456*K-.0378 3 6*K+2-. 33079E-02*Kf

21. 60 s UR=FEXP (UR)

22. 12 s RC+UR*1E04/(2*R(I) ) ;S X=TK(J)-D;S TR=X/RC

22. 14 s XK=<RJ (J) +lE-07-UR>/<RJ (J) +UR>

22. 16 I (TK(J+1)-.1)22.22

69
22.18 I (T(J) -T(J+1) ) 22.22,22.42

22.22 S K=1;I (TR- . 1 ) 22 . 92 ; I (TR-99) 22 . 23 ; S XM=-.184;G 22.32

22.23 I (TR-TO(K) ) 22.26,22.26;! (TO (K+1) -TR) 22 . 26

22.24 S XM=IN(K+1)-(IN(K+1)-IN(K) )*(T0(K+1)-TR)/(T0(K+1)-T0(K) ) 22.25 G 22.32

22.26 S K=K+1;G 22.23

22.32 S XX=TR*XM*FEXP< . 2*FL0G (FABS (XK) ) > ; S P=10*X/SF;S Z=l

22. 33 I (230-P) 22. 35;S Z=l . 8923- . 01528*P+1 . J2(364E-J2(4 *P 1

22.34 S Z=Z-2. 7879E-07*P+3+l. 895E-10*Pt4

22.35 S CF=Z* (1+1 . 4*FEXP (XX) ) ;G 22.94

22.42 S K=1;I (TR- . 1) 22 . 46 ; I (TR-99 ) 22 . 43 ; S XM=.48;G 22.48

22.43 I (TR-TO(K) ) 22.46,22.46;! (TO (K+1 ) -TR) 22 . 46

22.44 S XM=CD (K+1) - (CD(K+1)-CD(K) ) * (TO (K+1) -TR) / (T0(K+1) -TO (K)

22.45 G 22.48

22.46 S K=K+1;G 22.43

22.47 S XM=CD(1)

22.48 S CF=2-FEXP (-XM*XK/TR) ; ! (CF- . 01 ) 22 . 92

22.52 S TP='(X+TK (J+1) ) /RC; ! (TP-99 ) 22 . 54 ; S TP=99

22.54 S TR=FSQT (UR/RJ (J) ) *FLOG (TP) ; ! (4 . 6-TR) 22 . 62 ; S TR=FEXP (TR) ; S K

22.56 I (TR-TO(K) ) 22.58,22.58;! (TO (K+1 ) -TR) 22 . 58

22.57 D 22.24;G 22.65

22.58 S K=K+1;G 22.56

22.62 S XM=-.18

22.65 S XX=XM*TP*UR/RJ(J) ; ! (-XX-100) 22 . 68 ; S XX=-100

22.68 S CF=CF* (1+1. 4*FEXP (XX) ) ; ! (.1-CF)22.94

22.92 S CF=.09

22.94 S CR=UR/CF;! ( 1 . 5-! ) 22 . 96 ; S LR=CR;R

22.96 S AV= (CR+LR) /2; S LR=CR;D 25

23.12 ! (T(J)-14)23.2,23.3

23.20 ! (CR-. 926)23. 22;S P=7.2E-17;S K=1;G 23.4

23.22 ! (CR-.0324) 23.23;S P=3.3E-11;S K=.65;G 23.4

23. 23 ! (CR-. 00755) 23. 24;S P=1.47E-14;S K==. 832;G 23.4

23.24 S P=4E-17;S K=.966;G 23.4

23.30 ! (CR-1.43) 23.32;S P=2E-16;S K=1;G 23.4

23.32 I (CR-.0847) 23.33;S P=6.97E-14;S K=.837;G 23.4

23.33 ! (CR-. 00715) 23. 34;S P=6.93E-09;S K=.543;G 23.4

23.34 I (CR-. 00128) 23. 35;S P=2E-i6;S K=.94;G 23.4

23.35 S P=1.43E-12;S K=.744

23.40 S NN=FEXP<FLOG (1/ (P*CR) ) /K>

24.12 ! (CF-.1)24.2

24.14 T %4.02,D,%11.04,CR," " % 3 . 03 , NN , %7 . 04 , CF , % 9 . 03 , R ( i ) , %8 . 04 , UR

24.15 T %6.03,RC, ;R

24.20 T %4.02,D," T/R TOO SMALL TO GET CF " , %14 . 03 , R ( I ) , %8 . 04 , UR

24.22 G 24.15

24.50 T depth resistivity doping CF SR";G 24.

24.52 T " UR RC" , :

, " (MICR) (OHM-CM) ";G 24.54

24.54 T " (CM-3) (OHMS) (OHM-CM) (M!CR)",!!;R

25.10 ! ( .1-CF) 25. 15;R

25.15 S SH(J)=SH(J)+SF*lE-04/AV;R

25.20 T !!;S Z=J-1;F P=1,Z;D 25.5

25.40 G 25.8

25.50 T "SHEET RES OF LAYER" , %2 , P

, " =" , %7 . 02 , 1/SH (P) , " OHM/SQ",!;R

25. 80 T! , "END" , ! ! ;Q

27.12 F K=1,9;S TO(K)=K/10

27.14 F K=10,19;S T0(K)=K-9

27.16 S TO(20)=20;S TO(21)=50;S TO(22)=100

27.20 S CD(1) = .063716;S CD ( 2

) = . 1173 9 ; S CD (3 ) - . 162256 ; S CD(4) = . 19951

27.22 S CD(5)-.23029;S CD (6) = . 255749 ; S CD (7 ) = . 27679 ; S CD (8 )=. 29 4377

27.24 S CD(9)=.309103;S CD (10) =. 321649 ; S CD (11) 383058

70
7.26 S CD (12)=. 404117,-S CD ( 13 )=. 414196 ; S CD ( 14 ) = . 4 19 8 67

7.27 S CD(15)=.423970;S CD ( 16 ) = . 4 27 66 6 ; S CD ( 17 ) = . 4 30601

'.28 S CD(18)=.433109;S CD (19) =. 435383 ; S CD ( 20) =. 44 3056

'.29 S CD(21) = .443031;S CD ( 22 ) = . 4 7 88 52

I'. 40 S IN(1)=34.3205;S IN ( 2 ) =13 . 54 69 ; S IN ( 3 ) =7 . 58 7 5 ; S IN(4)=4.9045

j'.42 S IN(5)=3.42615;S IN ( 6 ) =2 . 5109 ; S IN ( 7 ) =1 . 8 9 8 9 ; S IN ( 8 ) =1 . 4 667 6 r.44 S IN(9)=1.146676;S IN ( 10) =. 908661 ; S IN (11) =. 024871

i'.46 S IN(12)=-.159883;S IN ( 13 ) =- . 21687 5 ; S IN (14 ) =- . 23553

r.47 S IN(15)=-.23995;S IN ( 16 ) =- . 2 37247 ; S IN (17 ) =- . 23304

i'.48 S IN(18)=-. 2267;S IN ( 19 ) =- . 2207 3 ; S IN ( 20) =- . 17056

.49 S IN(21)=-.138155;S IN ( 22 ) =- . 18 42

Appendix II

Variable List

SCALE FACTOR (MICRONS/POINT)

i ORIENTATION (111 OR 100)

(J) THICKNESS OF JTH LAYER

(J) TYPE (N OR P) of JTH LAYER

id) SPREADING RES (OHMS) OF ITH POINT

POINT INDEX

LAYER INDEX

TOTAL NUMBER OF POINTS

; (J) NUMBER OF POINTS IN JTH LAYER

' UNCORRECTED RESISTIVITY (OHM-CM)

; CORRECTED RESISTIVITY

CORRECTION FACTOR

DEPTH (MICRONS)

RADIUS OF CONTACT (MICRONS)

< Coimnent Cards

j.20 Read Tape

M29 Calculate true R (I)

' .40 Correct to bevel edge

'43 Edit bad points

< 50 Do first layer

2 60 Do remaining layers

i 10 Calculate UR

1 20 N <100>

2 30 N <111>

2 40 P <100>

2'50 P <111>

2ilO Calculate CF

2 20 Insulating boundary

2 40 Conducting boundary

2 50 Correct for insulating boundary below cond layer

2 10 Calculate doping

2 05 Calculate sheet resistance

iilO CF data matrix

ii

5-448 O - 75 - 6
Appendix III

SLICE:H40488 SFr.ll ORNT:100 POINTS ON 0XIDE:4

THK:3.25 TYPE:N THK:250 TYPE:N THK :

ENTER TAPE ::::::::::::::::::::::::::::::::::::::::: 9999

HOW MANY BAD POINTS? :

DEPTH RESISTIVITY DOPING CP SR UR RC 1 (MICH) (OHM-CM) (CM- 3) (OHMS) (OHM-CM) (MICR) ^

0.00 0.4695 0. 129E+17 0. 6968 591.560 0.3271 2.765

0.11 0.4573 0. 133E+17 0.6886 570. 162 0.3149 2.761 ( 0.22 0.4712 0. 129E+17 0.6779 578 .094 0.3194 2.763

0.33 0.4766 0. 127E+17 0.6670 575. 438 0.3179 2.762 . 0.44 0.4781 0. 126E+17 0.6555 567.542 0.3134 2.761 ( 0.55 0.4889 0. 123E+17 0. 6440 570. 162 0.3149 2.761 \ 0.66 0.4800 0. 126E+17 0.6344 552 .075 0.3045 2,758 ' 0.77 0.4793 0. 126E+17 0.6234 541. 999 0.2988 2.756

0.88 0.4787 0. 126E+17 0.6125 532 . 106 0.2932 2.755 1 0.99 0.4915 0. 122E+17 0.5993 534 . 562 0.2946 2.755 \ 1. 10 0.4901 0. 123E+17 0.5869 522 . 395 0. 2876 2.153

1.21 0.4843 0. 124E+17 0.5745 505. 824 0.2782 2.750

1.32 0.4827 0. 125E+17 0. 6502 492.038 0.2704 2.748

1.43 0.4884 0. 123E+17 0.5459 485.288 0.2666 2.747

1.54 0. 4860 0. 124E+17 0.5307 469.893 0.2579 2.744

1.65 0.4897 0. 123E+17 0.5144 459. 197 0.2519 2.743 1 1.76 0.4941 0. 122E+17 0. 4979 448 .744 0. 2460 2.741 ' 1.87 0 . 5022 0- 119E+17 0.47 85 438.529 0.2403 2 . 740

1.98 0.4696 0. 129E+17 0.4658 399.944 0.2187 2.734

2.09 0.4564 0. 134E+17 0.4488 374 . 972 0.2049 2.732

2.20 0.3983 0. 157E+17 0.4390 320. 626 0.1749 2.727

2.31 0.3474 0. 1B5E+17 0.4323 275. 422 0.1502 2.726

2.42 0.3056 0. 216E+17 0.4226 236. 591 0. 1292 2.730

2.53 0.2243 0. 312E+17 0.4394 179. 473 0.0986 2.746 i 2.64 0.1349 0. 573E+17 0.4876 117.489 0.0658 2.799 ! 2.75 0.0744 0. 127E+18 0.5733 73 . 451 0.0427 2.904 1 2.86 0.0469 0. 297E+18 0. 6554 50. 816 0.0308 3.027 ;! 2.97 0.0224 0. 116E+19 0.7931 26 . 546 0.0178 3.352 \ 3 .08 0.0140 0. 275E+19 0. 8911 16.982 0.0125 3.681

3.19 0.0108 0. 448E+19 1.0001 13 .932 0.0108 3.861

3.30 0.0106 0. 462E+19 1.0001 13 . 614 0.0106 3.884

3.41 0.0106 0. 459E+19 1.0001 13.677 0.0106 3.879

3.52 0.0106 0. 462E+19 1.0001 13.614 0.0106 3.884

3.63 0.0105 0. 468E+19 1.0001 13 . 490 0.0105 3.893 1 3.74 0.0106 0. 462E+19 1.0001 13.614 0.0106 3.884 , 3 .85 0.0106 0. 459E+19 1.0001 13.677 0.0106 3.879

72
v = o

AT 00

Figure 1. Potential distribution due to equipotential probe on semi-infinite solid

of homogenous resistivity, p.
INITIALIZE

EIITER DATA TAPE CALCULATE CORRECTED RESISTIVITY

CONVERT TAPED DATA

EDIT -BAD" POINTS

CALCULATE CARRIER CONCENTRATION

^

PRINT OUT DATA FOR l'"^POINT ^

SET 1-1, SET J-1

CALCULATE 3NP(J) •—(»)

CALCULATE RESISTIVITY OF

LAST POINT IN j'^" LAYER

CALCULATE DEPTH AND

UNCORRECTED RES OF POINT

JSMUNDRY INSULATINC::

YES ,

CALCULATE COND. CF CORRECT FOR LOVER

INS eOUNDRY

CALCULATE INS. AND EDGE CF

SET J-J + 1

Figure 3. Flow Diagram o£ SRPROF,

I

• POINT INDEX

J • LAYER INDEX

SP • TOTAL NUMBER OF POINTS

NP(J)- POINTS IN j'f" LATER

1020

10'9

1018

1017

,016 -

A988 - 7

"**i'iniiiej3r

o

•o

o

J I

I I

1019

10«

1017

1016

1015

RLS-1

_•

I I I

1 2 3 4 5 6 7

Z (/tm)—

• SPREADING RESITANCE O DIODE C-V Figure 4. Comparison of Spreading Resistance and Diode C-V profiles.

74
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Multilayer Analysis of Spreading

Resistance Measurements

Gregg A. Lee

Texas Instruments Incorporated

Dallas, Texas 75222

Spreading resistance measurements provide a highly flexible technique for the determination

of dopant profiles in semiconductors. However, because each measurement samples a greater depth into the sample than the depth difference between successive measurements, the direct conversion of resistivity readings to dopant concentration values will not yield a correct profile.

The technique discussed in this report analyzes direct spreading resistance readings to deduce a "true" dopant profile. The model used is that of circular contacts to a laterally infinite medium which is partitioned vertically into layers of homogeneous resistivity, each layer

corresponding to one spreading resistance measurement point. The analysis is performed by a computer program. Some detail in the development of the program is discussed.

The results of this analysis technique compare favorably to profile results of other profiling

techniques such as capacitance voltage and incremental sheet resistance on profile types to which

they can be apphed. The program execution time is usually fast enough that the computer charge

is less than the direct charge billed for making the spreading resistance measurements.

Key Words: Correction factors, computer modeling, dopant profiles, multilayer spreading

resistance model, resistivity, semiconductor dopant concentration, spreading resistance.

' 1. Introduction

Ij Spreading resistance measurements provide a potentially powerful method for determining dopant concentration

trofiles in semiconductor materials, because continuous profiles can be obtained over several orders of magnitude of

IjDncentration change and across p-n junctions. The profiles are obtained by stepping the probe points down a bevel

lipped at a small angle to the original surface (fig. 1). Each measurement point is assumed to approximate a iieasurement on a flat surface formed by removing all material from the sample above the depth of that point on the

3vel. By using small angles ( 1 7' to 5° ) it is possible to obtain profiles in which consecutive points differ in depth by

ss than 200 A [ 1

] '

1' Unfortunately, the precision of the geometry is negated by the comparatively large volume in the material being

rofiled which is sampled by the electrical measurement. This volume may extend one to several microns into the

laterial (which in shallow devices may involve orders of magnitude of resistivity change). As a result, the

laractenstics at a given depth in the material being profiled affect not one, but several of the measurement points on

bevel Thus, the direct result of spreading resistance measurements is somewhat like a profile of local averages,

Ither tlftn of discrete point values. Figure 2 shows a hypothetical example of this effect. Concentration rather than

jsistivity is plotted since this is the value of interest in process modeling and design.

\, The method described here, which is performed by a computer program, alleviates this problem by deducing the

|rue" profile from spreading resistance data as originally recorded.

f'igures in brackets indicate the literature references at the end of this paper,

i 75

i
2. Theoretical Model

The theoretical model employed is similar to that utilized by several other authors [2,3 ,4 ] . The continuou

resistivity profile is approximated by a stack of layers, each of homogeneous resistivity, with thicknesses equal to th spacing of the spreading resistance data. The potential distribution in this structure can be solved numerically an^ employed to derive the actual profile from the originally measured values.

2a. One Probe Potential Distribution '

The general solution of Laplace's equation in cylindrical coordinates (r, d , z) for a circularly symmetric potentii|

such as that resulting from a single probe is:

oo

V(r,z)= J

[A(X)jQ(Xr)e^2 + B(X)Jo(Xr)e-^2] dX

where V is voltage and A and B are arbitrary functions of the integration variable X. This can be rewritten as:

oo

V(r,z) = K y* -Xz sin(Xr„)

°' Jo(Xr)dX + K J

9(X)e-'^2

o

sinCXr^)

Jo(^r)dX

OO /

+ K

J

^(X)e

o

Xz

sin(XrQ)

Jn(^r)dX

where

sin Xr^ A(X)= K [1 +d{\)]

sin Xr,o B(X)= Ki//(X) -

and Tq is the effective radius of contact of the probe, which is assumed to be circular. In the case of a layer' structure, a separate voltage function, Vj, is defined for each layer, such that:

Vi(r,z) = K

-Xz

sin(XrQ)

^ Jo(Xr)dX +

oo y 0j(X)e- -Xz

sinCXr^)

Jo(^r)dX

(2.0)

OO

+ y '/'i(X)e o

sin(Xr„)

J„(Xr)dX

At this point boundary conditions are imposed which assume that current is flowing, which may be inconsiste with Laplace's equation if charge accumulation exists. However, the expected error introduced is not large[5],a

the results of the method do agree with other profiling techniques.

76
The boundary conditions are these: (refer to fig. 3)

I. No current flows through the surface of the structure beyond the radius of the probe contact:

] 3Vi

^1 9z 0 z=0

II. At each layer interface

a. V is continuous:

Vj (r,hi) = Vi + 1 (r,hi)

b. The current component perpendicular to the interface is continuous:

1 9Vj(r,z)

Pi 9z

1 aVi+i(r.z)

Z=h;

''i+l 3z

Z=h;

III. Two possible appropriate boundary conditions exist for the bottom layer. One assumes that the last layer is semi-infinite and of homogeneous resistivity. The other assumes that a junction exists beneath

the last layer.

In the first case, the boundary condition is that

lim VN(r,z) = 0

In the second case, no current crosses the junction:

1 dY^(T,z) = 0

z=hN

When the expression for Vi(r,z) is substituted into these equations, they reduce to the following set of equations,

ote that 9 j and \p[ are functions of X only, as previously defined.

or the first case:

or the second case:

-^j =0

-2Xhi -2Xhi

(-ej+^i9j+l)e i + (^j_/3jV/i+i)-e ^(l-/3j)

-2Xh

'N N +</'N = e -2Xh-N

(2.1)

(2.2)

(2.3)

(2.4a)

(2.4b)

ir

77
Where

^i+1

This gives 2N equations, which are sufficient for the solution of the N0's and N xIj's. An additional bound

condition involving the current distribution under the probe contact has been used by some authors to resolve t equation 2.0[6] . However, because the final form of the current distribution will be affected by the second prob(

apparatus, in this treatment its resolution is deferred until after the potential distribution of the two probesi

combination is determined. '

The solution of the system of equations derived above will be treated in detail in a later section. At this p( just note that only the solution of Vj, and thus 0 j (since equation 2.1 shows that \p \ - d is necessary, since surface potential is the only potential encountered by the probe.

2b. Two Probe Potential Difference Measurement

The voltage measured by the spreading resistance apparatus is the potential drop between the two probe poi

This is derived from a superposition of the one probe solution for each of the two probes. For this solution pi contacts are assumed. This is not too unreasonable since the ratio of the probe spacing to the physical con

diameter is 600 to 10, and that of the probe spacing to the effective electrical contact diameter 600 to 3.

The measured potential difference between the probes Vm, is

- Va - Vb

where V^ and V|j are the potentials at probe a and probe b.

Each potential consists of two components: the potential due to probe a and that due to probe b. Note thaijn one probe solution coordinates of b relative to a and a relative to b are both (r = D, z = 0), where D is the p

'y spacing. Their coordinates relative to themselves are of course (0,0). That is:

So

Va= Vi(0,0) - Vj(D,0)

Vb= Vi(D,0) - Vi(0,0)

Vm = Va - Vb

= Vi(0,0) - Vi(D,0) - Vi(D,0) + Vj(0,0)

-2 [Vi(0,0)-Vi(D,0)]

78
Noting from equation 2. 1 that 9 j = i// j

, expressing Vj in the form derived in equation 2.0 yields:

oo v^ = 2K y (l + 2ei)Jo(X • 0)

o o

oo sin(XrQ)dX

sin(Xr„)dX r sin(XrQ)dX

2K / (]+20,)J(XD)

X y X o

Vm (1 +20i) [1 - Jo(XD)l

where the 2 has been absorbed into K.

The method of performing this integration is discussed in Section 5.

2c. Resolution of the Proportionately Constant K.

The boundary condition imposed in order to resolve K is that the measured voltage on a semi-inifinite substrate of homogeneous resistivity should equal the voltage measured on that same substrate covered by a finite layer of

equal resistivity. That is, a two layer problem:

Surface

4

V], 9

J,

i// ], p I

V2, '''2'

Two layer problem on semi-infinite medium.

In this case the boundary equations, in matrix form, are:

P\- P2

(2.1)

(2.2)

(2.3)

(2.4a)

which solves to:

1

-2Xhi

-2Xh

1 0

1 —e

^

p-2Xhi

1 1^

0 0

0

-1

-1

1

~

^1 ~

^1

X ^2

_ ^2 _

-2Xh,

(1 -/?i)

01 = ^1

(/3i - l)e

-2Xh,

-2Xh,

((3l + l)-e '(/Jj-l)

Since pj=p 2, |3j = l.So0j = V'| = O and

00 sin(XrQ)

Vm2 [1 -Jo(XD)] dX

79
oo sin(XrQ)

dX -K

OO /

sinCXr^)

Jo(XD) dX

X

sin D

On a semi-infinite substrate the measured spreading resistance voltage would be:

^1

Vml=I

2r.

The defined boundary condition is that Vj^j = ^m2'

K —^ -1 — sm

2 -)D / 2r^

and

2r^

^ -1 sm

2

This expression could have been developed directly from the model of two discs on a semi-infinite medium. The

direct result of this development is:

V p (7t . _i 'o\ — =

I sm ' — I 1 Trr^ V2 d/

However, it has been traditional to neglect the second term and write

V__ p

1 2r„

The approach just shown was used primarily to employ standard formulations as much as possible for familiarity.

It is necessary to keep the sin""^ (fo/D) term because the iterative technique (Section 3a) employed in the

solution tends to reinforce this small error on successive iterations resulting in an error several times as large as that in the initial approximation.

3. Solution Technique

Replacement of K in the expression for Vj^ yields:

n-1

[1 +20i(X)]

_IP1 — -If —sm ' 2

-1-1 oo sinCXr^)

[l-J^CXD)] dX.

_l o

80
Previous authors[2,3,4] have chosen to reorder this equation to: n 1

2r Vm

= Pi —

^ -1

-sin

2

_J /o

(1 +26^)-

sin(XrQ)

[1-J (\D)] dX

A

and to define

^o - 2r.

Sincepo would be the correct resistivity if the measurement of Vm and I were taken on a semi-infinite sample of

homogeneous resistivity. (This is the usual calibration procedure for a spreading resistance probe.) In addition, the bracketed factor is defined as a "correction factor", so that

sin(X r ) (1 + 20) [1-J_(XD)] ^ dX, (3.1)

and thus

(3.2)

As Hu has pointed out [4] , this is not an entirely appropriate terminology since "correction factor" implies an

arbitrary adjustment on "fudge factor" rather than a logical data reduction scheme. However, in spite of the name,

the format is a convenient one and is used here.

3a. Iterative Technique

The last equation can be reordered to

Pl=Po/C (3.3)

where C is a function of Tq, d, and d d \ is itself a function of hj h2 . . . hjsj and p] P2 • • • Pn- other words, the equation for the "corrected" value of p j is not explicit in that C is a function of p j. In general the integral factor of C

has no analytical solution, and thus the equation cannot be solved explicitly for p'j.

The approach to solving for p \ taken here is to define Pq as an approximation of p j and to obtain successfully

better approximations of p ] from an iterative solution of 3.3. Since the calibrations obtained with the Texas

Instruments apparatus allow rQ to be assumed constant, P2 . . .PN hj . . . hjsj do not vary throughout the

solution. Thus C may be treated as a function of p j only.

Simple Relaxation: ^ 1 , i + 1 ~

^ ,^

always converges, but often very slowly in terms of the number of repetitions required. In addition, the only available convergence criterion is comparison of successive values ofp). The iteration is terminated when Ap/p falls below a predefined limit. However, in some cases the convergence is so slow that Ap/p may reach .001 when p j is still 10%

aways from the correct value.

81
A Newton-Raphson technique, which uses both the last value of p j and its derivative to compute a new pj,

converges 3 to 5 times as fast as relaxation, but suffers the same weakness of convergence criteria and may oscillate in some cases, especially if the input data is not smooth, rather than converge. The relations used for iteration is:

^l,i+ 1 " ^l,i

1 + C (Pl,i)

C'(pi^i)

where Cj = AC/Ap| from the previous iteration or from an extra (pj, C(p\,)) pair generated if Apj would be too

large.

Both relaxation and the Newton-Raphson method can be characterized as analytic techniques. Another

technique which can be employed is a pragmatic hunting method which converges about one-half as quickly as the Newton-Raphson technique, but converges absolutely and to a known absolute accuracy. The technique is a familiar one, and best described as "bracketing". If a criterion can be found to determine if the correct value of p j lies between two other values of p ], a search along the p | axis can be conducted using an arbitrary step size Ap until the

criterion is met. Once this has occurred, the correct value of p ] is bracketed to a known accuracy. By splitting the bracket and retesting either of the two new brackets created for the presence of the correct value the bracket size can be reduced by one-half. Repeating the process results in a one digit accuracy improvement each 3.322 (=(log 2)"^

iterations.

The correct value of p i will have the following characteristics:

^1 C(pi) 1

rr

. „i To — — sm —

2 \ D /

(1 + 20) [1-J, (XD)]-

sinCXr^)

dX^

In other words, two relationships must be simultaneously satisfied:

-1

A:

1 C(pi) sm M

2 Vd

sin(X

(1 +28) [I-Jq (XD)]

X

^o) } — dX/

The relationship of these two equations is depicted qualitatively in figure 4. Curve B is clearly a straight line. The

shape of curve A has been determined from numerical solutions of C (p j) and, except for local curvature reversals associated with noisy data, the shape has been qualitatively the same for every case tested. Since the two curves cross

at the correct solution of pj, C^-Cg will change sign at this point. This is the bracketing criterion discussed

previously. The initial search is always conducted upward to avoid the trivial solution at p i = 0. Figure 4 also

[ illustrates a hypothetical series of approximations toward the correct value of p j.

The program normally uses a combination of Newton-Raphson and relaxation techniques to achieve short | running time. However, bracketing is selected for use on profiles which are ill-suited to the Newton-Raphson analysis.

3b. Bootstrap Solution

An iterative solution is applied to only one layer at a time. The method for correcting the entire structure is a i bootstrap process proceeding from the deepest to shallowest layer. In other words, the deepest layer is corrected on

the basis of the semi-infinite substrate or a junction boundary condition. Then the next is corrected on the basis of

the corrected value of the bottom layer and boundary conditions, the next on the basis of these two corrected

values, etc. The shallower layers, of course, do not affect the layer being corrected since they were not present at the point on the bevel at which the measurement was made.

82

J
3c. Summary

The sections which follow represent the greatest practical difficulties in performing the solution. However, they

are in fact sub-procedures to the scheme just discussed. So before proceeding a more concise summary of the overall method is in order:

Resistivity layers are corrected one at a time, proceeding from the bottom to the top of the layer structure using

the previously corrected layers in the solution of later ones. The corrected .resistivity value is obtained from the

iterative solution of the implicit equation:

P\ = Po/C(^l)

In this equation, C (p ]) represents the following numerical integration:

C(pi) =

The values of fljCX) in this integral are obtained from the numerical solution of 2N simultaneous equations

where N is the number of layers in the structure.

4. Numerical Integration of C

In Section 3 it was found that

-1 oo

, ,

. J'o\ \ r sin(ArQ)

C(pi)= --sm-M— / (1 + 20) [1-J^(\D)] d\.

This integration is performed numerically using Simpson's Rule, which can be applied successfully since all functions

in the integrand are quite smooth. Two problems in performing the integration exist, however. First, the upper

integration Hmit is not finite; some way of approximating the upper limit with some finite limit must be found. And

second, the integrand is a product of three factors whose characteristics, or at least those pertinent to numerical

integration, are quite different.

The first problem is solved by breaking the integral into two parts and evaluating them separately:

oo /

sin(Xr ) (1 + 20) [l-Jo(XD)] ^dX -

L /sinCXr^) f (1 +20) [I-JqCXD)] — dX + / (1+20)[1-J (XD)]

sinCXr^)

dX

The first integral can be evaluated by usual numerical techniques, but the second integral still has an infinite upper

limit. If L is chosen large enough, however, 0 j can be made arbitrarily close to zero. (See Section 6, fig. 6 and fig. 8). In this situation, the second integral becomes

oo /

sin(Xr ) [1-J^ (XD)] : dX

83
which, in a reversal of the process used above, can be rewritten as

oo

[I-Jq (^d)]

sin(Xr ) dX =

CO L

Io

[1-Jo aO)]

sinCXr^) sinCXr^)

•dX - [1-Jo (^D)] dX.

X X

The first of these two integrals can be solved analytically. The second can be evaluated numerically to an

arbitrary accuracy. Because the integral from L to o° has been approximated by an integral which does not involve d \

its value will be independent of the layer structure. Thus it can be stored as a constant, so long as Tq and D do not

change.

When all physical dimensions (h, Tq, and D) are measured in multiples of Tq, a value of L = 50 is adequate to

justify the approximation just discussed. (Tq and D in this case are on the order of 1 to 3 microns and 600 microns)

The second problem mentioned manifests itself chiefly as a conflict between the maximum value of X required

to drive 6 \ to 0 and the small value of AX required to adequately approximate the Bessel function. D in units of Tq is approximately 400. This means that a zero of Jq occurs for every change in X of approximately .008. Even the questionable allowance of 5 points per zero would require 31,250 integration points to reach X = 50. Fortunately, Jq

decreases in magnitude with increasing argument value. As X increases, the value of (I-Jq(XDJ)) becomes dominated

by the 1 allowing the size of the integration increment, AX, to be increased. However, near X = 0 the size of AX must

be greatly reduced to prevent truncation errors caused by the subtraction of Jq(XD) from 1, inasmuch as Jq(XD)

approaches 1 as X approaches 0. This rapidly diminishing number cannot simply be ignored (i.e. assumed to be zero)

because in some cases (1 + 26) rises as fast as (I-Jq(XD)) falls. In the case of the first layer above a junction, (1 + 26)

may rise nine orders of magnitude as X decreases from 10~- to 10"^ 1, while the value of the entire integrand rises

1 order and then falls eight.

The solution to these problems lies in careful selection of integration increments and some adjustment during

execution. The necessary number of integration increments is between twenty-two and twenty-three thousand.

Each layer requires 3 to 20 iterations for the solution of equation 3.3 to converge. Each iteration requires that the integral in equation 3. 1 be evaluated once. Finally, each evaluation of the integral requires that a value for 6 j (X) be determined at nearly 23,000 values of X. Thus it is quite important that a fast method of solution for the system of equations 2. 1 and 2.4 be used. The next sections describe this method.

The set of simultaneous equations is solved numerically, but before the solution is performed, it is possible to analytically reduce the size of the coefficient matrix by two in each direction by eliminating two equations and two

variables. Equations 2.1-2.4a, restated in matrix form, are:

5. Solution of 6

j

5 a. Reduction from 2N to 2N-2 to Equations

84
1 1

Ej 1 -El -1

-El 1 /3iEi -m

E2 1 -E2

-E2 1 02^2

-1

-(52

En-2 1

-En-2 1

-EN-2

^N-2EN-2

En-1

-En-1

-|3N-2

1 -En-J 1

1 (3n-1En-1 -*5n-i

1

91 0

0

El (1 -01)

0

E2(l -(32)

0

En-1 (1 -(^N-l)

0

where Ej= e ^^j^. The geometry is as in figure 3 with hjyf °°. The areas of the matrix not shown are entirely zeros.

The case shown is for the infinite substrate boundary condition (2.4a). For the junction boundary

condition (2.4b) the last row of the matrix would become:

-En

J hJ

with the junction at h-^ in figure 3.

In both cases \l/ j and i/zj^f, and the outside rows and columns of the coefficient matrix can be eliminated. Since

the first equation is 0 j = \p \

, the first two columns represent the same variable and so can be added and the top row

eliminated. For the infinite substrate case, is zero and so can simply be removed, along with its coefficients, the

right most column. The junction case for t/z^ is similar to that for i// j. Since the last equation expresses i//]vf as a function of only, this expression can be substituted into the previous two equations and the last row and column

eliminated. The result for a semi-infinite substrate is

El +

-El + 1

-El

lEl

E2

-E2

-1

-0\

1 -E2 1

1 |32E2 -132

En-2 1 -En-2 -1

-En-2 1 (3n_2En-2 -0N-2

En-1 1 -En-1

-En-1 1 ('n-iEn-i _

*1

9N-1

*N-1

9N .

0

El (1 -(3i)

0

E2(l -(32)

0

En-2(1 -(3n-2)

0

_En-1 (1 -^N-l)

85
For the junction case the last 2 rows become

En

En_i +;3n_i (En-En-i)

The eHmination of the two equations and variables just discussed does reduce the solution time somewhat, but

especially for large, N, not significantly. It does, however, put the matrix into a better format on which to perform a diagonal solution algorithm.

5b. Matrix Solution

The high sparcity and regularity of the coefficient matrix make it possible to construct a "diagonal algorithm"

which solves for 6, in onepass of an iterative calculation along the diagonal of the matrix. Its development is straightforward from consideration of a Gauss reduction in which steps for which the result is known because of zeros involved in the calculator are eUminated. The algorithm is constructed to end at 9, rather than 6^, as would be

conventional for the matrix as it has been presented.

The matrix need not be stored as a 2N X 2N away, but can be compressed to 2N X 4. This saves considerable

storage and is convenient for programming the diagonal algorithm as well.

Finally, to repeat a point made earlier, no back substitution to solve 6 2, ^ \ , • • ., ^N' "^N necessary since only

6 1 appears in the expression for V j.

5 c. Intermediate Coefficient Storage

As mentioned previously, the only coefficients in the matrix which change between iterations are those which

involve p|. This fact, and the fact that the matrix can be solved in one pass, make it possible to save the values generated by the reduction at the last step before it enters the final two rows, and restart at this point on subsequent

iterations. This reduces the number of operations required for the matrix solution to those required for the solution of a 3 X 3 matrix on all but the first iteration. Of course a different set of coefficient values must be stored for each

value of A at which 6 j is evaluated. This is practical only if the number of A's is relatively small. This is the case as explained in the next section.

5d. Approximation of 0 J by Interpolation and Extrapolation

The greatest time savings in evaluating 9 \ is not in finding a fast way to solve for 9 \

, but in avoiding the solution

entirely. It is possible to compute values for 0 j at a relatively small (typically about 50) number of values of X and

interpolate or extrapolate 9 j at other values. The importance of this fact is made clear by the fact that the integration involves nearly 23,000 values of X.

Figures 5, 6, 7, and 8 illustrate the behavior of (1 + 20 1) for two different situations. Figures 5 and 7 show

original and corrected profiles for a steep gradient away from a junction, and for a steep epi interface. Figures 6 and 8 show the associated values of ( 1 + 20 ) vs X at various values of N.

The boundary condition in figure 5 is that of a junction at the bottom layer. The (2 + 29 \ ) function for this type profile is fitted very well by a power law, at least in the region 0 < X < 2.

It can be demonstrated that for the junction boundary condition, as X 0, 0 j ^ °o.

This would present a serious problem to numerical integration were it not for the fact that the entire integrand converges to 0 at X = 0. If X is taken near enough to 0, the contribution of the the integrand at that point becomes

immaterial.

Values of (1 + 29 j) generated by a profile similar to figure 7 are best fitted by a parabola. The actual system

used is a fitted parabola to each set of three consecutive points, with overlaps averaged. The overlapping is done to avoid problems at inflection points.

En-1 1 -(En-1+En)

-en-1 1 (En-1 - En)

<//N-l

On

86
The criterion of "good fit" used in both cases is the agreement to .1% of the value of (1 + 29 i) computed

exactly and interpolated at the midpoint of two successive values of X to be used as a basis for interpolation. If adequate agreement does not exist, the midpoint is incorporated as an exactly calculated point in addition to the two

original points, and the test performed again in each of the two new intervals.

I For intermediate values of X, a parabola fit is used with either boundary condition. For large values of A, 1 + 29

approaches 1 asymptomatically. 9 1 can be approximated in this region by an extrapolation of an exponential fit to two selected values of 5 1 at relatively low values of X. This extrapolation is used to calculate a few point values of 9j and the rest are linearly interpolated between them. The purpose of this exercise is to avoid excessive time consuming

exponential calculations. (In no case, has the approximated value of 0

1 in the "tail" region differed from an exact

value by an amount affecting the first three significant digits.)

6. Data Pre-Processing

i When input data is not "smooth", the Multilayer Analysis may magnify input irregularities into the output

profile. Figure 9, the original and analyzed profile of an epi-substrate interface, is an example of this effect. The

output profile is quite irregular even though the input appears smooth to the eye. The effect occurs when layers beneath the layer being corrected make a major contribution to the measured voltage. When this is true, the program

decides that minor variations in the measured voltage must be caused by major ones in the single surface layer since its

' contribution to the total measured voltage is relatively small. In figure 9 this is particularly true since the surface

I layer at the point where irregularity begins is underlain by layers of from one to three orders of magnitude higher

i conductivity than the surface layer.

j The problem is not in the program per se, but in the fact that the theoretical physical model used does not

j consider the problem of noisy data and also in the fact that although the model is a reasonable approximation of a

I smooth profile, it is a poor one for the derivative of the profile. The problem, then, cannot be solved by any change

j to the analysis technique short of complete revision. It must be solved at the input data. This is reasonable anyway,

since one normally believes that the profile is really smooth and that variations of the type discussed here are indeed

, noise.

Modifying the input data presents two problems. The first is to define criteria of "smoothness". The second is to smooth the data while avoiding both the loss of information originally contained in the data and the introduction of

I an arbitrary shape to the data profile from the smoothing technique.

The second problem may not be completely avoidable, and in any case cannot be measured quantitatively, so the

j best approach is to do as little as possible and accept some irregularity in the output profile if it is not severe.

Since the problem arises from the poor model of the derivative supplied by a step function profile, the basic

j

i criterion of smoothness is a locally monotonic set of first differences, which are the finite difference analog of the

I I first derivative. The first difference between two data points is:

; AiVi=Vi+i-Vi

'i (Voltage, V, is normally smoothed since this is the form of the raw data, but R or p could be smoothed as well.) No

'consideration of A^, the depth change, is necessary, since it is constant. The second difference is defined as:

: A2Vi= AjVi+i -AiVi

i| Notice that if the set of first differences varies monotonically, then all second differences have the same sign.

I Since the first differences must be smooth, it is these values on which the smoothing routine operates. However,

I data may be too noisy to allow this operation to be performed directly. The routine followed is this:

• The initial data values are smoothed.

• First differences are computed from the smoothed values.

• These first differences are smoothed.

• The final profile is recomputed based on the smoothed differences. 87

565-448 O - 75 - 7
The smoothing procedure referred to is as follows:

• A best fit parabola is generated for each set of five consecutive original points. • The center point of the five is recomputed from the parabola.

This avoids imposing a functional shape because no two points are adjusted using the same parabola. It also avoids

displacing the profile because only initial data is used to generate the smoothed result. That is, the parabolas are fitted only to initial values, not to the smoothed results for previously adjusted points.

Second order smoothing does occur, however, when the first differences computed from a smoothed data set are themselves smoothed. When a smoothed data profile is recomputed from the smoothed differences, displacement of

the profile from its original envelope is avoided by allocating the change in the first difference equally to the positions

of the data points at each end of the interval. Expressed algebraically for a non-end point:

1 1 '^smooth,! - ^i + 7 (^1 ^1 smooth,i-l "^1 ^l,i-l>- "^^1^1 smooth,! "^1 ^l,i>

Thus, the resulting profile contains not the smoothed differences, but differences changed in the direction of the smoothed values, but hmited by the original data envelope.

Two tests of this technique are particularly important. First, does the profile drift from its original position?

And second, does originally smooth data remain smooth? Both can be tested by smoothing profiles generated from

various polynomial and transcendental functions whose values and first derivatives are continuous. These profiles are by definition already smooth. It was found that after five iterations of smoothing previously smoothed output, the maximum deviation at any data points was .055% from the original. The results of the first smoothing operation

deviated at most .049%. The deviations on subsequent iterations did trend further in the same direction as the first iteration deviations. This and the fact that the greatest parts of the deviations appear on the first iteration suggest that some arbitrary shaping occurs. However, it is small.

At this point, the smoothing program makes no judgment as to the adequacy of the smoothing. In fact, no firm

criteria have been developed. The program simply performs the smoothing routine and suppUes the initial and

smoothed data along with first and second differences. Neither does it attempt to remove grossly erroneous data

values from the initial data before smoothing. Occasionally it does change the shape of the profile, but only at very

sharp peaks or bends. Obviously it is still necessary to screen the results of smoothing before using them.

j As an example of the results of this data preprocessing, figure 6 was obtained from the data used in figure 9, but

after smoothing. The smoothing routine cannot handle really noisy data at all. The best procedure in this case is very much as in the past. A best fit curve is drawn by eye and smooth data read from this curve for input to the analysis program.

7. Results

The effect of this analysis on different profile types has been illustrated in figures 5 and 7, but these only verify that the results are quaUtative as expected. Some measure of quantitative accuracy can be obtained by comparison

of dopant profiles obtained from analyzed spreading resistance data and other profiling techniques. The techniques

used were junction and mercury probe capacitance-voltage measurements and incremental sheet resistance. While

these techniques cannot be used on all types of profiles, they do have a known reliabiUty for specific profile shapes.

The result of such comparisons is general agreement, but certain discrepancies exist. The first is illustrated ir figure 1 0, a comparison of analyzed and unanalyzed spreading resistance profiles and capacitance-voltage profiles ol an epi-substrate structure. The dip in the analyzed spreading resistance profile at the interface of the flat section ol the profile and the steeply rising section is a program artifact. Fortunately, it is one which is easily recognized by an

experienced user and thus need not be confusing. The absolute dimensions of the structure involved determined tlie| importance of this defect; the feature is quite prominent in figure 10, but not nearly so in figures 5 and 7, whose!

absolute depth is greater.

88
The effect seems to arise from a discrepancy between the probe model and reality. Recall that the model used

or the probe contact was a single circle of uniform potential. However, optical microscopy and SEM of the probe tips

nd the probe "prints" left on a sample reveal that the contact is actually composed of a large number of smaller

ontacts over a generally circular area. Furthermore, when a calibration of spreading resistance versus resistivity is ttempted using the equation R = p/2ro, the value of Tq obtained is significantly less than the radius of the probe

rint[ 1 ] . Unfortunately, an analytical solution for a model more resembling the probe geometry has not been possible ecause of the complex boundary conditions involved in a tight array of contacts, either in a density distribution or ome arbitrary pattern.

A simple "non-real" model can explain the value of Tq obtained by the calibration. If the contact is viewed as aving a constant voltage, but a limited number of conducting areas in a uniform distribution so that the probability

'lat a contact touches a given point within the limits of the array is 5 , then the development of the two probe

quation is nearly identical to that of the conducting disc model. The final form is

. _i p sm

25 rj-) fSro D 25 rj)

'here rp is the radius of the damaged area of the probe point, or the limit of the contact array. Since 6 is the

jTobability of contact to an arbitrary point, 5 = Aq/Aj), where Aq is the total area of contact and Aj) is the area of

lie region of the array of contacts, or the damaged area. Thus the Tq measured in calibration is

Ac

J-o = -7-

This allows a solution for A^, but this is of little help since neither the density nor the size of the individual

bntacts is revealed in the calibration procedure. Also, observation of probe point hardly suggests uniformity. This

j^odel does help to confirm the conjecture that A^ is less than Aj), however.

The value of Tq given by a R vs p caHbration is usually called the "effective" radius, and is treated as though it |ere the radius in a calibration for uniformly doped samples. This is reasonable since the lateral displacement between

le points of contact is small compared to the probe to probe distance.

Multilayer analysis, however, is concerned with the potential distribution immediately beneath the probe, so the

istribution near individual contacts is important. Figure 1 1 is a hypothetical representation of the real problem. In a istributed contact array with individual contacts small enough for the potential distribution near each contact to

Jisemble that of an isolated small circular contact, the previously developed contact model indicates that the voltage par the small contact will fall off more quickly than that near a large one.

1 The single contact probe model then may look too deep in calculating C, and for certain geometries it Ipvercorrects"; thus, the dip. But the problem is more than one of depth alone; the shape of the potential under the ^obe is also important. Simply reducing the value of Tq does indeed remove the dip, but it also moves the rest of the

^ jlialyzed profile away from the capacitance-voltage data. Figure 12 repeats the C-V curve of figure 10, but with the

^ jj-V data reduced to a smooth curve. The two analyzed spreading resistance curves are for rQ = 1.556 /jm, the value

jjven by calibration, and for Tq = .5 ^m, the largest value which removes the dip. Intermediate values produce profiles

A typical comparison of an incremental sheet resistance profile to an analyzed spreading resistance profile of a

j jiallow phosphorus diffusion is shown in figure 13. The results are in good agreement on the steeply inchned portion

I the profile, but they differ near the surface. It is not completely clear whether this is a program artifact or whether

I arises in the measurement technique since unexpected deviations of the original profile near the surface may occur

I all shapes of profile, as in figure 7. Reducing the value of Iq for this type of profile produces no better correlation

lid no improvement in the analyzed profile shape near the surface. Removing the coating used to enhance the quality

Tthe surface-to-bevel comer on the sample reduces the effect, but does not eliminate it.

tween the two shown.

89
Since the multilayer analysis is performed by a computer program, an important consideration is speed of

execution, which will significantly affect the practicaUty of the measurement by affecting cost. Figure 14 is a plot of run time vs points in the profile. These are typical; noisy data and abrupt corners will increase the run time.

The analysis program cost is usually about one-half or less of the cost of the original data acquisition.

Conclusions

The multilayer analysis of spreading resistance data provides a significant improvement over directly calibrated

j data when exact profile shape is of interest.

However, the analysis makes certain mistakes related to deficiencies in the probe contact model now used. These,

errors are easily recognized, but require that the analysis results be screened by someone familiar with the problem.

An improved contact model will be necessary to correct the problem. This is a logical npxt step to consider.

The cost of the analysis is reasonable for routine use.

Acknowledgements

The author wishes to thank Gordon Gumming for considerable discussion both on modeling and on;, programming techniques, and Francois Padovani and Fred Voltmer for providing spreading resistance measurements.

I References

[ 1 ] F. Voltmer, personal communication. :

[2] P. A. Schumann, Jr., and E. E. Gardner, "Spreading Resistance Correction Factors," Solid-State Electronics] Vol. 12, pp. 371-375 (1969).

[3] T. H. Yeh and K. H. Khokhani, "Multilayer Theory of Correction Factors for Spreading Resistance Measurements,"/. Electrochem. Soc. Electrochem. Tech., Vol. 1 16, No. 10 (1969). \

[4] S. M. Hu, "Calculation of Spreading Resistance Correction Factors", Solid-State Electronics, Vol. 15, No. 7F.

pp. 809-817(1972).

[5] See also: P. A. Schumann, Jr. and E. E. Gardner, "Multilayer Potential Distribution," Technical Report 22,404,

IBM Components Div., East Fishkill.

[6] E. E, Gardner and P. A. Schumann, Jr., "Potential Distribution in Multi- Layered Structures," IBM Technical Report 22, 191.

[7] H. Ruiz, "On the Calibration and Performance of a Spreading Resistance Probe," this publication. j

j

I

90
TRUE PROFILE OOOOO SPREADING RESISTANCE DATA

^ DEPTH

2. Hypothetical Concentration Profile and Resulting Spreading Resistance Readings if the Left is Nearer the Top of the Bevel.

SURFACE

hi 1 v-), e-f, <|'|p^

V2. 82- 'l'2' P2

, V3, 93, i//3,P3

h4 V4, 64, i;'4_ P4

1

1

1

1

1

1 Vfj, Sm, <iif^, pivj

Figure 3. Multilayer Structure. 91
( 1 / ( 1

Figure 4. Qualitative Representation of

Bracketing Convergence Technique and a Typical Set of Consecutive Approximations

of p

Figure 5. Original Data and Result of

Multilayer Analysis for Epi-DUF-Junction

Structure.

10"^ 2 S 10"' 2 5 lO"-' 2 5 10" 2 5 lo' 2 S lO'

A-

' ORIGINAL DATA

o AFTER ANALYSIS

J \ I L

3 4 5 6 7 DEPTH (urn)

J I \ L

9 10 11

Figure 6. 1+26 versus X for Profile

Shown in Figure 5.

92
• ORIGINAL DATA

o AFTER ANALVSIS

J \ L J L J I L

DEPTH (um)

gure 7. Original Data and Multilayer

alysis Results for an Epi Layer on

finite Substrate Structure.

1 _

-T 1—I—I

1—

J i_ J I L_

10"^ 2 5 10-2 2 5 10-' 2 5 10° 2 5. lo' 2 5 10^

Figure 8. 1+20 versus A for Profile

Shown in Figure 7

ORIGINAL DATA a AFTHR ANALYSIS

J I I I \ I \

I I I 3 6 : 3 9 10 n

DEPTH (um)

gure 9. Result of Analysis of Data

fthout Preprocessing. Figure 10. Comparison of Spreading Resistance and Capacitance-Voltage Profiles.

93
Figure 11. Hypothetical Comparison of

Single and Multiple Contact Probe Voltage

Equipotentials Showing Deeper Penetration

of Single Probe Field Near the Surface,

1.0. 1-S' DEPTH Cum)

Figure 12. Effect of Changing Effective

P>adius of Contact, r^, on the Analyzed

Spreading Resistance Profile.

'3 licEEM aJTSl BES ISTAHCE

Figure 13. Comparison of Analyzed

Spreading Resistance and Incremental

Sheet Resistance Profiles.

O PROFILES UNDERLAIN BY JUNCTION

.60 Q PROFILES UNDERLAIN BY SEMI-INFINITE SUBSTRATE

Figure 14. Execution Time versus Number

of Layers in the Profile for Two General

Types of Profiles. Times Vary Considerably Due to Noise and Shape of Individual Profiles.

94
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS , Gaithersburg, Md. , June 13-14, 1974.

An Automated Spreading Resistance Test Facility

James C. White, Jr. Western Electric Co.^ Inc. 555 Union Blvd.

Allentown, Pa. I8IO3

An automated spreading resistance test facility has been designed

^ and constructed at the Allentown Works of the Western Electric Co. This system has been shown' to provide a rapid, semi -nondestructive,

and reproducible measurement of epitaxial layer resistivity which can

be used in a production environment. The system has the advantages

of operator independence, well protected probes, and four-inch capability. Surface or in-depth measurements can be performed with on-line

calculations of resistivity and impurity concentration. Cycle time is

less than five seconds per measurement and system reproducibility is +

1.3/= (IS).

|j Key Words: Automated testing; epitaxial silicon; impurity concentration;

I resistivity; semiconductor materials; silicon; spreading resistance.

1. Introduction

k. Probably the first question that comes to mind when the automation of a test facility

'lis proposed is "Why Automate?". The motives for automation range from a desire to remove

operator variability from a measurement to a need for rapid reproducible measurements. At

i/festem Electric - Allentown, the spreading resistance technique was investigated as a

ftool to satisfy the need for a rapid, nondestructive method for measuring epitaxial layer

{resistivity. A rapid technique was desirable for use for epitaxial reactor control. A

iiondestructive technique was attractive for a measurement directly on product with minimal

,^amage to the wafer.

1:1

2. Alternative Measurement Techniques

The most widely used measurement technique for determining epitaxial layer resistivity

ip-s the four-point probe or control wafer technique (l)-*-. While this technique is rapid,

',lt is not directly applicable to a majority of the epitaxial material being processed

today. An isolating junction must exist between the epitaxial layer and the substrate,

lllierefore, n/n+ and p/p+ structures are not directly measurable nor is the technique

I easily applied to wafers with subdiffused patterns. For these structures, substrates of

'Opposite conductivity type from the layer to be deposited are placed in the reactor and

-ayers deposited on these wafers are evaluated using a four-point probe. The assumption

-S made that the growth conditions on these control wafers do not differ significantly

, :rom those on the product wafers.

i Other techniques such as diode voltage-capacitance and MOS voltage- capacitance (2) are

iestructive and/or reqmre extensive sample preparation prior to measurement.

Because the spreading resistance technique appeared to satisfy the reqiolrements for

ooth a rapid and a" semi -nondestructive measure of epitaxial layer resistivity directly on

any type of structure, it was investigated as a possible tool for use in a production

Ipnvironment.

figures in parentheses indicate literature references at the end of this paper.

' 95
3. Why Automate?

A manual system was first constructed to determine the -precision and to gain a working knowledge of the technique. The experience gained from use of this manual system

demonstrated that the technique had the resolution and precision required for an epitaxial

layer resistivity measurement. However, many of the advantages of the technique were lost

in the manual system.

To satisfy the requirement of rapid feedback for epitaxial reactor control, it was felt necessary to provide for on-line calculation of resistivity and/or impurity

concentration incorporating the relevant calibration and correction factors. Because of

the importance of reproducible contacts between the probes and the wafer surface, it was deemed imperative that lowering and loading of the probes, application of current, and

measurement of voltage all be done in a controlled manner with no operation interaction

if possible. Moreover, because of the ability of the spreading resistance technique to detect small fluctuations in resistivity, several measurements on a wafer were desirable

to obtain an average resistivity. Based on these criteria, the decision was made to automate the spreading resistance facility (Fig. l).

h. Automated Facility Description

A block diagram of the automated test system is shown in Figure 2. The heart of

the system is a Hewlett-Packard 21l6c digital computer with 16k words of memory and a 16 bit word. Control and timing of all measurement functions are handled via this

computer. The computer is programmed in BASIC. A conversational language was chosen in

lieu of machine language because of the versatility and programming ease offered by

conversational languages. Calibration curves, correction factors, sequencing, and other

variables are easily changed by anyone with a minimum of programming experience. The

constant c-urrent supply is marketed by COSAR and is continuously programmable over the

range of one nanoampere to one ampere with a compliance voltage of 50 volts.

The wafer stage is positioned by two 500 steps/revolution stepping motors driving

an X-Y movement with a twenty pitch lead screw. This provides 0.0001 inch resolution and

a total travel of four inches in both the X- and Y-directions

The remainder of the electronics consists of a high impedance digital voltmeter, a digital thermometer for temperature corrections if desired, and an X-Y recorder and a Teletype for output of resistivity and/or impurity concentration.

The probing arrangement selected is manufactured by Jandel Engineering Limited

(Figure 3) • This probe consists of three t\xngsten carbide needles individually loaded by

gram gauges. These gauges are readily adjustable in the range of 0-100 grams. A

kinematic needle guidance system employing precision ruby ball guides and polished tungsten

carbide rods eliminates any sideplay of the needles and keeps friction to a minimum.

Because of the subsequent availability and industry acceptance of the Mazur two-probe

spreading resistance test system, the decision was made to convert the Western Electric

system for a two-probe measurement. The three probes have been maintained, however,

providing the versatility of performing a one-, two-, or three-probe measurement at will.

5. Measurement Sequence

The testing sequence begins with a series of questions to be answered by the system

operator. The conductivity types of the layer and the substrate, crystallographic

orientation, and thickness of the epitaxial layer are input via the Teletype. The wafer

is then automatically positioned under the probes and the measurement sequence begins.

To insure a reproducible contact between the probes and the wafer surface and to keep

wafer damage to a minimum, the probes are lowered to the wafer surface under their own

weight. The loading is then applied at a controlled rate through an air dashpot. Uo

current is forced until the probes are at rest on the wafer surface and are fully loaded.

This precaution . is taken to protect the integrity of the probes and to further reduce wafer j damage . I| 96 i
The constant current supply is automatically ranged to produce a voltage at the probes

of between five and fifty millivolts. At each measurement location, voltage measurements

are taken with current flowing in both the forward and reverse directions to minimize

'erroneous measurements due to injection and electrical noise. For most samples, measureI ments can then be performed with normal incident light. An added benefit of the forwardj reverse current pair is the capability of detecting the presence of p-n junctions from

j large forward- reverse voltage differences.

I From each resistance measurement, an uncorrected resistivity is calculated using

I calibration curves developed from four-probe measurements on bulk polished wafers. This

I result is then corrected for finite layer thickness using a routine similar to that

j described by Dr. Bernard Morris (3) and the impurity concentration is calculated from a jpiecewise-linear fit to Irvin's curves (h) . If desired, on-line plotting of resistivity

lor impurity concentration vs. wafer position is available.

For surface measurements, a series of measurements are taken in an X-pattem as shown

;in Figure h. When all measurements on the wafer are complete, the wafer is returned to its

I home position, well away from the probes. Radial resistivity gradient, average resistivity^

I and standard deviation for the wafer are output on the Teletype.

While the chief use of the automated spreading resistance system is for measuring

average surface resistivity, in-depth capability has also been provided. The surface

preparation for this method involves a rotary grooving technique which produces a icylindrical groove in the wafer surface. This technique was chosen over angle-lapping

ibecause of the sharp angle produced by the groover at the wafer surface and the subsequent

'; lease with which this edge can be aligned. An interference-contrast microscope mounted at

|a known fixed distance from the probes is used for the alignment.

I An initial dialogue similar to that for surface measurements is answered with the

jadditional input of groove width. The edge of the bevel is automatically aligned with the

i|probes and a series of measurements is taken. If small steps, less than 0.0005 inch, are

;to be taken, a zig-zag motion is incorporated to prevent overlapping of damaged areas.

jiAt each measurement location, the depth of the measurement is calculated, based on the

'iwidth of the groove and the lateral distance moved, and the resistivity is corrected for

this depth. As for surface measurements, output can be selected on the Teletype and/or

the on-line plotter.

6 . Summary

The decision was made to develop an automated spreading resistance test system to provide versatility not available in any other system. A system was developed which has

the reliability, versatility, and reproducibility necessary for daily use in a production

environment. The system has the advantages of operator independence, well protected

j;probes, and four- inch capability. Surface or in-depth measurements can be performed with

iPrograramable cycle times, on-line calculations and corrections of resistivity and impurity

i3oncentration, and on-line plotting of these corrected results. The system is able to accomplish this with a total cycle time of only five seconds per measurement and has been

Ifound to be reproducible to + 1.3^ (iS).

7. References

(1) W. J. Patrick, Solid State

I Electronics 9, 203 (1966).

I2) w. C. Niehaus, W. VanGelder, T. D. Jones, P. H. Langer, Silicon Device

Processing (National Bureau of Stand

ards Special Publication 337), 256-72

(1970).

(3) B. E. Morris, Symposium on Spreading Resistance Measurements

(U) J. C. Irvin, Bell System Tech. J. 4l, Wo. 2, 387-410 (March I962).

97
COSAR 501 CONSTANT CURRENT

SUPPLY

DORIC

DIGITAL THERMOMETER

H.P. 34801

DIGITAL VOLTMETER

H.P. 2116C DIGITAL COMPUTER

H.P. 7004B

X-Y RECORDER

KSR-35 TTY

PROBE CONTROL

SLO-SYN

STEPPING MOTORS

BLOCK DIAGRAM OF

AUTOMATED SPREADING

RESISTANCE TEST SYSTEM

Figure 2 Block Diagram of Automated System

Figure 1 Automated Spreading

Resistance Test FAciLnY

^ u MEASUREMENT LOCATIONS

Figure 3 Probe Guidance System Figure ^ Radial Resistivity F^asurement Locations

98
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Galthersburg, Md. , June 13-14, 1974.

Angle-Bevelling Silicon Epitaxial

Layers, Technique and Evaluation

P.J. Severin

Philips Research Laboratories

Eindhoven, Netherlands

The properties of a steel probe for a spreadingr^sistance system are discussed stressing the effect of

micro- and macrocontacts. The need is explained for

producing small-angle bevels and a lapping jig for

making such bevels is described. With small-angle bevels the slice topography cannot be neglected and a simple instrument is described by which the surface

topography of the whole slice can be recorded. By re- cording the slice topography before and after bevelling

the local reduction of thickness by the bevelling process is determined. This method can be used for angles

between I/5OO and 1/2000. It is indispensable for the

proper interpretation of spreading resistance measurements on bevelled N on N junctions.

Keywords: bevel, interferometer, jig, microcontacts , silicon,

spreading resistance, steel probe, topography.

1. Introduction

For advanced applications of epitaxially grown structures the dope

concentration profile and the extent of the concentration gradient between substrate and epitaxial layer are of paramount importance. This is

of particular interest for thin layers, a few microns or less thick. The

, capacitance-voltage technique flj^is very well suited for study of the

|1 charge carrier distribution up to a level of about 10^7 cm~-^ , but for

study of the full interface properties surface probing techniques should

be used and therefore the interior should be exposed by bevelling the

slice. The method for surface probing is the spreading resistance technique, which is accepted now as a very powerful tool for investigating

epitaxially grown structures.

For obtaining a large resolving power with the bevel technique the

probe averagingdepth should be as small as possible. ¥ith the spreading

resistance probe used by us the horizontal averaging lengthis fairly

large, about 25 |am. Therefore the bevel angle must be very small. This

l) implies, however, that for precise correlation between horizontal position and depth below the original surface the departure from ideal flatness of the slice is taken into account. In the next section the spreading resistance probe used in our laboratory for several years is discussed and a number of details essential for understanding the mode of

I operation is presented. A polishing jig and a laser-operated interferometer are described in the third section. Their use in producing the

bevel and for evaluating the local bevel angle, taking into account

any departure from perfect flatness of the slice, is explained in the

^Figures in brackets indicate the literature references at the end of this paper

99
fourth section. The method is illustrated with a fully worked-out example: an N on N"*" epitaxial layer is bevelled, evaluated and spreading-resistance measured. The formalism for deducing the resistivity profile is

critically discussed in another contribution to this Symposium [z]

2. The steel spreading resistance probe

The spreading resistance probe system now in use in our laboratory

£3 , ^ > 5] for several years is based on the use of a specially hardened

steel probe taken from a conventional Dumas four-point-probe head. This

probe is broken and sharpened until the untouched bottom of the tip is

about 25 Min across, which yields a mechanical contact diameter of about

1 5 |Jin.

Microscopic evidence proved conclusively that the bottom surface of

the probe is multi-tipped and that the mechanical contact to the silicon

is made up of a number of microcontacts. ¥ith high-power dark-field illumination the most pronounced prints made by the microcontacts are visible

and with a chromic etch these prints stand out more clearly. With an interference contrast microscope more details can be seen of the etched

print, but the size and depth of the microcontacts cannot be assessed and

must be less than 0. 1 |jjn. With a scanning electron microscope the print

could not be found, because the minute damage due to the microcontacts

is more wide than it is deep. For a given probe the print pattern is

completely reproducible , and shown in figure 1. It is well-known that below a circular metal contact to a semiconductor of resistivity ^ the potential drops from the applied potential

V to about 0. 1 V at a depth of about twice the' radius. This holds for

o o each of the many microcontacts of radxus a. At that level the equxpotential lines are almost horizontal and the microcontacts cannot be distinguished individually any more. This occurs at a depth which is very

shallow compared to the diameter 2A of the total contact area and therefore this new, deep, macrocontact is again subjected to the spreading

resistance phenomenon.

In this model the micro- and macrocontact resistance R . and R

can be considered acting in series. The currents through the microcontacts are supposed to be independent and the series combination of the

macro- and microcontacts yields the equivalent circuit shown in figure 2

with

where n and . a are the number and average radius of the microcontacts. For

a steel probe total spreading resistance was found ^3'^! *° ^® proportional to

J) over four decades, both for N- and P-type Si ~ ' (2)

where A represents the equivalent radius of the contact. A number of

authors have reported that for their, harder, probes

^ = -TlT^ ' (3)

where k(^ ) is a correction factor of order unity attributed to a variety

of causes, generally ^-dependent zero-bias-barrier resistance in series

to the true spreading resistance.

Although it appears possible to experimentally separate the two con- tributions R and R . because they have widely different thermal time

constants, aif(X non-1 A^e^rities can readily be generated in the microcontacts

we simply measure A and A and apply eqs (1) and (2).

The value of A is found from microscopic examination of the print

100
md the value of the equivalent radius A is found from calibration

measurements. The latter depends weakly on the nature, surface texture

md preparation of the semiconductor. It is slightly different for each

jrobe and decreases slowly during a probe lifetime.

Normally a large contact resistance is undesired because it spoils

;he proportionality to ^ of the spreading resistance in series, as shown

.n eq. (3)« The resistance of the microcontacts shows a spreading resis-

;ance controlled proportionality to p and their contribution is welcomed

because of the ensuing small information collecting depth a. This will be

liscussed below in connection with the resolving power.

It is an essential property of this type of steel probe that the mijrocontact distribution after a short formation process shows hardly any

ilteration in many thousands of measurements on polished silicon. Evilently the probe is loaded elastically only. When the probe is applied

;o a lapped sample the distribution pattern of the microcontacts changes,

mt the value of na remains very nearly the same. It is well-known from

aechanical and thermal contact studies and experiments in friction and

vear that any metal surface has protrusions. These are referred to as

lisperities. The protrusions, often harder than the matrix material by

m order of magnitude, have been the subject of many controversial experiments and speculative theories. Their nature and origin are problems

'»eyond the scope of this paper. The reproducibility of this steel probe

bpreading resistance amounts to about ^'fo, as shown by some surface proving tracks, presented in figure 3.

Typical values of the various parameters for a load F = 150 gram on

)olished N-type silicon are A =2.2 |jm, A = 12.5 |-ini, hence na = 2.7 Mm,

rhich with n « 100 yields a « 0.03 M^; also R . /R 5^5' Generally a small

:ontact radius is considered desirable for spreadxng resistance measurelents. However, with a steel probe the load cannot be reduced without

eriously degrading the performance of the spreading resistance probe.

The following experiments were done with the intention of shedding

ome light on the dependence of A and A on the load F. The probe is

)roken in order to expose a large number of asperities and sharpened

mtil the contact area left untouched is only slightly smaller than the

table area found after plastic deformation with the lowest load used

.n the experiment. Then with successively increased loads the probe is

pplied on a lapped and subsequently on a polished surface. The values

f A ^ and A on both types of surface and of A on the polished sur-

'ace are determined. On a lapped surface no prin? is visible so that Aj^

|;annot be determined but at a given load must be between Ap at the same

ijoid the lower load. It turns out that A ^ increases linearly with F, as

i|ihown in figure k, whereas the radius A is almost constant. Below a load

if lOOg a very erratic signal was produced. Apparently the spreading re-

||iistance on polished material can only be properly measured with a probe

mich is on the verge of yielding. Above 100 g the probe is again load

jjed up to the yield strength on polished material. The contact on lapped

jiaterial at low loads is determined by na only, but at about 100 g the

Influence of A is dominant. On lapped material not only the probe aspej'ities, but also, probably even more important, the roughness of the

i|ample determines the microcontact contribution. Because the asperity

pattern is completely rearranged by application of the probe to lapped

laterial, the value of A determined by the asperities, does not show

'. very systematic dependeSce on F.

In figure 5 the results of similar experiments with another probe

nd sample are presented, the only difference being that the starting

robe radius A was about lOjjm. Here the signal on polished material at

ow loads was again very erratic, but A ^ again increases almost linearly. As mentioned above, the experiments on polished silicon are influenced

jy the measurements on lapped material in between. This procedure is nej|essary to keep an unfractured probe tip over so long a load range,

jver a shorter range the probe reshaping on lapped material is not needed

101
and the curve labelled A is found. The slope, A «>jF , is more or less equal to the slope fo? A and for A* above 100-^g. It is also clear

that the microcontact contribStion plays §n important role. It is interesting to note that in figures k and 5 the three values of the equivalent radius for polished slices are almost equal at 150 g. That is why

this is chosen as the working load.

As mentioned above , the double-stage probe structure has a bearing

on the resolving power of the spreading resistance probe. With surface

probing both the micro- and macrocontact stage average horizontally over

about 2A. A relatively large contribution R . could be a drawback for

surface probing. ¥hen the horizontal resistxvity distribution in a sili- con slice is the desired information, this could be shielded by the va- riations in a one micron thick top layer. However, it has been found that

spreading resistance tracks with pronounced maxima and minima do not

change when a one micron thick layer is removed. Hence although the microstage represents about three quarters of the total resistance, the

microcontacts penetrate any surface layer which may be different due to

circumstances beyond control. More important, surfac e probing of a thin

epitaxial layer can be done advantageously with an shallow stage which

contributes significantly to the total resistance. It ranks among the

most favourable properties of the steel probe that for the microcontact

stage which represents about three quarters of the spreading resistance,

any isotype thin layer can be considered as a sample of infinite thickness. The thickness correction should be applied to the deep contribution

only, if necessary. For a heterotype structure the thickness correction

is a function of both the micro- and macrocontact contributions, as shown

elsewhere f 2,5j . In general the thickness corrections have been calculated for an abruptly layered structure and evidently some doubt exists of

the value of d in a real structure. In case the shallow stage contribution

is sufficiently large, the improvement obtained by applying the more or less accurate correction is good enough.

In summary, we use a probe which averages horizontally over a circle

about 2a ^ 25|jm across and in depth over a length of about 3a ^^0. 1 (jm.

For surface probing the small information sam.pling depth is a great asset.

For profiling averaging horizontally over 25 Mm is quite a nuisance

for, with a desired resolving power of 0.05 MJn in depth, the angle should

be 1/500 or more. ¥e shall describe in the next section how bevels up to

1/2000 can be produced and evaluated.

3- The bevelling jig and the interferometer

Conventional angle-lapping jigs have been used before for bevel and

stain measurements at relatively large angles. The reliability of these

instruments is limited by mechanical tolerances. Here we first describe a more stable and versatile tool, which matches well the interferometer to

be described later.

As shown in figure 6, the slice S to be bevelled is mounted on a piston A. It can slide without play in the holder B and can be fixed at any

height and position by screw C. This assembly rests on three balls on the

support ring D and can be moved with respect to the support by two screws

E. With one screw the assembly can be tilted about the axis between the

other screw and the third ball. In this way the angle between the axes of

B and D can be varied in a simple and precise way. The holder B and the

support D are held in position by three resilient clamps F. The jig rests

on a number of pieces of silicon G glued to the support D. Hence during

lapping and polishing no foreign garticles are produced and because their

total surface area of about 10 cm is much larger than the area to be

bevelled the pressure and rates are constant during the process. The slice

is mounted on the piston A in a thick layer of beeswax by heating. When

it is allowed to cool slowly, the slice .assumes its equilibrium position.

102
The lapping and polishing is done on a machine on which the slice is

^subjected to three different motions. For the lapping a slurry of water

land AlpO„ is used. The subsequent polishing is done with diamond paste unitil the roughness is reduced sufficiently to make the surface mirror-

|like. At this stage the surface shows som.e pits and scratches due to deep

Ilapping damage, but usually the polishing process is not continued. It

jhas been found that there is about 20^ difference in spreading resistance

between touched and non-touched parts. Because profiles are measured geinerally on a logarithmic scale, this difference in calibration is unimportant. It can be reduced by chemtmechanical polishing.

A bevel of relatively steep slope and mirror surface quality can

easily be evaluated with an interference microscope. In order to obtain

a reliable value for the slope at least a dozen contour lines should be

visible, and it has been found that for steep angles up to, say, 1/200

reliable results can be obtained. However, for small angles the slice

turns out not to be flat enough to unambiguously define its slope with

respect to the reference flat. Moreover, the method is time consuming

and it is impossible to obtain an overall impression. In this section an

(instrument of greater field of view is described with which the untouched

part of the surface of a bevelled slice can be seen and used as a horizontal reference in determining the slope of the bevel.

The optical layout of this interferom.etric instrument, which is not

i at all critical, is shown in figure 7. A HeNe laser (l) operating at

1 6328 X at about 2 m¥ power level provides an extremely monochromatic,

ijcoherent, relatively intense and narrow light beam. The light is incijjdent on a diffuser ( 3) , which serves as an intense and monochromatic

{jlight source. Via a semi-reflecting mirror (5) the enlarged-diameter pahrallel beam is incident on the polished side of the silicon slice (7)

i {which is positioned face to face with a semi-reflecting optical flat (8),

ijabout 1 cm thick. The fringe system arising from multiple interference

iljat the positions of appropriate slice-flat distance is imaged by a lens

|i(9) onto a screen, a television camera or a photographic camera (1 0) . As

Ijjthe light turns out to be still so coherent that speckles can be seen,

!;the diffuser (3 ) is mounted on a motor axis which revolves sufficiently

.fast that they disappear. ¥ith the instrument shown in figure 7 the com1 plete topography of slice (7) with a diameter up to the diameter of the

I parallel light beam is obtained in a single picture. Examples of such a

! picture are given in figures 8 and 10 below. In these pictures the disf'tance between two contour lines corresponds to a height difference equal

to \ /2. = 0.316 |am and the resolving power is about O.O6 jjm.

h. Evaluation of bevel angle

In general a slice is not flat and, although the bevel as produced

Way be flat, local thickness of a bevelled epitaxial layer plotted vs

jihorizontal position may not be a straight line. Typical surface topographs

|iof silicon slices can be seen in figure 8. Usually the contour lines

rishow a maximum or a minimum, manifested by closed lines, and sometimes

ijjsaddle points* . The radius of curvature of an extremum is roughly between

2 and 20m for 250 |am thick slices. Hence the slope may change over 5 mm

by an angle I/5OO. However, with the procedure to be described such variations in slope do not present a real problem because the profiles of

both the original surface and the polished bevelled surface can be measured accurately. To produce a bevel the slice is mounted on the jig of

i^l) This implies that concavity measured as a standard routine £6] and

commonly called bowing or dishing, does not adequately describe the

topography of silicon slices.

103
figure 6 and the mirror (8) of figure 7 is placed on top of the silicon

pieces G of the jig. Using the screws E the piston A is adjusted such that

on the television monitor a pattern arises with easily recognizable features. This pattern is photographed. Then the desired angle is adjusted

with screws E and the piston is lowered until the slice touches the optical flat and is fixed again with screw C. After lapping and polishing

the slice is positioned again such that the pattern on the non-touched

part of the slice compares well to the photograph made earlier and photographed again.

In practice the procedure runs as follows. A mark, labelled A in the

inset of figure 9> is scratched on the slice. In order to see this mark

on the photograph a small rectangular patch of paper, noted B in figure 9,

is glued to the slice. The slice is adjusted to such an angle with the

optical flat that a number of closely spaced interference fringes perpendicular to the patch is visible, and photographed (figure 10a). The slope

of the part to be bevelled may correspond to the desired angle, otherwise

the desired angle is adjusted, the patch of paper is removed and the slice

is bevelled. As before, a patch of paper is glued on the slice and the

slice is adjusted as well as possible in the same position as before bevelling and photographed (figure 10b). Then, from the photographs the profiles

along the spreading resistance track to be made, are measured and plotted.

Of course it will not be possible to reproduce precisely the pattern on

the non-touched pait. This is shown clearly in figure 9> where curve A re- presents the profile as measured on the original photograph. After bevelling, the profile labelled B is measured, which is different from the original one, though the left-hand side non-touched parts should be identical.

This arises from the fact that the angles with respect to the optical flat

in the two cases were slightly different. This can be corrected by pivoting curve B around the origin so that A and B are coincident. The difference between curve A and the first part of curve B turns out to be, as expected, a straight line, labelled C. Extrapolating this correction, due

to slightly different tilt of the slice, over the range where the slice

has been bevelled, the true surface profile curve Ag is obtained from the

measured curve B. The difference between curve A^ and A^t plotted as a curve labelled D, is the true depth below the orxginal surface. Due to the

surface topography and the nature of the polishing process, there is no linear relation between depth and horizontal position. Therefore some method to obtain a curve like curve D of figure 9 is definitely indispensable for precise and accurate work on spreading resistance profiles.

. 5. Discussion and conclusions

With a specially hardened steel probe spreading resistance measurements can be done on chem-mechanically polished and epitaxially grown sur- faces with a precision of about ^'fo. Because of the large contact area,

about 25 |im across, which cannot be made smaller, the slope of a bevel

should be 1/500 for a resolving power of about 0.05 Mm in depth. For such

slopes a procedure has been developed which takes into account the original

surface topography. In this way the horizontal and vertical scales are correctly correlated. When the bevel is chem-mechanically polished the

spreading resistance can be measured with a precision also of about ^'fo. The inference of the dopant atom distribution from the measured spreading resistance profile is obstructed by a number of serious difficulties,

which are itemized below.

1. The correction formulae which should be applied to the spreading resistance measured on a layer of finite thickness have been critically discussed elsewhere [2] and the sensitivity of the solution to the boundary

conditions chosen makes the validity of these expressions dubious within

about 10^.

104
2. The transition of the layered structure is not abrup-t so that the

thickness, particularly of thin, layers or near the bevel edge, is not well

defined.

3. The measured data should be corrected for the proximity of the bevelled

layer edge, particularly in the case of steep bevels.

k. The charge carrier density n can be deduced from the resistivity ^

only with the well-known curves, which are valid, however, only in uniform and neutral material; neither condition is satisfied, because mobile

charge carriers generate a space charge in any steep atom profile. Moreover the spreading resistance correction formulae have been derived using

Laplace's equation, implying the absence of space charge.

5. The space charge is perturbed due to the exposure on the bevel

I" 2 j.

The micro- and macrocontact contributions should be distinguished carefully. A dominant macrocontact resistance, which is more common for small

than for large contact area probes, is more sensitive to corrections. A

large probe with dominant microcontact contribution hardly needs any

correction for finite thickness. Therefore the items 1 to 3 do not apply

to our probe system. The problem of the necessary small-angle bevel where

the original surface topography is important for the correlation between

depth and horizontal scale, has been solved.

, Acknowledgement

The assistance of Mr.G.Poodt and Mr. H. Bulla in the experimental work and

of Dr. J.D. Wasscher in carefully reviewing the manuscript is gratefully

acknowledged.

References

1. P.J. Severin and P. Poodt, J.Elec- h. P.J. Severin, Silicon Device Protrochem. Soc. 1 19 (l972) 1384. cessing, NBS Special Publ. 337

2. P.J. Severin, Proc. Symp. Sprea- (l970) 224.

ding Resistance Measurements, NBS, 5- P.J. Severin, Philips Res. Repts.

Gaithersburg, 197^. £6 (l97l) 359.

3. P.J. Severin, Sol. St. Electr. J_k 6. Monsanto Evaluation Standards,

(1971) 247. Monsanto Electronic Materials,

St. Peters, Missouri, 1973, no I6-ME-OO5-O472.

Figure 1. The print of a steel probe

as seen with an interference contrast

microscope.

105
1

I

I

D

SI

sa n

Figure 2. The equivalent circuit of

the spreading resistance probe contact

as measured with a specially hardened

steel probe. R^^ is the microcontact

contribution of ohmic, low-resistance,

high-pressure contacts and diodic,

high-resistance, low-pressure contacts

which can be neglected. Rg^ is the

microcontact contribution acting in

series

Figure 3. The reproducibility of the

steel probe system is demonstrated by

some tracks on an epitaxial layer (a)

an N substrate (b) and a longitudinal

section (c)

106
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108
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

I Spreading Resistance Measurements on Silicon

with Non-blocking Aluminum-Silicon Contacts

J. Krausse

1

I Siemens AG, UB B GE 1

; 8 Munchen 46, Frankfurter Ring 152

P.R. Germany

The paper concerns the measurement of resistivity fluctuations in n-type silicon starting material in the resistivity

range from 1 to 1000 Q cm. The microscopic resistivity fluctuations that £ire associated with the well-known striations require a measurement technique of high accuracy and high local

resolution. We chose the spreading resistance method. However,

in contrast to the conventional method, in which the metal

probe is pressed directly onto the silicon surface, we supply

the silicon slice with non-blocking aluminum-silicon contacts.

The radius of the contact area is exactly defined. Any contact

radius can be realized according to the resolution desired in

lateral direction and in depth. V/hen the metal probe is applied

to the aluminum-silicon contact, the contact is not destroyed.

Thus it is possible to perform spreading resistance measurements and four-point probe measurements along one and the

Scune measuring track and in this manner at the same time to

vary the local resolution. A comparison of both measurement

results will in particular yield information on the conditions of the resistivity in axial direction of the slice.

Essential prerequisites for an absolute measurement are fulfilled with the aluminum- silicon contact. However, the investigations made up to now show that the resistivity calculated

from the spreading resistance is smaller than the one obtained

with the four-point probe measurement by approximately a factor

of 0.8.

Key words: Absolute measurements; aluminum-silicon contact;

four-point probe measurements; local resolution; n-type silicon;

resistivity inhomogeneities ; spreading resistance; striations.

I 1 . Introduction

The lateral and the axial distribution of the resistivity in starjting silicon is e.g. in several respects of importance for the electrical properties

Ipf power devices. Since resistivity variations as low as 5 to 20% can be distinctly

^effective, it has to be the aim to measure such variations as exactly as possible.

'iThe microscopic resistivity fluctuations associated with the well-knovm striations

l&re of the order of AQ

^ + 10 to 20^^ (see [l]-[4])and therefore require a measiireifnent method with high accuracy and high local resolution.

j Figures in brackets indicate the literature references at the end of this paper.

I 109

!

I

;i
Our interest is concentrated mainly on n-doped silicon material with a resistivity in the range of 10 to 1000 Qcra, as it is used for manufacturing power devices.

For the manufacture of devices silicon slices are processed that are cut perpendicular'

ly from rods grown in -direction. We perform measurements of the resistivity J fluctuations on such slices. '

2. The Conventional Spreading Resistance Method

The well-known method of MAZUR and DICKEY [5] presented itself as a suitable

measuring procedure. This procedure at present is an important method to detexTiiine

the doping distribution of diffusion profiles and multilayer structures. However, as yet it is not clear if it is suitable for an exact quantitative measurement of the

relatively small resistivity variations in starting silicon. The reason lies in the

fact that the physical properties of the contact between metal probe and silicon

surface are hard to define. This manifests itself in the calibration factor k which

is rather obscure. For the spreading resistance of a circular, two-dimensional

contact of radius a

(1)

holds. However, the conventional spreading resistance method yields a resistance R

for which one can write

Rc=k-Rs=k-7^ . (2)

The factor k contains the whole problematic nature of the conventional

spreading resistance method. It depends on several details of the handling of the

metal point as well as on the properties of the bulk and the surface both of the

silicon to be measured and of the metal point. KRAMER and VAN RTJYYEN [6] published

a compilation of k-factors that were measured in different laboratories, figure 1. Note that the k-values scatter by approximately a factor of 10. In addition, in the

range of high resistivity that is of interest to us, the k-factor always depends

strongly on the resistivity of the silicon material, k decreases with increasing

resistivity. According to eq (2) this means that Rq depends less than proportionally

on Q . This in turn means an increase in the inaccuracy of the measurement for a Ad -determination.

5. The Non-blocking Aluminum-Silicon Contact

In contrast to the conventional spreading resistance method, in which the probe

is pressed directly onto the silicon surface, we supply the surface with non-blocking

aluminum-silicon contacts. In [4] and [lO] we have already described the reasons that

led us to take this step, as well as the structure and the preparation of the

aluminum-silicon contact.

A cross-section of the structure of an aluminum-silicon contact as we use it

presently is drawn in figure 2. Etching the polished cross-sections makes visible

the phosphorus diffused n-region. The etch patterns obtained in this way confirm the

well-known observation that the underdiffusion amounts to about 2/3 of the penetration depth b of the phosphorus. The radius of the contact is thus given by '

2 3 I

110
In order to measure the spreading resistance, a metal probe is applied onto the

aluminum of the contact. The resistance of the contact is ohtained from a currentvoltage measurement between the probe and the back surface of the slice which is

diffused and contacted across the entire area. Normally \^e operate with a constant

Idc-current of 10 jaA. The polarity is always "probe plus". The thickness d of the

I silicon slices is normally approximately 500 ycm. As the penetration depth b of the

j phosphorus diffusion we choose for routine measurements "b 6 to 12 pn, in contrast

jto OUT first investigations [4,10] .By this means an ohmic behavior of the currentIvoltage characteristic could be obtained over a wide voltage range. Figure 5a- gives

itwo typical examples of characteristics that were measured on silicon of very

Idifferent resistivity. (This result and all the following ones were obtained for

|a temperature of 25°C). Here, as in the following, indicates the resistivity

Ithat was calculated according to eq (5) from the contact resistance of the aluminum-

|silicon contact (see section 5)« Even for the case of the high-resistivity silicon

'the characteristic shows ohmic behavior in the wide voltage range between approximately 50 mV (a*1kT/e) to IV (c5*40kT/e). For the polarity "probe plus", the ohmic

behavior continues even up to voltages of approximately 20V, while for the polarity

"probe minus", an overproportional increase of the current is observed with rising

voltage

It should be mentioned here already that four-point probe measurements, for

khich four probes are lowered onto four adjacent aliiminum-silicon contacts, show

la purely ohmic behavior independent of the current direction (see figure 5b;

jlindicates the resistivity measured by the four-point probe measurement). Here again

rwe would like to emphasize the wide voltage range in which Ohm's law holds even

for the case of the high-resistivity silicon. In contrast to a conventional fourpoint probe measurement, the characteristic shows ohmic behavior into the range

llof IV.

We see two essential advantages in the aluminum-silicon contact:

J a) The possibility to vary the local resolution (by a variation of the radius a;

1' by a combination of spreading resistance measurement and four-point probe

measurement).

lb) The aluminiim-silicon contact constitutes a spreading resistance contact with

! clearly defined reproducible properties that are homogeneous across the contact

" area and across the area of the wafer. Essential conditions for an absolute

measurement of the spreading resistance are fulfilled,

jjin the following two sections we will discuss these two topics in detail.

4. Local Resolution

I The volume in the silicon that is covered by the spreading resistance measurel^ent is approximately a hemisphere with a radius 5a (approximately 80^^ of the

spreading resistance is concentrated in this vol.Tome). In contrast to the conventional

_ spreading resistance method, the radius a of an aluminum-silicon contact is

[jl'learly defined. Since any contact radius larger than 2 jam can be realized

ij technically, the local resolution in axial and lateral direction can be vsiried in

hhe desired way by a proper adjustment of the contact radius.

h A typical example for an experimental realization is shown in figure 4« Results

||if spreading resistance measurements are plotted here that were measured along two

Marallel tracks of aluminum- silicon contacts. The distance between tracks was 180 pm,

jjhe distance between aluminum-silicon contacts 60 ;im. The tracks ran from wafer rim

ijio wafer rim through the center of the wafer. The measurement curves are interjjrupted every 2 mm over a distance of 200 pm. This representation should indicate

i'ihat the sequence of aluminum-silicon contacts had gaps every 2 mm of 200 jim length,

; or technical reasons during the preparation of the structure. In the figures the

a resistivity Q5(x) at the location x is plotted, normalized to the mean value of all

Measurement points along the track. The way the value of Qs(x) is calculated from

Nhe spreading resistance will be treated in detail in section 5 (see eq (5) ).

Ill
The two contact tracks differ only in the radius a of the alTiinimam-silicon

contacts. By meeins of a very shallow phosphorus diffusion (b = 0.7 ysn) , it was possible to obtain aluminum-silicon contacts with a very small radius. The measuring

track of figure 4a consisted of such contacts with a radius a = 3«0 }xm. In contrast,

the aluminum-silicon contacts of the track of figure 4b had a radius of 16.5 pa.

Thus, while in figure 43- a depth of about 9 was resolved, in figure 4^ the wafer

was covered to a depth of approximately 50 pm.

Qualitatively, one can recognize the same macroscopic resistivity profile for

both tracks. However, quantitatively, in the case of figure 4h the decrease of the

resistivity in the center is larger by about ^(yfo than in figure 4a. This comparison

shows the inhomogeneous resistivity distribution in axial direction. This is in

accord with observations made by VOSS of the infrared breakdown radiation from

diodes which were prepared from silicon wafers cut from the silicon rod parallel

to the pulling direction [11] .

While in figure 4a- microscopic resistivity variations were observed in the

center of the wafer, figure 4b shows a quite undisturbed, continous resistivity

profile in this area. Obviously, the resistivity variations in figure 4a are very

inhomogeneous in axial direction and were therefore averaged out in figure 4b.

In contrast to this, the quite strong microscopic resistivity variations outside the center of the wafer change only slightly in the transition from figure 4a

to figure 4b. This is demonstrated further in the section figure 4c v/here both

measurement curves are plotted together. (The separation of the two curves on the left side of the figure is caused by the different macroscopic resistivity

profile which is superimposed over the microscopic variations. This also reflects

the different depth resolution of the two measurements). The investigations in

[10] suggest that here we are dealing with resistivity variations associated with

the well-known striations.

The example chosen in figure 4 demonstrates that no essential information is

lost for the manufactTirer of power devices with the relatively large contact radius.

This statement could be verified for various rods and led us to normally use contact

radii of asrflO to 20 ym for routine measurements. The advantages are:

a) We can diffuse phosphorus with deep penetration (b?«6 to 12 jam). Thereby the

current-voltage characteristic obtains an ohmic behavior over a wide range

(see figure 5a).

b) An exact determination of the radius a is necessary for an absolute measurement

of the spreading resistance (see section 5)» The accuracy of the measurement

becomes better with increasing radius.

In order to save measuring time and in order to ensure a proper handling of the

measurement apparatus for routine measurements, we furthermore normally use

structures in which the aluminum-silicon contacts have a distance of 200 ym.

For a routine measurement of a silicon slice we provide the entire surface of

the slice with alujninum-silicon contacts in a square grid arrangement. The distance

between contacts is 200 jam in x-direction as well as in y-direction. The arrangement

permits a measurement along two tracks that are perpendicular to each other and run

through the center of the slice, see figure 5« The flat is already ground into the

rod to indicate the position of the wafers in the rod.

Since the al-uminujm-silicon contact is not destroyed by the application of the

metal probe, one and the same contact can be measured several times. Hence, it is

possible to start out with a spreading resistance measurement along a track, then

remove the coTonter electrode of the wafer and repeat the measurement along the same track using four probes as a foux-point probe measurement. Here the probes are arranged in the direction of the track . Since the distance between probes is 200 jun

Investigations of this aspect showed that in this arrangement the lateral resolution

is better than when the probes are applied perpendicular to the track.

112
now the resolution in lateral and axial direction is distinctly reduced. The silicon

wafer is certainly covered into a depth of at least 200 ]im. In the following two

examples (figures 6 and 7^) we will show that by a comparison between spreading

resistance measurement and fo\ir-point probe measurement valuable information on

the axial resistivity distribution can likewise be gained. In the upper part of the

figures in each case spreading resistance results are depicted, in the lower part

the four-point probe results.

In figure 6 a high-resistivity silicon wafer was measured. As an unusual

feature it can be seen that for the spreading resistance measurement in y-direction

jthe resistance increases from rim to rim by about a factor of three. In the case

of the fovir-point probe measurement the increase of the resistivity is significantly

lless. The comparison shows that the resistivity increase measvired with the spreading

[resistance method cannot be homogeneous in axial direction, since it would have to

|be noticeable to the same quantitative degree with the four-point probe measurement.

I Figure 7 depicts results taken from a silicon wafer in which the resistivity

[variations associated with striations are very distinct. The figure can be considered

|as a typical example for a strong resistivity dip outside the center of the wafer.

|The corresponding four-point probe measurement, in comparison, yields only a very

islight indication of the dip. The comparison of both results leads to the conclusion

[that the resistivity dip is highly localized in axial direction even more than in

jlateral direction.

5. Absolute Measurement

For the calculation of the spreading resistance of an alvunintim-silicon contact,

toe approximate the geometrical shape of the s^-n junction in figure 2 by a semijellipsoid with radius a of the circular base and height b. Then the spreading

resistance is given by

Q arc cos ^ 7-r-a2

jiccording to eq (j) the radius a can be calculated from the diameter (j) of the SiOgifindow and the penetration depth of the phosphorus diffusion.

Prom experience with the conventional spreading resistance method, we know

[;hat we cannot equate the contact resistance Rc of an aluminum-silicon contact and

|S;he spreading resistance Rs from the start. We therefore write in formal analogy

-0 eq (4)

arc cos g

Tl2 a2

(5)

[ere Qg is the resistivity as calculated from the measurement of the contact resisi;ance. This measured value is plotted in figures 4> 6, 7 and 8. Only in the case

};hat the resistance Rg of an altiminum-silicon contact is determined solely by the

^jpreading resistance, i.e., if

Rc" Rs

(6)

|As to the calculation of see section 5» especially eq (5)«

fPor the calculation of eq (4) based on eq (55b) and (54) of [12] the author wishes

Ito thank E. Spenke. For the limit of b = 0 one obtains the well-known relation of

eq (1) for a circular two-dimensional contact, for b = a the relation R = Q /ZTCO of

a semispherical contact.

113
holds, the calculated Q3 -value equals the actual resistivity Q of the material.

In order to check if the assujnption in eq (6) holds true, a second method is

required that also permits an absolute measurement of the resistivity. For this

purpose the four-point probe measurement with aluminum-silicon contacts presented

itself, as was treated already in section 4«

The exact theory of the four-point probe measurement requires that the contact

radius a of the aluminum-silicon contacts and the phosphorus penetration depth b be

small as compared to the probe distance s of 200 }im. This was not fulfilled. Thus, we first of all had to make sure that the finite dimensions of the aluminiam-silicon

contact do not distort the four-point probe measurement. For this check one takes

advantage of the fact, that the distance between the probes, s, can be varied very

easily, e.g., by just using every second (s = 4OO ytm) or every third (s = 6OO ym)

aluminum-silicon contact for the four-point probe measurement. In this fashion,

four-point probe measurements could be performed with greatly varying distances

between probes. The probe distance s and the thickness d of the investigated

wafers 5 were varigd in the range

s = 200 to 5000 )im

d = 150 to 2000 ym

d/s = 0.2 to 10.

Here, a was never larger than 20 jam. The -values were calculated according to

SMITS [14] for d/s < 1 .4 and according to VALDES [15] for d/s > 1.4. Within the

measuring accuracy of + 2^ no influence was noticed of the distance between probes

on the -value. In addition, in deviation from the normal case by feeding the

current into the two inner probes and measuring the voltage at the two outer ones, we were able to verify that the -value is independent of such exchange of probes.

Similar results had already been obtained by SEVERIN [16] when investigating

his unconventional four-point probe method, in which mercury is used as a contact.

In this case, too, the diameter of the mercury contact was already of the order

of the probe distance.

In order to check the assumption in eq (6), spreading resistance measurements

and four-point probe measurements (s = 200 ym) were performed in x- and y-direction

(figure 5) J "the latter measurements after the bottom diffused layer was removed.

The spreading resistance measurements were evaluated according to eq (5). For both

tracks (i.e. for approximately 2 • I50 measurement points) the average values

and were calculated and compared with each other.

Typical results that so far were confirmed quantitatively by all our measurements are shown in figure 9. Plotted are the results obtained from 55 silicon

slices. The slices were taken from three different silicon rods that differed as far as their average resistivity and their microscopic resistivity variations were

conceimed:

group 1: 11 wafers in the range Q"^ = 207 ^om + 16^.

"Short wave-length" microscopic resistivity variations with small

"eimplitude" . Figure 6 shows the measured resistivity distribution of one of these slices. (The slant of the curve measured in y-difection is not

typical, though).

Included in these investigations was neutron activated silicon with very

homogeneous resistivity [I5] which will be treated in connection with figures 8

and 9«

114
I^roup 2: 12 wafers in the range = J?*"! Qcm + 45^.

} "Long wave-length" microscopic resistivity variations of large "amplitude"

Figure 7 shows the measured resistivity distribution of one of these

slices. (The resistivity dip in x-direction is not typical, though).

^oup 5s 10 wafers in the range = 3. ''9 Q cm + 2.5^.

Neutron activated silicon [15] » no microscopic resistivity variations.

Figure 8 shows the measured resistivity distribution of one of these

I slices".

1 Since the spreading resistance measurement reaches into a much lower depth of

the silicon wafer than the fovir-point probe measurement, the values and do

iiot correspond to the same volume in the specimen. Hence, it is not surprising that

Values Qs/Qe, smaller than one are measuxed. However, it has to be noted that the

relation Qc/^/, is always smaller than one. On the average it is approximately 0.8.

i?his result cannot be explained by the differing local resolution of the two

lethods, especially since it was also obtained with the homogeneous silicon of

proup 3'

Analogous to the conventional spreading resistance method we are forced to

ntroduce a calibration factor

k=-|p- (7)

'or the aluminum-silicon contact in eq (5)s

0 arc cos -fc

aturally, this step rests on the ass^unption that principally ^ =

Q/^ holds true and

[hat there can be no doubt as to the accuracy of the four-point probe measurement.

j The k-values of figure 9 were plotted in figure 1 . It should be noted that

(AZTJB and DICKEY [5] and KRAMER and VAN RUYVEN [6] also measure k-values smaller

ban one, although only in the high resistivity part of their measurements range,

f one takes into account that the k-value is detenained by many factors (descrip-

~ ion of the s^-n junction by a semi-ellipsoid, which holds only approximately; the

pproximation: underdiffusion = 2/5 • b; the measurement of the penetration depth

f the phosphorus, b, and the diameter (J) ; current-voltage measurement etc.), a

jeviation of the k-values from the theoretical value of k = 1 by 20^ is basically

pt surprising. However, it is disturbing that k is always smaller than one by

pproximately 20^!^. This points to a systematical error.

l^e could not determine xinequivocally whether the two -dips measured with the

spreading resistance method in y-direction had to be considered as properties of

(phe material or whether they rather were pure measurement errors

I

115
For this reason we varied drastically the experimental conditions:

a) a from 2.5 to 50

^ 1 where the distance between two contacts and the

b; d from 150 to 2000 thickness of the wafer were always larger than 10a.

(figure 9 also comprises two different values of a and in the case of the

homogeneous silicon also different values of d).

c^ b from 0.7 to 12_pa _

d) measiirements of aind on wafers that were cut along the <111> -direction

from a rod pulled in that direction'.

e) measurements of and on contacts without metallization. The metal point

was applied directly_onto the phosphorus diffused silicon.

f) ac -measurements of Q^. The frequency was approximately 150 Hz.

In none of these cases was there a noteworthy influence on the k-values. The k-values

were always scattered statistically around kiwO.8.

The term "statistically" applies here only with restrictions. Unfortunately, at

the time of these investigations silicon with homogeneous resistivity was not yet

available to us. Since the local resolution of the two measurement methods was different, ve would have had to investigate a large number of wafers in order to arrive

at a statistical interpretation. It would have been too time-consuming. Therefore,

in some cases only four silicon slices were measured with one experimental condition varied. We can thus not claim true "statistics". It is only recently that in

the neutron activated silicon we have a material with homogeneous resistivity. The

investigations are to be repeated with this material. Surely, results with still

higher certainty will be obtained with respect to the k-value.

6. Pinal Remarks

A disadvantage of the aluminum-silicon contact consists in the time-consuming

and costly processing steps needed for the preparation of the contacts. As far as simplicity is concerned, the conventional spreading resistance method in many cases would be better suited, since it requires only a simple surface treatment of the

silicon slice. Therefore, it is now our aim to help answer the technically interesting question whether the conventional spreading resistance method permits

measurement of relatively small resistivity variations in starting silicon with

satisfactory accuracy. Ve intend to perform measurements of comparison between

the conventional spreading resistance method and our method of measurements with

al\imin\im-silicon contacts. The measurements are to be performed on the same wafer

on adjacent tracks. In order to arrive at a result as general as possible, we have

sent silicon wafers of groups 1 , 2 and 5 in figure 9 after they were measured by us

to a number of laboratories. These laboratories are concerned with the conventional

spreading resistance method and will use it to measure our silicon wafers.

7. Acknowledgements

The author would like to thank J. Burtscher for helpful discussions. He also

would like to thank G. Schuh for supplying the wafers with altuninum-silicon contacts

and H. Windisch for taking the measurements.

In contrast to the investigations of GARDIIER et al. [7] (see figure l) and

lOTREl^IANN , SEDLAK [17] , with aluminum-silicon contacts there is no indication of a dependence of the k-factor on crystal orientation.

116
8. References

Muhlbauer, A., Kappelmeyer, R., and

Keiner, F. , Widerstandsfeinstreifung

in tiegelgezogenen Si-Kristallen,

Z. Naturforsch. 20a 1089 (1965).

Mazur, R.G., Resistivity inhomogeneities in silicon crystals, J. Electrochem. Soc. rij. 255 (1967).

Krausse, J., Widerstandsschwankungen

in Siliziumkristallen, paper presented at the 2. DFG-Kolloquium in

Burghausen (1970).

Burtscher, J., Dorendorf, H.W. , and

Krausse, J., Electrical measurement

of resistivity fluctuations associated with striations in silicon crystals, IEEE Trans. Electron. Dev.

ED- 20 702 (1973).

Mazur, R.G., and Dickey, D.H., A

spreading resistance technique for

resistivity measurements on silicon,

J. Electrochem. Soc. 113 255 (1966).

Kramer, P., and van Ruyven, L.J.,

The influence of temperature on spreading resistance measurement,

Solid-St. Electron. 1^ 757 (1972).

Gardner, E.E., Schumann, P.A. , and

Gorey, E.P., Measurement techniques

for thin films, p. 258, Electrochem.

Soc. (1967).

Pinchon, P., private communication

to P. Kramer and L.J. van Ruyven,

ref . [5] . Keenan, W.A., Schumann, P. A. Jr.,

Tong, A.H., and Phillips, R.P.,

Ohmic contacts to semiconductors,

p. 263, Electrochem. Soc. (I969).

[10] Burtscher, J., Krausse, J., and

Voss, P., Inhomogeneities of the

resistivity in silicon: two diagnostic techniques. Semiconductor Silicon

(Ed. by H.R. Huff and R.R. Burgess),

p. 581, The Electrochem. Soc. (1975).

[11] Voss, P., private communication

[12] Ollendorff, P., Grundlagen der ErdschluB- und Erdungsfragen, Berlin,

Verlag von J. Springer (1928).

[13] Schnoller, M. , Breakdown behavior of

rectifiers and thyristors made from

striation-free silicon, IEEE Trans.

Electron. Dev., to be published.

[14] Smits, P.M., Measurement of sheet

resistivities with the fo\ir-point

probe, Bell Syst . Techn. J. 7II

(1958).

[15] Valdes, L. , Resistivity Measurements

on germanium for transistors, Proc.

IRE 42 420 (1954).

[16] Severin, P.J., private commtmication,

to be published.

[17] Murrmann, H., and Sedlak, P., Spreading resistance correction factors

for {111} and {lOC} surfaces,

published in this volume.
2a

Sn-silicon

Figure 2. Cross-section through a non-blocking aluminum-silicon contact.

U

Figure 3. U-I characteristic: a) spreading resistance measurement, a = 10 ym

(2.67ficm) or 12.5 ym (134J^cm) ; b) four-point probe measurement, s = 200 ym.

118
a=3.0^lm

a=15.5^lm Figure 4. Lateral resistivity fluctuations along a diameter of a silicon

slice (average resistivity 55 ficm)

a) a = 3.0ym {(^ = 5pni; b = 0.7iJin)

b) a = 16.5Mm ((() =32uiii; b = 0.7ym)

c) comparison of the two results in

a) and b) for the 0-6 mm positions

>^100|anT«-

E & )ti=ip\im or 30jim

200iim

Figure 5. Arrangement of the aluminum

aluminum-silicon contacts for a routine measurement.

119
10 15 20 25 30mm

X

20 25 30mm

y

10 15 20 25 30mm

y

Figure 6. Lateral resistivity fluctuations along two diameters of a silicon slice

(average resistivity 207 Qcm)

p^: spreading resistance measurement, a = 12.5 vim

Pt^: four-point probe measurement, s = 200 ym.

120
1,5--

1,4-

1,3-

1,2-

i

1,1 -

1.0-

0.9-

0.8-

0.7-

0.6-

0,5-

0,4-

0.3-0

1,3-

1,2-

if

1.1 -

1

1.0-

1 0.9-

1

0,8-

0,7-0

5 10 15 20 25 30mm

X

J I I I L

10 15 20 25 30mm

X

1.5-

1.4-

1,3-

Qs(y) 1,2- Q

1,1

-

1,0-

1 0,9-

0,8-

0,7-

0.6-

0,5-

0,4-

0.3-

1,3

Q.jy) 1,2-

i 1.1

1,0-

09-

Q8-

0.7'0

"5 10 15 20 25 30mm

Figure 7. Lateral resistivity fluctuations along two diameters of a silicon slice

(average resistivity 38.7 ficm)

Pi+: four-point probe measurement, s = 200 urn P^: spreading resistance measurement, a = 10 ym

121
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lor122
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

The Preparation of Bevelled Surfaces for Spreading Resistance

Probing by Diamond Grinding and Laser Measurement of Bevel Angles

A. Mayer and S. Shwartzman

RCA Solid State Division

Somerville, N.J.

A rapid and reproducible method for preparing bevelled surfaces on silicon has been developed as a preliminary to spreading resistance probe measurement of doping

profiles or junction depth determination by staining.

Several chips can be bevelled simultaneously. The sample

is mounted on a carrier which is clamped on the tilting

table of a microtome. The tilt is adjusted until a laser

beam reflected from the surface to a calibrated wall

chart is deflected to the desired angle. The bevel is

then ground with a high-speed diamond wheel momted on the

microtome, taking cuts of several micrometers at a time.

The bevel edge is clearly defined even for very shallow

angles. The angle is accurately measured with the same

laser.

Because the ground surface is highly reflective, in

contrast to a lapped surface, a good reading of very small

angles of less than 30 minutes can be obtained. Up to a

6 meter base line is used with a Imw He-Ne laser and the

reflection is visible in normal room light.

Factors entering into spreading resistance are discussed, such as mechanical damage incurred in bevelling,

probe impact damage, and surface cleanliness. Judged by

spreading resistance, the amount of damage incurred during

grinding is small and reproducible, provided care is taken

to maintain the spindle so that it runs without vibrating.

Key Words: Bevelling, diamond grinding, laser bevel

angle measurement, layer thickness determination, materials,

resistivity measurement, silicon doping profiles, spreading

resistance measurement, surface damage.

I 1. Introduction

1 Solid state device properties depend on the distribution of carriers

'tound p-n junctions. The bevel-and-stain method [1,2 J in conjunction with

pur point probe resistivity has been the most widely used procedure for this

wrpose, but the spreading resistance probe (SRP) is gradually supplanting it.

I The major reasons for the slowness of the introduction of SRP into dejlgn engineering and process control are (a) the slowness of sample prepar-

':ion, (b) the slowness of obtaining the SRP readings, (c) the lack of inforation about the effect of sample preparation on the precision of the resisance readings, (d) the lack of standard samples of sufficient uniformity to

fisure that the choice of the area was not the main reason for an observed

, iiange in the calibration graph and, by implication, the stability of the

cobe including the contact points and internal electrical circuits. Only
recently has sufficient work been done in commercial SRP* design and in the

study of sample uniformity by Subcommittee 6 of the ASTM Committee F-1 to

show that calibration graphs are reasonably stable and approximate straight

lines. The speed and reproducibility of sample preparation present a bottleneck inhibiting the use of the SRP as a production control tool.

The work reported here was undertaken to improve the rate of sample preparation (bevelling) to provide a basis for mechanizing the procedure. Highspeed grinding offered a chance to achieve this goal and it also provided a shiny bevelled surface which permitted the angle to be measured by optical

reflection; the normal method consists of lapping, (which leaves a matte surface) and measuring the angle by depth of focus of a toolmakers microscope.

Precision equipment was developed which led to the establishment of

grinding at any desired angle as a routine method for bevelling samples and a novel high-precision method for measuring bevel angles with a laser as part

of the total mechanical package.

It is known that the measured spreading resistance is the sum of series

resistance terms and the spreading resistance [3,4]. It has also been observed that surface preparation contributes to the observed value and its

stability on storage. In order to make the bevelling procedure useful for

production control it became necessary to provide some insight into the con- tributing factors, such as the degree of mechanical damage of bevelling in

relation to that added by the impact of the probe points; the contribution

due to the multiple contact points on each probe and the reason for the increased contact resistance when probes were used to measure only smooth surfaces. This report describes the development of the novel bevelling and

measuring system which resulted from these enquiries.

2. Surface Grinding Development

2.1 Consideration of Surface Damage

A survey of the literature on spreading resistance measurement indicates

that the method of surface preparation plays a major part in the reproducibility of SRP readings.

Severin I5J. observed that the contact to silicon is multipoint. Gorey

et al., [6] deliberately prepared multipoint tips by sandblasting. The

makers of the SRP suggest that apparent high spreading resistance , Rg , readings

obtained on a standard sample can be brought back to normal by allowing the

points to impact on a roughly lapped silicon surface, a procedure which is

called reconditioning. We agree with these observations and have also found

that continued operation of the probe tips on only chemically polished surfaces gradually leads to high Rs readings and that these can then be made to

read the normal, lower value after reconditioning.

The high readings probably result from the multiple contact points

gradually wearing away on the smooth sample surface giving a smaller effective contact area and reconditioning then roughens the probe points again.

The rough appearance of a normal imprint of a probe point is shown in the

scanning electron micrograph, figure 1. This effect is different from the

observation that the Rs of a lapped surface is greater than that of the polished surface of the same wafer. The reason for the latter effect is the

degree and depth of damage incurred during sample preparation. That uncon- trolled (impact) damage causes variable change in measured Rg can also be inferred from the observation that the drop rate of the probe tip on the silicon surface has to be well controlled. This is illustrated in figure 2; here,

the probe tip was allowed to impact repeatedly on the same area of a polished

wafer and this led to a rapid increase of the measured Rg with each extra

impact. It is similar to the observation that insufficient damping of the

probe descent leads to high Rs readings. The effect of damage is most pronounced on highly doped silicon and disappears in the 10-100 ohm-cm range and

i *We use a Model ASR-100 made by Solids State Measurements, Inc. i Murrayville, Pa. '

124
aay even reverse at higher resistivities. This effect is discussed in more

iietail and quantitatively later on.

j Similar conclusions about damage were reached by Gupta et al . [7] who meaI'.ured the Rs of lapped samples after progressive removal of damage by etching

j/ith hydrogen chloride, and also by Chu and Ray [8] who worked on germanium.

I 2.2 Grinding Machine

' The importance of the above observations in the choice of a grinding

jiachine for preparing bevels becomes clear when it is considered that vib-

-ation of the spindle is likely to cause uncontrolled damage. The best

lachines tried so far are an air-driven, pressure-mist lubricated spindle*

j'hich has been in operation on a daily basis for a year and a similar, but

iielt-driven one for 4 months. Most of the data reported here were obtained

Ith the former. It is being operated on 25 and 40 psi air pressure at

'peeds of 30,000-60,000 rpm. The main problems in the installation were

'lounting the spindle rigidly on a level platform and the balancing and dressing of the h" O.D. diamond cup wheel** to reduce vibration. Periodic rejlressing with an aliomina or carbide stone is necessary to maintain reproduciiility. Cutting is performed with air or oil cooling and an "elephant trunk"

|s used to exhaust the small amount of dust and mist generated. As can be

jeen from the photograph, figure 3a and the schematic, figure 3b the spindle

"S mounted on a microtome bed***; this has a ratchet feed capable of lifting

'he specimen in 1 to 25ym increments per stroke. The specimen is mounted

igidly with wax  on a steel block which is indexed so that it can be lined

.p in the microtome clamp by means of a .5mm wide steel key.

2.3 Bevelling by Grinding

The microtome is supplied with a tilting table which can be set so that

he waxed specimen is level with the sliding plane. It is then a simple mat-

||er to tilt the specimen to subtend the desired angle to the sliding plane

jnd to measure this angle by means of a Helium-Neon laser mounted parallel

lith the spindle. After setting the tilt the grinder is started and allowed

[o take a 3-5iJm cut per stroke. Each stroke takes less than 4 seconds so pat even a lOOym thick layer can be sectioned in less than 2 minutes,

jlinishing strokes of l-2ijm at a time help to produce a finish with minimal

amage on the bevelled surface. For examining very thin layers we routinely

evel at a 34 minute angle to obtain a tangent of about 0.01 or a magnifica-

|ion factor of 100, while a 0.2 tangent {"^11 degrees) is used to obtain comjllete cross-sections of wafers or for thick epitaxial layers. Table I can be

iised as a guide for selecting bevel angles and step length in relation to

layer thickness.

Table I. Guide to Bevel Angles & Step Length in Relation to Layer

Thickness. To obtain the true thickness multiply the SRP

step by the tangent.

Layer Thickness

tm up to 3 2-15 10-60 50-150

;U1 up to .12 .1-.6 .4-2.5 2-6

Jrp step,ym 5 10 10 10

ian a .008-. 012 .018-. 025 .08-. 12 .2-.

pprox. a h° 1° 60 11°

H.P.Smith, Assoc., Cheshire, Conn; AVON spindle

Sample Marshall Labs . ,Lyndhurst ,N . J. ; 100 concentration ,9 ym diamond,

plastic bonded cup wheel.

'{**  Reichert Sliding "Om E" microtome.

Sticky wax. Coming Rubber Co., N.Y.

1

i

125
2.4 Surface Cleaning

When a suitable bevel has been ground, the block is transferred to the

SRP, the surface is wiped with a Q-tip moistened with solvent* and air dried

before measuring the Rg . This treatment removes oil mist and debris from the

surface. In contrast to surfaces which have been prepared by lapping or chemical-mechanical polishing which is usually carried out with water based

slurries, we have found that the surfaces prepared by dry grinding and sol- | vent cleariing are stable. They show no significant drift upon standing in \ laboratory air, and give reproducible Rs when a fresh surface is prepared by i grinding as shown by the following example: The surface of a test wafer \ having n- and p- type epitaxial layers was measured regularly each morning,

then reground, cleaned and its Rg re-read each day for about a month. The

longest time between regrinding was 6 8 hours, the shortest 30 minutes. The

mean resistivity recorded was 17.57J^-cm on the p-type layer, with a standard

deviation, SD,of 4%. The n-type layer measured 13.3n-cm with a 6% SD. It

should be noted that these figures include errors due to the true differences

in resistivity of the sample as more of the sample was ground away. .' The probable reason for this stability of the surface is that the j freshly exposed silicon sees only the relatively dry room air. It is believed that surface charge effects are often due to charge separation and mi- u gration of impurities ionized in the presence of the highly hydrated silicon ; oxide film that forms when silicon is abraded under water. Similar stability :; could be achieved on surfaces prepared with aqueous media by baking them at ; 150°C for about 15 minutes. The suggested new method of surface preparation

is simple and provides the basis for routine process control because of its

relative insensitivity to what would normally be regarded as a very crude sur-; face treatment. An illustration of the effect of iirpurities when samples are prepared by wet-lapping with, silicon carbide is given in figure 4. Here, | th_e surface was just rinsed In water after lapping, air dried and the Rg I measured, then the sample was cleaned with hot ammonia-hydrogen peroxide

(SC-1) solution and dried at 150°C for 15 minutes before remeasuring. Note

that the apparent noise as well as the average level of the Rg value has

changed significantly. When this series of experiments was repeated with

the above sample the freon-solvent cleaning and drying step consistently pro- ! duced less noisy readings than the aqueous treatments. The absolute level of

the Rg varied by more than 10%.

2.5 Standard Sample Preparation

\ It became clear in the course of this work that the reproducibility of

Rg on lapped surfaces, and later also on mechanical-chemically prepared surfaces required standardization of the cleaning and drying procedure. It was • noted when this was done that the day-to-day reproducibility of the Rg still , showed variations which were traced to the fixturing used in the lapping or j polishing process; the pressure applied during the operation could vary con- / siderably and give rise to various degrees of surface damage. Bevelling with

an aqueous silica gel slurry on a glass or Lucite plate was also found to be j a process difficult to control routinely so as to guarantee the same level of

residual damage. This may have been the main reason for the changes in the

slope of the calibration graphs prepared daily when the SRP was first introduced into service. Kim, et al.ISJ also found that surfaces prepared with

0.0 3 to lOym alumina gave Rg readings which were too noisy to resolve re- sistivity striations.

When the grinding procedure was introduced as a routine process the calibration graphs remained constant over long periods (months) and also became straight lines when plotted as logarithms of Rg against resistivity, as shown in figure 5. This graph was constructed from 18 samples of (111) and T: samples of (100) oriented silicon, which had been selected for being reason- ! ably homogeneous, a very difficult task for the high resistivity range.

There is no significant difference statistically, when both the (111) and

(100) or only the ClU) samples are plotted. This is in contrast to private

L *51% Freon-TF with 49% methanol was a satisfactory solvent. j 126
I

information indicating that some workers find that the n-type and some that

the p-type curves for (111) and (100) are significantly different. Much of

|this sort of discrepancy is. probably due to bulk resistivity measurement

Iproblems. The next point of interest is the marked difference between chemiically polished and ground surfaces : note that the surface damage due to

[grinding affects the n- and p-type highly doped samples in a similar manner

jand very markedly and that the effect almost disappears at high resistivities.

jWe have no reliable samples for a good comparison in the greater than 100J2-cm

irange . Perhaps this effect is due to the introduction of crystal defects

•which change the effective carrier mobility, i.e., the trapping cross-section

Ifor large carrier densities is greater than for the low carrier densities.

2.6 Factors Affecting Reproducibility

I The confidence placed in any measurement procedure rests on the ability

to calibrate the instrument so that this calibration can be reproduced over

ilong periods of time. Our data suggest that the following factors enter

into this: grinding and impact damage, condition of the SRP points, and

[standard sample uniformity.

' The grinding process appears to introduce somewhat less damage than lapping, and is more reproducible on a routine, long term basis. The major

problems are vibration in the spind] e due to bearing wear, a loose clamp or

jsupport block, or a grinding wheel which requires dressing. A good mainten-

^ce schedule is essential. A daily check is easily made with a low resistii/ity sample by observing the height of the step in the Rg readings between

-he chemically polished and the ground surface as indicated in figure 6. In

:he range 10^0 to lO-^-^ carriers per cc a chemically polished surface gives

|:he lowest spreading resistance. Even with the greatest care in adjusting

the descent rate on our probe the surface is damaged. As can be seen in

I:igure 2 , repeated impact on the same point causes drastic changes in the

iipparent resistivity. Slight changes in the descent rate can change the dejree of damage and the observed Rg. This is most obvious with low resistivity

lamples, for example a O.Ollfi-cm n-type polished sample which was measured

.repeatedly over a 6 week period, often two and three times a day gave a Rs

between 14 and 24 ohm, the average was 19.8 ohm and the SD was 12.4%; the

'baximum fluctuation during a day was 9%. To evaluate the variation in Rs

tkue to variation in grinding these figures were compared with Rg readings of

|j:he same sample after bevelling. The calibration graph covering the range

il.02O to 10l4 carriers per cc shown in figure 5 is based on the statistical

liiverage of samples read at least 10 times. It indicates a difference of 14

jfhm between polished and ground surfaces of the test sample while the average

jijiif ference observed was 12 ohm with a SD of 11.8%. No difference was observed between samples which had been freshly ground and ones which had been

jleld for 16 hours after bevelling. The SD in a similar test for a in-cm nIjiype sample (Rs-10-^ ohm) was 5.4% and for a p-type, 20fi-cm sample (Rs==10^

i|hiai it was 10 . 8% .

r.{ The data suggest that the variation in grinding damage contributes

jlightly less to the total noise than the variation in impact damage. The

f pain practical benefit of this test is that it provides a ready means of

lionitoring the impact damage, by routinely checking the Rg of a low resisJivity standard sample having a damage-free, preferably an epitaxial, sur-

|iace. We can then set a limit to the value that is acceptable, and take

propriate action if it is too high - adjust the impact height or recondion the points on a lapped surface.

L- jj If we read the Rs on a freshly bevelled portion of the same sample we

jlan again set a limit to the step height we wish to tolerate. If the ob3 prved value is greater, re-balancing the grinder will usually obviate the

nbult . It has already been noted that silicon reference samples prepared

- [pom bulk crystal more often than not exhibit considerable resistivity

hariation across the diameter. These gradients or striations are known to

pflect the crystallization phenomena of the solid-liquid interface, varie itions of an order of magnitude over less than millimeter distances are not

ncommon. We have regularly prepared material by epitaxial deposition of 50

1 127
to lOOyin thick layers on high resistivity opposite type substrates.

Spreading resistance measurements made on these epi layers show less than a 10% variation in Rs values over the surface of a 50mm diameter wafer and suggest that this is probably the best method for the preparation of standard

samples for the calibration of the spreading resistance probe. These layers

can be measured by the four-point probe technique in conjunction with a thickness measurement and the only uncertainty then lies in the calculation

oftthe integrated resistivity over the thickness and the p-n junction correction for the built-in field when the two kinds of measurements , -four-point

probe and spreading resistance- are compared. Si±)committee 6 of the ASTM

Committee F-1 on Electronic Materials is working on this approach to

standardization

The work mentioned above on the evaluation of impact and mechanical damage required a large number of repetitive readings to be made by several

operators. It became apparent that once the initial shyness of a new operator

faced with a complex looking apparatus had worn off, no problems arose in the

rapid acquisition of the necessary skill for bevelling, de teimiination of the

bevel angle and SRP readings.

In normal day-to-day practice we find grinding to give us satisfactory

Rs data in terms of process control. In addition it is rapid and lends itself to the preparation of multiple samples and to mechanization.

3. Angle Measurement by Laser Reflection

3.1 Choice of Method

Process control requires the routine measurement of the width of subsurface layers. In order to convert the track marks of the SRP to width

measurement it is necessary to know the bevel angle precisely. The suggested

procedure for the ASR-100 probe is to use the calibrated toolmaker's microscope as a depth gage; the precision of the tangent measurement depends on thai ease of focusing at the start of the bevel and at some known distance along

the bevel; this procedure is time consuming and requires well trained personnel for reliable output. A somewhat improved measurement of the angle, in common use at RCA, depends on reflection of a collimated light beam from the

top surface and from the bevel ,. followed by measurement of the displacement

of the two rays at a distance of about 50cm. This method cannot be applied

to lapped samples because the surface is not sufficiently reflective but

ground bevels do give reasonable reflections. However, to measure small

angles accurately a much longer pathlength is necessary and then the light

intensity is insufficient.

3.2 Use of Laser

We have successfully substituted a He-Ne laser for the collimated light

beam. A Imw He-Ne laser* is mounted on the microtome used for grinding the

bevels and serves in the first instance to adjust the tilt of the stage to

obtain any desired bevel angle, and after the bevel has been ground it is

used to measure the tangent of the angle precisely, without having to handle

the sample further. It obviates the need for lapping blocks with different,

precisely machined angles, it has great flexibility in permitting angles

from 20 degrees to less than 30 minutes i.e. angles with tangents of 0.2 to

0.01 to be selected and measured accurately, giving a range of multiplicattion factors from 3 to 100. The arrangement for measuring the tilt of the i. sample before grinding and the finished angle after grinding are shown in

the photographs figure 8a and b. The laser beam which has a diameter of

0.8mm is allowed to impinge on the top surface of a sample waxed to the prealigned and levelled carrier block. The tilting stage is then adjusted so that the reflected beam is deflected to the desired angle, a, or rather j

* RCA Model L1540 4 and Exciter Model L1542 7A.

u

128

-J.
|to the desired tangent of a. This is determined by the distance between the

linitial reflection of the level sample, and the new position Y (after tilting)

idivide d by twi ce the optical pathlength ABC between the sample and the scale:

[tan a=XY/2

It is essential to ensure that the laser beam is at near normal incidence

|to minimize errors in calculating the tangent of the angle. After grinding

the bevel, its angle is measured precisely using the same laser and the same

bptics. This time two reflected beams are visible one from the sample surjface and one from the bevel. The sequence of operations is shown in figure

l8a,b,Cid.

I The longer the baseline ABC between sample and scale, the more precise

(is the reading of the beam separation. We have used a 6m baseline to measure

langles smaller than 20 minutes. In the existing permanent apparatus a 1.8m

paseline is used which gives a 36mm separation of the reflected beams from a

34 minute angle with a tangent of 0.01 (corresponding to a magnification of

:iOO). The laser beam we use has a nominal diameter of 0.8mm and a divergence

of 1 mrad. Surface scattering causes the reflected spot to widen to about

5mm in practice, as compared to a calculated 2.6mm. With silica gel polished

jevels the reflection tends to be more diffuse or elongated, especially with

small angles, due to some edge rounding. Excessive periodic vibration in the

opindle can produce deep ridges which cause a diffraction pattern to form and

chis makes it difficult to detect the center of the reflection. Figure 9

! shows photomicrographs of bevels obtained with a well balanced wheel.

4. Coirparison and Reproducibility of Bevel Angle Measurements

The reproducibility of the laser measurement was determined by 10 repeat

:ests by each of two operators who measured the bevel angle on one piece of

silicon over a 5mm bevel length over a period of days. The average was a :angent of .0533 with a SD of 1.25%. The measurements were also compared

fith the depth of focus technique suggested by the SRP manufacturer and with

tracing the profile of the angle using a calibrated surface profilometer* as

s'ihown in Table II.

Table II. Comparison of tangent measurements of the bevel angle. Each

figure consisted of 6 readings taken by two operators over

a one month period.

Laser Profilometer Depth of Focus

'.verage .00 73 .00 75 ' " .00 87

pre ad ± .0008 .0059 .002

verage .0143 .0153 .0155

pre ad ± .0009 .0014 .0010

.verage TTUl TTOS . 100

Jpread .001 . 002 .004

The depth of focus is not only the most tedious but also gives the

east reproducible results, and the laser method is the most convenient and

jgrees well with the profilometer procedure.

I In conclusion we can say that the combination of laser angle measurement

nd SRP track distance measurement produced values for the thickness of epiaxial layers which were in excellent agreement with infrared interferoptric methods, and that the procedure is well suited for routine process

pntrol and engineering design work.

S;aramary

High speed grinding has been shown to be a usefral method for the prepar-

'tion of bevels prior to spreading resistance profiling of silicon samples.

Talysurf 4, Engis Equipment Corp.

129
The main advantages of the new procedure are its speed, convenience , cleanliness and accuracy. Multiple samples can be bevelled and their angles

determined rapidly on one block which is designed to fit directly onto the

SRP. Simply wiping the surface with solvent is sufficient to get reproducible

surface conditions. This method reduces the variability of R- readings by

suppressing surface hydration and charge separation from impurity ions. By

combiring the grinder with a laser it is easy to select the desired angle and

to measure it precisely without removing the samples from the apparatus. Also

a wide range of angles can be selected so that full cross-sections of ISOym

thick wafers are as readily made as very shallow bevels of less than 30 minutes to measure thin layers with equal ease. In addition, the bevel edge is

readily visible and sharp. It should be noted that the bevel preparation by

grinding is a useful technique on its own because the ground surface is shiny

and can be stained by the methods used on polished samples.

An examination of the factors which contribute to the total resistance

measured by the spreading resistance probe indicate that damage due to the

method of surface preparation can be separated from damage caused by the impact of the probe points provided homogeneous standard samples are available.

The SR difference between the damage-free and the bevelled surface is a good

guide to set up procedures which ensure that the grinder and the probe are kept in good operation condition in routine use. Lastly, we have found that

the operation is readily learned and is relatively insensitive to operator

experience

We are happy to record that Paul Delpriore's an.d Eric Cave's help, ideas

and encouragement, and Bemice Upton's devoted detailed work have contributed

greatly to the success of this project.

6 Acknowledgements

7. References

[1] "Test for Thickness of Epitaxial

or Diffused Layers in Silicon by

Angle Lapping and Staining Technique", ASTM Method F 110-72, 1972

Annual Book of ASTM Standards,

Part 8, p American Society for

Testing Material Philadelphia.

[7] Gupta, D.C., Chan, J.Y. and

Wang, P., Rev. Sci. Instr.

,

1681, 1970.

[6] Gorey, E.F., Schneider, CP. and

Poponiak, M.R. , J. Electrochem

Soc, 117, 721, 1970.

41,

[2] Bond, W.L. and Smits, P.M.,

Bell System Technical Journal, 35

1209, 1956.

[8] Chu, T.L. and Ray, R.L. , S

State Tech., 14, 37, 1971.

Solid

[3] Mazur, R.G. and Dickey, F.J. , J.

Electrochem, So., 113, 255, 1966.

[4] Gupta, D.C. ibid 116, 670, 1970.

[9] Kim, K.M., Kumagawa, M.

Lichtensteiger , M. , Mugai, A. andf

Martin, E. , Annual Reports 1972-7

Research in Materials, ! Massachusetts Institute of

Technology, p. 299. '! [5] Severin, P.J., Solid State Electronics, 14, 247, 1971.

130
Figure 1. Scanning electron micrograph of a spreading resistance probe impact area on silicon.

Magnification 10,000 X; 70° specimen tilt.

E

hJU

Z

w

CO

ui

q:

o

z

o

<

lU

a:

a.(O

AB - SURFACE TRACE* EACH POINT \Ofim MOTION

B - MOTION ARRESTED.

BC - NET INCREASE IN RESISTANCE DUE TO

PROPAGATION OF DAMAGE .

I - n-TYPE SILICON

.OI4Acm

1000

100 r10 =- B

1

I p-TYPE SILICON

.OI2Xicm

1

c =

feure 2.

0 130/tm 0 130/im

DISTANCE ALONG SURFACE, /iin

Change in resistance from repeated impact of spreading resistance probe points on

p same place on the surface of a silicon wafer.

! 131

I.OOO.OOOe

.10 I RESISTIVITY, ohms -cm

Figure 5. Spreading Resistance vs. Resistivity.

133
E

UJ (O

(LliJ

lOOcr

10

U r-^

-

1 r

....

— T

1 1-

1

:

.-•••*•-.. " H 1 1

SURFACi

PRO

: BEVEL

BE MOTION, lO^n ^

SURFACE

1 PER

: BEVEL

STEP

Figure 6a. Spreading resistance

profiles of polished surface and

ground bevel of 0.11 ohm-cm n-type

silicon. Left, before dressing the

grinding wheel. Right, after dressing

the wheel.

J

O

So

a:(o

a.iu coo:

100,000

10,000

T r 1 1 r

SURFACE BEVEL

PROBE MOTION. \Ofim PER STEP

Figure 6b. Spreading resistance

profile of polished surface and

ground bevel of 23 ohm-cm p-type

silicon.

Figure 7a. Laser Beam Impinging

on The Silicon Chip.

Figure 7b. Holding Fixture

with Alignment Blade.

134
60^ iH e O

u

C 0)

a

O o •H CN > o LO

<u T3 II (U in

rH XI iH

0)

O ^

CO Xt (U

M <N

0) X3 •H II 0) o 4-1 x: d (U •u n) 00 4J C3 w iH 0)

(U c •HU to x:

•H -a bO CO 4-1 13 (U •H •H C XI o

FnU to 4-1

m

T3

<U U

CJ

<U • iH 4J

(U Id

1-1 x:o

x;M

to

x;u o

CO fio

<u3

4J 4J

!«! •H •rl

•4-1

O

ft

60C x:

•H +j

•i-i iH & O

x: to(U X! •Ha

(3 4J •H M Oo

•r-) tj

cq

<Ja

to to 00 01 XI

(U

)-l ^1 3 (U 00 to •H CO

0)>oa

CO X!

4JO

CO

(UU3

4J

i«S •H

M-l • 4-> 60 H C to •H x: -a o

iHO iH

x: r-l

to cu 3

x;

4J 0) XI

4J 4-1 to3 CO

to X!

cu 4JC

•HO o

CO o

0) 4-1 u3 ^

60

O

•H to

135
tan a « . 106

MAG. 148 X

(c)

tan a = .1 MAG. = I48x

Figure 9. Photomicrographs of 38' and 6°, ground bevels.

136 f

Hi
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Spreading Resistance Correction Factors

for (111) and (100) Surfaces

H. Murrmann and F. Sedlak

Siemens AG, V/erk Halbleiter

Munich, Germany

The effective contact radius for spreading resistance

measurements on Si has been evaluated by comparision of

S.R. for epitaxial la^/ers limited by a pn-junction or by

a v/ell conducting buried layer for different crystal orientation. The contact radius on (100) surfaces showed to be

greater by a factor of 1,26 than for a (ill) plane. Furthermore measurements were made on samples for both (100) and

(111) orientation in the resistivity range of 0,01 to 80 /I cm with n and p-type doping. Data for spreading resistance and

resulting from the predetermined contact radius for the resistivity dependent correction factor are given.

Key words: Contact radius, correction factors, silicon,

' spreading resistance, surface orientation.

1 . Introduction

The spreading resistance underneath a flat circular contact (radius a)

n a semiconductor (resistivity^) can be expressed in the form

^SR=

^ ' ^(5) • k(^) ( ') In this formula the first term represents the spreading resistance (S. R. ) of an ohmic contact on top of a semi-infinite medium of

jietal with resistivity ? (figure 1). If energy barriers have to be consii.ered betv/een the contact and the medium (as is the case for most contacts

|ietv;een metal and semiconductor) a generally ? -dependent factor k(?) despribes this effect. If furthermore the resistivity of the sample is noniniforra, the distribution of the electric field { will be influenced,

|;iving rise to a correction term k dependent on the s -distribution

jn the vicinity of the contact.

jl V/hen applying the spreading resistance technique to quantitative

leasurements on semiconductors, both these corrections have to be taken

into account. This generally includes a calibration of the specific

jjquipment with samples of known uniform resistivity, in which case the

|l' (c }-correction can be neglected.

Curves of measured spreading resistance vs. resistivity for n- and

|-type silicon have been published for different probe tip material and

jontact radius f^J, f2.J, f^J , /"^/.^From these graphs the ^-dependent

,'orrection can be derived provided the contact radius is sufficientlv

jell known.

figures in Brackets indicate the literature references at the end of this paper.

' 137
Only very limited data exist for the influence of crystal orientation on the correction factor [2.] . On the other hand there is strong experimental evidence, that differences exist between SR-measurements on

(111) and (100) surfaces.

Figure 2 shows plots of Rs.R. for (111) and (100) samples. In this

case p-type Si-substrates (8 cm) were used with a buried layer diffusion

(As, Xj = 4,5/um, R = 25 ^/o) and a n-type epitaxial layer (As, depi

= 2,5 /um, % - 0,8i?cm). Though the thickness and resistivity in both

samples are the same, the SR-values show considerable differences. As the

resistivity distribution in the first approximation can be assumed to be

identical, the reason for such discrepancies can only arise from differences in k(S) or in the contact radius for the two surface orientation.

In the following investigations we tried to distinguish between these

two effects.

2. Determination of contact radius

2.1 Theoretical consideration

The question of what the effective contact radius will be, when a probe with a spherical tip is pressed onto a flat surface is very difficult to answer. Several investigators have dealt with this problem considering more or less idealized contact areas /"V, f^J resulting from application of the Hertz formulas fSJ as well as arrangements of multipoint

contacts f3j. Optical evaluation of the surface depression after removal

of the tip in general only gives on approximate, figure for the contact

area. We have decided to try an evaluation by S.R. measurements making

use of equation (l):

As stated above the S.R. -value for a given ? at the surface is dependent

on the field distribution . The potential and hence the factor k(^) has

been calculated for the special arrangement of a layer 1 with resistivity

?1 on top of a layer 2 with ^2 respectively (figure 3).

Two configurations are of specific interest:

a) 5 2 =^ ! This implies that an insulating boundary limits the region of

layer 1 . Technologically this is realized by a pn-junction.

b) 9 2

- ^' Here the conductivity of layer 2 is assumed to be much greater

than in layer 1 . This case can be approximated by an highly

doped underlay of the same conduction type.

In both^ cases the field correction factor is only dependent on the ratio

of d/a .In figure 3 the results of a calculation following Schumann

and Gardner f7j are plotted as a function of d/a. If we furthermore com- pare two configurations with ^2 = *** and f 2 = 0 respectively but otherwise

identical and d, the ratio of the corresponding spreading resistances

is merely given by k(oo)/k(0) independent of 9 and barrier effects but

only dependent on the ratio of d/a (figure 4).

RSR \ll = 0]

^ ^ ^ /^|) (2)

So we may derive from the S.R. -ratio a certain value of d/a from

figure 4 and, when the thickness of layer 1 is known, the effective con- tact radius of our spreading resistance equipment can be found.

1 )

' There exists a slight dependence on the spacing between the probes used

for measurement, but this effect is neglible for our considerations.

138
2.2 Experimental

For the experiments Si-wafers (1,25" diam. ) with (111) and (100)

orientation and both p-type material (8^2 cm) were used. After a thermal

oxidation (1 /um Si02) the oxide was removed from a half of each wafer and

I buried layer diffusion was carried out (Sb, 25P/o, xj = 4,5/um) while

;he other half of each slice was masked by the oxide. Following complete

>xide-s tripping, As-doped epilayers were deposited (1150°C, SiCl4) in

Tour different runs with projected thickness of 2, 3, 5 and 8 mm. The

ppithickness was evaluated by both IR-reflection and stacking' faults above

l;he buried layer diffused halves. S.R. measurements were made with a Mazur

jiutomatic Spreading Resistance Probe (ASR-100) with two probes loaded with

ji force F of either 20 g or 45 g each. The measurements were taken on the

inprepared Si-surface after epitaxy on the half above the buried layer

jdenoted as Rsr (O)) and on the other half, where the n-epilayer is iso-

|.ated from the adjacent substrate by a pn-junction (Rsr (<^))« Table 1 jihows data of some of the slices examined.

Wafer F := 20 g F = 45 g ^epi

Nr. R(oo) R(0) R(o) by IR

l\a] //W

2 12,0 1,55 8,7 0,98 2,10

4 11,3 1,50 7,5 0,83 2,02

6 5,95 1 ,26 5.4 0,88 2,95

7 6,40 1,75 5,6 1,03 3,02

12 5,80 2,40 5,0 1,6 5,36

14 2,55 1,53 2,08 1,07 7,85

15 3,35 1,97 2,70 1,35 8,16

01 10,5 0,84 1,94

03 10,2 0,82 2,02

07 5,2 0,98 4,72 0,58 3,12 o

08 5,8 0,92 5,3 0,54 2,98 o

09 3,75 1 ,41 3,28 0,97 5,92

012 3,40 1 ,26 2,97 0,84 5,68

016 2,52 1,35 2,12 0,94 8,72

Table 1: S.R. above a pn-junction (R(<»)) and buried layer

(R(0)) for different probe loading F

(asR-100, 2 tungsten probes with spacing of 600 /um,

measurement voltage 10 mV, resistivity of the ' epilayer 0,6 - 1,3 cm).

139
2.3 Results

From the ratio R(oo)/r(o) using figure 4 and the determined epithickness, an effective contact radius (a) was evaluated with the results shown

in table 2.

Table 2. Contact radius for different probe loadings and two orientations

F = 20 g F = 45 g a (20 g) a (I11)/^um7 2,20 2,82 1,26

a (lOO)/~/uin7 2,90 3,45 1,25

Within an experimental error of ± 8 % the values of (a) showed no dependence on the epi thickness within the range examined, indicating that

the thickness effective for S.R. and the thickness deduced from IR-reflection is approximately the same ^

)

According to an early study of Hertz /67, the radius of the contact

area resulting from a spherical probe (radius A, modul of elasticity E>i

)

elastically pressed onto a flat medium (elasticity modul E2) by a force F

is given by

a = 1,1 ^ '•A

(3)

If the S.R. -contact mainly follows the laws of elasticity, the ratio

of the effective radius for two loadings F-^ and F2 is given (independently

on orientation) by

a (F^)

^2

(4)

The result derived from the measurements show a very good agreement with

this simple theoretical model (table 2).

3. Measurement on (111) and (100)

3^1 Experimental

In order to compare different crystal planes of otherwise identical

material the following procedure for sample preparation was chosen: The

resistivity of a number of n and p-doped Si-slices (orientation (ill),

thickness 200 /um) with homogenous doping was measured by conventional

4 point probing. From the middle part of each slice we subsequently cut

two samples of 4 x 4 mm^. Taking one sample of each slice we stacked them

together and mounted them on a fixture under a certain orientation (figure 5).

The only difficulty showed up for depi less than 2 /um at (100) orien^

tation with 45 g loading, where obviously the pn-junction got leaky

giving rise to R(oo)-values lower than expected. The data for this

special case have not been considered in the evaluation for table 2.

140
I Then the sample block was polished ' in order to expose the desired

crystal plane as predetermined by the sample orientation and the angle on

I the mounting fixture. By repeating this procedure we finally got two cali-

'bration blocks, one with (111) and one with ( 100 )-surfaces, each consisting

I of 8 samples covering a range of 0,010 to 20 cm for n-type and 0,013 to

178 cm for p-type material^'^. Then S.R. -measurements were made with the

! two-probe arrangement of the ASR 100. The polishing procedure and measurejment was repeated a total of five times within three months.

I 3.2 Results

I The S.R. -data as received from the calibration blocks is given in

jfigure 6, Each point is a mean value of the five different measurements.

iFrom this we finally plotted in figure 7 the ^ -dependent correction factor

,as a function of resistivity using the different contact radii for (111)

land (100) as determined in section 2 for 1 iZcm n-material and assuming

these values to be valid for the whole resistivity range and p-type as

jwell.

4. Conclusions

From the data given in section 1 and from additional analysis of the

measured values we finally can summarize the following conclusions of our

jexaminations:

ta) The effective contact radius of our probes is a factor of 1,26 greater

jj on a (100) than on a (ill) surface (n-material).

jib) The spreading resistance on a (111) surface is always greater than for

I a (100) surface within the resistivity range of 0,01 to 20 cm. This

holds for n- as well as for p-type material. The difference is greatest

in the region of 1 ilcm, where we find a factor of 2,1 (n) and 1,8 (p)

respectively.

to) This behaviour can partially be attributed to the difference in the

effective contact radius.

i) There remains at least in the 1 ^2 cm region a clear difference in the

resistivity dependent correction factor between (100) and (111).

) The spread of the values from repeated measurements is much smaller

for (100) orientation than for (111)

We hope that these experimental investigation are of some use for

bthers dealing with S.R. -measurements and their theoretical explanation.

l' Polishing was done first with Linde A abrasive and a final finish with

li Syton polish.

y It was checked by X-ray measurement, that each sample surface had the

desired orientation within ± 2,5°«

141
5. References

[ ^ ] Mazur, R. G. and Dickey, D. H. , A Spreading Resistance Technique

for Resistivity Measurements on Silicon, J. Electrochem. Soc.

113 . 255 (1966).

[ 2 ] Gardner, E. E. , Schiamann, P. A. and Gorey, E. F. , Measurement

techniques for thin films, p. 258, Electrochem. Soc. (1967).

f3 J Keenan, W. A., Schumann, P. A., Tong, A. H. and Philips, R. P.,

Ohmic contacts to semiconductors, p. 263 » Electrochem. Soc.

(1969).

[ k J Kramer, P. and van Ruyven,L,J., The Influence of Temperature on

Spreading Resistance Measurements, Sol. State Electr. 15, 757

(1972).

[ 5 J Severin, P.J. Measurement of Resistivity of Si by the Spreading

Resistance Method, Solid-State Electron. 14» 247 (1971).

[ 6 J Hertz, H. , Uber die Beriihrung fester elastischer Korper und iiber

die Harte. Ges. Werke, Bd. 1 (Leipzig 1895).

[ 7 J Schumann, P. A, and Gardner, E. E. , Application of Multilayer

Potential Distribution to Spreading Resistance Correction Factors,

J. Electroch. Soc. 116, 87 (1969).

o) RsR. = -L

4a

( metal )

b) Rs.R. = Z • k(p) k(jf)

( semiconductor )

Figure 1. Schematic for S.R. of a circular contact area (radius a) on

a semi-infinite metal and a semiconductor with inhomogenous resistivity.

142
( Sum

Figure 2. SRM on n rTp structures

with (111) and (100) orientation but

with identical dopings.

Figure 3. Correction factor due to

d. distortion of the electric field I

° by a two layer configuration. (Two

probe arrangement with a spacing of

0 , 6 mm)

Figure 4, Ratio of the field cor- rection factor for a two layer

arrangement with P2 = °°. and P2 = 0 respectively (two probes with 0,6 mm

spacing)

ir-^

143
"t1 ) resp. ( 100)

Figure 5. Calibration block con- sisting of several samples with

different resistivities and (111) or

(100) surface orientation.

Figure 6. Spreading resistance for n and p-type material and for (111)

and (100) surface orientation. (ASR100, probe spacing 0,6 mm, two tungsten probes (tip radius 25 ym)

with a load of 20 g each).

k(5>: A < 1 11 >

< inn \

y A

-w y > 1—

® •

V

(E)

Figure 7. Resistivity dependent cor- rection factor derived from figure 6 with values of contact radius from

table 2.

144

,1
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

On the Calibration and Performance of a Spreading Resistance Probe

H. J. Ruiz and F. W. Voltmer

Texas Instruments Incorporated

Dallas, Texas 75222

In this paper, techniques are presented for material standards

selection for calibration purposes, materials and calibration block

preparation, and techniques for data collection and processing for

the spreading resistance probe. A description of the variation with

time of the calibration of a spreading resistance probe is presented.

Problems encountered with characterization of high resistivity p-type

silicon are discussed, and examples of the probe performance in the

characterization of germanium are also presented.

Key words: Automated resistivity measurements, calibration, germanium characterization, sample preparation, silicon characterization,

! spreading resistance, surface effects.

1. Introduction

I Spreading resistance measurements [1]^ are currently being used throughout the semicon-

^ctor industry to characterize semiconductor materials in the bulk [2,3], in epitaxial,

iffused, and buried layers [1], and in some cases in finished devices [4]. The method con-

: ists in measuring the total resistance of a metal-semiconductor point contact and relating

t through empirical calibrations of the bulk resistivity of the material.

Spreading resistance measurements today provide the most practical tool for characterping semiconductor materials, especially those involving n/n"*" and p/p structures. The

preading resistance, Rg, of a circular contact [5] of radius a on a material with resistivity p is given by

Rg = p/4a (1)

1 ibwever, it has been shovm [1] that the exact relationship between spreading resistance and

jpterial resistivity must be modified by an empirical factor K such that

' Rc = KRg (2)

ijiere R^ is the total electrical resistance between the metal probe and the silicon. Defending on the probe material used and the experimental conditions, several authors [6] have

pwn marked variations in the behavior of K as a function of resistivity. Nevertheless,

f.1 previous work seems to agree that the effective contact radius of the probe increases

j)wards low and high resistivity values for both n- and p-type silicon. In obtaining accuiite calibration data, the parameters of importance in achieving good accuracy and

igures in brackets indicate the literature references at the end of this paper.

145
reproducibility are sample surface preparation, temperature control of the samples, a good

set of bulk material standards whose resistivity has been determined by a different method

such as the four-point probe, and properly conditioned probes. Careful selection of material standards cannot be over-emphasized.

2. Equipment Description

2.1. Probes

Two different apparatuses were used in obtaining the data presented in this report.

One of the apparatuses was an in-house design with electrically activated mechanisms for

all moving parts. The probe tip material was an osmium-ruthenium alloy which has a 6 ym

tip radius and operated under a 20 gm load. The other spreading resistance probe had airaccuated relays for all moving parts, an osmium-tungsten alloy probe tip with a 25 ym

radius, and operated under 40 gm loading. The probe assembly and the stepping motor were

obtained from Solid State Measurements, Incorporated.^

2.2. Electronics

Two probes make contact with the material surface to be characterized. The probe

spacing is 600 ym. The sample to be measured is generally electrically floating and the

probes are biased at +10 mV and -10 mV. By measuring the current flowing between the

probes, one calculates electronically the value of R^, and a logarithmic amplifier provides

a signal proportional to the value of the spreading resistance. By adjusting the value of

Rq, the bias resistance for zero current flow, one can cover values of spreading resistance

from 1 f2 to 100 Mfi. The electronics are calibrated by shunting the probes with a 1% resistor of the appropriate value, and adjusting the electronics so that the appropriate reading

is obtained. Shunting resistors from 1 to 100 Mfi are available in the instrument. To avoid the erratic behavior of rotary switches in the calibrate mode, push-button switches

are used to activate mercury-wetted relays. Thus, in the calibrate mode, one can for ex- ample change the shunting resistor from 1 to 10 Kfi without having to go through the decades in between.

2.3. Data Processing

The signal in millivolts which is proportional to the value of the spreading resistance is digitized through a millivoltmeter , passed through an interface card, and fed into

an HP9810 minicomputer. The data can be on line converted to spreading resistance, resistivity, carrier concentration, and plotted simultaneously on either a linear or logarithmic

scale. A program is also available for providing on line single layer correction factors

when characterizing single layer epitaxial or diffused films. The data obtained from the

minicomputer can be stored in magnetic tape, punched tape, or IBM cards for further processing, as is the case when one performs multilayer analysis of the data.

3. Calibration Block Preparation

3.1. Material Standards Selection

Silicon wafers in the range .01 to 100 fi-cm were selected as potential material standards for calibration blocks. Using a 4-point probe for resistivity measurements, approximately 100 wafers were found in the desired resistivity range for both n- and p-type material. Out of these wafers, '^'20 were selected for each type as material standards for

calibration. The wafer selection was achieved through the following procedure:

(a) Each wafer was measured 10 consecutive times on 10 different occasions (a

total of 100 measurements) near the center of the wafer. For example, see table 1.

2 Solid State Measurements, Inc., 600 Seco Rd. , Monroeville, Pa. 15146.

146
(b) The measurements were corrected for temperature and thickness variations.

(c) Near the center of the slice, resistivity readings were made .5 mm apart,

and slices which exhibited more than 10% variation in the readings were

rejected as material standards. Spreading resistance measurements were

also used to determine which wafers had less than 10% microsegregation

of dopant.

(d) The resistivity value of the wafers chosen was the average of the 100

readings described in (a), and an attempt was made at obtaining a mini- mum of 4 different material standards per decade in resistivity.

3.2. Materials Preparation

The wafers chosen were individually waxed down on microscope glass slides. Using a

tiamond wafering saw, .5 mm x 1.0 mm x 20 mm bars were cut out from each wafer as indicated

'.n figure 1. One bar from each of the wafers selected as material standards was waxed down

in a 0° stainless steel block which was threaded for mounting under the spreading resistance probe. All of the bars were waxes down adjacent to each other and in order according

l';o resistivity to facilitate measurements to be made. Using a silicon carbide 1200 grit,

he samples were ground to the same thickness. Lustrox^ 1000 was then used to chemicallylechanically polish the samples until a scratch-free mirror-like surface was obtained.

Table 1. Example of Four Point Probe Readings Taken for

Material Standard Evaluation for Calibration Purposes

1 2 3 4 5 6 7 8 9 10

Sample 1 1 040 1.057 1 051 1.056 1.042 1.043 1.060 1.045 1.043 1.035 No. 2 1 030 1.053 1 055 1.054 1.053 1.034 1.052 1.051 1.042 1.035

11 3 1 040 1.059 1 059 1.062 1.051 1.044 1.051 1.054 1.052 1.036 4 1 .040 1.053 1 055 1.068 1.050 1.037 1.052 1.042 1.054 1.043 N-Type 5 1 050 1.060 1 051 1.065 1.051 1.037 1.056 1.051 1.040 1.040

(111) 6 1 050 1.060 1 058 1.058 1.060 1.040 1.048 1.048 1.035 1.034

7 1 046 1.055 1 067 1.050 1.051 1.046 1.059 1.048 1.042 1.037

8 1 050 1.056 1 057 1.060 1.054 1.042 1.045 1.050 1.045 1 .043

9 1 057 1.062 1 .054 1.049 1.055 1.039 1.049 1.043 1.048 1.041 10 1 055 1.068 1 .058 1.053 1.063 1.045 1.058 1.051 1.050 1.047

Average 1 0458 1.0583 1 .0565 1.0575 1.053 1 .0407 1.0530 1.0483 1.0451 1.0391

Average = 1.0497; Standard Deviation = .00695

4. Probe Calibration

4.1. Technique

j 4.1.1. Data Collection

' The calibration block containing the prepared bars is mounted under the probe apparatus

\)V spreading resistance measurements. Twenty measurements, one every 20 ym, are made on

kch one of the bars. The measurements are made automatically, the data is electronically

jransf erred on line to an HP9810 computer, and the computer computes the average value of

preading resistance of each bar, and stores it along with the standard deviation of each

&t of measurements. The process continues until all of the bars in the calibration block

Hve been read. The computer has stored the resistivity value of each one of the bars.

'

i'-trademark of Tizon Chemical Corporation, Flemington, New Jersey.

I 147
4.1.2. Data Processing

Once the measurements have been completed on the calibration bars, a linear least

square fit is performed on the logarithm of the spreading resistance and the logarithm of

the resistivity of each bar. A printout is obtained of the least square fit parameters of

the data and the correlation of the data points in relation to a linear fit. At the same

time, a plotter, on command from the HP9810 computer, plots the data points and the line

representing the linear fit of the points on log-log graph paper. An example of the type

of graphical display of the calibration data is shown in figures 2 and 3. Figure 2 corresponds to calibration data on n-type material, and figure 3 corresponds to calibration data

on p-type material.

4.2. Calibration Parameters

The expression for spreading resistance is given by

Over the range of interest, let us neglect the dependence of the empirical factor K on the

resistivity of the material p. We thus have

P = Y Rg (4)

where y is a constant. A linear fit through the calibration data points shown on figures

2 and 3 gives an equation of the form

Log p = A Log Rg + B (5)

where A is the slope of the line and B is its intercept (A and B will be called calibration

coefficients). For figure 2, the values of A and B are*1.025 and -3.466 respectively. In figure 3, A and B are .989 and -2.99 respectively. From the calibration coefficients we

can compute the resistivity of material of spreading resistance Rg through

p = IqS Rg^ (6)

4.2.1. Variation of Calibration Coefficients with Time

Weekly during the past two years, we have performed calibration runs of the spreading

resistance probe using the same calibration block. Figure 4 shows the statistical distribution obtained from the measurements made on each one of the different samples on the calibration blocks. One should note that the standard deviation of the measurements becomes

larger with increasing resistivity, specially in p-type material. Figure 5 shows a plot of

A and B as a function of time for three sets of identical probes. The places where the

value of coefficient A took a sudden deviation appeared to correlate very well with that

point in time in which the probes became erratic with an increased amount of scatter. After

the probes were replaced, the behavior of the calibration coefficients was back to "normal."

The model proposed in equation (3) implies either a linear relationship between Rg and p or

a functional dependence of K on p . In the range over which our calibrations are made, it

is important to know whether or not the linear relationship holds. In equation (5), the

value of A determined over 100 calibration runs is such that A = 1.000 is within the a limits of the frequency distribution of A. This implies that the linear model described in

equation (3) is valid. While we use the specific value of A as determined in the weekly

calibration runs for determining sample resistivity, it would be equally valid from a statistical point of view to set A equal to unity. However, our data definitely establish

that n- and p-type silicon behave differently. The difference in the value of B must be

due to a dependence of K on the semiconductor material, its orientation, and type. Figure

6 shows a variation of the calibration coefficients for different probe materials. Figure

5 corresponds to data taken with 25 ]sm radius probes made of osmium-tungsten alloy at 40

gms loading. Figure 6 corresponds to 6 ym radius probes made of osmium-ruthenium alloy with

20 gms loading. Figure 7 corresponds to histograms showing the frequency distribution of

148

1
coefficients A and B for both n- and p-type calibrations. Each set of probes that exhibited

a marked deviation in the calibration coefficients as shown in figure 5 was discarded. This

occurred after about 250,000 measurements.

4.2.2. Comparison of Two Probes

The performance of the two probes has been similar, except that the osmium-ruthenium

jprobe exhibits larger scatter in the high resistivity end, specially on p-type material.

Typical calibration factors for both probes are summarized below for p-type material.

6 pm Radius, 20 gms Load 25 ym Radius, 40 gms Load

Osmium-Ruthenium Probe Osmium-Tungsten Probe

A .992 .990

B -3.25 -2.950

% scatter at 70 cm p-type 'X'20% <5%

: The range over which A varied for the osmium-tungsten probe was from .91 to 1.08. For

,the osmium-ruthenium probe, the range of variation of A was from .90 to 1.07. The difference in B of the probes is indicative of the difference in the electrically active radius

,iof each probe.

5. Probe Performance

5.1. Characterization of N- and P-Type Silicon

In the resistivity range of .01 to 100 f2-cm, the performance of the probe was very

'jsat is factory on n-type material. Measurements obtained in this range were within 10% of

jineasurements obtained on the same material using other characterization technqiues [7],

'i.e., C-V measurements, 4-point probe measurements, etc. Characterization of p-type material had similar performance in the .01 to 10 Q-cxa range. For resistivities larger than

10 fi-cm however, the measurements were not as reproducible and were very sensitive to the

conditions of the sample surface. The empirical factor K in equation (2) has a different

value for p-type material than it does for n-type material. As can be seen from the calibration plots of figures 2 and 3, the parameter K is more sensitive in the high resistivity

ijCegion of both n- and p-type calibrations.

5.2. Problems with High Resistivity P-Type Silicon

We have observed that surface preparation of the samples can contribute considerably

lO error in the characterization of high resistivity p-type silicon. A mechanically

polished p-type high resistivity sample (^^70 H-cm) was used in the measurements to determine the effect of surface preparation on spreading resistance measurements. The sample

pas first measured as received and the point is the first one on figure 8. The sample was

then placed in boiling water for the amounts of time indicated in figure 8. At the end of

each time cycle, the sample was allowed to dry in air and reach room temperature before mea-

'jsurements were made. The bars in figure 8 indicate the range over which the data scattered,

jtt is important to note that neither an HF dip nor a boiling water bath affected the readliLngs obtained on a sandblasted piece of silicon from the same slice. This clearly indicates

jthat surface effects on a polished slice are a dominant factor in resistivity determination

|)f high resistivity p-type material. In an effort to determine if surface conduction was a lominant factor in the phenomena, the following experiment was performed. A piece of the

^lice being used in this experiment was sandblasted everywhere except for two circular areas

kbout 200 ym in diameter. The distance between the center of these areas was '^-600 pm, the

probe separation. It was believed that microcracks introduced into the surface this way

I'ould impede carrier motion along the surface. However, this did not occur and the behavior of this specially prepared sample was identical to that shown in figure 8. We also

iiad a slice cleaved in two pieces and placed on the sample holder such that each probe

^'ould fall on a different piece. The two pieces were far apart physically so that the only

149
current path was through the vacuum chuck. Again, the behavior was the same. In an attempt

to gain understanding of this phenomenon, the following experiment was also performed. A

high resistivity slice, p-type, was placed in an oxidizing ambient for various times. The

resistivity of the slice as determined by the spreading resistance probe was measured as a function of oxide thickness and the results are shown in figure 9. The measurement accuracy

of oxide thickness below 50 A was questionable; however, the data point out an interesting

surface phenomena. At this point, the only conclusive statement we can make about our observations is that we are not dealing with a problem of surface conduction, but rather a problem having to do with metal-semiconductor contacts which are markedly' affected by sur- face treatment or condition of the material. Again we must point out that we do not observe

this phenomena in n-type material up to "^150 Q-cm in resistivity. In performing our measure

ments and calibration on p-type material higher than 10 f2-cm, we have had to re-polish the

calibration block previous to any characterization of freshly polished material.

6. Summary

Techniques have been presented for the calibration of spreading resistance apparatus

and the preparation of material standards for calibration purposes. It has been shown that

with proper care in the material standards selection and preparation, one should be able to obtain an accuracy of 10% for measurements on both n- and p-type silicon in the range .01 to 100 J]-cm. However, for resistivities higher than 10 fi-cm, special attention must be paid

to surface treatment and condition of the samples to be measured. The relative accuracy of

the probe can be '^'l%, as has been shown by shunting the probes with a resistor of value between 10 and 10 KQ,, and observing that the variations in repeated measurements are ±.5%.

Potential problems have been outlined concerning the characterization of high resistivity p-type silicon. It has also been shown that the performance of the probe on germanium is comparable to its performance on silicon material.

7. References

[1] R. G. Mazur and D. H. Dickey, "A Spreading Resistance Technique for Resistivity Measurements," J. Electrochem. Soc. 113 (1966) 255.

[2] F. W. Voltmer and H. J. Ruiz, "Use of the Spreading Resistance Probe for the Characterization of Microsegregation in Silicon Crystals," 1974 Spreading Resistance Symposium, Gaithersburg , Maryland.

[3] A. F. Witt, M. Lichtensteiger , and H. C. Gatos, "Experimental Approach to the Quantitative Determination of Dopant Segregation During Crystal Growth on a Microscale," J. Electrochem. Soc. 120 (1973) 1119.

[4] H. J. Ruiz and F. W. Voltmer, to be published.

[5] R. H. Holm, Electric Contacts, pp. 11-19, Springer, Berlin (1969).

[6] P. Kramer and L. J. Van Ruyven, "The Influence of Temperature on Spreading Resistance

Measurement," Solid State Electronics 15 (1972) 757.

[7] Gregg Lee, Walter Schroen, and F. W. Voltmer, "Comparison of the Spreading Resistance

Probe with Other Silicon Characterization Techniques," Spreading Resistance Symposium,

1974, Gaithersburg, Maryland.

150
GLASS SLIDE

Figure 1. Technique for Obtaining Calibration Bars from Material Standards.

Figure 2. ^^-Type Calibration Curve - Figure 3. P-Type Calibration Curve -

I Spreading Resistance vs. Resistivity. Spreading Resistance vs. Resistivity.

151
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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Comparison of the Spreading Resistance Probe

with other Silicon Characterization Techniques

Walter H. Schroen, Gregg A. Lee, and Fred W. Voltmer

Semiconductor Research and Development Laboratories Texas Instruments Incorporated

Dallas, Texas 75222

j Range and precision of doping concentration data in silicon materials gained by the spreading resistance technique

litre compared to values obtained by other characterization methods. They include junction and MOS capacitance-voltage

echniques, mercury probe, four-point probe, incremental sheet resistance technique, ion microprobe, and optical

jTiethods. The comparison considers precision and resolution of each technique, range of silicon resistivities and layer

lihicknesses, experimental effort, analytical interpretation, and time and cost of data acquistion and evaluation. Examples are presented which demonstrate the range of applicability of each technique and how they can supplement

jach other so that they cover the total doping range of silicon devices.

Key Words: automation; bevelling; comparison; four-point probe; incremental MOS capacitance-voltage; ncremental sheet resistance; infrared spectrometer; ion microprobe; junction capacitance-voltage; lap and stain; mercury

jrobe; Schottky capacitance-voltage; scanning Michelson interferometer; spreading resistance.

'i

1. Introduction

' The spreading resistance probe has recently been widely applied as a means of determining semiconductor

[esistivity. Some uses to which it has been or may be put are shared with other measurement techniques. Thus it has Decome pertinent to review the general capabilities of the spreading resistance probe and its alternatives and, where

jossible, to make direct comparisons of the results of one or more techniques.

I Spreading resistance is presently employed for three general purposes: production control, measurement of

ijesistivity laterally across a silicon slice, and measurement of dopant concentration versus depth into a sample. The key

jiidvantage provided by spreading resistance for production control is its ability to probe small areas within an integrated

fircuit to measure a local resistivity value. In this application reproducibility is extremely important. For scanning across

l'i silicon slice, the probe measurements must be not only reproducible but also of high precision and volume resolution

:in order to detect micro-segregation or local oxygen content in crystals. The spreading resistance probe is the only tool

ivhich has sufficient spatial resolution to perform this function. Other papers presented at this Symposium discuss the

I (ipplication to production control and scanning measurements of the spreading resistance technique [1 to 6] *, thus this

|>aper is restricted to the comparison of techniques used to measure dopant concentration versus depth, commonly

lalled the dopant profile.

I This comparision is performed with two questions in mind. First, for a given measurement, which is the best |echnique to choose from a number of alternatives. Second, however, how may the capabilities of different techniques

be employed to supplement each other to provide a more complete or accurate measurement. A number of points of homparison are pertinent; they are listed in figure 1. Precision and spatial resolution have already been mentioned above,

ipor the present purpose, the range of silicon resistivity and the range of layer thickness which can be resolved are also

.important. Furthermore, it is useful to know whether or not the measurement process destroys the sample and to know

|he degree of effort required to obtain the experimental data and then to analyze it. Last and by no means least, is the

tost of equipment required for the technique, the cost of making the measurement and of analyzing the data.

155
A point worth mentioning is that the spreading resistance probe and many other techniques discussed here measure

electrically active dopants. For many investigations it is advantageous to supplement this capability with a technique

able to measure the total concentration, or active plus neutral dopants. The comparison of this paper will first be

concerned with techniques measuring only electrically active dopants; for the purpose of supplementing the spreading' resistance probe, it will then list briefly the capability of total concentration techniques. '

2. Capabilities and Limitation of the Spreading Resistance Probe

The local impurity concentration tj is inferred from the local measured resistivity according to the expression ]

n = l/piq^ln), '

where the mobility, m, is inferred as a function of the carrier concentration n, and p-| is the measured local resistivity. In the spreading resistance technique, the contact resistance of the small metal-semiconductor contact is determined and

related to the resistivity by the fundamental relation

y PO PI X C

'

s

I

^ I 2rn 2r,o t

\ where rg is the effective radius of the probe contact, determined by calibration with known resistivity standards. C is th^i "correction factor" [7] which reduces the measured resistivity p i to the true resistivity pg. ^

I! The spreading resistance probe lends itself to automated operation, data acquisition and data evaluation. A:

sophisticated probe is capable of operating as either a "one-point" or two-point probe. The descent rates on static; loading may be controlled independently for the two probes to ensure a constant and identical contact area for each

probe. The probes have been calibrated for silicon, and the linear slope of unity, when spreading resistance is plotted versus resistivity, verifies a constant contact area. A highly developed mechanical system allows stepping in 2.5, 5, 10, 25, 50, 100, and 250pm steps automatically, through a 1-inch translation. Smaller steps can be taken, but the] mechanical damage to the silicon owing to probe impact would overlap, and it is still debated whether actual measurement can be taken under these conditions. The entire mechanical control system is pneumatic, ensuring thai during electrical measurement of the resistivity, the system is otherwise in a quiescent state.

A constant 10 mV potential is applied to the probes after they contact the surface, and the current is measure

using a log converter which is linear over 8 decades. Standard resistors are used to calibrate the spreading resistance. The

calibration between spreading resistance and resistivity is obtained by measuring silicon samples of known resistivity and

from the resistivity and spreading resistance determining the contact area. The resistivity can be determined using either

a calibrated 4-point probe or by making Hall measurements. The precision of these calibrations depends on the homogeneity of the reference sample, which can be determined by qualitative spreading resistance measurements. i

1

3. Comparison of Profiling Techniques i in Reference to Sample Processing i

I Figure 2 lists five profiling techniques which are generally used for determining the concentration of electrically active dopants: spreading resistance, incremental sheet resistance, incremental MOS capacitance-voltage, junction

capacitance-voltage, and MOS and Schottky contact capacitance-voltage. In addition to these techniques, the four-point

probe and lap and stain techniques are listed for supplying reference points. Section 6 of this paper discusses supplementary techniques for determining active plus neutral dopants, namely the ion microprobe, several optical

methods, and the nuclear activation analysis.

I A comparison and overlay of the most appropriate and accurate profiling techniques is presented in figures 3, 4, and 5. (see also [8] ). The sequence of transistor processing steps is illustrated for typical impurity concentrations and 156 \
depths. The superposition of the techniques is shown at decisive processing stages: in figure 3, after the diffusion of the

buried layer, in figure 4, after epitaxial deposition, and in figure 5, after base and emitter diffusions. The symbols

Indicating the various techniques have not been selected as actual data points, but rather to indicate the qualitative

j;apabilities of the techniques. The connecting line has been added for clarity, but does not represent an actual

Theoretical model.

The most versatile technique is the spreading resistance probe. It is shown qualitatively as "uncorrected data," this

j-neans the data as measured by the probe and translated into concentration values as though each measurement were

;Tiade on a homogeneous sample. By applying a multilayer model analysis these data points can be brought into close [agreement with theoretical predictions and also with other techniques such as the junction CV data [7,9] . The spreading

I'esistance probe can cover the widest range of doping concentrations, it can be used to measure both very shallow layers

jand deep diffusions. It can probe close to pn-junctions and can measure both n- and p-type conducting material. It is the

pnly convenient technique to monitor buried layers and deep diffusions.

{ 3.1. Incremental Sheet Resistance Technique

The incremental sheet resistance technique for determining concentration profiles had been used extensively in the

)ast several years [10] for the identification of control problems in the manufacture of shallow devices (<1 /jm). The

nethod consists of measuring the sheet resistance after removing thin (about 200 A) layers of silicon by anodic

)xidation and stripping in HF. From the resistivity profile, a concentration profile is obtained by using suitable ponversion data, such as that of Irvin [11]. The incremental sheet resistance is an absolute technique since it compares

differences of resistivity data. It is the best technique known for measuring profiles in the high concentration regime and

i'|n extremely shallow layers. It fails, however, to measure concentrations lower than 1 X 10^^ carriers/cm'^, so that it is

Slifficult to probe close to junctions. The primary drawback of the technique is the long period of time necessary to perform the anodization and stripping experiments. An experienced technician may take at least one day to measure a

|*)rofile. The evaluation of the data can be automated, but little automation can be applied to the experiment itself.

3.2. Incremental MOS Capacitance-Voltage Technique

The relatively new incremental MOS CV technique [12] is capable of acquiring precise data in extremely thin

ayers, such as ion implanted layers and bases of microwave transistors. The technique is best applicable at lower doping

oncentrations, in particular concentrations where the incremental sheet resistance technique can no longer acquire data

i.e., at concentrations lower than 10^^ carriers/cm^). The incremental MOS CV technique removes thin layers of silicon

ly the growth of anodic oxide. MOS CV measurements are made after each oxidation. The oxide is then removed, a new

ixide is grown and another MOS CV measurement is made. The process is repeated enough times to acquire data for a

|f!omplete profile. For each MOS CV curve the maximum width of the space charge layer is determined and plotted

ijtersus Xg, the total thickness of silicon removed. The impurity profile is found by calculating the curve W^p (Xg) for a

(0ries of theoretical profiles. The profile whose Wm (Xg) curve matches the experimental curve, is taken as the correct

rtrofile. The difficulty with this technique is its very time consuming experimental procedure, which is even slower than

he incremental sheet resistance technique, and the instability of the anodic oxide. It turns out that only for aluminum

netallization is the anodic oxide stable enough for precise capacitance measurements. Processes have unfortunately not

et been developed to grow oxides stable enough for mercury probe contacts or gold ball bonds, either of which would

jcceierate the data acquistion. Another requirement of the incremental MOS CV technique is an extensive analytical

i|:omputer program to convert the depletion region measurements for concentration data. This analytical technique is

particularly demanding when very steep profiles are considered, such as a three order of magnitude change in loncentration over a depth of .2 /im [12]

3.3. Junction Capacitance-Voltage Technique

The junction CV technique is one of the most effective methods of determining the concentration profile in

i^pitaxial material. An automated real-time system is shown in figure 6; it permits acquisition of CV data, transfer of the

^ata into a computer, evaluation of the data for the plot of doping concentration vs. geometrical distance, and output of

|lhe data in printed form or by an x-y recorder. The expected profile as it relates to the cross sectional geometry of the

(ample-under-test, is shown in the upper left portion of figure 6. 157
'1

In addition to automated data taking, computer programs have been developed [13] which take into account

several corrections of the junction capacitance-voltage data. One correction is for the toroidal capacitance surrounding c. circular capacitor dot; the smaller the dot area relative to diffusion depth, the more important the contribution of thi toroidal capacitance. Another correction is the contribution of the capacitance caused by the space charge layet penetration into the heavily doped side of the diffused junction. In figure 7 the two corrections are seen to pull the

profile in opposite directions and in this sense are compensating corrections. In the example shown, the importance o1^ the corrections is that the resistivity of the epitaxial material varies from 3.1 to 3.7 ohm cm (18% variation) and th« thickness of the epitaxial material varies from 5.0 to 6.1 ijm at 10^^ carriers/cm~3 concentration (20% variation).

For efficient process evaluation, electrical data acquisition and evaluation should be automated through the largesl extent reasonable. Not only does automation save time, it also reduces the involvement of human operators anc

simplifies data retrieval. An example of an automated data reduction scheme is shown in the lower part of figure 6, Another more general example is given in figure 8. A coupler system connects standard laboratory instrumentation with

a programmable calculator and allows data output on paper tape; an x-y recorder displays the evaluated measurements,

3.4. Mercury Probe and Schottky Capscitance-Voltage Technique i A modification of the junctions CV technique is the mercury probe or Schottky CV method. It employs a mercury dot of precisely determined and reproducible area to contact silicon surfaces directly without the need of fabricating < junction. Consequently, it lends itself for investigating unprocessed material (except for cleanups) with regard to dopim

concentration and layer thickness. The method is thus nondestructive except for some possible but reversible mercury contamination of the semiconductor surface. The relatively minor limitations of the mercury CV technique are: A

back-side contact is required for the slice; the sample should be flat to the order of the mercury contact area; and th( operation is limited to the breakdown voltage of the Schottky contact. The Schottky CV and the MOS CV technique

are applicable only to thin or lightly doped epitaxial layers. When thick or heavily doped epitaxial layers have to b( measured, one has to resort to the junction CV technique where part of the layer is used up by the diffusion. It shoulc be stressed again that because of its nondestructive operation, the mercury contact or multiple mercury contacts lent themself for automated real-time on-line production control.

3.5. Examples for Comparison of Techniques

Figure 9 shows an overlay of actual data points for spreading resistance measurements, junction capacitance-voltagi

measurements, and mercury probe capacitance-voltage measurements. For the spreading resistance probe, both data "aj j

taken" and after multilayer analysis are shown. It can be seen that there is very good agreement for the surface value om.

the concentration for all three techniques after the spreading resistance data has been analyzed. The profile thei'

'

proceeds to show the epitaxial concentration and the interface of the epitaxial layer and the diffusion of the burie(

layer (see figure 7). There is also very good agreement between the three techniques for the definition of the epitaxia thickness and the slope of the buried layer. The dip of the concentration displayed by the analyzed spreading resistanol data is an artifact of the multilayer analysis and is discussed in other papers at this Symposium [7,9] . In brief, the dip iJ caused by an overreaction of the multilayer analysis to this steep increase of concer tration under the epitaxial layer, h j

addition, the multilayer analysis assumes that a circular contact is made between the probe and the silicon while ii, reality there are many microcontacts in an array. Since it is an artifact, this dip can be disregarded.

Figures 10 and 1 1 illustrate the outstanding capabilities of the incremental sheet resistance for determining profiled

in very shallow layers. This technique has been used in the past few years as a tool for ion implantation investigation]

and the development of models for doping profiles. Figure 10 shows the capabilities of the incremental sheet resistanol technique for ion implant boron modeling. A dense array of data points can be acquired in very shallow layers and aj

relatively high concentrations. The data points fit very well the model predictions developed by Prince anci Schwettman [14] . The technique has successfully identified small discrepancies between theory and experiments, suclf as indicated in figure 10 for the conditions of 1000°C annealing temperature at 30 minutes steam oxidation and thi choice of the segregation coefficient k = 10. On the other hand, figure 10 clearly exhibits the limitations of thi incremental sheet resistance technique. Carrier concentrations smaller than about 2-10^^ cm~3 cannot be resolved. Thij

technique is therefore not able to probe close to p-n junctions.

{

158
Figure 1 1 demonstrates the capabilities and limitations of the incremtnal sheet resistance probe for implanted

[arsenic and comparison with As implant models. The probe is able to detect the arsenic tail observed in ion implanted

arsenic layers and the relative immobility of this tail with annealing times and temperatures. As stated earlier, the incremental sheet resistance technique detects only the electrically active dopants. There is, therefore, a discrepancy

between the theoretical model, which accounts for the total amount of dopants, and the electrically active part of it. Models are presently being developed [15,9] to account for the percentage of electrical activation in implanted arsenic.

It is important that the spreading resistance values are "corrected" by the multilayer analysis [7] before they are jcompared to incremental sheet resistance data. Figure 12 underlines dramatically the shift of the original data points

''(crosses) towards the corrected values (diamonds and squares). There is good agreement between incremental sheet

[resistance and spreading resistance values after multilayer analysis has been applied to the spreading resistance data.

[Right under the surface, however, the spreading resistance technique (diamonds in figure 12) seems to suggest a

^{significant decrease in the phosphorus concentration. The probable origin of this drop is an effective reduction in carrier [concentration caused by the formation of a depletion region under the surface generated by the deposition of the

iprotective silicon nitride film. As figure 12 shows, the depletion region is partially reversed and eliminated

(square-shaped data points), when the silicon nitride film is removed. Consequently, this doping dip can be disregarded

as an artifact.

4. Small Angle Bevels for Spreading Resistance Probe

Figure 13 demonstrates the importance of the protective silicon nitride layer mentioned above. It is mandatory for

the extremely shallow bevels of angles of 0.3 degrees or less to have a very well defined edge between the original silicon •Surface and the slope of the bevel. It has been found that unprotected silicon slices, or silicon oxide-covered slices, may

jgive rounded interface edges. Silicon nitride covered samples, on the other hand, turned out to result in very

;/vell-defined sample slope edges when the films exhibited the correct hardness achieved by the right composition

laetween silicon nitride and silicon. Only with this well defined edge is it possible to probe very close to the surface, and

thus to measure the very high concentration parts of the doping layers.

5. Techniques for Acquisition for Singular Data Points

^1 Figures 3 and 4 mention two techniques which can supply singular data points for material characterization: The

our point probe and the lap-and-stain technique.

5.1. Four-Point Probe

l' The four-point probe measures the average resistivity or net impurity concentration of substrates or diffused layers,

t has been employed as an indispensable material characterization tool for many years. Only recently have test lUquipment, specimen preparation, measurement procedure, evaluation, and precision been subject to detailed hvestigation with regard to reproducibility, and has a concise description of the standard method for measuring

lesistivity of silicon slices with a collinear 4-probe-array been published by the ASTM [16]. The four-point probe

determines average resistivities from current and voltage measurements. The evaluation assumes layers whose lateral lUimensions are large and whose thickness is small in comparison to the spacing of the probes. For typical probe spacings,

ithis condition is amply met by diffused layers and also by 1 to 3 inch diameter wafers. If either the wafer thickness or

sj:he lateral dimension of the semiconductor sample is comparable to the probe spacing, correction factors must be

Applied [17]

5.2. Angle Lap and Stain Technique

It is the junction between opposite conductivity types where the angle and stain technique delivers an important

Hata point on the concentration profile for material evaluation. Lap-and-stain is destructive. The semiconductor sample,

(vhether large or small, is affixed to a rigid support, whose surface angle (i.e., perpendicular to its long axis) may lie in

'he range from 90 degrees to approximately 0.1 degree, and this support is held in alignment with a polishing plate by

I 159
use of a precision collar. Using the silicon nitride overcoat shown in figure 13, the integrity of the bevel-surface interfac can be preserved. After obtaining a fresh, scratch-free polished surface at some specified angle which will reve; diffusion, ion implantation, epitaxial or even damaged layers, the- sample is subjected to a combination of illuminatio and chemical (usually acidic) etchants which will sharply distinguish such subsurface qualities as junction depth, abrup

concentration changes (in like-type material), shapes of penetration areas, and anomalous defects such as spikes, pipe or induced damage.

6. Techniques for Determination of Concentration

of Active Plus Neutral Dopants

6.1. Ion Microprobe

The ion microprobe is able to determine the profiles of diffused or ion implanted layers even for two-componer

interactive situations. Figure 14 gives an example of boron and arsenic implanted layers which show a significant effe( on the boron distribution after the arsenic implant, the so-called base retardation. The ion microprobe is an importar

analysis tool to acquire data for developing two-component interactive doping models [18] , and for determining tf- factor of electrical activation of dopants during annealing or diffusion heat treatments. The ion microprobe

destructive. ;

6.2. Optical Methods '

Two nondestructive techniques to measure the thickness of silicon epitaxial material are the dispersive infrare spectrometer and the scanning Michelson interferometer. The IR interferometry, using the reflection inteferen(

spectrum obtained on an IR spectrometer, has been reviewed recently by Severin [19] and has been exploit^'

extensively during the past decade. A standardized procedure based on I R interference has been adopted by ASTM.

Even though IR interferometer measurements have contributed considerably to simplify the measurement J' epitaxial films, in particular when based on a computerized system, the problem of mechanical wear resulting fro repeated cycling of the scanning mechanism in an IR spectrometer, remains. An automated scanning Micheisc interferometer has been developed [20] , based on computer handling of the required Fourier analysis. Since r restrictive slit mechanism is required and a reasonably wide angular aperture can be used without impairing performanc|

the radiation throughput of the system is quite large. All wavelengths are viewed simultaneously by the detector, and ! a detector noise-limited system, this multiplexing of the spectrum will especially improve the signal/noise ratio. Tl complete system for the measurement of epitaxial layer thickness utilizing the scanning Michelson interferometer is routine use for volume slice evaluation.

It should be kept in mind, however, that I R measurements are employed for epi films on buried layers of the sa conductivity type, and the value measured is somewhat within the high concentration side of the interface profile (s- figure 4, arrow "Reflected IR") since it is there that the absorption and reflection take place. IR measurements cann

read epitaxial layers on opposite conductivity type because there is no absorption in the depletion region.

7. Conclusions and Recommendations

When compared with other resistivity profiling techniques, the spreading resistance probe has been shown to bet^ most versatile. Its precision approaches that of incremental sheet resistance for shallow layers, yet can provide ent' doping profiles. It is rapid, and is easily adapted to automation. No special processing is required, other than am

lapping, and therefore does not suffer from profile changes owing to oxidation or junction formation as in the C

techniques. Spreading resistance profiles can be obtained from finished devices as well.

5 There are, however, several areas where care must be taken in making spreading resistance measurements. Samp; must be carefully and reproducibly prepared and the probe tips must be adequately conditioned. Adequate standar must be available for conversion of spreading resistance to resistivity.

'

160
Several explicit recommendations for further work include extremely shallow angle sample preparation, i.e. less lan 1 5', definition of procedures for reproducible surface preparation, establishment of calibration procedures as being

lefined by ASTM to provide multi-laboratory precision development of on-line multi-layer correction factors for bmplex profile evaluation, and reduction of probe spacing to 25 ^nn for probing smaller bars.

8. References

il] White, J., An automated spreading resistance

test facility, NBS/ASTM Symp. on Spreading

I Resistance Measurements, Gaithersburg, Md., June 1974.

i ,&] Ruiz, H., and Voltmer, F. W., On the calibration and performance of a spreading resistance probe,

NBS/ASTM Symp. on Spreading Resistance Measurements, Gaithersburg, Md., June 1974.

^ Goldsmith, N., Experimental investigation of two probe spreading resistance correction

factors for diffused layers, NBS/ASTM Symp.

on Spreading Resistance Measurements,

Gaithersburg, Md., June 1974.

Edwards, J., Spreading resistance and MOS C-V

radial resistivity profiles of silicon wafers — a direct comparison, NBS/ASTM Symp. on

Spreading Resistance Measurements,

Gaithersburg, Md., June 1974.

Voltmer, F., Bulk microsegregation in silicon, NBS/ASTM Symp. on Spreading Resistance Measurements, Gaithersburg, Md., June 1974.

Vieweg-Gutberlet, F., Investigation of local oxygen distribution in silicon by means of spreading resistance, NBS/ASTM Symp. on

Spreading Resistance Measurements,

Gaithersburg, Md., June 1974.

|] Lee, G. A., Rapid multilayer correction factors, NBS/ASTM Symp. on Spreading Resistance Measurements, Gaithersburg, Md., June 1974.

j] Schroen, W., The impact of process control on

parameter stability — a review, Semiconductor

1 Silicon 1973, ed. by H. R. Huff and

R. R. Burgess, (Electrochem. Soc, Princeton,

New Jersey, 1973), pp. 738-758.

Schroen, W., Application of the spreading

resistance technique to silicon characterization

for process and device modeling, NBS/ASTM

Symp. on Spreading Resistance Measurements,

Gaithersburg, Md., June 1974.

[10] Donovan, R. P., and Evans, R. A., Incremental

sheet resistance technique for determining

diffusion profiles, Silicon Device Processing, ed. by Ch. P. Marsden (NBS Spacial Publ. 337,

Washington, D.C., 1970), 123-131.

[11] Irvin, J. C, Resistivity of bulk silicon and of

diffused layers in silicon. Bell Syst. Techn. J. 41,

387-410 (1962).

[12] Kronquist, R. L., Soula, J. P., and Brilman, M.

E., Diffusion profile measurements in the base

of a microwave transistor, Solid-State El., 16,

1159-1171 (1973).

[13] Buehler, M. G., Peripheral and diffused layer

effects on doping profiles, IEEE Trans. Electron

Devices, ED-19, 1171-1178 (1972).

[14] Prince, J. L., and Schwettman, F. N., Diffusion

of boron from implanted sources under

oxidizing conditions, J. Electrochem. Soc. 121,

705-710 (1974).

[15] Shah, P. L., to be published.

[16] 1971 Annual Book of ASTM Standard,

(American Society for Testing and Materials; Philadelphia, 1971), Part 8, 697-711.

[17] Smith, F. M., Measurement of sheet resistivities with the four-point probe. Bell System Tech. J. 37, 711-718 (1958).

[18] Fair, R. B., Quantitative theory of retarded base

diffusion in silicon npn structures with arsenic

emitters, J. Appl. Phys. 44, 283-291 (1973).

[19] Severin, P. J., On the infrared thickness measurements of epitaxially grown silicon

layers, J. Appl. Optics 9, 2381-2387 (1970).

[20] Cox, P. F., and Stalder, A. F., A Fourier

transform method for measurement of epitaxial

layer thickness, J. Electrochem. Soc. 120,

287-292 (1973).

161
COMPARISON OF TECHNIQUES

FOR SILICON DOPANT PROFILING

• HOW DO THE CHARACTERIZATION TECHNIQUES COMPARE?

• HOW CAN THE TECHNIQUES SUPPLEMENT EACH OTHER?

Figure 1. Comparison of Techniques

PRECISION for Silicon Dopant Profiling RESOLUTION

RANGE OF SILICON RESISTIVITIES RANGE OF LAYER THICKNESS

SAMPLE CONSERVATION

EXPERIMENTAL EFFORT

ANALYTICAL INTERPRETATION

EQUIPMENT COST

TIME AND COST OF DATA ACQUISITION AND EVALUATION

SILICON CHARACTERIZATION TECHNIQUES

• CONCENTRATION OF ELECTRICALLY ACTIVE DOPANTS

SPREADING RESISTANCE

INCREMENTAL SHEET RESISTANCE

INCREMENTAL MOS CAPACITANCE/VOLTAGE

JUNCTION CAPACITANCE/VOLTAGE

MOS AND SCHOTTKY CONTACT CAPACITANCE/VOLTAGE

-r u FOUR POINT PROBE

Figure 2. Silicon Characterization Techniques LAPANDSTA'N

• CONCENTRATION OF ACTIVE PLUS NEUTRAL DOPANTS

ION MICROPROBE

OPTICAL METHODS

NUCLEAR ACTIVATION

Figure 3. Profile in Techniques Processing Steps — DUF Through Emitter Diffusion

— THEORY

A INCREMENTAL SHEET RESISTANCE O JUNCTION CV

SPREADING RESISTANCE (UNCORRECTED) L

:-Faoc]o-C)oa>GE)

1

SURFACE

1

1

DUF

I

1

<

A SUBSTRATE

1 1

1021

1020

1019

1018

1017

0

(Aim)

10l6

(\ POINT PROBE

1015

1014

ANGLE LAP AND STAIN 162
THEORY

O SCHOTTKY BARRIER OR MOS CV

SPREADING RESISTANCE (UNCORRECTED)

REFLECTED IR

-,1021

-1020

1019 i

1018 tt(-z

UJu

z

1017 8

1016

1015

1014

SURFACE

ANGLE LAP & STAIN

Figure 4. Profiling Techniques. Processing Steps - Dotted Line: After DUF, Solid Line: After Epitaxial Deposition

1021

SURFACE ANGLE LAP & STAIN ANGLE LAP 8. STAIN

Figure 5. Profiling Techniques. Processing Steps - Dotted Line: After Epitaxial Deposition, Solid Line: After Base and Emitter Diffusion

163
-V

DATA REDUCTION SCHEME

TEST DIODE -> CV

SLICE OR CAN APPARATUS

PUNCH TAPE CV DATA COMPUTER

TELEPRINTER

IMPURITY PROFILE

Figure 6. Epitaxial Layer Impurity Profiles Using the Diode Capacitance-Voltage (C-V) IVletliod

DISTANCE (tim)

Figure 7. Capacitance-Voltage Technique for Various Corrections

164
X-Y RECORDER

i OTHER L/C BRIDGE

OPERATOR

CALCULATOR

i r

BUFFER )

COUPLER 4

AMMETER

Figure 8. Multifunction, Interactive Data Aquisition and Evaluation Facility

TTY

PPT OUTPUT FOR

• FURTHER DATA

ANALYSIS

MULTIMETER MULTIMETER

EXPERIMENT IN PROGRESS

Figure 9. Multilayer Analysis Verification

SPREADING RESISTANCE

VS.

CAPACITANCEVOLTAGE

ANALYZED

SPREADING

RESISTANCE

^ UNANALYZED

SPREADING RES.

[71 JUNCTION

CAPACITANCE

VOLTAGE

0 Hg PROBE

CAPACITANCE

VOLTAGE

1017 r

<on

81016

165

1.0 1.5 2.0

DEPTH (um)
1.2 1.6 DISTANCE (Mm)

Figure 10. Predicted and Experimental Boron Profiles for 30 Min Steam Oxidation

Figure 1 1. Ion-Implanted Arsenic Profile, Model and Experimental Data

1020

1019

Z, 1018

1017

^—120 MINUTES

O \ •

• O \

• O \

>

r

°

y •

DOSE = 5 X 1015 cm -2 \

ENERGY = 120 keV - ANNEAL = 900°C • 10 MIN O 120 MIN — THEORETICAL >^

1 1 1 \

0.2 0.3 DISTANCE (Mm)0.4 0.5

166
Figure 12. Multilayer Analysis Verification

SPREADING RESISTANCE

VS.

INCREMENTAL SHEET

RESISTANCE

ANALYZED SPREADING

RESISTANCE NITRIDE

STILL ON SURFACE

a ANALYZED SPREADING

RESISTANCE NITRIDE

STRIPPED

-0- INCREMENTAL SHEET

-f UNANALYZED

SPREADING RES.

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1. DEPTH {[im)

Figure 13. Well Defined Shallow Angle Lap

4r167

565-448 0-75-12
10 Arsenic dose 5 E 15 -- 60 KV

900 C 10 min steam oxidation

1000 C 30 min anneal Boron dose I E 14 -- 80 KV

900 C 60 min anneal ^ L_ 1 1 I

f

\ I 0 1500 3000 4500 6000 7500 9000 1G5G:

flNGSTRDMS

Figure 14. Ion Microprobe for Ion-Implanted Boron and Arsenic

168
iMATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

;?roceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

!

I Preparation o£ a Lightly Loaded, Close-Spaced

I Spreading Resistance Probe and its Application

to the Measurement o£ Doping Profiles in Silicon

J.L. Deines, E.F. Corey, A.E. Michel, and m.r. Poponiak

IBM System Products Division, East Fishkill

Facility, Hopewell Junction, New York 12533

A commercially available spreading resistance probe,

the ASR-100, was modified to operate with lighter probe loading and smaller probe spacing. The advantages of

device structure profiling, increased resolution, and

reduction in the "correction factor" in the converted

impurity concentration profile are realizable with

smaller probe spacing. The effect of the probe

modifications on sample profiles and profile quality

is discussed for thin epitaxial layers, bipolar transistor structures, and ion-implanted layers. Sample

preparation, as influenced by the beveling technique,

is also shoisTi to have an effect on profile quality.

A novel m.ethod for precise measurement of very small

bevel angles is described.

Key words: Bevel angle measurement; correction factor; epitaxial

layer; impurity concentration; ion- implanted layer; neutron activation; probe loading; probe spacing; spreading resistance

1 . Introduction

The trend toward development of high density integrated circuits

as heightened existing problems in device characterization. Thin

pitaxial layers, ion- implanted layers and micron-size devices require

'ccurate and precise measurement of electrical and physical parameters,

;he spreading resistance technique has been shown to be an effective

Leasurement tool [1-6].* The commercial availability of an automatic

spreading resistance probe the ASR-100 [7], has made production control

isalizable by decreasing the time required for a measurement and

'screasing operator measurement error. The existence of an automatic

robe provides the potential for measurement standardization, which

;,js highly desirable as the need for accuracy and precision increases,

||' This paper describes efforts to improve the spreading resistance

jpasurement , determine optimum sam.ple preparation procedures, and

^btimize the capability of the commercial probe. Accordingly, a leveling procedure employing diamond paste and water was used to

|p.gnif icantly decrease data scatter by yielding smooth, beveled

prfaces and sharp bevel angles. Probe spacing was reduced to 25 jam,

prmitting device profiling, greater profile resolution, and a reduction

'ii correction factor used for computer correction of spreading resistance

fofiles. Probe loading was decreased to minimize probe penetration,

Figures in brackets indicate the literature references at the end of

jthis paper.

169
adding a high degree of sensitivity. A technique for more accurate measurement of the very shallow bevel angles required for thin layer resolution is

presented as an inexpensive addition to the spreading resistance probe. The

effect of these probe modifications is shown in example profiles. Correlatioi

of spreading resistance profiles of ion- implanted layers with neutron

activation analysis demonstrates the accuracy and validity of the measurement:

The correction program for spreading resistance profiles will not be discusse

here except to say that it was an APL program developed by S.M. Hu [8]

utilizing the multilayer approximation of Schumann and Gardner [9] for a circular contact to compute the resistivity profile and the Irvin's [10] curv

to convert to concentration.

2. Probe ^'Modification

2.1 Probe Spacing 1 The ASR-100 Automatic Spreading Resistance Probe provides the semiconductor industry with a machine capable of a high degree of reproducibility

and accuracy in measurements. Installation of the ASR-100 was followed by a period of experimentation to determine the ability of the machine and to

ascertain and implement modifications for improvement. Among the first point."

considered was a modification of the detachable probe mount to permit close

probe spacing. Schumann, et.al., [11] described the benefits of using a closi

probe spacing of the order of 12 ^m. Close probe spacing permits the profili]

and measurement of very small regions on device wafers. In addition, the clo:

spaced probe arrangem.ent requires a smaller correction factor when converting

the raw spreading resistance vs. depth profile to an impurity concentration

vs. depth profile. The as-delivered ASR-100 permitted varied probe spacing

down to 635 \im. Shorting due to the geometry of the probe mount prevented

closer spacing. A simple redesign of the probe mount permitted probe spacing

of 50 to 75 ]jm without shorting or probe tip modification. Grinding of the

tungsten carbide probe tips to a chisel-like geometry permitted 10 |jim spacing

The development of the close-spaced probe is illustrated in figure 1.

The effect of probe spacing on a sample with a thin (~.6 ^m) ion-implant

layer is shown in figure 2. In this case, probe spacing was varied from 20

to 606 |im. The large changes in the uncorrected profiles dramatize the effec

of close-probe spacing. Note that the uncorrected profile at 20 ijim spacing

is closest to the corrected profiles and that the neutron activation profile ' compares reasonably well with the corrected profile at 20 ]im. spacing. The j large probe spacing appears to accentuate deficiencies in the correction j theory, resulting in inadequately corrected profiles.

Figure 3 shows the effect of probe spacing on raw spreading resistance i profiles obtained in laboratory room light and shielded from room light. ? There is no observable difference between the close-spaced profiles. i Although junction depth is not affected by probe spacing, the photovoltage

at the junction is affected by probe spacing and lighting conditions.

Significantly more photovoltage is developed for wide-spaced probes than | for close -spaced probes . This effect can be used to advantage; wide spacing ' and room light can make junction determination easier.

The obvious advantage of close-spaced probes, the ability to profile i very small areas, is shown in figure 4. Three corrected profiles of an i epitaxial layer over arsenic and boron diffused areas and a non-diffused ; area are shown. The width of the diffused pattern was 5.0 m.il. All three ; profiles were obtained on a single bevel in the key area between the devices " measuring 20 mils. Probe spacing in this case was 30 ]xm. \

i

170
2.2 Probe Loading

Loading on the probe tips can affect profile quality, machine integrity,

nd profile reproducibility [12] . Light loading has an obvious advantage in

linimizing probe penetration that can distort or result in inaccurate profiles,

eyond this, excessive loading can change the probe calibration. This can be

;jeen if the condition of the probe tips is described. The probe tip is not a phere or single point of contact. Rather, it contains a number of sharp,

jmall tips which are necessary to penetrate native oxide and insure reasonable

iietal-silicon contact. Reduction in probe loading reduces the force with

hich the probe impacts the silicon, decreasing the chance of changing this

ulti-tip configuration and consequently the probe calibration. Light

oading can reduce probe wear, offering longer probe tip life. It can be

nferred that light probe loading and close probe spacing are features with a igh degree of interdependence. Probe loading was changed by adjusting the

osition of the probe arm weights. The load was measured by counterbalancing

gainst known weights.

The effect of probe loading on an N-type epitaxial layer over an n"*" ubstrate is shown in figure 5. The 40 gram load profile indicates a 0.25 ]im. hift in the apparent junction depth as compared to the 10 gram load profile,

n addition, all the uncorrected data points indicate a higher impurity

oncentration in the 40 gram profile than the 10 gram profile. This discrepancy in the uncorrected data and the junction depth is due to probe penetration

fr "punch- through . " The probe tip in the heavier load case penetrates the

ilicon and the measurement is influenced by the higher concentration layers

jelow the beveled surface. A larger correction factor compensates for the

larger effective radius of contact seen by the probe tip yielding corrected

jrofiles at very nearly the same concentration level. The lightly loaded

irobe produces less penetration, requires less of a correction factor, and

introduces minimal error in the junction depth determination. It is possible

n certain simple structures, such as shown here, to compensate the

Concentration levels for excessive probe loading and punch-through via the

orrection scheme. The effect of punch -through on very thin layers, however,

an result in gross error in the resolution of the junction depth and profile

hape. The effect of a 0.25 \im shift in X. for a 0.3 or 0.5 ^im layer would

e disastrous. ^

The effect of probe penetration on a complicated structure is shown in

igure 6, where the sample was P-type epitaxy over a diffused P-type region

n an N substrate. The uncorrected and corrected reference profiles of the

gram load are given in figure 6a and for t^^ 40 gram load in figure 6b.

|he surface intercept at 10 grams is 2.9 x 10 At/cc and at 40 grams is

1.3 X 10 . Note also the trend of higher impurity concentration in the

pitaxy and the lower peak height in the 40 gram profile. The 40- gram

Irofile shows higher epi concentration and lower peak height due to punchhrough, its effect on the radius of contact, and influence by the buried

layers. For this case the correction program is unable to yield an dequately corrected profile.

Calibration curves are influenced by probe loading. The calibration

nd sample profiles should be done at the identical probe load. Differences

n calibration due to probe loading for P and N-type (100) are shown in

iligure 7. The 40 gram load calibration is shifted downwards from the 10 gram

l^libration by a factor of approximately two in both the N and P standards,

'gure 8 goes further in showing differences in calibration resulting from

|rystal orientation. The P-type (100) and (111) calibration curves were

lound to be virtually identical for the different probe loadings. There were

ifferences in the N (100) and N (111) calibration for both probe loadings,

he 40 gram load appears to mask the differences below 0.4 ohm-cm. At 10 gram

pading the differences in the curves are evident throughout the range

jjeasured

! 171
3. Sample Preparation for Spreading Resistance

3.1 Beveling

a. Surface Preparation

Spreading resistance is an extremely useful and sensitive tool for

determining impurity concentration profiles, junction depth, etc. Its

sensitivity makes sample preparation an extremely important step in the

measurement process. Rounded bevels make the determination of the bevel

edge and zero depth measurement difficult. Excessively rough bevels can cause significant scatter in the data, which is amplified when corrected.

The abrasive beveling medium most used in spreading resistance measurements has probably been 0.3 ^m AI2O- in water. Care in the beveling procedure can result in fine, uniformly abraded surfaces. Scratches or other

imperfections and irregularities in the beveled surface can cause appreciable

scatter in obtained data, particularly on profiles requiring high resolution.

Figure 9a gives the raw spreading resistance vs. depth profile of an N

epitaxial layer over an N substrate which was beveled by lapping with 0.3 ]xm

AI2O, in water on a frosted glass plate. The sample had been mounted with

glycol -phalate on a bevel block for lapping and transferred to the special

mandrel for mounting on the spreading resistance probe. Scatter in the data

is evident in this high resolution profile of 2 log cycles. The sample was rebeveled with water on a frosted glass plate which had been prepared by

working with a silicon slug and 0.25 ]im diamond paste. The excess paste was removed and the imbedded grit with water was used for beveling. The

resultant bevel edge was sharp, the bevel quite smooth, and scatter in the

data was significantly reduced as shown in figure 9b.

b. Bevel Angle Measurement

Shallow bevel angles in the order of 30 minutes or less are necessary

for satisfactory investigation of thin structures. Of critical importance

to such shallow bevel profiles is the bevel angle measurement. The

goniometer is not accurate enough to resolve these shallow angles. Tong,

et.al.,[13] introduced the Small Angle Measurement (SAM) apparatus as a means

of measuring shallow bevel angles with far greater precision than the

goniometer. Beyond this, certain modifications in the SAM technique have

been made to permit small angle measurements on any laboratory m.icroscope [14

Use of the ASR-100 microscope and rotatable stage facilitates the MSAM

(Microscope SAM) measurement and completely eliminates the need for the

specially constructed SAM apparatus. Measurement of the bevel angle at the

location where the profile was taken is now insured, thus increasing the

accuracy of the depth measurement.

The MSA^i apparatus is shown in figure 10. The ASR-100 rotatable stage

and sample mounting block can substitute for the base plate and protractor

assembly. A thin wire of diameter s_ is inserted within the barrel assembly

of the 3X measuring objective or any long working distance lens. During

normal microscope use, the wire and the wire image projected below are not

visible because the lens has a short depth of field. In angle measurement

use, the beveled sample actually yields two images of the wire, one reflected

off each of the flat and beveled surfaces. An angle measurement is made by

focusing on the images of the wire. Rotation of the sample causes a rotation

of the images, each rotating about its own axis. The images are aligned by

rotating the microscope stage until the side of one image barely touches the

opposite side of the other image. At this point an angle reference reading,

al, is recorded as in figure 11. The stage is rotated until the images cross over each other as in figures 12 and 13 and are aligned edge to edge on the

side opposite from that used for the reference reading, as shown in figure 14

A second angle reading, a2 , is miade here. The total angular rotation, a, is

calculated, a= al - a2 . The rotation angle a is converted to the sample

bevel angle 0 by t^e relation:

172
sin 0 = S , where d is

2d sin a

he distance from the wire to the sample bevel edge (0.805" in this case) and

is the width of the wire, 0.0153".

MSAM data on several shallow angle beveled samples is compared with

nterferometer and SAM data in table 1. The MSA>1 data is an average of ten

iieasurements taken oyer a period of ten days.

Table 1. Comparison of Shallow Bevel Measurement Techniques

ample Interferometer SAM MSAM* Ave 0 MSA^^ Ave % Dev

1 16 2

' 16.2' 16 3' 1 .41

2 22 7

' 23.3' 23 1

' 1 .61

3 52 0

' 52 .0' 51 6" 0 5%

* s = 0.0069 inches

d = 1 . 049 inches

The addition of a second wire parallel to, and a known distance from,

he single wire gives an effective increase in s_, enabling a wider range of

ngles to be measured with a single objective lens attachment.

4 . Summary

' Modification of a commercial spreading resistance probe to operate with

fmall probe spacing and light probe loading has resulted in more accurate

'rofiles requiring less correction than wide, heavy probes. The sensitivity

|f the probe has been increased and beveling procedures improved to reduce

Ijjata scatter. Shallow bevel angle measurement has been shown to be accurate,

iuick, and inexpensive.

5. Acknowledgement

The authors would like to express their appreciation to Dr. S. M. Hu for

|is comments and suggestions on spreading resistance correction and Dr.R. H.

lastl for the neutron activation analysis.

6. References

1] R.G. Mazur and D.H. Dickey, [5]

J. Electrochem. Soc, 115 , 255 (1966). [6]

t2] E.E. Gardner, P. A. Schumann, Jr.,

and E.F. Corey, Electrochem. Soc. [7]

Symposia Proceedings "Measurement

Techniques for Thin Films,"

April 1967.

3] D.C. Cupta, ibid, 116, 670 (1969).

[8]

4] C.K. Chu, ibid, ILS, 192c (1968).

R.C. Mazur, ibid, 1L4, 255 (1967).

D.C. Gupta, J.Y. Chan, and P. Wang, ibid, n6, 301c (1969).

Reference Manual and Operating

Instructions for the ASR-100

Automatic Spreading Resistance

Probe, Solid State Measurements,

Inc., 1971.

S.M. Hu, Solid State Electronics

15, 809 (1972).

173
[9] P. A. Schumann, Jr., and

E.E. Gardner, J. Electrochem.

Soc. , ne, 87 (1969) .

[10] J.C. Irvin, Bell Syst. Tech. J.,

41, 387 (1962).

[11] P. A. Schumann, Jr., E.F. Gorey

and C.P. Schneider, "Small

Spaced Spreading Resistance

Probe," Solid State Tech.

(1972) .

[12] P. A. Schumann, Jr., J.M. Adley,

M.R. Poponiak, C.P. Schneider

and A.H. Tong , J. Electrochem.

Soc. , n6, 150c (1969) .

[13] A.H. Tong, E.F. Gorey and

C.P. Schneider, Rev. o£ Sci.

Instruments, 43, 320 (1972).

J.L. Deines, E.F. Gorey and

M.R. Poponiak, IBM Tech.

Disclosure Bulletin, 15, #10,

"Measurement of Small~l^ngles

with a Microscope, " (1973).

Figure 2 Effects of probe spacing

on spreading resistance prof iles of

thin structures as compared with

neutronactivation analysis.

174

Figure 1 Close spacing

probe tip modifications.

DEPTH FROM SURFACE m)
Figure 4 Corrected spreading resistance profiles

of small device structures. Probe spacing 30 \im.

175
Figure 5 Probe penetration effects Figure 6 Probe penetration effects

as a function of probe loading on a as a function of probe loading on a simple N/N+ structure. complicated P-/P+/N- structure.

Figure 7 Calibration curves of (100)

orientation P and N-type silicon at 10

and 40 grams loading.

10-" 10-3 10-2 ig-l ,qO iqI ,g2 RESISTIVITY (n-cm)

176
Figure 9a Spreading resistance profile

utilizing 0.3 uinAl202 in water on a frosted glass.

igure 9b Spreading resistance profile

tilizing only water on a glass frosted

ith 0.25 urn diamond.

0 SURFACE

Figure 10 Microscope small angle

measurement assembly (MSAM)

SUBSTRATE PROTRACTOR

OPTIONAL ASSEMBLY

BARREL

SLEEVE

" BONDED WIRE WIRE RING WITH TAPE ACROSS LIGHT PATH RETAINER

BEVELING DISC

SCRIBED CIRCLE

AX

BASEPLATE REFERENCE LINE

ROTATABLE STAGE OF ASR 100 REPLACES BASE PLATE AND PROTRACTOR. 177
Figure 11 Photograph taken with MS/'i! system

showing double images (1 & 2) of wire. Images

are positioned edge to edge at this orientation

of sample stage: 91°. This is the starting point

of specimen bevel angle measurement. By a second

exposure, image (b-b') of sample's bevel surface

is also shown. NOTE: microscope focal point must

be changed between these exposures.

Figure 12 Double exposure photograph of wire

images (1 & 2) and sample's bevel surface.

Sample stage orientation is 72°. Dark band is

overlap of wire images.

Figure 13 Double exposure photograph of wire

images and sample's bevel surface. Sample stage

orientation is 54.5 ; wire images (dark band)

have crossed over each other.

Figure 14 Double exposure photograph of wire

images and sample's bevel surface. Images have

completely crossed and are positioned edge to edge. This is the final step of measurement.

Orientation is 44°. Total a = 1/2 x 47° =23.5°.

Specimen bevel angle = 69.5' where s = 0.0153 in.

and d = 0.0805 in.

178
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

A Direct Comparison of Spreading Resistance and

MOS-CV Measurements of Radial Resistivity

Inhomogeneltles on PICTUREPHONE® Wafers

J. R. Edwards and H. E. Nigh

Bell Laboratories

555 Union Boulevard

Allentown, Pa. 18IO3

Small scale (~ 50 |im) radial Impurity concentration

Inhomogeneltles In silicon wafers have been measured

using both the MOS-CV method and the spreading resistance

technique. The MOS-CV measurements were made using photollthographlcally defined 50 |j,m square capacitors placed

on 75 um centers and the spreading resistance measurements were made using a model 100 ASR probe on the same wafers after removal of the MOS capacitors.

A direct comparison between these methods Is presented for three specific types of (111) oriented silicon

wafers with an Impurity concentration range between 5 and

10 X 10l^/cm3. In addition^ a photograph showing the

direct effect of radial resistivity variations on the

dark field coring of a PICTUREPHONE® target Is Included.

Key words: Dark field coring; MOS-CV techniques;

PICTUREPHONE®; radial resistivity inhomogeneltles;

silicon resistivity; spreading resistance techniques.

I 1. Introduction

li In this paper we report the direct measurement of small scale (~ 50 |j,m)

ladlal resistivity inhomogeneltles in silicon crystals using the MOS-CV

pthod . In addition, spreading resistance measurements using the ASR-100

I'joreadlng resistance probe were done on the same wafers which allows a ilrect comparison between MOS-CV and spreading resistance measurements. In

||lie past, the spreading resistance probe technique has been used by several

Kperimentalists to measure small-scale radial resistivity inhomogeneltles

a silicon crystals [1,2]-'-. Since this technique is empirical, reliable

'jalibratlon Is necessary. Most Investigators use four point probe measurepnts for calibration, but the four point probe does not give adequate

.allbration for the small spatial resolution desired in studying the radial

ahomogeneities in PICTUREPHONE® target material or in IC's. In particular,

Y will demonstrate that the video shading which occurs in the dark field

ilsplay of silicon PICTUREPHONE® targets can be caused by substrate

ii

i

i''igures in brackets indicate the literabure references at the end of this

paper

179
resistivity variations in the target material as small as \0% over a distance

of 0 . 01 inches [3]

2. Experimental Procedure and Discussion of Methods Used

Although spreading resistance measurements can be made over a wide

impurity concentration range (lO^'^/cmS to lO^O/cm^)^ precise measurements

are more difficult for the low range. Fortunately this range is particularly well suited for the MOS-CV method [3j>'^] ^^^d is also the impurity con- centration used for PICTUREPHONE® target material. As a consequence, the

wafers used in this study were (111) oriented n-type silicon wafers with an impurity concentration 5 to 10 x 10l'^/cm3 (10-5 Q-cm resistivity). Both

float-zone refined and Czochralski pulled wafers were used.

The silicon wafers were chemically etched to remove saw damage and one side was polished using Syton polishing compound. An 1100°C thermal oxide

of 15OO-I8OOI was grown on the wafers after suitable chemical cleaning. The

MOS capacitors were made by vacuum depositing aluminum and subsequently

photollthographically defining 50 |j,m square pads on 75 M-in centers. This

choice of MOS pad size allows approximately 270 measurements on the diagonal

of the 0.850 inch diameter wafer used for PICTUREPHONE® targets. After the

MOS measurements were made, the aluminum and the SIO2 were chemically re- moved to prepare the wafer for spreading resistance measurements. Thus,

both types of measurements could be made without any heat treatment altering

the radial resistivity profile.

The C-V measurements were made at 1 MHz using a Boonton Model 7I-AR

capacitance meter. The choice of thermal oxide resulted in capacitance

values approximately 1/2 pfd or less which allows full use of the 1 pfd

range. The analogue output from the capacitance meter was recorded to 3

significant digits using a DVM and the data reduction was done by computer.

Since the MOS-CV method averages the impurity doping over a region about

1 |j,m below the surface, there are two different methods which can be used

to evaluate the Impurity concentration for absolute calibration of the

spreading resistance probe. In the first method, only two measurements are necessary for the max-min high frequency technique [3]: oxide thickness,

and the accumulation - Inversion capacitance ratio. This means that

absolute values of capacitance are not necessary, which in turn eliminates

absolute capacitance calibration. Only the linearity of the analogue output

of the capacitance meter is necessary. Because the thermal oxide is uniform

to ± 30I, only a single oxide measurement by a U-V Spectrophotometer is. necessary to obtain the oxide thickness. Since the MOS-CV method uses only

known constants and measured parameters, it is estimated that the precision

with this method is ± 2% and the absolute value of the impurity concentration calculated is 10^. This precision clearly allows determination of

impurity concentration inhomogeneities across a slice which vary ± 10^ over

a distance of 50 ^m. The second method of MOS-CV evaluation uses the change

of capacitance in the depletion region with respect to the applied voltage

in order to calculate the doping as a function of the depth. For this

measurement, the absolute value of the capacitance and the differential

change of voltage are needed 'in addition to the oxide thickness. The precision of this method is estimated to be ± 5^ with an accuracy of 15^.

Since the MOS-CV measurement techniques complement each other, a high

degree of precision with a spatial resolution of approximately 25 M' is

assured

When the spreading resistance probe is calibrated relative to the MOSCV measurements, a precision of ± yfo is possible for the spreading resistance

measurements using the ASR-100 spreading resistance probe on chem-etched,

Syton polished silicon wafers. In comparison, we observed that the precision,'

and reproducibility for the probe is only ± 20^ to 30^ on a mechanically

lapped surface.

180 I
Using the wafers calibrated by the MOS-CV, it was found that additional

lyton polishing allowed the sample to be reused as a standard. This is

mportant when considering day-to-day calibration of the spreading resistance

srobe. Several other factors were observed which affect the precision of the

preadlng resistance technique ^ the primary one being the probe wear. It was

ound that a 5^ deviation from the control measurements indicated excessive

robe wear. This usually occurred after about ten thousand measurements on Syton polished surface. The probes could be regenerated by using the probes

in a mechanically lapped silicon wafer for a few hundred measurement cycles.

j 3. Experimental Comparison

I The ASR-100 spreading resistance probe was operated in the two probe

'ode with the probes spaced about 40 mils apart. The actual values of

jeslstivlty measured at 100 |j,m increments are plotted in figures 1-3 for a ypical float zone refined wafer^ a typical Czochralski pulled wafer and a peclally prepared Czochralski wafer. The next three figures show the re-

.istlvity data converted to impurity concentration using the MOS measurements

h calibration points. This change was done to enable a direct comparison to

he MOS-CV impurity concentration data shown in figures 7-9. Both typical

iafers show dark field coring and also clearly demonstrate variations of

"npurity concentration greater than ± 10^. Routine four point probe measurepnts would not reveal these inhomogeneitles, but both spreading resistance

|id MOS-CV do allow a direct measurement. As a direct example of the effect

p resistivity inhomogeneit ies , figure 10 shows a silicon PICTUREPHONE®

jlirget made from a wafer whose radial resistivity profile had been measured,

bte the dark field coring corresponding to the resistivity variations of

i 10^ for this Czochralski wafer.

In concluslonj it has been shown that the spreading resistance probe can

;asure the radial resistivity profile of a wafer to a precision of ± 3% fo3?

'properly prepared wafer. This has been verified using MOS-CV measurements,

id the effect on dark field coring has been demonstrated by an actual target

jiotograph

4. References

] Mazur, R. G., J. Electrochem.

1 Soc. Vol. Il4, No. 3, March

i 1967, p. 255.

•i] Gupta, D. C, Chan, J. Y., and

j: Wang, P., J. Electrochem. Soc.,

: Vol. 117, No. 12, December 1970,

p. 1611.

[31 Grove, A. S., Snow, E. H.,

Deal, B. E., and Sah, C. T.,

Jap. 3S, 2458 (1964).

[4] Kennedy, D. P., Murley, P. C,

and Kleinf elder, ¥., IBM J.

Res. Dev. (1968) p. 399.

l3

181
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184
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Investigations on Local Oxygen

Distribution in Silicon Single

Crystals by Means of Spreading

Resistance Technique

Fritz G. Vieweg-Gutberlet

Vacker-Cheraitronic GmbH.

Physical Laboratory

D-8263 Burghausen, West Germany

By means of spreading resistance measurements subsequent

to heat-treatments at approx. 450°C and llOO^C alternatively

the local distribution of oxygen in the donor state in Silicon

single crystals was examined. Oxygen striations have not been

found which is in correspondence to a distribution coefficient

of ko = 1.25 + 0.17 for oxygen in Silicon. The radial distribution of oxygen in the donor state is more or less uniform

except for an edge area of about 1.5 mm where the oxygen content

seems to be considerably lower. A very strong relationship

between electrically activated oxygen (donor state) and swirls

was found: in regions containing swirls a smaller amount of

oxygen was activated to the donor state. This result fits

De Kock's model describing swirls as consisting of vacancyOXYGEN-clusters.

Key words: Oxygen in Silicon, Silicon single crystals,

spreading resistance measurements, swirls.

'J 1 . Introduction

I More or less knowledge exists about the local oxygen distribution in Silicon

ingle crystals. In connection with swirls the question arises if swirls may be

llated to oxygen striations. The experiments carried out in the past either by

;ifrared transmission or by resistivity measurements have been handicapped by a very

or local resolution. We selected the spreading resistance probe to continue the

lectrical measurements from the past with the best resolution one can obtain up to

(W.

It is well known that oxygen in Silicon may be changed from the electrically

jutral (interstitial) into a donor state by a heat-treatment at 450°C. It is also

11 known that oxygen may be removed from the donor state by a heat-treatment at

igher temperatures and "crash cooling" of the sample, ^ij

Figures in brackets indicate the literature references at theend of this paper

185
The change between the electrically neutral and the donor state with respect

to the heat-treatment is detectable by resistivity measurements. In our experiments

we employed the spreading resistance probe for the resistivity measurements in order

to get highest local resolution.

Under the assumption that oxygen in Silicon does not change its local position

by diffusion during a heat-treatment at ] lOO^'C for approx. 90 minutes and for very

small differences in concentration, the local distribution of oxygen in form of

striations must be detectable by a change of the magnitude of the striations with

respect to the heat-treatment.

2. Procedure

A large number of samples of Silicon single crystals zone floated as well as crucible pulled was taken. The following procedure was applied to the samples:

The as grown sample was polished and measured

by spreading resistance.

The sample was heat-treated at llOo'^C (open air)

for 90 minutes. Within a few minutes the sample

was brought to room temperature ("crash cooling")

to avoid any activation of the donor state of

oxygen due to the 450°C temperature range.

After relapping the surface the sample was polished

and measured by spreading resistance.

The sample was then heat-treated at 1100°C

(open air) for 90 minutes and very slowly cooled

down to room temperature so that the sample was kept

for approx. 1 hour in the temperature range of

approx. 450°C. That means that oxygen will be

activated from the neutral to the donor state. After

relapping the sample was polished and measured by

spreading resistance.

Relapping of the sample after the heat-treatment was found to be necessary due

to the formation of a surface layer by the heat-treatment which is quite uniform in

resistivity. After removing this layer by If oping off a few micrometers the bulk

resistivity characteristic was found.

The spreading resistance measurements subsequent to the heat-treatment or on

the as grown material were taken in the same trace as correctly as possible. The

obtained spreading resistfmce profiles have been compared qualitatively by superimposing one over the other. A quantitative evaluation was done by converting the

spreading resistance readings into values of carrier concentration and comparing the

values obtained by crash cooling and 450°C treatment respectively.

The difference " ^ " (cm~-^) between the values obtained by heat-treating the

sample for a long time at 450°C and the so called "crash cooling" is related to donors generated by converting oxygen from the neutral into the donor state.

3. Results

In all our experiments we could not find any indication for oxygen striations.

The result is the same in cross section and longitudinal s:iction for zone-floated

as well as for crucible pulled Silicon. This can be explained by the results of

Yatsurugi et al . who claim from their experiments that the distribution coefficient

of oxygen is k^ = 1.25 + 0.17 [2] 186
For crucible pulled Silicon the radial distribution of the activated oxygen

iras found to be more or less uniform except for an edge area of approx. 1.5 mm.

"his is in agreement with Graff's results obtained by IR absorption at 9 /um waveength [3] . /

The average change of carrier concentration due to the oxygen activation

donor state) at 450°C is quite different for zone floated and crucible pulled

Silicon crystals. This is related to the different oxygen content in these crystals,

in most of the zone floated crystals no change in carrier concentration was

observable. For crucible pulled crystals having an oxygen content of about 10^7-10^^

items cm~^ ( IR absorption [4] |^5] ) the average change in carrier concentration

[iras approx. 10^^ cm~^ which corresponds to the results obtained by Fuller and Logan

rj] for a heat-treatment at 45U^C for approx. 1 hour. In this case the change in

:arrier concentration in the edge area (which is near to the skin of the as groim

|trystal) is approx. 10l3 cm .

Plotting the calculated values of donor generation (" ", era ^) in radial and

.xial direction of the crystal sample under test some areas have been found where

,he donor generation was much lower with respect to the other parts of the crystal,

'he distance between those regions of lower donor generation gave us the impression

.hat these areas might be related to swirls. Therefore the samples have been etched

or swirls applying Chromium Acid etch ^6] . A comparison between areas of a lower

'|.onor generation obtained by spreading resistance measurement with areas showing

jwirls after etching gave a 100^ correlation for swirls and areas of lower donor

|:eneration. The correlation is of such a quality that substructures in the density

If shallow etch pits in the swirl bands correspond to substructures in the spreading

jesistance curves.

4. Discussion of the Results

With respect to the literature there is no doubt that additional donors

enerated by a heat-treatment at 450*'C are related to oxygen. Therefore the local

istribution of the additional donors is related to the local distribution of

etivated oxygen atoms. Two effects obtained by our measurements must be discussed;

4.1. The Edge Area

In an area of approx. 1.5 mm from the. skin of the crystal a much lower amount

f activated oxygen exists. Therefore we assume that the oxygen content is lower than

n the entire crystal which is in agreement with Graff's results £3) • his may be due to out-diffusion of oxygen or Si-O^^ -formation on the Silicon surface

f

evaporation of oxygen from the melt in the miniscus area near to the liquidus

lidus interface. Indications are that all of these effects work together.

4.2. Swirls

In the swirl bands oxygen is bound to the swirl forming complexes in such a

ilorm that the single oxygen atom cannot be activated to the donor state. That means

lihat in the swirls oxygen is still there but will not be activated by 450°C heatj^jreatment. This is in agreement with De Kock's model describing the swirl forming

!]»mplexes as VACANCY-OXYGEN-CLUSTERS.

This also explains some of the difficulties in the comparison of the 9 /um

R absorption coefficient with chemically obtained oxygen contents because oxygen

lound to the swirlforming complexes does not show the 9^nm -resonance.

187
On the other hand our results may explain what the reason for the svirl

formation is: We found that oxygen is incorporated to the Silicon crystal in a uniform distribution. With respect to the rotation rate and the growth speed the

crystr.l will be supersaturated by vacancies in form of spiral bands. This

nonunif ormity of vacancy supersaturation generates the nonuniform arrangement of

vacancy oxygen clusters WHICH IS SWIRL.

A discussion of this mechanism will appear in a later publication.

Acknowledgement

I am greatly indebted to ray coworkers P. Siegesleitner (spreading resistance

measurements) and Mrs. A. Mayer (sample preparation and the heat- treatment

experiments )

I also have to express my thanks to my colleagues at Wacker-Chemitronic for

providing me with samples and for critical discussion of the results.

This work was supported by the German Federal Ministry of Research and

Technology, contract Nos. NT 381 and NT 506.

5. References

[l] Fuller and Logan

J. Appl. Phys. 28 (l957)

p. 1427

^2] Yatsurugi , Akiyama, Endo and

Nozaki

J. Electrochem. Soc. 120 (l973)

p. 975

Graff, Grallath, Ades, Goldbach

and Tolg

Solid State Electr. I6 (l973)

p. 887

[5]

ASTM, F 121-70 T Annual Book of Standards,

part 8 (1973).

The American Soc. for Testing

and Materials

Kaiser and Keck

J. Appl. Phys. 28 (l957)

p. 882

Method of Test for the Detection

of Swirls and Striatlons in

Chemically Polished Silicon Wafers,

ASTM Standard, to be published.

188
O 1.0 2.0 3.0 4.0 5.0 6,0 7.0 8,0 9.0 10.0 POSITION (mm) '

jFig. 2 Spreading Resistance Profiles of Trace A (fig. 1)

Profile "a": 1100°C, 90 minutes, "crash cooling"

.Profile "b": 1100°C, 90 minutes, slow cooling (approx. 1 hr. for 450°C)

II

0 1.0 2 0 3.0 4.0 5,0 6,0 7.0 8,0 9,0 10,0

j POSITION (mm)

3 Difference "A" (donors cra""^) calculated by deducting carrier concentration

med from profile "a" from carrier concentration of profile "b" of Fig. 2.

189
I

enPiM

<:

1.0 2.0 ao 6.0 70 8.0 90 100 POSITION (mm)

-3

Fig. 4 Comparison of "A" (donors cm ) profile of figure 3 with the swirl-pat ;n obtained by etching the sample. The two horizontal lines in the photograph ind: at the spreading resistance probe traces.

9 lO'"-

-.14,

S S s

0 1,5 10

S S

20 30 40

-10'

10"

-10"

49.5 51 0["

Fig. 5 The Radial Profile of donors generated at 450°C equivalent to the oxyg

distribution. Note the edge area of approx. 1.5 mm. and the swirl bands mark^

190
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Use of the Spreading Resistance Probe for the Characterization of Microsegregation

in Silicon Crystals

F. W. Voltmer and H. J. Ruiz

Texas Instruments Incorporated

Dallas, Texas 75222

A technique for using the spreading resistance probe to quantitatively characterize microsegregation in single crystal siUcon is presented. For the first time, the use of Fourier

Transformations of the resistivity is developed to provide accurate quantitative information as to the periodicity and amplitude of the various components giving rise to the resistivity variations. It

is demonstrated that the probe is reproducible and is capable of measuring fluctuations in resistivity to ±1 percent, which is well below the normally observed microsegregation. Examples

of the use of the technique are given by characterizing microsegregation in two Czochralski

grown crystals and one modified float zone crystal. The periodicity of the principle resistivity fluctuation of the Czochralski grown crystals is evaluated by Fourier transform analysis and

agrees well with the anticipated fluctuations in impurity incorporation based on growth

parameters.

Keywords: crystal growth; Czochralski-, Fourier transform; microsegregation; resistivity characterization; siUcon; Spreading resistance.

I The growth of doped single siUcon from the melt or by the floating zone technique results in periodic variations

ji impurity incorporation, the magnitude and frequency being determined by the impurity species and growth

I nditions. Recently, the spreading resistance probe has been used to qualitatively characterize the fluctuations. [ 1 ]

this paper, a technique is presented for the first time, to use the spreading resistance probe in conjunction with

Durier transform analysis to quantitatively characterize the impurity microsegregation.

i A number of 2000 gm, 2" diameter phosphorus doped (nominally 0.8 ohm-cm) sihcon crystals were grown by

»? Czochralski technique under various growth conditions (viz. crucible and seed spin, pull rate and thermal

vironment) for characterization of microsegregation of the dopant impurity. Material was pulled from melts heated

' radio frequency induction and by radiant heat from resistance heaters. The Czochralski crystals were principally

jpwn in the (111) direction, although crystals were also grown oriented along the <100> and (115) directions,

bsphorjs was chosen as the dopant impurity because of its relatively low effective segregation coefficient (.45) Impared with boron and therefore its enhanced microsegregation. In addition, a crystal was grown by the modified

lating zone technique for comparison. The growth conditions included variation in pull rate from 2.75 to

. 9 cm/hr and seed rotation rates from 1 rpm to 75 rpm. The crucible was counterotated at 10 rpm for the most of

'< crystals.

(. "

^gures in brackets indicate the literature reference at the end of this paper.

1. Introduction

2. Experimental Technique

2. 1 . Crystal Growth

191
2.2. Sample Preparation

The crystals as grown were approximately 12 inches long and 2 inches in diameter. Axial slabs 1/2 inch long were cut from the crystal at one inch intervals for axial microsegregation characterization of spreading resistance, and

for interface delineation by etching. The configuration and location of the slabs are depicted in figure 1. Slabs were

taken at intervals to determine the influence of fraction sohdified on the microsegregation. In order to allow for single

point spreading resistance measurements, the slabs were chemically-mechanically polished on one side and a gold

ohmic contact formed on the other side. The backside gold contacts were flash evaporated directly on the cleaned back surface. The contact resistance of the gold-silicon interface was negligible when compared with the spreading

resistance contact.

2.3. Spreading Resistance Measurements — The Apparatus

Single point spreading resistance measurements using a modified Solid State Measurements^ mechanical prober

station and TI control system and electronics (figure 2) were made on samples from various positions along each of ji the crystals.

The probe tips were Tungsten-Osmium with a probe radius of 25 /zm and a loading of 40 gms. The value ofi^ spreading resistance measured is electronically fed to a minicomputer which is used for on line conversion of

spreading resistance to either resistivity or carrier concentration.

The sample is mounted on a copper vacuum chuck which is electrically isolated from any equipment. This allows us to use the vacuum chuck as part of the current path when making single probe measurements.

2.4. Spreading Resistance Measurements - The Technique

The spreading resistance measurements were made on samples approximately 2" X 1/2" X 1/16" cut from the

crystal as shown in figure 3 so that the axial resistivity could be profiled. The sample was placed on the spreading

resistance probe chuck with the gold side down and held fast with a vacuum. The probe chuck was electrically isolated and allowed a return current path for the probe bias.

A diagram of the locations of the measurements on the sample are also shown in figure 3 along with the interface demarcation. Because the solid-liquid interface in crystal growth is usually curved, single point probe measurements

were made to optimize the spatial resolution. Use of two probes would have resulted in measurements which gave the average resistivity of the regions being sampled by the two probes. Alignment of the probes coOinear with the growth

direction is critical to insure accurate determination of the spatial frequency. A misalignment would increase the apparent periodicity of the striations. Accuracy of the alignment is estimated to be better than 0.2 degrees.

The measurement sampling frequency was chosen a lO/um/step. A sampling frequency of 5 nm/stcp was alsoi; tried, but did not provide any more information than the 10/jm/step frequency which was finally chosen. The

distance over which measurements were taken ranged from 1.5 to 4.5 mm.

The measurements were done automatically at the rate of 10 measurements per minute. The data, either measured spreading resistance or computed resistivity values, were stored on either magnetic or punched paper tape.

It was subsequently transcribed to data cirds for processing on an IBM 360 using an FFT (Fast Fourier Transform)

program. The data were also plotted such that any abnormal points (such as those caused by dust, scratches, etc.)) could easily be corrected in the data card file before the FFT program was run.

2.5. Spreading Resistance Measurements — Reproducibility

In characterizing microsegregation using the spreading resistance probe, one is concerned with measuring small fluctuations in the resistivity over small dimensions. To determine the instrument's capabiHty, three experiments were; performed; the first to establish the variations inherent in the electronics of the apparatus; the second to establish the variations inherent in the mechanics of the apparatus; and the third, to estabhsh reproducibility.

The first of the experiments consisted of connecting a 1000 ohm resistor across the probe input to the log detector and cycling through a series of pseudo-measurements. The results of this sequence of measurements are

^ Solid State Measurements, Inc., 600 Seco Rd., Monroeville, Pa. 1 5 146 i 192 F
plotted in figure 4 as resistivity as though one were measuring a sample of uniform spreading resistance such that 2Rs = 1000 ohms. Fluctuations in the converted resistance (i.e., resistivity) were thus due to instabilities in the

electronics of the log converter and the A/D converter. As is apparent, the resistivity variation is less than ±0.5%. This

is more than an order of magnitude better than the resistivity variations due to microsegregation which are typically measured.

The second experiment was to measure the resistivity variations on a unifomi surface diffusion in order to determine if the resistivity variations measured in the virgin material were due to impurity variations or mechanical

instability of the probes. It was assumed that the diffusion surface concentration was relatively constant. The

diffusion was adjusted such that the resistivity after diffusion was approximately 0.1 ohm-cm on a 10.0 ohm-cm

substrate. The results, again plotted as resistivity, are given in figure 5. The results are only slightly more than ±0.5%

indicating the stabihty of the mechanical system. These measurements constitute a worst-case situation, and the probe

stabihty is Hkely to be even better.

The third concern is the reproducibihty of measurements of microsegregation where the resistivity fluctuations

are on the order of 10%. Two sets of resistivity measurement were made adjacent to one another, and the resultant

resistivity profiles are shown in figure 6. The reproducibility is apparent; only the absolute values are different owing

to the slight lateral displacement of the probes for the two measurements.

The results of these three experiments indicate that the probe as configured is adequate to characterize microsegregation in bulk silicon in a reproducible manner.

3. Analytical Technique

Earlier attempts to describe the microsegregation of dopant impurities in semiconductors on solidification have

been largely qualitative. Determining the frequency distribution has resulted from counting striations or resistivity

?! variations in plotted data. For very periodic functions, with a single dominant frequency, this technique yields reasonable results. In crystal growth, however, there are often a number of parameters, both thermal and mechanical,

which influence the impurity incorporation. Each of these parameters is likely to have a different frequency and

j hence the impurity distribution may be a composite of a number of frequencies. In order to grow crystal with

I uniform resistivity distribution, it is necessary to identify the source of the various resistivity fluctuations and this requires analysis of the composite resistivity profile. The technique presented in this paper for determining the

relative strength and the periodicity of the various components of the resistivity fluctuations is Fourier Transform

analysis.

The axial resistivity profile constitutes a complex spatially periodic function p(x). The fundamental frequency

components making up this function are derived from the temporally periodic conditions during growth. The

I temporal spectrum of the resistivity is thus obtained from

pCco)- / p'(x)ei"Xdx (1) /

p| The function p(cd) is complex and the spectrum is evaluated from

lp(w)l=Vp*(w) • p(w) (2)

iwhere p*(a)) is the complex conjugate of p(a;).

The actual integration was performed numerically using FFT algorithm on an IBM 360 computer.

! The non-zero average resistivity and the gradual change in the average resistivity owing to normal segregation give

rise to a large spectral peak at zero frequency (i.e., the transform of a constant is a zero frequency component to the spectrum). This peak complicates the evaluation of the spectrum. In order to minimize the problem, a linear least ^square fit to the resistivity was obtained and subtracted on a point-wide basis to ehminate all ramp and square wave

ibomponents of the function. Thus the actual resistivity function which is transformed is p'(x) = p(x) - p(x) where

3(x) is the actually measured resistivity profile and p(x) is the resistivity as determined by a least square fit to the

actual data. 193
4. Results

In this section, representative results of measurements made on several single crystals of silicon are presented.

The resistivity plots and transformed resistivity spectra are given for data taken on three crystals grown under varying

conditions. Two of the crystals were grown by the Czochralski technique and the third by a modified float zone

technique. In figure 7, the actual resistivity profile is shown for measurements made at the center and edge of one of

the crystals. This crystal was pulled at 13.7 cm/hr, with the seed rotated at 35 rpm and the crucible counter-rotated at 10 rpm. The sample was taken at g = 0.6, where g is the molten fraction remaining at the time of solidification. [2] The transform of the edge resistivity modified by subtracting the average as derived from a linear least square fit is given in figure 8. The obvious spectral line at 58.8 nm agrees well with the observed frequency on the resistivity plot, while the resistivity fluctuations corresponding to the 2000 /im peak are not as readily apparent. In this case, the 58.8 nm periodicity can be accounted for by the growth of crystal during one revolution to within 10%. This value is arrived at by determining the length of crystal grown in one revolution, i.e., periodicity = (seed pull rate ± crucible lift rate) ^ (seed spin ± crucible spin). The peak at 2000 fjm corresponds to approximately one minute of growth which is very near the thermal time constant of the crystal puller.

The resistivity measurements made on the second crystal, pulled at 1 1.0 cm/hr and with a seed rotation of 1 rpm

and a crucible counter-rotated at 1 rpm is presented in figure 9. The sample is taken at g = 0.6. The transform of this spectrum is shown in figure 10. Here again there is an obvious spectral line, however, at a wavelength of 875 fim,

although the low frequency peak 2000 ^zm is not present. The peak at 875 jum agrees within experimental accuracy to the calculated growth of the crystal in one revolution, viz 9\4 nm.

The resistivity profile of a modified float-zone grown crystal, as distinct of the Czochralski grown crystals

described above, is shown in figure 1 1. The growth conditions for this crystal were pull rate, 15 cm/hr; pull spin,

20 rpm. The transform of the resistivity spectrum is given in figure 12.

5. Conclusions

It has been shown that the spreading resistance probe can be used to quantify the resistivity microsegregation in

silicon crystals. Instrument noise is shown to be less than ±0.5% and measurement reproducibihty has been

demonstrated. An analytical technique is described which allows calculation of the fundamental frequencies which

contribute to the microsegregation. The results allow identification of those mechanisms which are dominant during

crystal growth in determining impurity incorporation, and determination of the relative strengths of those! mechanisms. A subsequent publication will discuss the results from a crystal growth point of view.

6. Acknowledgments

The authors wish to acknowledge the assistance of Roy O. Byrd in making the spreading resistance measurements.

7. References

[1] Witt, A. F., M. Lichtensteiger, and H. C. Gatos, "Experimental Approach to the Quantative Determination ofj Dopant Segregation During Crystal Growth on a Microscale: Ga Dope Ge, J. Electrochemical Society 120 1 1 19 (1973).

[2] See for example Pfann, W. G., Zone Melting, John Wiley & Sons, Inc., New York 1958.

194

DISTANCE

Figure 5. Variations in surface

resistivity of a uniform diffusion.

DISTANCE

q,4320

Figure 4. Variation in instrument output for 1 000 ohm ; 4300 constant impedance across input to electronics. (See text

- .4280

+1.0

.0695

.0690

.0685

-1.0 DISTANCE

Figure 6. Reproducibility of microsegregation measurements determined by measuring resistivity in two adjacent regions.

196
0.9

0.8

:0.7

>

; 0.6

0.5

)

>

: 0.4

0.3 _L

SAMPLE NO. 73-042-10

_L _L _L _L I 2.0 4.0 6.0 8.0 lO.O 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 DISTANCE X lO'^(MICRONS)

Figure 7. Axial resistivity of sample 73-042-1 0 measured at edge and center. (See text for growth conditions)

0.016 0.033 SPATIAL FREQUENCY (/im^)

Figure 8. Transform of edge resistivity shown in Figure 7.

0.049

197
>-

tozUl

0 0.0068 0.0136 0.04 SPATIAL FREQUENCY (^nrM , Figure 10. Transform of edge resistivity shown in Figure 9.

198
0.5 0.6

DISTANCE X lO'^(MICRONS)

Figure 1 1. Axial resistivity profile of modified float zone crystal. (See text for growth conditions)

0.031 0.062

SPATIAL FREQUENCY ifim^)

Figure 1 2. Transform of resistivity of float zone crystal.

0.093

199

565-448 O - 75 - 14

iNHiIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Effects of Oxygen and Gold on Silicon Power Devices

Jacques Assour

RCA Solid State Division

Somerville, New Jersey 08876

Several important features that make the two-probes spreading

resistance technique a unique process control tool for designing and

manufacturing silicon power devices are elucidated in terms of the effects

of electrically active oxygen and gold centers on the characteristics of

transistors, thyristors, and rectifiers. The effectiveness of the spreading

resistance technique is compared to other commonly practiced techniques

for the investigation of diffusion mechanisms of oxygen in homotaxial

NPN transistors and of gold in fast switching rectifiers and thyristors.

Key Words: gold in silicon, oxygen in silicon.

1. Introduction

The internal structures of silicon power rectifiers, transistors, and thyristors are laracterized by multiple diffused and/or epitaxially grown junctions ranging in depth from

D to 125 microns with doping concentrations varying from 10l3 to 10^-'- A/cm-^. The control

E diffusion and epitaxial processes used in designing and manufacturing these power devices

as relied mainly on two commonly practiced techniques. The first is angle lapping and

taining(l) to detect the presence and to determine the depth of a single junction or

Ijltiple junctions. The second is the measurement of sheet resistance by the four-probe

2thod, which is used in conjunction with the staining technique to determine average

jsistivities and surface concentrations of diffused and epitaxial layers. The intent is

Dt to discuss the reliability of each technique in terms of accuracy and reproducibility,

it rather to review their limitations as process control tools in a present day manufacjring environment.

The results of studies based on spreading resistance measurements have shown that the

imitations of the staining and sheet resistance techniques reviewed below can be satispctorily resolved by the two-probe spreading resistance (SR) technique. In this paper,

he unique features of the SR technique that aided the investigation of the effects of

ygen and gold centers on the internal structure and electrical characteristics of power

vices are discussed.

2. Limitations of the Staining and Sheet Resistance Techniques

The limitations of angle lapping, staining, and four-probe sheet resistance measurements

brrently experienced in a manufacturing environment are noted in Table I. It is no surprise

lat angle lapping and staining is operator-dependent, since this technique is considered by

pny as something of an art, and since it is greatly dependent on the topography of the lapd surface, chemical reaction of the staining solution, and relative doping concentrations

the adjacent layers. The factors influencing the accurate delineation of n/n+ and p/p+

Jtf fused layers are complex and little understood. Therefore, the delineation of multiple

fLffused or epitaxially grown layers in power devices is often fortuitous. The staining

pchnique is also time consuming in terms of measuring junction depth and recording data

jbr permanent reference.

[Figures in brackets indicate the literature references at the end of this paper,

ll 201
Because of analytical boundary problems, the sheet resistance technique is not readily

applicable to multiple layer structures, and consequently, special test samples of controlled

geometry are required so that consecutive diffusions or epitaxial growth process can be

monitored. This technique also inherently requires samples with areas 10 times larger than

the spacings of the probes in order to reduce the influence of geometrical correction factors,!

Therefore, this technique cannot be used to study manufacturing problems in single, practical,

power devices. The sheet resistance technique provides average values for a given volume

and is incapable of detecting micrononhomogenities . Therefore, it is incompatible with control requirements of current, sophisticated device designs. It is needless to add that the

above technique is cost prohibitive for diffusion profile studies in a manufacturing environment.

3. Calibration of the Spreading Resistance Probe

The spreading resistance probe used at RCA as a process control instrument has been

purchased commercially from Solid State Measurements. To date, over 400,000 points have

been recorded with excellent reproducibility and minimum maintenance. Sirice the calibration

of the SR probe is essential for accurate and reproducible data, the following procedure was

adopted to calibrate the Instriment. Several n- and p-type silicon wafers ranging in resistivity from 0,001 to 1000 ohm-cm were first profiled in bulk form by the SR probe for homogeneity. The resistivity of each wafer was then measured by the four-probe technique followii' ' ASTM Standard F84-72. The homogeneous n-type and p-type calibration samples were then lapped

with an alumina abrasive, AO #305, and profiled by the SR probe. Using the SR and resistivit

data, a least-square straight line was calculater to fit the data. The resulting calibration

curves relating the measured spreading resistance with resistivity data for n-type and p-type

samples are shown in Fig. 1. The reproducibility and accuracy of these calibration curves

has been found excellent.

Other surface finishing methods based on mechanical and chemical polishing of the calibration samples were also investigated. Although polished surfaces reduced the noise level

of the recorded data, these surfaces were found extremely sensitive to ambients and probe

pressure, thus resulting in nonreproducible calibration curves.

SR Profiles of Multiple Layer Structures

Figs. 2 and 3 show that the limitations of the staining and sheet resistance techniques

experienced in a manufacturing environment can be resolved by means of SR profiles. The SR

profile of a multiple epitaxial layer structure used in the manufacture of high voltage transistors is shown in Fig. 2. This structure consists of three epitaxial n/v/ir layers grown

consecutively on an n"^ substrate. This single profile yields complete and accurate data on

the width and resistivity of each epitaxial layer, including the resistivity of the starting n+ substrate. Clear delineation of the n/n+ and v/tt interfaces and the non-uniformities in

the resistivity of the v layer can be uniquely achieved with the SR probe. Without the SR

technique, angle lapping, staining, and sheet resistance measurements of two p-type control

samples would be needed to evaluate the n and v layers; the same techniques would have to be applied to the epitaxial structure to evaluate the t: layer. No information would be

available on the uniformity of the grown layers and on out-diffusion and auto-doping effects

at the various interfaces. The data available from the SR profiles of epitaxial structures,

when properly corrected for p-n junction effects, allow the accurate calculation of the !f breakdown voltages (2).

The second SR profile shown in Fig. 3, is that of an asjrmmetricai thyristor structure

profiled through the Tl surface. This device consists of four layers diffused into a homogeneous n-type silicon region. It is sufficient to say that a detailed evaluation of the

width and doping concentrations of all the active layers would have been a horrendous task

by any known characterization technique other than the spreading resistance technique.-

The next two discussions on the effects of oxygen and gold centers on power devices

can only be investigated with the spreading resistance technique because of its unique

ability to detect, jreproducibly , raicrononhomogeneities in complex diffused structures.

202
5. Effects of Oxygen on NPN Homotaxial Transistors

I A cross section of an NPN homotaxial transistor is shown in Fig. 4. This device is

fabricated by simultaneous diffusion of an n-type impurity from each side of a homogeneously

doped p-type base. A mesa is etched on one side of the wafer to define the emitter and exi)ose the base region for metal contacts. The starting p-type wafer is Czochralski grown,

joron doped silicon crystal. Inherent to their growth process, these crystals contain rela-

:ively high concentrations of oxygen atoms, approaching lO-^-^ A/cm^. It has been shown(3)

:hat under certain heat treatment cycles, the oxygen atoms form donor centers which greatly

-iffect the resistivity and lifetime of Czochralski grown n-type and p,-type crystals. The

Influence of oxygen donor centers on the resistivity of one sample from a p-type crystal

jifter heat treatment at 450°C for one hour in an H2 ambient is shown in Fig. 5. An SR profile

.n the radial direction of a 2-inch diameter wafer shows an initial resistivity of about 11

|)hm-cm. Infrared measurements performed on this wafer revealed a strong peak at 9 micrometers,

jzhich is characteristic of oxygen absorption. A concentration of approximately AxlO-^^ A/cm^

pxygen was determined from the absorption peak. After heat treatment, the SR profile in the

Game radial direction reveals several resistivity peaks with values exceeding 2000 ohm-cm.

j'he resistivity upgrading is the result of oxygen donor formation whose detailed mechanism

J.s not known, but it has been found (3) to be dependent on the parameters of crystal growth,

jliuch as heating or cooling rate, rotation rate, gaseous ambient, and crystal diameter. TherePore, as far as wafer processing is concerned, the device manufacturer is completely at the

fnercy of the impurities that the crystal grower has incorporated into the material. For

Oxygen, in particular, there is no way to remove what has been grown in. Consequently,

Jinpredictable non-uniform concentrations of oxygen donor centers can form in both the radial

jmd axial directions of p-type wafers. The spatial distribution and magnitude of the high

fesisitivity peaks shown in Fig. 5 were found by SR profiles to vary in wafers sliced from

;he same crystal.

The influence of resistivity upgrading on the structure of NPN homotaxial transistors

I'abricated with Czochralski crystals containing high oxygen concentrations is dramatically

.llustrated in Figs. 6 and 7. Fig. 6 shows the doping profiles determined from SR profiles

if an NPN homotaxial transistor before and after heat treatment at 450°C for one hour. The

i.oping profile measured from the emitter surface clearly delineates the base width and doping

oncentration, the emitter base, and base collector junctions. After heat treatment, however,

|he p-base has converted to an n-type region with no apparent junctions. Similarly, in Fig, 7 he doping profile measured from the base contact surface clearly delineates the width of the

ase region width and the base collector junction. After heat treatment, the p-base has

lonverted to n-type and, consequently, the junction appears displaced at the new p+/n boundary.

Sim.ilar profiles have been measured for several NPN transistor chips located in different

|ireas of a processed wafer. The rate of resistivity upgrading and conversion of the p-base

legion from p-type to n-type resistivity varied with time and is assumed here to be dependent

in the relative concentration of oxygen donor centers across the wafer as shown in Fig. 5.

ilhis phenomenon is shown in Fig. 8 for a transistor heated to 450°C. The SR profiles measured

rom the emitter surlace have been superimposed to illustrate the rate of resistivity upgrading

ind final conversion as a function of time in hours. In this sample, total conversion of the

iase region from p-type to n-type silicon occurred after seven hours. It has also been

Reported C3) that these oxygen donor centers can be neutralized by heating the crystal to

elevated temperatures. This phenomenon has been confirmed in several bulk wafers and processed

levices. In fact, the sample shown in Fig. 8 was heated to 1000°C for 60 hours to obtain the

(|R profile shown before heat treatment.

I Changes in the electrical characteristics of NPN homotaxial transistors with the type of

|iesistivity changes explained above may be summarized as follows; all of these changes lead

|0 yield rejects.

(1) Uniform resistivity upgrading in a device together with narrowing

of the base region results in breakdown from premature punchthrough.

': (2) Localized resistivity upgrading in the base region results in

!; high leakage currents, IecO*

1

i (3) Conversion in the base region from p-type and n-type resistivity

ii results in Vceq of zero volts.

203
(4) In all cases, transistors with high donor center concentrations

exhibit very low current gains as a result of poor minority carrier

lifetime in the base region. This result is also true in narrow base

transistors and has been substantiated for transistors heat treated

at 1000°C to neutralize the oxygen donor centers. In other words,

oxygen complexes precipitated in the base region can act as effective

recombination centers for electrons.

A closing note on this topic is the fact that NPN transistors fabricated with epitaxially

grown p-type bases with structures identical to those of the NPN homotaxial transistors

exhibit none of the oxygen phenomena discussed above,

6. Effects of Gold Doping in Power Devices

Gold is widely used to control the lifetime of minority carriers during the fabrication

of fast switching power devices. Despite extensive studies (4) of the characteristics of

gold doped silicon, there remain significant gaps in the understanding of the properties of

gold doped silicon. These gaps, or problems, have left the industry without a complete model

for gold diffusion into silicon. As a result, in a manufacturing environment, control of

gold diffusion is empirical and often elusive. Examples of the unsolved problems are the

accumulation of electrically active gold centers near the surfaces of silicon wafers, the

diffusion mechanism of gold through heavily doped n and p regions, and the lack of correlation between the total gold concentration and resistivity upgrading of n-type and p-type

silicon.

A typical example of gold accumulation near the surfaces of wafers of finite practical

thickness is shown in Fig, 9. These are SR profiles of a gold doped n-type wafer for various

diffusion times. The wafer has one mechanically polished surface and one lapped surface (12

micrometers alumina) . An oxide layer 1 micrometer thick was grown on both surfaces and then

removed from the polished surface only, A 508 gold layer was evaporated on the polished surface. The wafer was divided into several samples which were diffused at 870°C for various

times in an argon ambient. The initial and final resistivity values in the bulk are noted

in Fig. 9 for reference. The SR profiles show evidence of the accumulation of gold centers near both surfaces even though one surface was masked by a thick oxide layer. The region of

accumulation extends about 60 micrometers from each surface after 1 hour diffusion and de- creases to about 20 micrometers after 4 hours. Excessive gold accumulation near surfaces has

been observed (4), and the degree of accumulation, in homogeneous bulk wafers, has been found

to vary slightly with surface and heat treatment of the samples. The diffusion mechanism

responsible for the accumulation of gold has been explained (5) theoretically and shown to be

related to vacancy generation in the bulk of silicon wafers. The difficulty with applying

this model for production processes, however, is that it is nearly impossible to predict the

concentration of defects and the accurate generation rate of vacancies in wafers that have

undergone various diffusion, oxidation, and cooling treatments.

In practical devices, the degree of gold accumulation near the surfaces is further com- plicated by the differences in gold solubility in heavily doped layers. Gold appears to be more soluble in phosphorous doped regions as compared to boron doped regions. This property

is illustrated in Figs. 10 and 11. Fig. 10 shows the SR profiles of p+/n and n+/n junctions

fabricated in the same wafer before and after gold doping. The resistivity upgrading in the n region adjacent to the p+ junction is much higher than that in the neighboring n+ junction.

This result is indicative of a difference in the concentration of electrically active gold

centers diffused into the respective n regions. In other words, heavily doped phosphorous

regions appear to getter gold atoms more effectively than boron doped regions. It is interesting to note that regardless of the diffusion mechanisms occurring at the p+/n and n+/n

junctions, gold accumulation near the far surface is evident.

The above phenomenon is also illustrated in Fig. 11 for the case of a gold doped thyristor structure. The SR profile measured from the Tl surface is shown for the structure both

before and after gold doping. In this example, gold has been diffused separately from the

Tl surface and from the T2 surface. The resistivity upgrading in the n region when gold is

diffused from the T2 surface is much higher and more uniform when compared to the Tl surface.

The differences in the Tl and T2 SR profiles are interpreted as resulting from differences

204
.n gold solubility and diffusion mechanisms in the n+ and p+ layers.

Although gold is used primarily to control the lifetime of minority carriers, its

omplex diffusion mechanism through heavily doped regions of power devices influences other

mportant electrical parameters. In rectifiers, for example, excessive gold concentration

n the n region of p+/n/n+ structures causes increases in the forward voltage drop at nomilal current rating, and extremely short recovery time; the latter causes "ringing" in typical

switching circuits. On the other hand, lower gold concentration causes yield depression be-

;ause of long recovery times. In the case of gold doped thyristors, gold accumulation near

surfaces can cause a significant decrease in the lifetime of minority carriers injected from

:he cathode into the p base; this results in higher gate currents and di/dt power dissipation

luring turn-on conditions. Secondly, excessive gold concentration in the n region, even if

|listributed uniformly, causes unpredictable, high resistivity upgrading which leads to prelature bulk punchthrough breakdown. Thirdly, the forward voltage drop of thyristors in the

m-state is also influenced by gold doping, which greatly decreases the diffusion length of

'jainority in the n region.

7. Summary

The advantages and uniqueness of the two-probe spreading resistance technique as a rocess control tool for designing and manufacturing silicon power devices have been compared

o other commonly practiced methods. The spatial resolving power of the SR method has been

sed to elucidate the effects of electrically active oxygen and gold centers on the electrial structure and performance of transistors, thyristors, and rectifiers. It is shown that

or NPN homotaxial transistors fabricated from Czochralski grown crystals, oxygen donor

enters in the base produced by low temperature heat treatment upgrade the resistivity of

hat region or completely convert the base to n-type. Moreover, the diffusion properties of

old atoms and their selective accumulation near the surfaces of finite, practical structures

re illustrated with spreading resistance profiles.

References

1) Research Triangle Institute, Integrated

Silicon Device Technology Volume IV. . .

Diffusion by A. M. Smith, ASD-TDR-6 3-316

Volume IV, Contract No. AF33(657)-10340

Durham, North Carolina, February (1964).

(2) R. A. Sunshine and J. M. -Assour, Avalanche

Breakdown Voltage of Multiple Epitaxial

pn Junctions , Solid State Electronics,

16, 459-466 (1973).

;3) Fuller, C. S. and Logan, R. A., Effect

of Heat Treatment Upon the Electrical

Properties of Silicon Crystals , J. Applied

Physics 28, 1427 (1957).

(4) An excellent bibliography of the literature on the properties of gold-doped

silicon has been published by W. R. Thurber

and W. M. Bullis, Resistivity and Carrier

Lifetime in Gold-doped Silicon , National

Bureau of Standards, Washington, D.C.

AFCRL-72-0076 (1971).

^5) F. A. Huntley and A. F. W. Willoughby,

The Diffusion of Gold in Thin Silicon

Slices , Solid State Electronics, 13,

1231-1240 (1970).

205
TABI,E I LIMITATIONS OF ANGLE-LAPPING AND STAINING TECHNIQUE

1. OPERATOR DEPENDENT

2. UNRELIABLE FOR n/n+ AND p/p+ DIFFUSED JUNCTIONS

3. TIME CONSUMING

LIMITATIONS OF FOUR-PROBE SHEET RESISTANCE TECHNIQUE

1. UNAPPLICABLE TO MULTIPLE DIFFUSED AND

EPITAXIAL STRUCTURES

2. REQUIRES LARGE-AREA SAMPLES

3. PROVIDES AVERAGE VALUES OF A GIVEN VOLUME

4. COST PROHIBITIVE FOR DIFFUSION-PROFILE STUDIES

Figure 1. Spreading resistance calibration curves for n-type and p-type

silicon.

UJ |o3

s

E

^

-| II 1 MM 1 . 1 II 1 1 II 1 Ml 1 in 1 1 II lo-i 10-5 10-2 lO-l 10° 10' RESISTIVITY (ohm-cm)

102 l(

Figure 2. Spreading resistance pro- file of a multiple epitaxial layer

structure.

Figure 3. Spreading resistance pro- file of an asymmetrical thyristor

structure.

rZO 140 160

206
DIFFUSED EMITTER.

EMITTER METAL CONTACT

r- BAbtSE METAL CONTACT

HOMOGENEOUS

BASE

DIFFUSED COLLECTOR

Figure 4. Cross-section of an NPN

homotaxial transistor.

^COLLECTOR METAL CONTACT

Figure 5. A radial SR profile of a Czochralski grown, boron doped silicon

wafer before and after treatment at 450" C for one hour in an H2 ambient.

I

'

I

' I i-Lt '

I

I II

I

I

I

I

AFTER HEAT

' TREATMENT

INITIAL RESISTIVITY

14 16 Imm)ZO 22 24 26

Figure 6. Doping profiles of an NPN homotaxial transistor before and after heat

treatment at 450°C for one hour. Profiles

measured from the emitter contact region.

-20

BASE-i COLLECTOR 0 20 40 60 80 ICQ 120 DISTANCE FROM EMITTER SURFACE, X —(^m)

Figure 7. Doping profiles of an NPN homotaxial transistor before and after heat

treatment at 450°C for one hour. Profiles

measured from the base contact region.

20 40 60 80 100 120 DISTANCE FROM BASE SURFACE , X —(/xm)

207
DISTANCE FROM EMITTER SURFACE ,X I /iir)

Figure 8. SR profiles of an NPN homotaxlal

transistor as a function of heat treatment.

DISTANCE FROM POLISHED SURFACE, X ( ;im) Figure 9. SR profiles of gold doped silicon

as a function of gold diffusion time.
lATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium, 'roceedmgs of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

The Evaluation of Thin Silicon Layers

by Spreading Resistance Measwements^

Gilbert A. Gruber

Solid. State Measurements, Inc., Monroeville, Pennsylvania 151^6

and Robert F. Pfeifer

NCR Microelectronics Division, Miaraisburg, Ohio ^53^2

The spreading resistance measurement technique is the only one capable of provd.ding precise thickness measurements and detailed

concentration profiles on any type of active device layer or structure

formed in silicon on a routine basis. The methods employed in the

evaluation of thin layer structures of the type used for microwave

devices is discussed and the application of these methods to thin

Nlf*", P'^'NIf*" and P'''N silicon structures formed by combinations of

diffusion, epitaxy and ion implantation is illustrated.

Key words: Diffusion; epitaxy; ion implantation; microwave devices;

profiling; spreading resistance; thin silicon layers.

! 1 . Introduction

Important criteria for the successful operation of a silicon high frequency device

•e layer thickness and impxarity concentration profile of the device. One of the major

iroblems of process control in the development and production of this type device is

Valuation of these two important parameters. Techniques such as infrared interference

Dectroscopy, angle lap and stain, anodic oxidation with differential four point probe

pasurements and various capacitance-voltage techniques, however, yield only limited

i[lformation on micrometer and submicrometer thick structures or are extremely time

'pnsuming. Only one method available today can provide precise thickness measurements

fid detailed concentration profiles on any type of active device layer or structure

brined in silicon on a routine basis, i.e., the automatic spreading resistance measurepnt.

; The purpose of this paper is to illustrate the application of the spreading resisPce technique to routine evaluation of thin N¥^, P'^'NN^ and P^ silicon structures

med by combinations of diffusion, epitaxy and ion implantation.

[ 2. Measurement Procedure

J The apparatus used for the meas-urements of spreading resistance for this study was

Model ASR-100 Mazur Automatic Spreading Resistance System (1) » ^. This system is

iiGim schematically in Figure 1 and features a two point probing arrangement with an

jWork was done at Westinghouse Research Laboratories, Pittsbiirgh, Pennsylvania 15235

|Solid State Measurements, Inc., Monroeville, Pennsylvania 151^

rFigures in parenthesis indicate the literature references at the end of this paper

ii

209
X-Y plotter and a digital acquisition system for computer processing. The "conditioned"

probe tips used for this study were each loaded to twenty grains and were spaced one-hundred

micrometers apart.

Calibration of the instrument is done by periodic measurement of a specially prepared

calibration block made up of a number of individual silicon samples of known resistivities.

The calibration samples were initially measured using a four-point probe to determine the

average resistivity of each. It was also foimd desirable to measure these standard sstmples

with the automatic spreading resistance probe in a radial fashion in order to determine

their doping uniformity since the accuracy and reliability of the measured sample resistivities is obviously no better than the calibration data to which the sample is compared.

The surfaces of the calibration samples were prepared by chem-mechanically polishing

with an alkaline colloidal silica solution on a plastic plate. A typical calibration curve resulting from measurement of standards prepared in this way is shown in Figure 2.

The samples to be measured are prepared by scribing, breaking and then mounting on a

bevelled polishing jig. A bevel is then chem-mechanical 1y polished down through the layers

to be measured. Surfaces prepared in this way are both smooth with no rounded edges and

are damage free. They therefore meet the most important criteria necessary for reliable

spreading resistance measurements, i.e. reproducibility.

After polishing, the sample was mounted on the mechanical subsystem of the probe, the

bevel edge aligned with the probes and the precise bevel angle measured with the microscope. The measurement cycle was begun and the spreading resistance plotted as a function

of position on the bevel edge. This position on the bevel is related to the actual thickness of the layer by:

T = NS sina

where T is the layer thickness in micrometers, N is the number of spreading resistance

points in the layer and S is the incremental step size in micrometers. For angles less

thaji approximately 15° then:

sinCL::! tanCL

therefore, since the tangent is measured directly, a convenient working equation is:

T = NS tanQ

A typical example of a profile of the kind obtained is shown in Figure 3« This is an example of a thin multiple epitaxial structxire measured with S = 2.5 micrometers per step and a tanCL = .020, therefore, each step across the bevel represents a 500A increment in the

thickness of the layer.

Once a sample is measured and a plot is obtained, the real advantage of this technique can be seen. The plot represents a map of the entire electrical structure obtained by the

various processing techniques employed. These "raw data" plots of spreading resistance as a function of position on the bevel surface can be used as process monitors without further

processing of the data, l^fhen necessary, however, these data can be converted to resistivities, by comparison with the calibration curve described above, and impurity concentrations by using the mobility data of Sze and Irvin (2).

3. Corrections for Insulating and Conducting Boundaries

Considerations of the geometric aspects of this raeasiirement require correction to the

value of resistivity obtained from measxarements taken in close proximity to either of the

210
:wo extreme cases of an insulating or a conducting boundary (3, ^, 5). For this study the

lorrection for the presence of an insulating boundary (a P-N junction) described by Dickey

k) and Mazur (5) was used. In this method the working equation for the correction of

'esistivity in the proximity of an insulating hcnmdscrj is:

jJcOTT. = ~ Rm

k(p) - 1 +

[liere Rm is the measured spreading resistance, /^corr. is "the corrected resistivity of a

ample at a particular point, "a" is the metal-semiconductor contact radius (3 x 10"^ cm.),

p" is the number of probes used in the measurement, kOO) is a measure of the "zero bias

larrier resistance" (4-) of the point being measured ana "C" is the geometrical correction

jactor for an insulating boundary. The parameter k is a function of the resistivity and

jan be determined by solving this equation for k(^) using the calibration data and the fact

ihat C = 1 in the absence of an insulating boundary. To apply this correction, an iteraive procedure is used. First, the resistivity, yO, corresponding to the measured resisance, Rm (assuming C == 1 and choosing a value for k^) corresponding to that resistivity)

iS found. Then a value of C is calculated from the equations of Dickey (^) given below:

C = 1 +J| In (D/2t) - 0.116 (t ^a)

or C In (2D/a) (t < a)

D" is the lateral spacing between a pair of spreading resistance probes (.01 cm in this

|Drk) and "t" is the thickness of the layer below the spreading resistance probes in centiters. From this data a value for ^corr. calculated. Then a new value for k(yO) is

sterrained for this new value otp. A few iterations are usually all that are necessary to

' ing the corrected resistivity value to within five percent of the previous value in the

eration procedure.

This correction is based on geometric considerations of the spreading resistance meapremcint. The following assumptions are made: 1. a perfectly circular contact of radius,

|l", 2. a perfectly insulating boundary, 3« a relatively uniform layer, k. no edge effects

jie to the pinching of the field as the probe approaches the edges of the sample and 5« an

jjcurate measure of the thickness at which the junction occurs. These assumptions do not

j)ld in all cases and are invalid in the vicinity of a junction. This procedure has the

flvantage, however, of being easy to apply and gives results that compare favorably with

iasurements made by other techniques (6, 7)«

The correction used for a conducting boundary is based on the work of Brooks and

-ttes (8). Since nearly all of the conducting boundary corrections are made to measiiresnts of lightly doped silicon layers on a heavily doped layer, e.g., an N-type epitaxial

yer on an I^r*" (N lO-'-^/cm.^) substrate, the substrate may be assumed to be a perfect conctor. A copy of the relevant correction curve is shown in Figure k. Here the ratio of

le corrected spreading resistance value Rcorr. 'to the measured spreading resistance Rm is

otted as a function of the thickness of the silicon above the conducting layer for a confct radius of 3 x 10"^ cm.

h. Results and Discussion

The example in Figure 3 above, is a "raw data" spreading resistance plot of a thin P'''N itaxial structure deposited at a pyrometer temperature of 1050°C. from a silane source on substrate (9). From this profile it can be seen that the spreading resistance ineases from the s\irface (the extreme left hand side of the plot) to the P-N junction (the

pdmum spreading resistance value). The spreading resistance of the N-type layer appears

latively uniform before dropping off to the substrate value. When these data are corrected

211
for the presence cf the P-N junction and for the conducting NN^ interface, the plot of con- centration vs. thickness shown in Figure 6 is obtained. Three rather interesting effects,

not apparent in the "raw data" plot, can be seen. First, the impurity concentration of the

region of the curve is uniform from the surface to the P-N junction. Secondly, a dip in

the concentration occurs at the M-fT*" interface and third, a steeper M to I>r*" transition gradient is seen at the N-N^ interface. Note again that none of these three effects is apparent from the uncorrected "raw data" plot. The uniform P"*" layer is typical for this type

of epitaxial growth and is expected. The "dip" in the impurity concentration at the N-N^

interface, however, is in contradiction to the normal case where the transition from a heavily doped substrate to lightly doped epitaxial layer occurs in a gradual fashion from

one concentration to the other. V/e believe the cause of this particular phenomenon is that

the N-type epitaxial deposition was purposely done in two steps in order to obtain the

steeper N to N+ transition gradient also observed. The first part of the layer was grown

with no dopant gas being injected into the reactor and so was doped only by the transported

and evaporated dopants from the substrates. After this initial growth which is designed to increase the abruptness of the to N-type transition, phosphine is injected into the gas

stream to dope the remainder of the layer to the proper impurity level. This belief is

supported by the series of profiles shown in Figure 6 which are results obtained by varying

the length of deposition time for the initial or undoped layer. This study was done using

silicon tetrachloride but other experiments indicate that the same relative result is obtained for the silane system. These are raw data plots and as such have not been corrected

for the presence of a conducting boundary as in the computer curve above, but the same effect is shoim. Curve A shows the effect of a zero time delay between silicon source gas

injection and dopant gas injection; and Curves B through D show the effects of delay times

of 1, 2 and 5 minutes respectively. As can be seen from the peak in Curve D, a higher resistance layer is formed at the N-N^ interface the longer the delay time. This peak in the

resistance is equivalent to a dip in the impurity concentration. The choice of proper delay time to give the sharpest N to N transition without forming this high resistance

layer, which would distort the electric field in this region, depends on the purity level

of the silicon source material and the backround purity in the epitaxial reactor.

The profiles shown in Figures 7 and 8 are the raw data plots of spreading resistance

and corrected impurity concentration as a function of layer thickness, respectively, for a

P"^ layer diffused into an N-type epitaxial layer grown on an N^ substrate. In Figure 8 the

gradual change in the concentration of the P"^ layer and the change in slope at approximately the midpoint of the layer which are not apparent in the "raw data" plot are typical for a boron diffusion done in two steps - a predeposition and a drive-in. Because each of

these steps was done under different source conditions, i.e, the predeposition from an infinite source and the drive-in from a limited source, the resulting profile is that of a double diffusion as shown. It is also noteworthy that the impurity concentration in the N region of this structure does not decrease as the M^N interface is approached and that the

N^ to N resistivity transition occurs over a wider region than seen in the previous example. Both of these effects are probably the result of the higher temperature used

throughout the growth of this layer, compared to that of the previous exainple, and the

subsequent diffusion of impurities from the substrate into the epitaxial la^'-er during both

the epitaxial deposition and the P-tj-pe layer diffusion.

The next example illustrating the use of the spreading resistance technique for profiling thin layers is that of a silicon P-K junction structure prepared by ion implantation followed by an anneal to eliminate damage. This strupture^is shown in Figures 9 and

10. The ion implantation was done at a B"*" dose of 6 x 10-^^/cm. The most interesting

feature to be seen from these profiles is the region of higher impurity concentration between the surface and P-N junction. Although this type of profile is not normal in the case of junctions formed either epitaxially or by diffusion, it is typical of junctions

formed by ion implantation (10). The position of the peak of this impurity profile and

the shape of the profile depends on the energy of bombardment and the crys tallographic

orientation of the silicon crystal during bombardment.

5. Conclusion

The automatic spreading resistance probe, by providing detailed evaluation of thickness and impurity concentration in thin layered structures has been shown to be iinique in

its ability to provide quick, reliable feedback on the effects of semiconductor processing.

212
General process features such as epitaxial resistivity uniformity and profile reproucibility can be monitored on a routine basis by use of the ra,w data spreading resislance profiles. In addition, computer processed resistivity or concentration profiles may

Is obtained from the spreading resistance profiles to be used by the device designer for

aterial evaluation and product improvement.

6 . References

L) R. G. Mazur and D. H. Dickey, J. Electrochem. Soc, ll^, 255 (1966).

2) S. M. Sze and J. C. Irvin, Solid State

J Electronics, 11, 599 (1968).

b) E. E. Gardner, P. A. Sch\iraann, Jr. and

E. F. Gorey, Measurement Techniques for

I Thin Films . Bertrara Schwartz and Newton

Schwartz eds.. The Electrochemical

Society (196?) p. 258.

) D. H. Dickey, "Diffusion Profiles Using

a Spreading Resistance Probe", Extended

Abs. of the Electronics Div. . Electrochem. Soc . Vol. 12, 151 (19637^

(5) R. G« Mazur, "Spreading Resistance Resistivity Measurements on Silicon Containing P-N Junctions", Extended Abs.

of the Electronics Div. . Electrochem.

Soc. . Vol. 15. Abs. No. 164, (1966).

(6) R. N. Ghoshtagore, Phys. Rev. B, 2,

389 (1971).

(7) R. N. Ghoshtagore, ibid. 397 (1971).

(8) R. D. Brooks and H. G. Mattes, Bell

System Tech. Jour. (1971).

(9) T. L. Chu and G. A. Gruber, J. Electrochem. Soc, m, 522, (1967).

(10) J. F. Gibbons, Proc. IEEE, 295,

(1968).

ASR-100

AUTOMATIC PROBf SYSTtM AND

MICfiOSCOPL

AUTOMATIC SIACE- SIFPPINC DEVICE (SELfCTtD UNIT STEPS

Of 25 TO 250 MICRONS'

CONTROL LtNtI ISYNCHRONOUS MOTOR

SEQUENCE PfiOCRAMMEfll

T« AL-TOWATIC SPREADING RESISTANCE PfiOBE

I 'WITH DIGITAL DATA OUTPUT OPTIONI

|

PROCESS FLOW

IN AUTOMATIC SPREADING

RESISTANCE MEASUREMENTS

X-Y POINT PLOmfi

ANALOG TO DIGITAL CONVERTtR AND DATA COUPLffi

DIGITAL DATA oinpuT Dtvias

ITlLfTYPE. CARD

PUNCH. ETC. )

DIGITAL COMPUTTR

(BATCH OR

TIMC-SHAHED)

PROaSSEO DATA

OICITAl X-Y PLOTTER (SUCH AS Tht CAl-COMP MODEL M5I

Figure 1. Diagram of ASR-100 Automatic Spreading

Resistance System.

213
Figure 2. P and N-type Calibration Curves for a Polished Surface, Probe Spacing: 100 Micrometers, Probe Load: 20g.

10-3 10 0° lOl

RESISTIVITY, ohm-cm.

Figure 3. P"*!^ Double Epitaxial Layer on an N - Substrate - Spreading Resistance vs. Position ^

i° on Bevelled Surface. 2

of

nUUPUi NO. 1 TH!N B'ITIXI>L

Distance on Beveled Surface

DATE 4-lf-72 FIG.BOOK& cnRo-^^x PAr,FNO. COND. ^ TYPF rN SURFACE

FINISH STTON NO.Of , f-STEP „ ,^ „ IMir.RONS:! i.i TAM a .020

PROBE „ ^ 1

Pi lOHMSl

fSOURrFI p(OHMCM)

'(SOURCE] REMARKS

Figure 4. Conducting Boundary Correction Curv Ratio of Corrected Resistance to Measured Resd

tance vs. Thickness.

12 3 4

LAYER THICKNESS , micrometers 214
Figure 5. P'''N Double Epitaxial Layer on an N"*" Substrate- Impurity Concentration vs. Thickness.

CURVE A CURVE B CURVE C CURVE D

0.5 1.0 1.5 2.0 THICKNESS , micrometers

igure 6. Effect of Time Delayed Dopant In-

,;ction on the Interface Between an N Substrate

ad an N-type Epitaxial Layer.

0 10 20 0 10 20 0 10 20 0 10 20

THICKNESS, micrometers

Figure 7. Boron Diffusion into an N-type Epitaxial Layer on an N"*" Substrate-Spreading Resistance vs. Position on Bevelled Surface.

Distance_on Beveled Surface 215

f 565-448 O - 75 - 15
Figure 8. Boron Diffusion into an N-type Epitaxial Layer on an N"*" Substrate-Impurity con- centration vs . Thickness

THICKNESS, micrometers

Figure 9. Boron Ion Implantation into an N-type « Substrate-Spreading Resistance vs. Position on I Bevelled Surface. '

10^

Tifflfrf

w

DATE 4-18-72 PAf-,F NO 50*0536 COND. _, TYPF TM

SURFACE

FINISH JTTC'J NO.Of _ PRORF?; z X-5TEP „ 9 a- -

TAM a .017 PROBE „ SFPtCM> 0.5X10-1

Pt (OH MSI

f SODfirpT 3(OHMCM)

'fsOURCEJ REMARKS

Distance on Beveled Surface

Figure 10. Boron Ion Implantation into an N-type

Substrate-Impurity Concentration vs. Thickness.

0.25 0.50 0.75 1.00 1.25 1.50 1.75 THICKNESS, micrometers 216
lilATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

jProceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Evaluation of the Effective

Epilayer Thickness by Spreading

Resistance Measurement

H. Murrmann and F. Sedlak

Siemens AG, Werk Halbleiter

Munich, Germany

Two types of double layer structure which

are dealt with in the multi layer theory have

been examined:

1 . a top layer is insulated against a bottom

layer (i.e. pn-j^ction, R (cd) )

2. a top layer is shorted by a bottom layer

(i.e. n'^'-buried layer, R(0)).

In both arrangements the Spreading Resistance

depends strongly on layer thickness d and on

the radius a of contact area. Knowing the effective radius the epilayer thickness can easily

be evaluated from Spreading Resistance Measurement and making use of the function R('^) = f (d)

This method is nondestructive and less time consuming than other common methods. A simple test

pattern is proposed for evaluating the thickness

on wafers in process. A comparison between this

method and an IR-reflexion method (Digilab FTG 12)

showed that both are in very good agreement in

thickness range of 2 6/um.

Key words: Epilayer thickness, silicon,

spreading resistance, test pattern.

1 . Introduction

Exact knowledge of the thickness of epitaxial layers is very important in integrated circuit technology. The methods commonly used to deter^

Lne thickness are:

angle lapping and HF-staining

i| stacking fault measurement

IR-reflexion measurement after epitaxial deposition

I base breakdown voltage measurement during

i IC-processing.

Lapping and staining is both destructive and time consuming. EvaluaJing stacking fault depth is very inaccurate for thin epilayers. The IRsflexion method requires heavily doped buried layers with concentrations

pcceeding 5 . 10^9 cm~^. Also using antimony as the buried layer dopant

;b reduce autodoping and out diffusion effects this concentration limit

217
may cause problems for successful application of IR-reflexion method. In

addition there is often a need to measure the epilayer thickness on wafers

being processed in order to optimize and control the deposition process

and to characterize the wafers themselves. Based on previous investigationso

/l/^we propose the Spreading Resistance Measurement (SRM) as a means to

evaluate epilayer thickness.

2. Method of Evaluation

We have examined two types of double layer structure which are dealt

with in the multi-layer-theory /2/:

1. a top layer is insulated against a bottom layer (i.e. pn-jvmction,

2. a top layer is shorted by a bottom layer (i.e. n+-buried layer,

R(0)).

In both arrangements the SR depends strongly on layer thickness and

on the radius of contact area. In addition the ratio R(oo)/R(0)=k(<»)/k(0)

is a unique function of the ratio of the epilayer thickness and contact

radius and there is no dependence on resistivity and barrier effects at

the probes. In this way we were able to determine the effective radius

of the probe by SRM on wafers with known epilayer thickness for different

surface orientations and probe loads Knowing the effective radius,

the epilayer thickness can easily be evaluated from SRM of R(p°) and R(0)

and making use of the function RCco)/R(o) = k(oo)/k(0) = f (d/a) in figure 1 and 2.

3. Accuracy of the Method

The graph in figure 2 shows the strong dependence of the function

R(oo)/R(0) = f(d/a) for d/a < 5. For larger values the curve will approach

1 asymptotically and the method becomes insensitive. To determine the

expected accuracy of the method within the region of interest we made

estimations using the error formula

[Aa . C|)] . [a . A(f)]

and applying it to figure 2 with

a = 2,90/um,Aa = 0,2/um,A (|{^) = 5 %

The result is shown in figure 3. The total error Ad in thickness in

the range d = 2 4 /um was less than 0,3/um. In this thickness region

the method will be a very useful tool for controlling the epilayer deposition process.

It is worth noting that generally the buried layer maximum concentration will not be located at the same point at which the epilayer starts

growing. The difference between the two depends on the buried layer and

epilayer deposition process. Therefore each evalution is strictly bound to a specific set of process conditions and because of the semi-empiric nature

of the evaluation method the SR probe has to be calibrated for each specific process. In addition there should be calibration standard wafers with

known epilayer thickness which serve as check routines and as samples for

upper and lower tolerance limits.

^Figures in brackets indicate the literature references at the end of this paper.

218
4. Experimental Results

In order to test the possibility of applying this SRM method a compaison was made with the IR-reflexion method. P-type wafers with (100) surace orientation were oxidized and from one half of each wafer the oxide

as etched off. Then a buried layer diffusion was carried out (R=25^2/o,

= 4,5 /um) and all the oxide was etched off. N-epilayers of different

ickness were deposited in the range of d = 2 10 /um /l/. Finally

hickness was evaluated by SRM on the wafer halves wixh and without buried

ayer using the graph of figure 2 with an effective contact radius of

= 2,90 /um. Thicknesses were also measured using a Digilab FTG 12 IRquipmenx. The result of the comparison is shown in figure 4. The data

Dints are very close to a straight line with slope 45° passing through

ero. Within the thickness range 2 6 ,um there is very good agreement

etween the methods. However at about 10yum the deviation becomes larger

s is expected 1).

5. Proposed Test Pattern

The experiment in section 3 was carried out with wafers without patterns. Now the question arises as to a suitable test pattern for the sucesful evaluation of epilayer thickness on wafers in process. This test

jattem should consist of two areas which are separated by a straight

loundary. One area should have a buried layer underneath while the other

hould be isolated by the substrate pn-junction. Test pattern dimensions

epend on the lateral influence of the field distortion by the low ohmic

uried layer. A theoretical evaluation is difficult but figure 5 shows

practiced SRM made over the boundary between the two areas. A travel of

bproximately 600/um is required to get out of the field distorted region,

aking this effect into account we propose the test pattern shown in filure 5» with area 1,8 x 1,8 mm^ for a 0,5 mm probe spacing.

j 6. Conclusion

il The SRM method proves to be a very useful tool for controlling the

toilayer thickness after the deposition process. It is nondestructive and

ess time consuming than other common methods. Evaluation can be carried

iut on wafers in process with a simple test pattern consisting of two areas

iith and without buried layer underneath the epitaxial layer. A comparison

ptween this method and a IR-reflexion method (Digilab FTG 12) showed that

0th are in very good agreement in thickness range of 2 6yum.

7. References

tl/ Murrmann, H. and Sedlak, F. , /2/ Schumann, P. A. and Gardner,

Spreading Resistance Correction E. E. , Application of MultiFactors for (ill) and (100) layer Potential Distribution

Surfaces Symposium on Spreading to Spreading Resistance CorResistance Measurement, rection Factors, J. ElectroGaithersburg, Maryland, 1974 chem. Soc. rL§» 87, (1969)

The error of the Digilab FTG 12 is i 0,05 /um in the film thickness

range of 1,5 10/um, provided there is'a sufficient high concentration in the buried layer.

219

i
220
-gure 4. Comparison of epilayer thickness measured by IR-reflexion and SRM.

dUR)

"J

1

1

10 1

—7

/

/•

/ —

/

5 —

—

/

'

(100> —

—

<— —. d (SRX ) [pm]

boundory

with

buried layer R(0)

without

burled layer R (oe.)

1,8 mm

•

•- 0,6 mm-* — 0,6mm-^

•

R(oo)

gure 5. SRM across boundary between area of R(0) and R(°°) the proposed test pattern (below)

(above). Dimensions

221
II

E
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposi

Proceedings of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

The Experimental Investigation of

Two-Point Spreading Resistance

Correction Factors for Diffused Layers

N. Goldsmith, R. V. D'Aiello and R. A. Sunshine

RCA Laboratories

Princeton, New Jersey 08540

Spreading resistance measurements have been made on a series

of erfc and Gaussian phosphorus diffusions into n and p-type

silicon. Conventional four point probe methods were used to obtain

! values of sheet resistance and surface concentration. Comparison

I between the two methods shows increasingly large disagreements as

I the diffusion depth is decreased. The Dickey formula for accounting

j for the presence of a junction is shown to work well for uniform (nonj diffused) samples but to fail to correct fully and properly for

diffusions less than- 20 um deep. Empiric curves for estimating

errors on lapped surfaces used in this study are given for a wide

variety of samples

I Key words: Correction factors; diffused layers; spreading resistance,

ij I . Introduction

j The availability of commercial two-point spreading resistance probes is bringing a new

llLmension to device fabrication, control, and analysis. With this tool, the internal dekils of devices having complicated doping profiles are reproducibly and rapidly revealed

b the device designer or engineer. However, as with any measurement technique, calibraion and correction factors play an important role in the interpretation and usefulness of

i|ie data.

1 In using the two-point probe spreading resistance method for analyzing diffused re-

||Lons in a semiconductor device, the Dickey [1]-'- correction factor due to the junction proximity is generally applied. However, Dickey's original formulation rests upon the assumpLon that the semiconductor layer beneath the probes is of uniform resistivity. Indeed,

(le early experimental work of Mazur and Dickey [2] showed this assumption to be quite uselil for uniform epitaxial layers and for very deep diffusions. In practice, this assumption

k violated in many devices and in particular, for shallow diffused layers where the resisLvity can vary by orders of magnitude over a distance of less than one effective probe

^dius 4 microns) . This can result in serious errors in converting spreading resistance

liita into a concentration profile, especially for devices having very shallow junctions and

jirrow or partially "covered" internal layers . Inaccuracies can also result when device

parameters such as surface concentration, sheet resistance, and total charge are calculated

'rom measured spreading resistance profiles. A particular case of extreme importance is

|ie base region under the emitter in a bipolar transistor where the sheet resistance and

'btal charge are parameters which must be controlled.

I In this paper we present an experimental study of the applicability of the spreading

fesistance measurements to the case of diffused impurity profiles. We have evaluated a bries of diffusions of phosphorus and boron into silicon in which the surface concentrations

jj 'Figures in brackets indicate literature references at the end of this paper.

I 223
impurity distribution and junction depth were controlled variables. Both junction and non- junction cases were examined for diffusion depths between 5 and 50 microns. Both four-point'

sheet resistance and concentrations determined from Irvin's [3] curves are compared to the ' corresponding values determined by an analysis of two-point spreading resistance measurements

The effect of the Dickey correction factor is examined for a uniform sample and for the

diffused samples containing a junction. All of the work reported here is for lapped surfaces)! A block diagram summarizing our procedure is given in figure 1.

\

2. Experimental Procedure

2.1. Diffusions

In this section we discuss the methods used to prepare diffused samples having either

Gaussian or complementary error function distributions. The majority of the samples were

diffused using doped oxides [4] as the source. For samples in which a complementary error function distribution was desired, the doped film was left on the sample for the full diffusion time. For samples where Gaussian distributions were desired, the doped film was com- pletely removed after an initial time at diffusion temperature. The sample was then coated

with an undoped film of deposited oxide and the impurities driven in by a second diffusion.

The second diffusion time was chosen to be at least 10 times longer than the first so as to approacii a Gaussian profile.

Doped oxides were selected since they are a clean and controllable impurity source yielding reproducible surface concentrations below lO^OAcm"^, The surface concentrations in

most of our experiments were kept below 5 x 10l9 a cm"^ to avoid anomalous diffusions

which can be caused by crystal damage due to excessively high impurity concentration [5,6].

Thus, with the use of doped oxides, following the procedure outlined above, one can expect

to obtain near theoretical complementary error or Gaussian profiles.

Doped oxide source films of one impurity type were deposited simultaneously on p- and

n-type wafers to obtain samples with the same surface concentration, both with and without a junction. Althougn we prepared diffusions from both boron and phosphorus doped oxides, we have restricted tne discussion in this paper to the diffusions using phosphorus in order to avoid possible problems associated with outdiffusion of boron at the oxide-silicon interface

2.2. Measurements and Data Analysis

The diffused samples were measured using a four point probe to determine the sheet re- sistance (appendix A-1) . Sections from each wafer were then prepared for measurement by

the spreading resistance probe using the technique given in appendix A-2. The spreading re- sistance measurements were collected in a manner suitable for analysis using an in-house

time-shared computer. By combining the junction depth measurement obtained from the spreading resistance probe with the four point probe sheet resistance, the surface concentration

for the junction samples was calculated with the aid of Irvin's curves.

A computer program was written to perform all of the necessary calculations, including

those detailed in appendix B. The output of this program was arranged to give both tabular

listings of the calculated quantities and a graphic output on a Calcomp plotter.

'- 3. Experimental Results

3.1. Test of Dickey Formulation

The first phase of our investigation was to experimentally verify the validity of the

commonly-used Dickey formulation for junction correction. Since this formulation was based

upon a uniformly-doped sample with a non-conducting boundary, we fabricated the sample shown

in the inset of Figure 2 . One micron of oxide was thermally grown upon a uniform, n-type

silicon wafer. A poly-silicon "handle" 10 mils thick was grown on the Si02, and the sample

was flat lapped to reduce its thickness. Four point probe measurements of the sample com- bined with the thickness obtained from spreading resistance measurements allowed us to calculate the resistivity of the bulk sample. In carrying out the spreading resistance measure- ments we made careful observations through the microscope to determine as closely as 224
jossible, when the points first contacted the oxide. This position of first contact was

assumed to correspond to the location of a p-n junction in the Dickey formulation. The nuaerical procedure used to apply the Dickey correction is described in appendix B.2.1.

In figure 2 we show the Dickey-corrected and uncorrected impurity profiles for this

sample. As can be seen, the Dickey correction is very small at distances greater than

several probe radii from the nonconducting plane, but is very accurate for distances as close

is 0.3 ym, which corresponds to less than 1/10 of a probe radius. The average resistivity

ietermined from the two-point probe data agreed with that determined using the four-point

»robe to within 2%.

3.2. Analysis of Diffused Samples

a. Dickey Corrections

Having experimentally verified the validity of the Dickey formula for uniform samples,

•e attempted to apply it to samples with diffused junctions . Following the procedures outined in Appendix B, we calculated sheet resistance for the diffused junction samples using

j.he Dickey corrected two point probe data. This calculated sheet resistance was then comfiared with the value measured using the four point probe method. The results of this comarison are shown graphically in figure 3, where the ratio of the two point sheet resis-

; ance to the four point sheet resistance is plotted vs. the junction depth for a variety of

[amples. This plot shows that the sheet resistance calculated from Dickey corrected spreadng resistance measurements begins to deviate from the four point probe values for junction

.epths less than 25 um.

If the conversion from spreading resistance to corrected resistivity is properly done,

Ihe sheet resistance calculated from two probe measurements should agree with that deterjined by four probe measurements regardless of the distribution of impurities within the

ample. Thus, even if our diffusion techniques failed to yield ideal distributions, the

allure to obtain the proper value of sheet resistance indicates that the Dickey procedure

oes not correct properly for diffused samples.

Since, in a diffused sample, the conductivity is predominantely determined by the

jarrier density in the top-most portion of the diffusion the disagreement in the sheet reJistance for the shallow junction cases implies a large disagreement in the surface conjentration. Figures 4a-4d are plots of the Dickey corrected concentration profiles for

|amples with Gaussian diffusions of increasing junction depth. Superimposed on these curves

,^ a Gaussian distribution calculated using four-point data and Irvin's curves. Figures Said are plots of similar profiles without any correction factors applied. As expected from

ne values of sheet resistance, there is very poor agreement between the theoretical and

jeasured concentration profiles for shallow junction depths.

Furthermore, as Figure 3 indicates, the spreading resistance procedure underestimates

ne concentration throughout the profile. The Dickey procedure corrects this data in such a

^y as to provide the largest correction factor for the points closest to the junction. It clear from Figure 5a, for example, that the correction factor for a diffused sample should

higher near the surface than the Dickey procedure provides.

b. Non-junction Samples

To determine to what extent the presence of a junction contributes to the errors found

a the samples just discussed, we analyzed the junctionless samples in the same manner as

inscribed above. Plotted in figure 6a-6d are the impurity profiles determined from the two

()int probe data for four such samples . These figures also have a superimposed Gaussian

stribution. The surface concentration for the Gaussian profile was chosen to be that calfilated from a simultaneously prepared junction sample. The departures from the theoretical

lirve are similar to those found in the junction case. Changing from a Gaussian profile to

[1 error function complement profile introduces comparable errors, as shown in figures 7a

'tid .7b. These results indicate that the discrepancies found are not solely due to the esence of a junction.

225
c. Comparison of Profiles

In an attempt to determine the range of errors associated with measurement of diffused

samples, we have plotted in Figure 8 the ratio of surface concentration calculated from four

point data to that calculated from two probe data vs. diffusion depth for a variety of

samples. The solid lines arbitrarily enclose the entire range of the data. It is clear that

the largest errors in surface concentration occur for the smallest diffusion depths. These

large errors are found not only at the surface but also over the whole profile as shown in

figures 9-12. No correction factors were applied to the data.

In Figures 9-12, to provide greater clarity, the distance scale has been normalized to the diffusion depth. The results given in figures 9 and 10 are for n"*" into p diffusions

while those of Figures 11 and 12 are for n+ into n-type substrates. The diffusion depth is

a parameter in all of these plots and is indicated in the figures. From figures 8-12 it is

apparent that the significant parameter in determining the error is the diffusion depth.

These graphs can be used to estimate the errors associated with the measurement of diffused

layers using a two point spreading resistance probe.

4. Discussion and Conclusions

In this paper we have demonstrated that the direct conversion of two point spreading

resistance data into concentration produces a very accurate representation of the impurity

profile for very deep diffusions (depths greater than 40 pm) . However, when the same procedure is applied to diffusions shallower than 10 pm, very inaccurate results are obtained.

The inaccuracies result from the diffusion itself, rather than the presence of a junction,

since comparable errors were obtained for n+ diffusions into both n and p material. Although the error is probably associated with the rapid variation of impurity concentration

over a depth comparable to a probe radius, we have found that the error is much more strongly correlated with total diffusion depth than local gradient with a profile. The errors grow extremely rapidly for diffusion depths comparable to, and less than, the

effective radius of the probe. Although we show that the Dickey correction procedure is

quite accurate for "step junctions" having uniform profiles, its application to diffused

samples results in a profile of the wrong shape. However, since the Dickey correction

factor increases rapidly as the junction depth decreases, its application to very shallow

junctions can produce results of the proper order of magnitude.

The data shown in figures 11 and 12 show that the maximum error occurs at a distance

roughly equivalent to a probe radius. Since there is no insulating boundary in these

samples, this effect can be interpreted as resulting from the presence of the high resistivity substrate below the diffusion. In principle, a multi-layer correction scheme, such

as that described by Schuman and Gardner [9] can be used to correct the data. In practice,

this procedure requires an inordinate amount of computer time to be used on a routine basis

Similar comments apply to the data shown in Figures 9 and 10, where there is a junction

present. As a practical matter, the degree of correction required for various types of

diffused samples can be estimated from figures 8-12.

It should be emphasized that the correction factor appears to be sensitive to the manner of surface. preparation. Based on a limited number of experiments, we have observed

that samples prepared by polishing, rather than by lapping, require less correction at the

surface

5. References

[1] Dickey, D. A., "Diffusion Profile Studies

Using a Spreading Resistance Probe,"

Abs. No. 57, Paper presented at the

Pittsburgh Meeting of the Electrochemical Society, April 15-18, 1963; See

p. 151, Extended Abstracts of the

Electronics Division, Vol. 12, No. 1.

[2] Mazur, R.G. and Mickey, D. A. "A Spreading Resistance Technique for Resistivity

Measurements on Silicon," J. Electrochem

Soc. , 113 (3) , 255 (1966) .

226
[3] Irvin, J.C., "Resistivity of Bulk Silicon

and of Diffused Layers in Silicon," Bell

System Technical Journal, 56_ (2), 388

(1962).

[4] Barry, M. L. "Diffusion from Doped- Oxide

Sources," in Silicon Device Processing,

N.B.S. Special Publication 337m p. 175

(1970) .

[5] Tannenbaum, E. , "Detailed Analysis of

Thin Phosphorus-Diffused Layers in p-type

Silicon," Solid State Electronics 2, 123

(1961)

[6] Niclcolas, K. H. , "Studies of Anomalous

Diffusion of Impurities in Silicon,"

Solid State Electronics 9_, 35 (1966).

[7] Swartzendruber , L. J., "Correction

Factor Tables for Four Point Probe Resistivitiy Measurements on Thin Circular

Semiconductor Samples," Technical Note

199, NB.TNA, Nt'l Bureau of Standards,

April 15, 1964.

[8] Caughey, D. E. and Thomas, R. E., "Carrier

Mobilities in Silicon Empirically Related

to Doping and Field," Proc . IEEE, p. 2192

December 1967.

[9] Schumann, P. A., Jr., and Gardner, E. E.,

"Application of Multilayer Potential

Distribution to Spreading Resistance

Correction Factors," J. Electrochem Soc.

116 (1) , 87-91 (1969) .

Appendix A - Measurement Procedures

A.l. Four Point Probe Measurements

j Four point probe measurements were made using a Fell head. Probe spacing was measured

l^fore the start of these experiments and was found to be 0,030". Voltage was read using a sithley 910B electrometer and current was supplied by a barrier driven source. Five readings

lire taken on each sample in a region near the center of the sample-, and these were averaged

jifore applying the appropriate geometric correction factor [7].

I

I A. 2. Spreading Resistance Measurements

'i

' All spreading resistance measurements were taken using a Model ASRIOO manufactured by

>lid State Measurements Corp. The samples were lapped on an angle block using 6 micron

I irnet grit as recommended by the probe manufacturer. The angle of the lap was determined

I' the use of the calibrated microscope mounted on the probe stage. Angles used ranged

rom 1 to 12 degrees depending upon the junction depth. The instrument was calibrated using

liform samples of known resistivity. This calibration is periodically checked to ensure

I'obe stability.

1 Appendix B - Data Acquisition and Analysis

J B.l. Data Acquisition

j Because of the large number of calculations involved in a study of this type, the outIt of the logarithmic amplifier was digitized using a 0-1. 999V panel meter. The digital

Itput of this meter was transferred, by means of a locally designed and built parallel to

irial data decoder, to punched paper tape in a format suitable for use with an in-house

tme-shared computer. At the start of each run the voltages corresponding to the fixed relistors built into the equipment were recorded on the tape. A section of the analysis proam calculates the curve relating resistance to voltage so that problems of meter linearity

id long term electronic drift are eliminated. This program also contains a mathematical

jipresentation of the measured spreading resistance vs. resistivity relationships for n- and

Itype material.

3.2. Numerical Formulation

I

i' B.2.1 Dickey correction

\ The Dickey correction factor for spreading resistance can be combined with the calibrabn data relating spreading resistance to resistivity to produce the following expression

k correcting the resistivity of a uniform layer in the presence of a junction.

i 227
R

sp RM + i- t£n^ - .116]

P TTt 2t

R

P =

t 1 a (1)

t < a (2)^

MpI ^ ^ 2D 1

p TTt a

where

R(p') is the relation between spreading resistance and resistivity

R is the measured spreading resistance

sp

a = effective probe radius

D = spacing between the points

t = distance from the junction.

This trancendental equation is solved iteratively using a rapidly converging numerical

procedure

B.2.2 Resistivity to Concentration Procedure

In order to convert from resistivity to concentration the following equations, modifications of those given by Caughy and Thomas [8], were used.

^ 65 1265 , .

Mp = 47.7+r . ..n (4)1

These formulations have been selected to provide agreement with Irvin's curves which were

used to analyze impurity profiles. A rapidly converging iteration procedure uses these re- lationships to calculate a carrier density for a given resistivity. In every case where

average properties over a number of data points are required, the concentrations rather than

the resistivities are averaged.

B.2.3 Sheet Resistance

Sheet resistance from data point j to sneet resistance data point k (not crossing a junction) is calculated using the formula

\

=

(5)

where p(i) is the calculated resistivity at data point i,

6 is the bevel angle

and s is the distance between measured points along the bevel.

228
DIFFUSIONS:

ER FC

GAUSSIAN

ANGLE

LAP

ASR-lOO

SPREADING

RESISTANCE

PROBE

Figure 1: Flow Diagram for

Experimental Procedures

TIME SHARING

COMPUTER

PROGRAM

A/D CONV.

PAPER TAPE

IMPURITY DISTRIBUTIONS

•SHEET RESISTANCE

PLOTTER

Figure 2: Calculated impurity profile,

wita and without Dickey correction, for a uniform sample having an insulating boundary

3.0

2.5

2.0

1.0

0.5

1

o

1 1 1 1

GAUSSIAN SAMPLES

" Jx

1 ERFC SAMPLES

- \\°

0

1 1 1 1 1 20 30 40 50 JUNCTION DEPTH (>xm)

60

DICKEY CORRECTION

SINGLE CRYSTAL

SILICON

'//////////////rmm. POLYCRYSTALINE

SILICON

<PZ > =.578 Xl-cm <p^ > = 584 Q.-cm

-l^im SiOg

20 30 40 50 DEPTH FROM SURFACE (>im)

Figure 3: Ratio of sheet resistance calculated

from Dickey corrected two point probe data

to that measured using four point probe as

a function of junction depth.

229

I
Figure 4: Theoretical and Dick, y corrected impurity profiles for Gaussian diffusions of

varying depths

230

'1

I
231

3SS-443

O - 75 - 16
Figure 6: Theoretical and calculated impurity profiles for Gaussian diffusions into bulk

wafers of the same conductivity type.

232
DISTANCE FROM SURFACE (/xm ) DISTANCE FROM SURFACE (^m)

Figure 7: Theoretical and calculated impurity profiles for erfc diffusions into bulk

wafers of the same conductivity type.

Fig. 9 Ratio of local concentration, cal-: culated from four point probe data and

Irvin's curves, to that calculated from

uncorrected spreading resistance data as

a function of distance (normalized to junction depth) for a series of Gaussi?n

diffusions with varying junction depths.

Fig. 8 Ratio of Surface Concentration 100 1 1 1 1

1

1 . . , c r J ^ z. ^

' GAUSSIAN derived from four point probe measurements - n*-into-p as a function of diffusion depth ' ~

NORNALIZED DISTANCE (X/Xj)

233
100

7.2/im

14.6/i.m

Figure 10. Ratio of local concentration, calculated from four point probe data and Irvin's

curves, to that calculated from uncorrected

spreading resistance data as a function of distance (normalized to junction depth) for a series

of erfc diffusions with varying junction depths.

100

0 .2 .4 .6 .8 1.0 NORMALIZED DISTANCE (X/Xp)

Figure 11. Ratio of local concentration, calculated from four point probe data and Irvin's

curves, to that calculated from uncorrected

spreading resistance data as a junction of distance (normalized to diffusion depth) for a series of Gaussian diffusions with varying

diffusion depths.

-i

1 r

GAUSSIAN

N*-1NT0-N

.2 A .6 .8 NORMALIZED DISTANCE (X/Xq)

Sit)

it)

ih Figure 12. Ratio of local concentration, calcu-: " lated from four point probe data and Irvin's

curves, to that calculated from uncorrected

spreading resistance data as a function of dis- ^mei tance (normalized to diffusion depth) for a series of erfc diffusions with varying diffusion

depths

2 4 6 .8 NORMALIZED DISTANCE (X/Xp) 234

iOfs,
•ATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10. Spreading Resistance Symposi

roceedlngs of a Symposium Held at NBS, Gaithersburg, Md. , June 13-14, 1974.

Application of the Spreading Resistance Technique

to Silicon Characterization for Process and Device Modeling

Walter H. Schroen

Semiconductor Research and Development Laboratories Texas Instruments Incorporated

Dallas, Texas 75222

In recent years, the interest in modeling of semiconductor processes and silicon device parameters has intensified considerably. Precise knowledge of the doping distribution in the semiconductor emerged as a key requirement for input and starting condition of many of

these models and for their verification. It turned out that the spreading resistance technique,

after careful probe calibration and multilayer data analysis, is able to supply some of the

required data better than any other characterization technique available. This paper

discusses these successful applications. On the other hand, this paper points out inherent

limitations of the spreading resistance technique with regard to resolution and precision, and

how this affects the verification of process and device models. Finally, the paper describes ways to supplement the spreading resistance technique by other material characterization or

electrical techniques so that the combination of these methods is capable of generating the

required experimental data for the analytical models.

Key words: arsenic; boron; design; device modeling; doping distribution; phosphorus;

process control; process modeling; spreading resistance.

1. Introduction

Stimulated by the trend toward increased automation of circuit design and improved process control in silicon

ice technology, new approaches and advances in modeling of processes, device and circuit parameters, and device

Dility have been discussed in the literature [1-9] *. It has been recognized that many device parameters and their

oility are controlled by the distribution of the dopants in the semiconductor. The knowledge of details of this tribution, such as variations of the concentration gradient with depth from the surface or with heat treatments

ing processing, becomes increasingly important as device structures become smaller and shallower. Since the trend

l ilicon device development is indeed in this direction — for reasons such as increased circuit speed, enhanced

jtking density, and reduced fabrication cost — the detailed understanding and control of the doping profiles comes mandatory. In addition, analytical expressions or empirical data of the doping distribution form the

sessary inputs to device models.

This paper emphasizes the outstanding features of the spreading resistance technique as a tool for acquiring

icise doping distribution data. This data is needed both for inputs as initial condition of the doping models and for

ification of the models. Analytical expressions for describing doping profiles in silicon have been derived for the

!p of semi-infinite medium, as well as infinite medium. For the semi-infinite medium, the situations of a limited

llgures in brackets indicate the literature references at the end of this paper.

/, 235
source, i.e., the drive-in from an initial condition (ion implantation and diffusion for base and emitter), and of an

infinite source, i.e., diffusion from a gaseous source or thick oxide have been treated. For an infinite medium, the

limited source situation, i.e., buried layer, is of particular interest. These doping distribution models comprise the category "process modeling" in figure 1.

Process models and device characterization measurements, in turn, serve as inputs to "device models", see

figure 1 . These models include diode models, intrinsic transistor models (forward active, dc, transient, etc.), and

actual transistor models (parasitics and geometry). The spreading resistance probe can supply precise input data

directly, or through process models. An example of direct device application for discrete diodes of small and large

geometries in epitaxial silicon was recently discussed by Morris [10]

The major part of this paper is devoted to applications of the spreading resistance technique to doping

concentration models. The examples are discussed in the sequence in which they appear in silicon device fabrication:

First, epitaxial layer growth and buried layer diffusions are described. Then, the formation of base and emitter is illustrated. Finally, complete transistor profiles are presented. The examples demonstrate the capabilities and

limitations of the spreading resistance probe for modeling. Supplementary techniques are outlined briefly to indicate ways of compensating for the limitations of the spreading resistance probe.

2. Application to Epitaxial Layers

and Deep Diffusions

Models for the doping distribution in epitaxial layers have to account for average doping, surface concentration,

and interface doping at substrate or buried layers. These models must therefore include not only doping redistribution during epitaxial growth, but also diffusions during epitaxy of any doped layer generated before epitaxial deposition.

2.1. Epitaxy Models

Calculations for the epitaxial process describe the effects of up-diffusion and autodoping, which have been

investigated for a number of years [1 1-14] and reviewed by Grove [15] . Since some epitaxial layers are thick

(2 to 10 Mm), the spreading resistance technique is ideal for precise impurity distribution measurements over this wide

thickness range. Figure 2 represents an example [16] of an n-type epitaxial layer, 5 Aim thick, deposited on a p-type

substrate of about equal carrier concentration. This substrate was measured to a depth of 15 /nm for detection of concentration irregularities. The data points represent analyzed spreading resistance measurements [17,18]

2.2. Buried-Layer Models

Buried-layer models describe limited-source diffusions in an infinite medium, with the boundary condition of

carrier conservation. The model has been established in strength for the case of linear diffusion constants [19,1] , such

as antimony doping, using Green's functions technique. The distribution, C, as a function of depth, x, is initially

C(x,0) = f(x).

Its subsequent redistribution at a given temperature, T, follows the differential equation, with time scaled by the

diffusivity,

ac a^c

at 3x2

236
The number of impurities has to be conserved, so that

+00

J"

C(x,t) = constant. —00

The solution is given by the usual superposition expression

+00

C(x,t)= Jf(x + 2t'/=|) exp

which can be calculated using standard numerical techniques.

For non-linear diffusion constants (such as arsenic doping) or field-aided effects different approaches have to

replace the linear model.

The spreading resistance probe proved to be the most suitable tool for acquiring the initial condition inputs, for jwhich only insufficient analytical expressions exist, as well as for verifying the buried-layer movements due to

{diffusion. An example of an antimony buried-layer diffusion is given in figure 3. Although the buried layer had moved

only slightly during epitaxial deposition, an additional 45 minutes at the given processing temperature was enough

!time to diffuse the buried layer all the way through the epitaxial layer. The data points in figure 3 are "as taken" by

the spreading resistance probe. Subsequent multilayer analysis will change the absolute values of the concentration,

but not the diffusion effect illustrated in figure 3.

The impurity distribution along the epitaxial layer/buried layer/substrate system displays two features perfectly

suited for investigations by the spreading resistance probe: deep penetration into the silicon slice, and a wide range of

(doping concentrations. It seems justified, therefore, to illustrate this system by a few more detailed examples. They

iwill also offer an opportunity to point out some important features of the spreading resistance multilayer analysis,

[which is indispensable for precise and reliable interpretation of raw spreading resistance data.

2.3. Multilayer Analysis

Figure 4 shows an n-type epitaxial layer of 2 nm thickness on an n-type buried layer almost 7 nm thick, which is diffused into a p-type substrate (beyond total depth of 9 iixr\). The impurity concentration range covered by the

spreading resistance probe is more than four orders of magnitude. The crosses in figure 4 represent data as taken by

the spreading resistance probe, while the diamonds indicate the same points after multilayer analysis. The

nathematical basis of the multilayer analysis [17] is discussed by Lee in another paper at this symposium [18] . In 3ssence, because each measurement samples a greater depth into the slice than the depth difference between

successive measurements, the direct conversion of resistance readings to dopant concentration values (crosses in igure 4) will not yield a correct profile. The direct result of spreading resistance measurements is somewhat like a Drofile of local averages rather than of discrete point values. The model used to arrive at the "true" doping profile

diamonds in figure 4) starts with the assumption of one circular contact to a laterally infinite medium which is partitioned vertically into layers of homogeneous resistivity, each layer corresponding to one spreading resistance neasurement point. The analysis consists of consecutive solutions of Laplace's equation for the potential distribution generated by the circular contact on top of this stack of layers. The solution actually proceeds from the deepest of

ithe stack of layers, with known boundary conditions, back to the top layer. Since the spreading resistance probe

[Sonsists of two contacts, the two-probe solution is then obtained by superimposing two one-probe potential solutions

|>t a suitable distance. Techniques for the rapid solution of the simultaneous equations have been developed [18]

liesulting in short enough execution time to allow economical routine use. The cost of the analysis is typically less |han the cost of the original measurement.

When input data is not smooth, the multilayer analysis may magnify input irregularities into the output profile,

igure 4 gives an example of this effect at the interface of the epitaxial layer and the slope of the buried layer. The

237
local concentration dip of the corrected data is an artifact of the analysis and can be disregarded. It occurs when

layers beneath layer being corrected nnake a major contribution to the measured voltage. Under this circumstance, the program decides that minor variations in the measured voltage must be caused by major ones in the single layer under

test, since its contribution to the total measured voltage is relatively small. The program thus overcorrects. In figure 4

this is particularly true since the layer at the point where the irregularity begins is underlain by layers having one to

three orders of magnitude higher conductivity.

In addition to the question of smooth data, the shape of the potential distribution under the probe is also important for analysis overcorrection. Real probe tips are not single circular contacts of uniform potential, but are composed of a large number of smaller contacts over a generally circular area. Simply reducing the value of the apparent tip radius to a more effective one does indeed remove the profile dip, but generates some side effects. An

exact analytical solution for a model of a real probe tip geometry is presently not available due to the complex

boundary conditions involved in a tight array of contacts.

The data in figures 2 and 4, and the following figures are analyzed data, thus representing "true" doping profiles.

Figure 5 gives another example of the epitaxial layer/buried layer/substrate system. The spreading resistance technique was able to cover a wide range of depths (total of 18 jum) and concentrations (5 orders of magnitude) with

both n- and p-type silicon involved. The location of the junction at about 14.25 (jtm depth can be clearly delineated.

3. Application to Doping of Shallow Layers

Recent advances in very small-angle beveling (< 0.3 degree) with precisely defined slope edges and scratch-free surfaces [20] opened a new field for application of the spreading resistance probe: the shallow, doped regions of emitter and base in bipolar transistors, and source, drain, and gate in MOS transistors. The data acquired by the spreading resistance probe serve, similar to the applications described previously, as inputs to and as verification of the doping distribution models.

3.1. Boron Distribution

Better understanding of the complex diffusion and redistribution processes in silicon and insulating layers has

made it evident that final doping distributions in silicon do not follow simple functional relationships. For instance,

dopant profiles were long thought of as characterized by a junction depth and sheet resistance. Consider the regime of

devices where both measurements are possible and even accurate. Simple functional forms for the profile

representation, namely Gaussian or complementary error function, were chosen and a preliminary device analysis constructed accordingly. Figure 6 represents an actual deposition and drive-in for boron and a functional approximation (Gaussian) with the same sheet resistance and junction depth. Sheet resistance of the Gaussian profiles were calculated using accepted mobility-concentration relationships. Experimental values for sheet resistance are accurate to ± 5%. Figure 6 indicates the problems which can arise because of segregation of the boron into the oxide. For a bipolar base this can lead to an error of a factor of 2 in the base sheet under the emitter, and for MOS

technology one might find a surface inverted (weakly) when it was expected to be accumulated.

A realistic diffusion model, as the one developed by Prince [21] for ion-implanted boron under oxidizing

conditions, starts with an initial condition for the doping concentration, N(x,t)

N(x,0) = f(x,0)

given either by experimental data (e.g., gained by spreading resistance measurements) or theoretical expressions (LSS

range theory [22] for ion implantation). Defining the origin of the coordinate system at the Si-Si02 interface, the

diffusion of boron atoms is governed by

238
aN _ a(D aN/ax) dx^ aw

at ax dt ax

where

D = boron diffusion coefficient in silicon m = thici<ness of silicon consumed in growing unit thickness

of Si02 (assumed to be 0.44 in this instance)

Xgft) = Si02 thickness

x = depth from Si/Si02 interface into the silicon

Boundary conditions are

N(°°,t) = 0, and —aN r -, (at X = 0) = [{K - m)/D] N(0,t) dx^dt

ax

L J o

where

K = segregation coefficient of boron in the Si-Si02 system.

,The last boundary condition is derived from the requirement of conservation of boron atoms and under the

! assumption that boron diffusion in the oxide is slow relative to the oxidation rate dx^/dt, which is true for steam

oxidation.

I 3.2. Arsenic Distribution

Comparing arsenic diffusion data with a Gaussian profile fit using sheet resistance and junction depth in an

pnalogous way to the boron data plotted in figure 6, would result in an even greater discrepancy due to the strongly

[ion-linear diffusion/annealing behavior of arsenic and its incomplete electrical activation at high concentrations. In figure 7, the true arsenic profile is compared with a linear approximation (complementary error function) by

fiormalizing the concentration. The model and data apply to diffused arsenic. As can be seen, the experimental data

rail well into the range of a 10% variation of the intrinsic diffusion constant, Dj, for the non-linear model, but not at

^11 into the range of the erfc approximation. The non-linear model [ 1 ,23,24] incorporates the effects of an internal

electric field and the variation of equilibrium lattice vacancy concentration into the continuity equations. For

i|on-implanted arsenic. Shah [25] employed field-aided diffusion, concentration enhancement due to enhanced

jjolubility of vacancies in heavily doped silicon, and electrical activation to formulate a realistic relationship for the

|iffusion coefficient D in the diffusion differential equation.

I D 1 + (2 C+/n:) — = 1 +

^ 7 ^

i Dj 1 +/3 (C+/nj)>^

239

565-448 O - 75 - 17

J
where

C"*" = concentration of electrically active arsenic

nj = intrinsic carrier concentration (temperature dependent)

i3 = fitting parameter for arsenic activation (temperature dependent)

As Shah has also pointed out, p can be chosen so that it fits the diffusion coefficient for boron previously used [1,21]

in the form

= [l + (C+Zn;)] jl + [1 + (2C+/ni)]-/^

|

3.3. Phosphorus Distribution

The third species used for base and emitter formation is phosphorus. Figures 8 and 9 give examples of spreading

resistance data acquired in support of phosphorus distribution models. Figure 8 relates to diffused phosphorus,

figure 9 to ion-implanted phosphorus. The model of Tsai [26] assumes a moving boundary separating two distinct phases, a constant concentration region and the transition region of the concentration profile. The phase boundary

reaction is the rate-limiting process and the phase boundary moves at a nearly constant rate. Subsequently,

Schwettmann and Kendall [27,28] have shown that the tail of the phosphorus profile is formed by enhanced

diffusion during low temperature heat treatments. The mechanism underlying this effect has been shown to be related to the one forming the kink in the original unannealed layer. However, the detailed processes occurring in the high

concentration region are still not fully understood.

Figures 8 and 9 stress the capability of the spresding resistance probe for acquiring a dense array of data points

in layers less than ^ iim thick. As mentioned, this capability is based on the recent advances of fabricating very shallow and well-defined angles [20] . it adds a new dimension to the investigation of emitter and base layers, since the spreading resistance probe is applicable to both n- and p-type silicon, and since it can cover a very wide range of doping concentrations, including steep doping gradients. A particularly important feature of the spreading resistance probe is its ability to probe closer to a pn junction than any other characterization technique. Figures 8 and 9 also compare spreading resistance data to measurements obtained by the incremental sheet resistance technique. There is very good agreement after the spreading resistance data have been corrected by the multilayer analysis. This

agreement is significant since the incremental sheet resistance technique supplies absolute values by monitoring the

difference between data.

A comment may be added concerning the doping distribution in the silicon layer right under the surface. Figures 8 and 9 show a discrepancy between spreading resistance and incremental sheet resistance data; the spreading

resistance values suggest a significant decrease in the phosphorus concentration close to the surface. The probable

origin of this drop is an effective reduction in carrier concentration caused by the formation of a depletion region

under the surface initiated by the deposition of the silicon nitride film; this film is needed for the precise definition of the surface/bevel edge [20] during the small-angle lapping operation. As figure 8 shows, the depletion region is partially reversed and eliminated (square-shaped data points), when the silicon nitride film is removed.

Profiles of implanted boron, arsenic and phosphorus, diffused to depths of 10 ^im, have been measured recently

[29] using the spreading resistance probe. The data confirmed diffusion calculations, and were in good agreement

with results of incremental sheet resistance measurements.

4. Application to Complete Transistor Profiles

An impressive summary of the capabilities of the spreading resistance probe as a tool for supplying doping

profile data for device modeling is the monitoring of a complete transistor profile. It demonstrates that the spreading

240
resistance technique can nneasure different conductivity types, many orders of nnagnitude difference in doping

concentration, and shallow layers as well as considerable depth into the silicon slice. It also is a means of monitoring

junction depths, or profile parts in selected portions of the transistor, when their shifts as a function of continuing

time-temperature treatments are to be studied.

Figure 5 described the cross section of a silicon slice with the diffusion of an n-type buried layer up to the point

in time of deposition of an n-type epitaxial layer. The examples given in figures 10 through 13 depict and continue a similar case history, namely an npn epitaxial test transistor with an experimental time-temperature sequence of the

diffusion processes. The major differences compared to figure 5 is that the remaining epitaxial layer is about 3 iim

deep. Using a much finer depth scale than figure 5, figure 10 reproduces the concentration detail of the boron base

after completion of all temperature cycles except the emitter diffusion. The surface depletion due to boron

redistribution into the grown oxide is clearly visible. The same depth scale is used in figure 1 1 to measure the diffused phosphorus emitter profile. The shoulder at intermediate concentrations is particularly prominent [27,28] . Figure 12

I shows the very narrow boron region of the original base of figure 1 0 that remains after the emitter of figure 1 1 has been predeposited and diffused. Figure 12 also emphasizes how close to pn junctions the spreading resistance probe is able to measure.

I Finally, figure 13 represents a composite of the measurements of the previous figures, resulting in a complete

1 transistor profile and illustrating the relative doping proportions. To avoid overcrowding only a few of the actual data

[ points have been plotted in figure 13. The connecting line has been added only for clarity and does not represent the

result of theoretical calculations. Cross sections like figure 13 are useful verifications of theoretical doping

distribution models, and they serve as inputs to device models concerned with the prediction of transistor

characteristics [3,30]

\

5. Conclusions and Recommendations

5.1. Capabilities of the Spreading Resistance Probe

for Modeling

This paper has pointed out the capabilities as well as the limitations of the spreading resistance probe for silicon characterization needed for process and device modeling. The most significant capabilities include the doping

Icharacterization of complete transistor profiles, covering the whole range from 1 0

' ^ to 10"^' carriers/cm"^, the 'measurement of layers from 0.2 ^nn to greater than 20 junri, and the determination of junctions between n-type and

jp-type silicon. Consequently, the dopant distributions can be measured as a function of time and temperature

jiprocessing, and thus supply inputs, starting conditions, and verification of process and device models. Therefore, the Spreading resistance probe is an indispensable tool in support of epitaxy models, buried layer, base, and emitter

'diffusion models, dopant deposition and redistribution models for both ion implantation and diffusion, and device

[models as much as they are based on doping profile inputs. These capabilities are summarized in figure 14.

I

] 5.2. Limitations of the Spreading Resistance Probe

i for Modeling

I The limitations of the spreading resistance probe for its application to process and device modeling are the

iDossibly insufficient density of data points, and the restriction to electrically active dopants. The density

knumber/depth) of the spreading resistance measurements is limited by the angle of the slice bevel (presently, smallest

fbngle routinely obtainable * 0.3 degrees), the probe tip diameter (presently, mechanical radius 25 nm, electrical

ll'adius'* Vm), and the minimum separation between tip placements (presently, no agreement on definition or |nninimum). The limited measurement density is particularly aggravating when the doping profiles in extremely shallow

layers « 0.2 ixm) or in very rapidly changing doping concentrations (> 3 orders of magnitude in 0.2 ^m) are to be

determined. High accuracy in these cases is required for some process models (e.g., doping profile shoulders [28] ) and

•fievice models (e.g., current gain hp^, injection efficiency, and cut-off frequency fj as a function of heavy doping of

the emitter-base profile [31 to 34] )

241
5.3. Recommendations for Improvements

More precise model predictions can be expected from improved inputs from the spreading resistance probe.

Consequently, efforts should be devoted to refine the angle-lap and surface-preparation techniques of the silicon sample, to decrease the effective electrical tip diameter of the probe, and to minimize the distance between tip

placings for reproducible measurements. The multilayer correction factors should be extended to represent the experimental situation of numerous micro-contacts forming the actual electrical tip geometry, and to accommodate

wider scattering of the data points.

5.4. Recommendations for Supplementary Techniques

In addition to improvements of the spreading resistance technique, it is recommended that the spreading

resistance probe be supplemented by the results of other and independent silicon profiling techniques. Most of these techniques are compared to the spreading resistance probe in another paper at this symposium [20] . Figure 14 lists three of these methods: incremental sheet resistance, incremental MOS capacitance/voltage, and Schottky contact.

The incremental sheet resistance technique for determining concentration profiles has been used extensively

during the past several years [35] , especially for the identification of control problems in the manufacture of shallow

devices (< 1 jum). The method consists of measuring the sheet resistance after removing thin 200 A) layers of

silicon by anodic oxidation and stripping in HF. From the resistivity profile, a concentration profile is obtained by

using suitable conversion data, such as that of In/in [36] . The technique is suited for relatively high doping

1 Q O concentrations (> 10 /cm"^).

-I o o The incremental MOS C-V technique [37] is best suited for low doping concentrations « 10 /cm ) and very shallow devices. Thin layers of silicon are removed by the growth of an anodic oxide. MOS C-V measurements are made after each oxidation. The oxide is then removed, a new oxide is grown and another MOS C-V measurement is made. The process is repeated a number of times. For each MOS C-V curve the maximum width of the space charge

layer, W^p, is determined. An experimental plot is made of W^^ versus Xg, the total thickness of silicon removed. The

impurity profile is found by calculating the curve W^(Xg) for a series of theoretical profiles. The profile whose

W^(Xg) curve matches the experimental curve is taken as the correct profile.

The Schottky contact C-V technique [20] is best suited for lightly doped silicon, since it is limited to the breakdown voltage of the Schottky contact. The depth resolution of its application is thus a function of the doping

concentration of the sample. This technique supplements the spreading resistance probe mainly for epitaxial silicon;

in addition, the low-concentration diffusion tails can be measured after the more highly doped layers have been

removed by anodization.

The three techniques described above measure the electrically active part of the dopants. For some models it is desirable to know the sum of the electrically active and neutral dopants. This information can be supplied by

techniques such as the ion microprobe, nuclear activation analysis, and optical methods [20] . More detail about these techniques can be found in the literature [ 1 ]

Experience has shown that the best way of acquiring the materials characterization needed for precise process and device models is a combination of the spreading resistance probe and the incremental sheet resistance or the ion microprobe techniques. This combination of methods is capable of generating reproducible, precise, and sufficient data for the analytical models. In this context, it can be stated with confidence that the spreading resistance technique will not only retain its place as an indispensable tool to acquire input and verification data for semiconductor process and device models, but will increase its importance and flexibility, as experimental (bevel, sample surface, probe tip) and analytical (multilayer analysis) methods are improved and standardized.

242
6. Acknowledgements

1 The author would like to thank Dr. F. W. Voltmer and Mr. R. Byrd for providing the spreading resistance

! measurements, and Mr. G. A. Lee for supplying the multilayer analysis. The author is also indebted to Drs. P. L. Shah

and J. L. Prince for numerous discussions of doping distribution models.

7. References

[1] Schroen, W. H., The impact of process control on parameter

stability — A review. Semiconductor Silicon 1973, ed. by

H. R. Huff and R. R. Burgess (Electrochem. Soc, Princeton, N. J., 1973), pp. 738-758.

[2] Jenkins, F. S., Lane, E. R., Lattin, W. W., and Richardson, W.

S., MOS-Device modeling for computer implementation, IEEE Trans. Circ. Theory, CT-20, 649-658 (1973).

[3] Edwards, J. R. and Marr, G., Depleti on-mode IGFET made

by deep ion implantation, IEEE Trans. Electron Devices, ED-20, 283-289 (1973).

[4] Sigmon, T. W. and Swanson, R., MOS threshold shifting by

ion implantation, Solid-State EL, 16, 1217-1232 (1973).

[5] Hachtel, G. D., Joy, R. C, and Cooley, J. W., A new efficient one-dimensional analysis program for junction device modeling, Proc. IEEE, 60, 86-98 (1972).

[6] Kleppinger, D. D. and Lindholm, F. A., Impurity

concentration dependent density of states and resulting Fermi level for silicon, Solid-State El., 14, 407-416 (1971).

[7] Poon, H. C, Modeling of bipolar transistor using integral charge-control model with application to third-order

distortion studies, IEEE Trans. Electron Devices, ED-19,

719-731 (1972).

processing, J. Electrochem. Soc, 121, 563-571 (1974).

[15] Grove, A. S., Physics and Technology of Semiconductor

Devices (Wiley, New York, 1967) pp. 43-83.

[16] DeVries, D. B., Lee, G. A., and Watelski, S., Integrated-circuit process control and development, Techn. Report

AFAL-TR-73-268 (1973).

[17] Hu, S. M., Calculation of spreading resistance correction

factors, Solid-State El., 15, 809-817 (1972).

[18] Lee, G. A., Rapid multilayer correction factors, ASTM/NBS

Symp. on Spread. Resist. Meas., Gaithersburg, Md., June

1974.

[19] Hu, S. M., Redistribution of diffused layers during epitaxy and other process steps, J. Appl. Phys., 39, 3844-3849

(1968).

[20] Lee, G. A., Schroen, W. H., and Voltmer, F. W., Comparison

of the spreading resistance probe with other silicon characterization techniques, ASTM/NBS Symp. on Spread.

Resist. Meas., Gaithersburg, Md., June 1974.

[21] Prince, J. L. andSchwettmann, F. N., Diffusion of boron from ion implanted sources and oxidizing conditions,

J. Electrochem. Soc, 121, 705-710 (1974).

([8] Whittier, R. J. and Tremere, D. A., Current gain and cutoff

11 frequency falloff at high currents, IEEE Trans. Electron

i Devices, ED-16, 39-57 (1969).

I:

'![9] Van Overstraeten, R., and Nuyts, W., Comparison of

theoretical and experimental values of the capacitance of

I

diffused junctions, J. Appl. Phys., 43, 4040-4050 (1972).

[10] Morris, B., Some device applications of spreading resistance measurements on epitaxial silicon, J. Electrochem. Soc, 121, 422-426 (1974).

j[11] Kahng, D., Thomas, C. 0., and Manz, R. C, Epitaxial silicon junctions, J. Electrochem. Soc, 110, 394-400 (1963).

112] Grossman, J. J., A kinetic theory for autodcping for vapor

phase epitaxial growth of germanium, J. Electrochem. Soc,

110, 1065-1068(1963).

.13] Grove, A. S., Roder, A., and Sah, T. C, Impurity distribution

in epitaxial growth, J. Appl. Phys., 36, 802-810 (1965).

.14] Langer, P. H. and Goldstein, J. I., Impurity redistribution during silicon epitaxial growth and semiconductor device

[22] Linhard, J., Scharff, M , and Schiott, H. E. Kgl. Danske

Videnskap Selskab, Mat.-Fys. Model, 33 14 (1963).

[23] Hu, S. M. and Schmidt, S., Interactions in sequential

diffusion processes in semiconductors, J. Appl. Phys, 39, 4272-4283 (1968).

[24] Fair, R. B. and Weber, G. R., Effect of complex formation on

diffusion of arsenic in silicon, J. Appl. Phys., 44 273-279

(1973).

[25] Shah, P. L., to be published.

[26] Tsai, J. G., Shallow phosphorus diffusion profiles in silicon, Proc. IEEE, 57, 1499-1506 (1969).

[27] Schwettmann, F. N. and Kendall, D. L., Carrier profile change for phosphorus-diffused layers on low-temperature

heat treatment, Appl. Phys. Letters, 19, 218-220 (1971).

[28] Schwettmann, F. N. and Kendall, D. L., On the nature of the kink in the carrier profile for phosphorus diffused layers in silicon, Appl. Phys. Letters, 21, 2^ (1972).

243
[29] Douglas, E. C. and Dingwall, A.G.F., ion implantation for threshold control in COSMOS circuits, IEEE Trans, on El. Dev., ED-21, 324-331 (1974).

[30] DeMan, H. J., and Mertens, R., SITCAP - A simulator of

bipolar transistors for computer-aided circuit analysis programs, 1973 IEEE Internat. Solid-State Cirucits Conf., Feb. 15, 1973.

[31] Mertens, R. P., DeMan, H. J., and Van Overstraeten, R. J., Calculation of the emitter efficiency of bipolar transistors, IEEE Trans, on El. Dev., ED-20, 772-778 (1973).

[32] Van Overstraeten, R. J., DeMan, H. J., and Mertens, R. P., Transport equations in heavy doped silicon, IEEE Trans, on

El. Dev., ED-20, 290-298 (1973).

[33] Mock, M. S., Transport equations in heavily doped silicon, and the current gain of a bipolar transistor, Solid-State El., 16, 1251-1259 (1973).

[34] DeMan, H. J., Mertens, R. P., and Van Overstraeten, R. J., Influence of heavy doping effects on the ij prediction of

transistors. Electronic Letters, 10, (May 1974).

[35] Donovan, R. P. and Evans, R. A., Incremental sheet

resistance technique for determining diffusion profiles, Silicon Device Processing, ed. by Ch. P. Marsden (NBS

Special Publ. 337, Washington, D.C., 1970), 123-131.

[36] Irvin, J. C, Resistivity of bulk silicon and of diffused layers

in silicon. Bell System Tech. J., 41 , 387-410 (1962).

[37] Kronquist, R. L., Soula, J. P., and Brilman, M. E., Diffusion

profile measurements in the base of a microwave transistor, Solid-State El., 16, 1159-1171 (1973).

PROCESS MODELING

EPITAXIAL SILICON

BURIED LAYER DIFFUSION

ION IMPLANTATION AND DIFFUSION

DEVICE MODELING

DIODE MODELS

INTRINSICTRANSISTOR

ACTUAL TRANSISTOR

Figure 1 . Spreading Resistance Technique Applied to Modeling

iU

10^'

lo"

10^ •

N-TYPE •

P-TYPE

1 1 1 1 1 1 1 1 1 1 1

1

1 1 1 1 1

° 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 DEPTH (pm)

Figure 2. Epitaxy on Substrate

244
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• • • •••45 MIN. DIFFUSION

_L _L

10 12 14 DEPTH ()jm)

16 18

Figure 3. N Buried Layer Diffusion

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R 10

+ +

4-

+

+

+

+

+

+ UNANALYZEO SPREADING RESISTANCE ^ANALYZED SPREADING RESISTANCE = P-TYPE SUBSTRATE. N-TYPE EPITAXY, - 60 MIN. DIffUSION

+

_L

0.0 2. 0 4.

6. 0 8.

DEPTH (pm)

10.0 12.0

Figure 4. N Buried Layer Diffusion: Spreading Resistance Data with Multilayer Analysis

EXPERIMENTAL DATA

(J. PRINCE)

Figure 6. Ion-Implanted Boron: Comparison

of Experimental Data [21] with Gaussian Model

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247

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,

Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Improved Surface Preparation

For Spreading Resistance Measurements

on p-type Silicon

J. R. Ehrstein

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

The interpretation and the precision of spreading resistance

measurements have been seen to be strongly dependent on specimen

surface preparation. A bakeout at 150°C for 15 min. following

specimen surface preparation with any aqueous polishing solution

is considered here. It is shown both to improve the precision of

the basic calibration curve for spreading resistance measurements

and to significantly improve the correlation between resistivity

values derived from spreading resistance measurements on a variety

of specimens, and resistivity values derived from other measurement

techniques. No bakeout appears to be necessary if specimen surface

preparation is done with a non-aqueous polishing process.

Key words: Bevel polishing; p-type silicon; resistivity depth profiling;

resistivity radial profiling; semiconductors; spreading

resistance measurements; surface effects; surface preparation.

1. Introduction

Spreading resistance measurements, despite their high degree of spatial resolution

nd versatility for measuring the dopant profile in multilayer semiconductor device

tructures, are nevertheless subject to reduced sensitivity and even to misinterpretation

jf the conditions of measurement are not properly defined and controlled. A recent change

(n the surface preparation of silicon specimens prior to measurement was necessitated by

jibservation of apparent changes in the dopant density on the bevel polished surfaces of

julk p-type specimens. The change in surface preparation, the addition of a thermal cycle,

|r bakeout, 150°C for 15 min. was subsequently found to significantly improve measurement

Ijesults of three different types. The three measurement areas were 1) the construction of

I calibration curve from spreading resistance to resistivity for p-type silicon specimens,

I) radial resistivity profiling of silicon slices being inspected for use as four-probe

' :sistivity standards, 3) depth profiling of bevel polished specimens.

2. Observation of a Surface Effect

The existence of a surface related problem in spreading resistance measurements was

imarily noted as a result of an attempt to study redistribution of dopant atoms in

J-licon resulting from thermal oxidation. For this study, because of the smallness of

te expected effect, it was necessary to run instrument electronics at nearly maximum gain:

11 scale covered only 2 decades of measured spreading resistance as opposed to the

(j decade full scale normally used for profiling of device structures by spreading resistance.

;ll wafers in this study were approximately 10 fi'cm boron-doped silicon wafers which had

'^n sectioned by polishing with a silica gel polish at a small bevel angle with respect

249
to the top surface. The bevel sectioning was done to allow profiling of dopant distribution

in depth below the surface, as shown in figure 1. An apparent redistribution of dopant, seen in the form of increased spreading resistance values, and hence of increased resistivity, was observed both for wafers which had undergone thermal oxidation and for control wafers

which were merely polished wafers from the same starting batch. The effect was such that even on the nonoxidized wafers the measured spreading resistance was higher on the freshly

polished beveled surface than on the original top surface by a factor greater than two.

It is to be noted that the nature of the bevel polishing procedure is such as to remove material only from a section of the silicon chip at a small angle with respect to the top surface. The rest of this original top surface, although it may be in contact

with the polishing solution, is not held under any load against the polishing plate, and

hence is protected from the effects of the polishing solution by the natural surface oxjde

of the silicon which remains intact. This surface oxide, generally of the order of 50 A

thickness is readily penetrated by the spreading resistance probes. If the bevel polishing

process were completely passive and simply removed silicon layers without leaving electrically active residue or changing the nature the surface states of the silicon, it is

expected that the bevel polished and the top surfaces of the nonthermally oxidized chip

would have shown differences in spreading resistance of 10% or less. This small change

might be expected because of possible changes in contact shape from a slightly different

angle of the spreading resistance probe against the silicon surface, small possible changes

of resistivity in depth due to the original crystal growth, and possibly a very small

effect due to the native oxide on the original top surface.

3. Experimental Results

3.1 Early Surface Treatments

Since the shift in spreading resistance observed in probing across the bevel vertex

was much larger than expected as a result of all the component causes that had been

considered, it was judged that the polishing process used for beveling was not in fact

passive, but changed the electrical nature of the silicon surface. Subsequent similar

specimens, without thermal oxide, were bevel polished by the same polishing process and were then variously bathed and swabbed in solutions of hydrofluoric acid, chromic acid,

ammonium hydroxide and ammonium hydroxide with hydrogen peroxide. Each of these chemical

treatments effected a change of the spreading resistance value of the bevel polished

surface from the value measured on the polished only surface, and all but the hydrofluoric

acid treatment left unaffected the spreading resistance value on the original top surfaces

of the chips which had been protected by the native oxide. However, in no case did one

of these chemical treatments bring reasonable agreement between the spreading resistance

value on the beveled surface and that on the original top surface. In fact, most of these

subsequent surface treatments caused increased measurement scatter as compared with the

polished only surfaces. Thermal cycling at 70 to 100°C under partial vacuum for 15 minutes,

subsequent to polishing also failed to change the measurement disparity between these two exposed surfaces.

Comparison of these observations with those of members of various other laboratories

led to a recommendation^ for a bakeout at a minimum 150°C for 15 or more minutes subsequent

to polishing.

3.2 Bakeout of Bevel Polished Specimens

The recommended bakeout procedure was implemented on a series of bevel polished boron

doped silicon chips, each having nominal resistivity value of 10 Q'cm and having only an ambient oxide layer prior to polishing. The effect of the bakeout procedure is shown in

figure 2 for chem-mechanical polishing using two different commercially available silica

Dr. A. Mayer, RCA Laboratories (private communication)

250
i polishing compounds, both in strongly basic aqueous solutions, and the first of which was

1 the polishing compound used when the original surface preparation problem was noted during

the study of dopant redistribution. In both cases, the bevel polishing was done against

a sheet of methyl methacrylate , The specimens here were sections of a silicon wafer

actually measured at 11 fi-cm by the four-probe method (1)^ and taken from a lot of wafers

for which capacitance-voltage measurements (2) and use of Irvin's curves (3) yielded

values of 10 to 12 fi'cm. The resistivity scales shown in figures 2 to 5 are derived from

a calibration curve which was generated from the spreading resistance values near the center

of silicon specimens whose resistivity values were carefully measured by the four-probe

; method and which show a high degree of uniformity of radial resistivity. Spreading

' resistance data for all parts of this work were taken at the same 2 decade/full scale gainsetting at which the surface preparation problem was originally observed.

It should be noted that there is a shift in apparent resistivity across the bevel

' vertex from the bevel polished to the original top surface of both unbaked chips. It should

, also be noted that reasonable agreement with the four-probe and C-V values of resistivity is not obtained on the freshly bevel polished surface, without the addition of the bakeout

I cycle. This bakeout, however, succeeds in producing resistivity values from spreading

resistance which are within 10% of those from both other methods. A limit of about 5% on

! the resolution of all data is imposed by the analog form in which data were acquired.

I In order to investigate whether this shift in spreading resistance was a particular

I result of silica polishing, further wafer sections were taken and were bevel polished

] with a zirconium compound in an alkaline solution and with an alumina slurry in water,

I the latter having a strictly mechanical polishing action. The results are shown in figure 3. Because of the relatively large particle size in both these solutions it was not possible

to obtain a sharp bevel vertex. Consequently, polishing actually occurred for a small

distance onto the original top surface of the wafer section, which would normally go untouched.

This results in an increased value for spreading resistance for a distance on both sides of

,j the bevel vertex as seen in the figure. Again, the point to be noted is that freshly

I polished surfaces yield spreading resistance, and their corresponding resistivity values

5 which are in marked disagreement with those obtained from the four-probe and C-V methods

(j whereas values obtained on specimens which have undergone the recommended bakeout are

i in good agreement.

I The cases of an etched surface and a surface mechanically polished in the only

non-aqueous based solution considered here are both shown in figure 4. Again, effects due

to the surface preparation are shown on both sides of the rounded bevel vertex because of

i the inability to maintain sharp vertices with these processes. A shift in measured spreadij ing resistance due to etching is seen which is also removed by thermal cycling. No measurable

j shift is seen for the case of non-aqueous surface preparation. The exact mechanism is

; unknown but the observations are in good agreement with the observations of Mayer and

1 Schwartzmann regarding the effects of aqueous preparations (4)

I Two other specimen configurations were also tested for the presence of such an effect.

The first, a piece of p-type bulk silicon from the same batch used for previous measurements,

, had a thermal oxide grown on the top surface before sectioning and bevel polishing. The

] shape of the spreading resistance data (fig. 5) is of course influenced by the presence of

the oxide; however, again, agreement with four-probe resistivity values can only be obtained

I by the addition of the bakeout subsequent to polishing. The second specimen configuration

f was a chip with p epitaxy on a p+ substrate. The value of the epitaxial resistivity using

, MOS C-V (5) measurements and Irvin's curves (3) was 12 n-cm. This particular epitaxial

I'l configuration was chosen since the effect of the high conductivity substrate, for data near

I the epi-substrate interface, is in the opposite direction from that previously experienced

|j from the polishing process. Again, an artificial increase of measured spreading resistance

; is seen for the epitaxial layer until the specimen has been baked-out, at which time

resistivity values within 10% of that obtained from MOS C-V measurements were achieved.

1 Figures in brackets indicate references at the end of this paper.

251

f
3.3 Effect on the Calibration Curve

The second area In which the thermal cycling of specimens was found to be of great

benefit was In the construction of the calibration curve Itself. As reported elsewhere (6)

early calibration data for p-type specimens showed scatter of 50 to 80% In spreading

resistance values for specimens closely grouped in terms of four-probe resistivity values,

lesser scatter being noted for n-type specimens. The observed scatter In data for p-type

silicon was particularly evident in the resistivity range from 1 to 100 J^-cm. Data from

a calibration on chem-mechanically polished p-type specimens, which had previously been

screened for radial resistivity uniformity of 10% or better, by use of spreading resistance

are shown in figure 6. The specimens used were chem-mechanically polished in an aqueous

solution against an artificial leather backing.

At first the data scatter seen in this figure may be judged to be insignificant

considering the total span and overall linearity of the data. However, our experience

Indicates such a judgement to be optimistic, at least for high resolution applications,

because shifts of measured spreading resistance values, of the type already shown, while

strongly linked to the aqueous polishing medium, also appear to be linked to other

parameters of polishing such as composition of polishing substrate and rate of material

removal. This can be seen in figure 7 where the scatter of the data from figure 6 is

expanded by use of a reduced ordinate scale: ratio of measured spreading resistance to four-probe resistivity; (also shown are data taken on the same specimens which had received

the bakeout after a fresh chem-mechanlcal polishing using a silica gel solution) . It is to be noted that there are both increases and decreases in measured spreading resistance,

rather random as a function of resistivity, resulting from the bakeout. This is particularly

to be noted for the three specimens with resistivity in the vicinity of 10 n*cm where two of

the specimens show an Increased spreading resistance after thermal treatment. This is

opposed to the strong decrease upon thermal treatment which was seen for all bevel polished

specimens, as discussed previously, which were chem-mechanically polished in the same solution but using different loading and a different polishing substrate from the calibration specimens.

It is expected as a result of this variability in response to polishing without

subsequent bakeout, that a given specimen may not maintain a specific high or low bias

with respect to the line of regression. Therefore, for any highly accurate analysis where

the local calibration over a small range of resistivity values becomes important, large

scatter In the data about the local regression, particularly if not reproducible point

by point, may make interpretation of data erroneous. By contrast, it can be seen from

figure 7 that bakeout of the same calibration specimens after a fresh polishing results

in highly improved distribution of data about the line of regression.

3.4 Effect on Radial Resistivity Profiling

A third area of improved results due to the bakeout procedure lies in the area of

radial resistivity profiling. During the original examination of incoming material for

possible use as resistivity standards, now issued by NBS^ uniformity of radial resistivity

was a key acceptance parameter. It was a rather common experience, however, to find that

a slice from a crystal, particularly at the 10 Q'cm level, would yield resistivity profiles

radially uniform to within 5% by both four-probe measurements and combined photovoltage/

photocurrent measurements (7) , while spreading resistance radial profiles showed as much

as 100% variation on the same diameter of the slice. Figure 8 shows a typical slice

profiled by spreading resistance both with and without a 150°C bakeout after polishing. The

sets of probe tracks were approximately along a diameter but were displaced laterally by

about 200 ym from each other. The measure of radial variation in the case of the baked-out

wafer is in quite good agreement with measurements on the same slice by both the four-probe

and photovoltage techniques.

-ly — SRM 1520, Silicon Resistivity Standards; Office of Standard Reference Materials,

NBS, Washington, D.C. 20234

252
4 . Summary

Although the mechanism for the surface effect is not understood, its inherent

association with aqueous based surface treatment is strongly indicated. Such effects may

be minimized by other variations in the polishing process such as loading, rate of

surface feed during polishing, or the nature of the polishing substrate, but bakeout

after polishing has been shown to remove such surface effects almost in their entirety.

It must be noted that the strength of the effect may well be related to conductivity

type and resistivity level; hence isolated experiments on a limited number of specimens

may be inadequate to characterize a particular polishing process for the full spectrum of

specimen types which may eventually be considered.

This research was supported by the Advanced Research Projects Agency of the

Department of Defense under ARPA Order No. 2397.

5. References

1. Standard Method for Measuring Resistivity of Silicon Slices with a Collinear Four-Probe

Array, ASTM Designation F-84, 1973 Annual Book of Standards, part 8, American Society

for Testing and Materials, November 1973.

2. Mattis, R. L. , and Buehler, M. G., Semiconductor Measurement Technology: A Basic

Program for Calculating Dopant Density Profiles from Capacitance-Voltage Data,

NBS Special Publication 400-11 (in preparation)

3. Irvin, J. C, Bell System Tech. Journal 41, No, 2, 387-410 (1962).

4. Mayer, A., and Schwartzman, S., this volume, pp. 123-137.

5. Lehovic, K. , Solid State Electronics 11, 135-7, (1968).

6. Bullis, W. M. , ed. , Methods of Measurement for Semiconductor Materials, Process

Control, and Devices, Quarterly Report; April to June 1973; NBS Technical Note 806

(November 1973), pp. 9,10.

7. Blackburn, D. L., Schafft, H. A., and Swartzendruber , L. J., Journal of the

Electrochemical Society 119, No. 12, 1773-78 (1972).

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I 565-448 O - "5 - 18

DISCUSSION SESSIONS

The material in this section was taken from tape recordings of discussion periods which

jere held at the conclusion of the Theory, Practice and Application Sessions with all the

speakers in the session forming a panel to respond to questions and comments. Such questions

is were asked directly after individual contributed papers, and their answers, are presented

iLn the appropriate discussion section. Since a list of all participants and their affiliations

Ls given at the outset, the respondents are inentified only by name in the discussions. Each

pespondent was given the opportunity to review his comments prior to publication. Such changes

jis were made were primarily grammatical or for clarification of intent. The content is substanhially unchanged. Editor's notes are also given where it is thought to benefit the discussion.

DISCUSSION SESSION PARTICIPANTS

R. P. Anand

Bell Telephone Laboratory

2525 North 11th Street Box 241

Reading, Pennsylvania 19604

Jacques Assour

RCA SSD

Somerville, New Jersey 08876

! Douglas A. Barth

I Westinghouse Electric Corporation

'Defense and Electronics System Center

P. 0. Box 1521 MS 3525

Baltimore, Maryland 21203

Dr. K. E. Benson

iBell Telephone Laboratories

555 Union Boulevard

Allentown, Pennsylvania 18103

David H. Dickey

'Bell & Howell

iPasadena, California 91107

|John R. Edwards

Bell Telephone Laboratories

555 Union Boulevard

Allentown, Pennsylvania 18103

|J. R. Ehrstein

I^Jational Bureau of Standards

jWashington, D. C. 20234

Stephen J. Fonash

t'ennsylvania State University

!231 B. Sackett Building

pniversity Park, Pennsylvania 16802

S. E. Gardner

tBM - SPD

;?. 0. Box A G37/B966

Essex Junction, Vermont 05452

Carl A. Germane

Motorola Semiconductor Products Division

P. 0. Box 2953, Mail Drop A-162

Phoenix, Arizona 85036

Gilbert A. Gruber

Solid State Measurements, Inc. 600 Seco Road

Monroeville, Pennsylvania 15146

Norman Goldsmith

RCA Corp. Labs

Route 1 Princeton, New Jersey 08540

Hans Mork Janus

Topsil A/S

Lindervpvej , Frederikssund

Denmark DK-3600

J . Korvemaker

Bell Northern Research

Department 8R81 - P. 0. Box 3511 Station C Ottawa, Ontario, Canada KIY4H7

Dr. J. Krausse

Siemens AG, LLBBGEl

Munich, Frankfurter Ring 152, F. R. Germany

Dr. Paul H. Langer

Bell Telephone Laboratories

555 Union Boulevard

Allentown, Pennsylvania 18103

Alfred Mayer

RCA - Solid State

Route 202

Somerville, New Jersey 08816

Robert G. Mazur

Solid State Measurements, Inc. 600 Seco Road

Monroeville, Pennsylvania 15146

257
Bernard L. Morris

Bell Telephone Laboratories

555 Union Boulevard

Allentown, Pennsylvania 18103

Dr . Helmuth Murrmann

Siemens AG. WH MB EA 511

Balanst. 73

Muenchen 80 West Germany

Steve Mylroie

Signetics Corporation

811 East Arques 9132

Sunnyvale, California 94986

Pierre Pinchon

RTC La Radiotechnique Complec

Code postale: boite postale 6025 - 14001 - CAEN CEDEX (FRANCE) 14001

Michael Poponiak

IBM - East Fishkill

Department 214, Building 300-94

Hopewell Junction, New York 12533

Simon Prussin

TRW Semiconductors

14520 Aviation Boulevard

Los Angeles, California 90260

A. J, Robinson

IBM

9500 Godwin Drive

Manassas, Virginia 22110

Dr. Walter H. Schroen

Texas Instruments, Inc.

P. 0. Box 5012, MS/72

Dallas, Texas 75222

Robert I. Scace

General Electric

Electronics Park, EP7 Box 41

Syracuse, New York 13201

Dr. P. J. Severin

Philips Research Laboratories

Eindhover - Holland

Stanley Shwartzman

RCA Solid State Division

Route #202

Somerville, New Jersey 08876

Fritz G. Vieweg-Gutberlet

Wacker-Chemitronic GMBH

P. 0. Box 1140

Burghausen, West Germany t)-8263

Fred W. Voltmer

Texas Instruments, Inc.

P. 0. Box 5936 MS 144

Dallas, Texas 75222

James C. White, Jr. Western Electric

555 Union Boulevard

Allentown, Pennsylvania 18103

Don E. Williams

Bell Telephone Laboratories

Reading, Pennsylvania 19604

Douglas Yoder

Delco Electronics, GMC

P. 0. Box 1104, Plant 10, Room 328

Kokomo, Indiana 46068

258
1. THEORY SESSION

F. MAYER : I think the only speaker who addressed himself on theoretical grounds to the

difference between what should be observed on (111) versus (100) material is Steve Fonash.

I am interested to know what the other members of the panel expect from theoretical con- siderations of an orientation dependence.

W. SCHRGEN ; The multilayer analysis is independent of crystalline orientation. It considers only potential theory. However, I do not exclude that there could well be

influences of the crystalline orientation and a complete theory would include crystalline

orientation, stress effects, specific contact resistance, and other effects mentioned this

morning. The pure potential theory neglects all these.

R. MAZUR ; I do not want to leave the question hanging with some of you who are not so familiar with the question of crystallographic orientation but I have gone on record in the

past as indicating that I have never seen a significant orientation dependence. Now I get

disagreement there from all of IBM combined with all of Bell Labs and a few other places to

boot. I may have to retract on this statement in the future; that is possible. I have not

had the time to do extensive research with different orientation samples. Bernie Morris

did supply me with a couple of wafers about six months ago and I have not had a chance to

irun them yet believe it or not. But the orientation dependence may, in many practical

cases, be so small as to be unobservable from a practical point of view. I see it as a

jcase of the jury still being out.

F. VIEWEG-GUTBERLET : We have had the same experience showing orientation dependence as Bemie Morris, and this is based on over 100 measurements. We got the same curves as shown

this morning by Morris. We feel there is a dependence on orientation.

, M. POPONIAK : In the last paper today [P-8], I will present some data showing the influence

of probe loading on the orientation or I should say the orientation effect due the probe

'loading. We do see a difference and it is a function of probe loading. The lighter the

i loading the more sensitive it is to the orientation effect.

, F. VIEWEG-GUTBERLET ; Does that mean that with constant probe loading you will get another

''effect of impressions depending on the crystal orientation, i.e., if you set your probe

loading with respect to crystal orientation, you should not get a difference for (111) or

(100) material.

|M. POPONIAK : What I am saying is that due to the atomic structure between (111) and (100)

(and their mechanical properties, there is a critical level of stress from which we get

(excessive fracturing, and that seems to be the problem.

K. BENSON : Steve Fonash this morning gave some numbers, about a factor of 10 I think for

^-type (100) versus (111) and I would like to hear from anybody here that has made a icalibration curve, does this number of a factor of 10 seem realistic?

|S. FONASH : I forgot to mention [T-1] the fact that the zero bias resistance also in the

(Contacts will depend on stress and I have a reference in my paper on that: Kramer and

Ivan Rcuyven did some experimental work on this and showed that the zero bias resistance of

lithe contacts does depend on stress also. I think this is rather well known but that is one

llparticular reference. There is another paper in which I made some comments on this which

jappeared in Journal of Applied Physics in January of 1974. This effect also depends on [crystallographic orientation so you have an interplay of those two effects both of which

||depend on crystallographic orientation. So regarding the factor of 10 which was brought

!up first there is this interplay of two effects which may change the factor of 10. Seclondly, it is based on data that were determined at lower stress levels and I do not think

Ithe silicon is behaving elastically underneath these contacts and so I question the use of

jthat data. I am just trying to show the existence of an effect which I think we better

jtake a look at it

259
H . MURRMANN ; We will present [P-5] in the afternoon experimental data showing a difference

between 100 and 111 material. We tried to split the data into mechanical phenomena including

the contact radius and other physical phenomena. I would like to reintroduce a p dependent

correction factor that Bob Mazur dropped some hours ago, [1-3] because I feel there is real

physical reason for it.

R . MAZUR ; I would like to make a comment here, Dr. Murrmann. I mentioned this to Bernie

Morris at the coffee break. I regret mentioning the K(p) factor in the way I did because

it was misleading. We did not really drop the physical model involved in that K(p)

function. I was referring to the fact that we had worked out a way to avoid using cumbersome

mathematics in making the corrections that get involved in having to plot an extra function:

K(p). You can treat it through the calibration data but the physical situation is still

the same and I would agree with you on that

J . KORVEMAKER : I would like to know if any of you have any results on other materials than

silicon which has been discussed all morning.

R. MAZUR. : There is data of course in the literature. I began making measurements on germanium. There is also data in the literature on germanium from T. L. Chu. Not in the

scientific literature, but in Solid State Technology; that is a testimonial to the lack of

clout of spreading resistance measurements several years ago. Ting Chu was unable to get it

accepted by the prestigious journals, but it is good data and it is available in Solid

State Technology of several years ago. We at Westinghouse, years ago, did make spreading

resistance measurements on silicon carbide. There is a real question about spreading re- sistance measurements on gallium arsenide. There are ways to do it; whether it is easy or not may depend on a lot of things that would involve more discussion. That is about the

size of what I know about it.

K. BENSON : There is also Witt and Gatos' paper looking at inhomogeneities in indium antimonide crystals. I believe spreading resistance was quite easy to use because this material was low resistivity.

B. MORRIS : I would say that probably in general as the band gap gets larger the measurement is going to become more difficult as in the case of gallium arsenide where you have a problem with four point probe measurements. From what I can see there should not be an appreciable problem on materials whose band gaps are similar to silicon or perhaps a little greater. If you can make four point probe measurements you should be able to make

spreading resistance measurements.

P . LANGER : I would like to find out what the panel thinks is the lower limit in terms of

the thickness to probe radius ratio to which one can extend the correction factor calculations on opposite conductivity type structures.

B . MORRIS : As I mentioned [T-5] we use a minimum value of 0.1 for t/a. This is somewhat

arbitrary. I would not say that this minimum value of t/a is all that good. I do not

know of any really good independent methods of experimentally verifying it . These methods

would be the only ones I would believe. I would not tend to believe any calculations that

close to the junction. Unfortunately the differential sheet resistance measurement has a lot of problems that close to the junction. I would be very interested in finding another

method which would work in this region. The ion microprobe of course will go right

through the junction but then you have first of all the chemical analysis technique and,

instead of the net carrier concentration, you would have to subtract, say, the boron from

the phosphorus profile and those readings as absolute numbers are not terribly good with the

values that you usually get near a p/n junction for most microprobe analysis.

R. MAZUR : Paul should clarify whether he is asking the question of how close you can come

to a junction with a good corrected value or whether he is asking the question of how thin

a layer you can get a good corrected value on? That is* measurement on a beveled surface, or on top of a thin surface. They are not the same question and it sounds to me that he

asked one question and Bernie answered another. On the subject of this layer measurement,

Gil Gruber's paper which comes up tomorrow, I believe, will carry good evidence of quite

reasonable results on certain sub-fractional micron layers in the range of 3,000 angstroms.

260
!J. GOLDSMITH : I would like to add a comment to that. In my paper [A-7] on the last day of

jthe session I will show an experimental model which you can use to test correction factors

Very close to an insulating boundary.

i E. GARDNER : I heard the Schumann and Gardner paper mentioned quite often this morning so I chink I should stand up at least and say hello. When Paul and I wrote the paper about 8 years ago we recognized a number of limitations in the spreading resistance technique and

ne tried to identify a number of them in our paper. I think many people today are recogaizing those same limitations and going beyond our work and that was originally part of the

intention of the work, to interest people in developing correction factors for the spreading

(resistance operation. It seems to me there are still a number of problems that have not

jreally been identified and one is that we, in our analysis, did a finite layer type of

structure in which we assumed a finite number of layers whether it was 2 or 40 and if we had

been smarter we thought that there should be some way you could do this, not on finite, but

on a continuous basis. That is problem #1. The second problem is one that people have

lalluded to and that -S that you do not have a single contact but you have many contacts and

how do you develop correction factors for many contacts? The third problem which is related

to this, is, how can one explain the spatial resolution that you get whenever you assume

jthat you have a 5 micron contact but you really show curves in which your resolution is 500

langstroms, or as some I saw this past week in which they were getting 50 angstroms resolution.

So those are some of the problems I think that still remain with spreading resistance.

; B. MORRIS : I have an answer to the last comment on how you can get the resolution that we

do get. This is, I believe, due to the fact that instead of having one big flat contact for

jwhich one could very nicely calculate a correction factor from theory, we have a large

number of small contacts, each of whose diameter is perhaps 1/10 micron, as opposed to 4 or 0 microns for the "flat" radius. Since the theory predicts a depth resolution of the order

bf magnitude of your radius, this allows us to get this very fine resolution in depth, while

jthe effective radius of four microns is still the value that you get from the calibration

(as defined by values you measure for p and R. Thus, on one hand the micro-contacts add

together so you can make real measurements, and on the other hand, you are also fortunate

j,in that, for fine resolution, you may take an average value of the depth, a weighted average

! is more likely, and while this cannot be calculated it lets us make some very fine resolution

I (measurements . I would say that from measurements with the Mazur probe using 45 gram loading

I Ithat the physical penetration of the damage is approximately 1/10 of a micron. I cannot

li(measure any better than that and perhaps this is an absolute limit as to how fine you can

jimake the measurement.

I J. ASSOUR : I have seen this morning several spreading resistance profiles through thin

epitaxial layers and nobody said how these were produced in terms of surface polishing or

lapping. I was wondering since we are worrying about correction factors and accuracy, how

freproducible are the results in terms of surface finishing?

Iw. SCHRGEN : You will hear data this afternoon [P-6] on this very question of how to preIpa.re the sample surface and the probe tip, how reproducible the data are, and what we need

Ito do to get those very shallow bevels.

jP. SEVERIN : May I comment on this question invoking the micro-contacts, which I talked about

in the Silicon Device Processing Symposium^ in 1970. With our steel probe the microjcontact contribution, p/4na (where n is the number of contacts which act in parallel to

hieach other) acts in series with the term p/4A, where A is the total contact diameter. The

jimicro-contacts represent about 5 times as large a resistance in the series combination as

:,!ithe large overall spreading resistance contact. In this case the resolving power of say

ilO.l micron is easily explainable. That we have indeed these micro-contacts and that this

Ihas nothing to do with contact resistance in the common physical sense is explained by the

fact that we find proportionality to p over 4 orders of magnitude which is a very unrealistic assumption for a contact resistance. Furthermore, micro-contacts are an extremely

interesting subject because there the mechanics and physics enter. Although the term microcracking has been. used today several times, direct evidence has been given in Russian

literature^' 3' that silicon behaves plastically at room temperature in a very shallow

; top layer. The thickness of this top layer increases with the applied load. ^Indirect^

evidence has been given earlier in various experiments of a different nature, > » » .

. 1 think that it is a pity that there are no people in this audience who have more experience

ion micromechanical properties. On a submicron scale you cannot just talk about the elastic

i\ 261
constant or hardness of silicon.

Ed. Note: In review of his comments, P. Severin supplied the following references.

Y. Silicon Device Processing, NBS Spec. Pub. 337 (1970) 224.

2. V.P.Alekhin, O.V. Gusev, et al.-Sov. Phys. Dokl. 14, 894 (1970).

3. V.P. Alekhin, O.V. Gusov, et al. -Sov. Phys. Dokl. 14, 917 (1970).

4. V.J. Nitenko, M.M. Myshlyaev and V.G. Eremenko- Sov. Phys. Sol. St. 9_, 2047 (1968).

5. G.R. Booker and R. Stickler-Phil. Mag. 8^, 859 (1963).

6. T.R. Wilshaw- J. Phys. D. 4, 1567 (1971).

7. M. Renninger- J. Appl. Cryst. 5^, 163 (1972).

8. W. Ridner and J, Braun- J. Appl. Phys. 34, 1958 (1963).

R. MAZUR : I would like to answer - this is also to that last question. We cannot leave it

said that way. I mean that I cannot just sit here and leave it in the record that Mazur

did not say anything. Regarding the third part of Ed Gardner's comment I need to point out, ^ of course, to be consistent, that the very high spatial resolution can be explained in many

cases again because of the work function potential barrier which has a very, very shallow

penetration. It is restricted to the immediate surface material. The second part of the i question is that using what I call a conditioned probe, which you will remember I defined

as one which although made up of multi-contacts, will act as a single contact if you get the 'i little contacts close enough together and distribute them properly. I would refer anybody

to a paper by Greenwood (Brit. J. A. P., 1966) which lays this out in great detail. I have 5 pointed out in the past to many people that I think that when the questions come up about

spreading resistance resolution, people are often talking about spreading resistance measurements with what I consider unconditioned contacts. If you damage the probes, you will

go on and get profiles and you will make measurements and you can even write papers but I do not know that it is going to get anyone anywhere. So you have to be careful about ., whether the original work and data that went into it was valid or not. i

i! J. KORVEMAKER : I would like to ask Dr. Severin a question. In regard to the plastic be- ii havior, is it similar to the behavior of glasses? }i

i' P. SEVERIN : We are talking about monocrystalline structures which are something quite

different from a glassy structure. I have given the reference of about 2 years ago about ; this microplasticity at room temperature of silicon.

D. WILLIAMS ; The question that keeps bothering me is that we have talked about accuracy say, comparing spreading resistance to capacitance voltage, but I think in the latest report as published by NBS^ they also say they have difficulty getting correlation between resistivities that are very close together and spreading resistance. If this is true, since you

have calibrated on a set of samples, what are you correcting when you get your profile.

Granted a profile may look very consistent but how valid is the calibration back to resis- t tivity? » ^Ed. Note : W. M. Bullis, Methods of Measurement for Semiconductor Materials, Process Control, and Devices, Quarterly Report; April to June 1973; NBS Technical Note 806 (November [ 1973), pp. 9, 10.

R. MAZUR : This is a point that should be kept in mind; i.e. that fussing with 2 or 3 or 5 even 5% on the thickness corrections and the other corrections may be senseless if the basic

calibration data limits you to ±10 or 15% accuracy. So you have to be practical. It is I quite possible still, even at this late date, to get hung up on the micromechanics of that ; contact and fail to keep your eye on the main thing which is control of silicon processing, > if it has to be 100% empirical then that is the way it is going to have to be.

\ 2. PRACTICE [,

): N. GOLDSMITH : Jim White, I noticed in your program you require the orerator to input the thick

ness. Don't you derive any thickness measurements from the spreading resistance data itself?

J. WHITE : Well, we use the test set for two functions; when making surface measurements,

of course, we cannot derive any thickness measurements. For depth dependent measurements

we could determine the thickness from the spreading resistance data but we do not use that

as an input because we could not correct our first values, we would have to store all the

values and correct them later.

262
i^. GOLDSMITH: That was my point.

' \ VOLTMER ; I wondered how you automatically align the probes at the bevel edge?

r. WHITE : We have an interference contrast microscope that is mounted a known fixed

.ateral distance from the wafer stage. We align the bevel edge with the microscope cross

.air and we move laterally by the known distance to position the probes.

r. AS SOUR : I do not know if you said it or if I missed it. How do you measure the depth

igain in the case of the groove? By staining technique?

I. WHITE : We measure the total width of the groove and from the width of the groove and

:nowing the diameter of the grooving mandrel you can calculate the total depth and then

:rom each lateral distance you move you can calculate an incremental depth.

". ASSOUR ; I take it that the depth measured by the grooving method was proven by other

echniques?

". WHITE: Yes.

. KORVEMAKER : I noticed in all the talk about spreading resistance that you never said

.nything about the quality of the silicon slice. In our company we have been looking at

lices, how much of the slice is really good and how much of the slice is not good. Does

his have any effect on the spreading resistance measurements?

'. VOLTMER : What do you mean by good?

. KORVEMAKER : We have been doing x-ray analysis of the slice to get an overall view of

hat part the slice would be suitable to get good devices from, and there is a fair amount

,hlch is not suitable because there are impurities or strains or stresses. How do these

.ffect spreading resistance measurements? I think I have also seen this reported in the

Microelectronics and Reliability magazine that is from the United Kingdom. There is, I jould say, atleast 30 to 40% of a wafer as such is not useable.

POPONIAK : I would like to comment. I think in one of the references by D. Gupta of

'ylvania, he showed that higher dislocation areas of a slice gave him different spreading

esistance values if that is what you mean. Well^he has shown it. Jimmy Hu and I have

ooked at a microscopic type effect. We looked at copper precipitates using the close

pace probing and an infrared microscope so we were able to directly correlate spreading

Resistance data as affected by a copper precipitate near the silicon surface and that was

iiublished 2 years ago (Phys. Stat. Sol. 18^, K5 , 1973), so there is a sensitivity to this

jjype of a defect.

i . LANGER : I would like to ask some of the people who discussed other types of equipment

Ifnd modifications of the Mazur equipment what they have experienced in terms of precision

|ior two types of specimens. Let's say 1 Q'cm n-type and 1 Q'cm p-type specimens that are

liniform throughout. Let's go around the table for those people who have automatic probing

:|quipment and consider precision on a long term basis, say several months.

J. MURRMANN : As I pointed out, we have done these measurements on our calibration

llocks for (111) and (100) material. For (111) material we approximately get a reproducibility of ±13%. For the (100) surface the reproducibility of the measurements was reiarkably better, approximately 1/2 of this. The reason for that we really do not know.

It looks like the (111) surface is more sensitive either to surface contamination or con-

(jensation of humidity. In addition, there is some indication that the (111) samples are

ore sensitive to the degree of misalignment between the exact (111) orientation and the

:)easured surface plane.

i j. VOLTMER : Most of our calibration deals with the entire block which is 22 samples and we

,b not very often compare an individual sample on that block. But from those times we have

'pne so, I feel that our reproducibility on a given sample is something like ±5% over a ong term. That is over a period of weeks. This must be qualified, however, since it

pplies to calibration samples which are chosen to be as free as possible from microsegreation.

263

f

jl
J . WHITE : We took an ion implanted slice which we had found to be rather uniform by making

repetitive probes across the diameter and got a short term reproducibility, say a one day

reproducibility, of maybe 10 different measurements, 5 mils apart, of +1.3%. A long term

reproducibility would be around 5%.

P. SEVERIN ; We use N-type (111) silicon substrate slices for calibration, and since I never have come across a substrate slice which has a resistivity uniformity better than 1 or 2 percent and since you cannot probe the same spot twice I think the reproducibility

should be determined as follows. When you measure a track and the next day make a track at

25 ym distance parallel to it, which is the most similar situation you can arrive at, then

you find the measured profiles are different by 1 or 2%. The main criterion however, by

which I think we should compare performances and quote precision is how much "grass" is to be seen on a smooth spreading resistance curve. In our case this spurious signal amounts to about 1%.

M. POPONIAK : All I have to say is that I agree with Severin. We have done some implanted

structures also and by independent measurements across the silicon wafer, say with resistor

type structures there were claims of 1% reproducibility or grading across the wafers and

what I saw with the probe is less than 2%. It becomes very hard to interpret data less than

2% so I am saying we are nearly at the limit either because of electronics or mechanical

stability of the probing system.

J . KORVEMAKER : I noticed that most of the panel speakers are of rather large multinational

companies and I wonder if they have any intercompany relations as far as how accurately they can measure, or at different plants how accurately they compare, or is there just one location where all these measurements are done.

F . VOLTMER : Within our plant we have two different probes in different buildings and we are able to get within 10% reliability on those two probes measuring the same samples when they

are calibrated by the same procedure. So between two completely different kinds of probes

we can get within 10% on a given sample.

J. WHITE : At Western Electric - Allentown we have essentially two measurement systems also,

because there is a Mazur set in Bell Laboratories in the same building with us. I do not

have a number to compare the two probes but we use the same calibration samples. We are in

good agreement that way.

F . MAYER : The question was raised about intercompany comparison. We ran a pilot round

rob in in Subcommittee 6 of ASTM. We prepared some 50 pm thick epitaxial specimens, and

exchanged samples with 5 laboratories. Our first comparison indicated 6.7% difference

between the 5 labs which is not bad at all. We tracked across the surface on 2 and 3 decade paper and found less than 10% variation in uniformity across the sample. Each lab

used its own method of calibration and surface preparation.

P. P INCHON : I would like to stress one point about the measurement of a thin low resistivity

layer deposited on high resistivity material, because in that case the correction factor

acts in such a manner that you measure something controlled by sheet resistance. By ex- periment it is nearly always the case that the spread in measurement is very much lower in

the case of low on high resistivity as compared with bulk material or high over low resistivity material. So for the case of calibration, the reported stability of the probe on

ion implantation is something optimistic in my point of view.

R . ANAND : My question is concerned with the conditioning of the probes. Bob Mazur pointed

out that's one of the most important tricks of the trade, and I was wondering if people who

are using other than Mazur type probes, how do they condition their probes and make them

stable.

P. SEVERIN : We use steel probes and they are taken from a four-point probe, in general a used one. In order to get a fine microcontact pattern the probe should be broken. Why are

the microcontacts there? They are there because there appears to be in steel little,

harder particles, therefore called asperities, which upon contact of a flat bottom surface

of such a needle with the flat surface of a silicon slice, act as protrusions. Under a scanning electron microscope we found these protrusions to be very small, at most several

264
;enths of a micron. But they are absolutely much harder than the steel and therefore the

iiteel acts as a softer matrix in which these asperities can move more or less elastically.

ilo the system is that you break the steel probe, and in some way that metallurgusts can

ixplain you expose a number of these asperities. Thereafter like a pencil you sharpen it

in a sharpening instrument so that the bottom remains untouched. You stop sharpening when

.he bottom has almost the size which you think will be the final size and then you start

ising it. At first the steel is too heavily loaded, and is plastically deformed until the

ontact has expanded and become so wide that it is not anymore plastically deformed. Then

|.t remains just the same for say 10,000 or 20,000 measurements. Upon contact to the silicon

hese asperities make very small, something like 0.1 or 0.05 micron, impressions which retain constant over the lifetime of the probe. When you use lapped silicon then you find

hat a rearrangement of the asperity patterns takes place, but the microcontribution deterlined by (na) remains the same.

WHITE : We use tungsten-carbide probes and I have found that I am able to use a new

robe with no conditioning and get very reproducible results

. SEVERIN : What is the depth of the damage and do you think the damage does really mean

omething to the result of the measurement? Tungsten carbide is harder than silicon and

he probe I am advocating is softer than silicon with only small protrusions which are arder than silicon. In this way less damage is generated.

. WHITE : I really do not have a number for the depth but when we compare our profiles

Ith profiles done on a Mazur set, they are similar. One thing you have to realize about

ur system is that we do lower the probes on the surface unloaded. We load them only after

hey come to rest on the surface so we probably get quite a bit less damage than a probe

hat would come down on the surface completely loaded.

. LANGER : Let me clarify that. I did work for Western Electric and helped in developing

heir automatic spreading resistance probe. It is possible with that particular probing

rrangement to make indentations or to lower the probes to the surface and raise them under

00 grams apparent load such as to leave no visible marks. By no visible marks Jyou certainly

•annot see them under interference contrast, and even with oblique microscope lighting you

lannot find any tracks on the surface, so that this probing arrangement may yield a completely

ifferent situation than lowering the probes under full load as is done with the Mazur probe.

I . SEVERIN : In order to increase the measurement cycle one could be tempted to increase the

anding velocity of the probe. It can be regulated from very small velocities up to about

, mm/sec with the air escape valve. We have found that above 1 mm/sec the probe shows retounding on a milisecond scale, actually losing contact and subsequently generating elastic

'.Sibrations. It is an interesting observation that the correct spreading resistance value has

ieen reached at the first impact. We have found that a landing velocity of 1 mm/sec, where

lio rebounds occur, and a measurement cycle of 5 measurements /min. produce most reliable

Jesuits.

1. ROBINSON : I address my question to Mike Poponiak. I noticed you showed a plot of conientration versus depth for the different probe pressures and there was difference in the

loncentration peaks. Is that attributed to the difference in the probe pressures or is it

ittributed to something else?

|. POPONIAK ; Well there were two profiles I showed [P-8] and I think you are talking about

jihe high concentration regions, right? On 40 gram versus 10 gram. What I am saying why

'there is an apparent difference is due to the inadequacy of the correction factor. They

jihould both be the same Cg. I am saying a 10 gram loading gives us a more accurate repreJjentation of the Cg than a 40 gram loading.

[. ROBINSON : Is it determined by the monitor wafers that you use in your subcollector , or

Itn your diffusion? When you say that that is a more accurate representation of the Cg^is

ihat Cg the determined Cg that is seen on another monitor wafer and not by spreading resistance?

L POPONIAK : We have done independent correlation with neutron activation or differential

heet conductance measurements. Independent techniques verify that the lower loading works

265
better with our multilayer correction scheme. Excessive probe penetration at 40 gram

loading causes the inaccuracy.

C . GERMANO : I was wondering if any of the participants have noticed the effects of taking

small delta X increments where the damage left by the probe marks overlaps the previous

steps

M. POPONIAK : This morning somebody showed data indicating repetitive measurements at the same point and the spreading resistance increased dramatically. Well, in our close space

probing where we have done beveling on the probes we are able to achieve a lateral movement

of 2 1/2 microns without overlapping. Now a way to test this is to start with something

large: 10 micron steps across the surface, reduce it to 5 microns, reduce it to 2 1/2,

reduce it to 1. When you see an apparent shift to higher spreading resistance you know you

cannot go below that last delta X movement. Someone else said they had a 1/2 mil resolution

delta X. I am saying we can go 2 1/2 microns by preparing the probe points properly, without

overlapping.

P . SEVERIN : May I ask a question to Mr. Poponiak. One of the key questions that has come here today is the potential distribution around the probe. For then we know whether there

is a contact resistance, either a physical contact resistance because of a barrier or a contact resistance because of microcontact . You mentioned 15 microns as the distance

between the probes. Could you bring them still closer and then just find out what the key

problem is?

M. POPONIAK : It is very difficult, but so far we see no influence.

F. MAYER : In answer to your question we did check on the overlap question, if you have

probes that step on each other so to speak. With 2 1/2 micron steps, you see something

like a 10% increase in resistivity, with 5 micron steps it is hard to say whether there is an effect: it is no more than 2 or 3%. With 10 micron steps you do not see any effect at

all. ^

I am a little confused about your data, Fred Voltmer, on the interpretation of the contact resistance that you showed. I think you showed a considerably increasing contact re- sistance after you dipped in HF and as a function of boiling in water. Now on the next

slide you showed an oxide growth of up to 700 angstrom. Are you implying that in an hour's

boiling you grow 700 angstrom of oxide? Most people consider the maximum oxide growth in

boiling water to be about 30 or 40 angstroms. What is your interpretation of that value?

F . VOLTMER : What we did was to take a slice and dipped it in HF to ensure that there was

no oxide and V7hen we did that we got a very high spreading resistance. We subsequently grew

an oxide in boiling water and measured the oxide thickness and the spreading resistance and

what we saw is a dramatic decrease in spreading resistance as the oxide thickness grew to about 100 angstroms. It remained relatively constant then until we grew about 700 angstroms

of oxide at which point the spreading resistance got quite large indicating that we were not

penetrating the oxide. We grew the oxide for the thin layers of oxide we use boiling water,

for the thicker layers they were grown in a furnace tube.

F. VIEWEG-GUTBERLET : I think, Fred, I can now answer for this effect of dipping in HF. We

have the same experience measuring p-type polished wafers by four point probe and if you dip

the wafer into HF the resistivity increases by about a factor of 10 or more, and if you

store the wafer in a temperature of approximately 150° C or you boil the wafer in water, or whatever you do^ this increase of resistivity goes down by a time constant of approximately

40 minutes. You can do the same by lapping the wafer and if you lap the wafer partly and

you position your probe in the lapped area you can see the decrease of resistivity readings

versus time. Our explanation for that is: you have a fluoric layer on the surface, which

is strongly n-type, so you bind a part of the holes to that electron layer on the surface,

i.e. the negative active layer on the surface. This is related to fluoric ions on the surface.

P . LANGER : Since we have gotten into the area of surface preparation I will just throw in

a few remarks and possibly Stan Shwartzman from RCA might want to comment on these. He has

the one technique that does not use a aqueous solution in his beveled sample preparation.

266
iJhat we have found when we went to a lighter loading probes was that you could affect

:hanges anjrwhere from 100 to 400% in the measured resistance on half ohm cm n-type by

leating for about 5 minutes at 180 - 190° C and then cooling the sample back down. These

ihanges have been stable right now up to 3 weeks. We have also found the same effect on

iob Mazur's QTA, we were able to decrease the measured resistance by a factor of 2 by using

:he same thermal cycle.

;. SHWARTZMANW : All of our samples including Bob Mazur's QTA remain stable after they are

iwabbed with methylene chloride solution with our probes loaded to 45 grams. When specimens

ire prepared in the presence of water the same degree of stability can be obtained by baking

:hem at 150" C.

' . LANGER : What I was saying was that since you are the only one that does not get tied up

'ith water during sample preparation you may not see this effect at all. I just wondered if

.nybody else had seen this type of effect.

". EHRSTEIN : I have just finished over the last month, following some very helpful suglestions from Fred Mayer, measurements using a modified surface preparation procedure. I :ope to have something to say on it tomorrow in the fashion of a late newspaper. I think,

.n terms of improvement, we have answered at least 3 problems which turned out to be re-

,.ated to surface preparation for the upper ranges of p-type material. I thought they were

, eparate problems, but they all seem to fall into consistent interpretation now, just because of a modified treatment, namely, the bake out procedure? 150° C for 15 minutes or more bllowing an aqueous chem-mechanical polish. Probably this time-temperature cycle could

e made hotter and shorter, but we have not tried it. Let me wait until tomorrow to discuss

'.t further.

I. AS SOUR : Since our experience has been concentrated on deep diffusions for power devices,

I'e are not really relating to the thin layers most of you have been talking here. We did

look at polishing techniques versus lapping techniques. The lapping technique is what we

[se constantly, but in terms of the polishing techniques that we tried on the same cali-

'iration samples, and that means syton finish, or chemical polish, or other polishing techjique, I must say that in these cases although we would reduce the noise level of our

Ipreading resistance readings we have not been able to reproduce our calibration curve in

lerms of time stability; I mean that we can polish by syton or chemically, measure, and repeat the measurement two or three hours later and get different points due to drifting. In

'ther words, the ambients, dirt in the room, or humidity, or what have you, seem to influence

jreatly the polished surface. Of course, since we have gone to the lap surfaces for the deep

lif fusion structures that we are interested in, we really do not see these effects.

'i

[ . WILLIAMS : The TI paper that you had on the calibration and performance of the spreading

jieslstance probe, was that (111) material, syton polished?

|

. VOLTMER : Yes, it was, it was all (111), but Lustrox polished.

j. WILLIAMS : In our case I used a least square linear regression. The numbers for the

jlope for both n and p- types are almost the same. I compared the residual sum of squares

irom the actual data to the fitted line and asked myself whether the slope was unity. With

5% confidence, both slopes included unity. Therefore as far as I can tell from the data

(he slopes cannot be said to be different from unity. Do you use a slope of unity in your

|lork or do you use the exact value of slope as calculated from your least square regression

||f the calibration data? I find it interesting that my calculated slope for n-type is

.'lightly larger than unity and for p-type it is slightly less than unity. This of course

jiould have implications for the simple linear model of the spreading resistance measurement.

I. VOLTMER : We use the actual values for slope and intercept from the least squares fit to nr calibration data for that particular week. For n-type, it is typically 1.03 and for pype it is 0.97. As I showed in my paper the long term distribution of the calculated

alues for these slopes maintain values slightly higher than unity for n-type and lower than

aity for p-type. These values are obtained from a linear least squares fit of the data in

og-log coordinates, but of course a slope different from unity in these coordinates implies

i non-linear relation between spreading resistance and resistivity in the model used.

I 267

f
D. WILLIAMS : Can you then determine resistivity values to better than 10%?

F . VOLTMER : Yes, I have the actual data for any given point in my calibration and the distance between that point and the spreading resistance value of the actual specimen of interest allows me to determine its resistivity to better than 10%.

3. APPLICATIONS SECTION

P . LANGERFred Voltmer, you mentioned that you have multiple peaks related in some way to tl the sum and difference of the rotation rates. Could you clarify that?

F. VOLTMER : Yes . For the multiple peaks , if you calculate the distance traveled for the

various rotation rates, for* example, just the crystal spin or just the crucible spin or the sum of crucible spin and the crystal spin, you will get peaks where the periodicity of the

fluctuation corresponds to the growth for that time. So that it is not always so simple

that there is just one well defined frequency for the microsegregation, but sometimes there

are multiple frequencies, and they all can be related to mechanical conditions during the

growth of the crystal. It is not always just a single frequency variatioti.

F. VIEWEG-GUTBERLET : Did you find for the distance between the peaks related to the ro- tational striations that the equation d = F/W is satisfied where F is the relative pulling

rate and W is the rotation rate?

F . VOLTMER : Yes, in fact that was the point. The peaks in the resistivity translate to a spacial frequency in the transform and that spacial frequency, i.e. the dominant frequency

is exactly that derived from the pull rate and the rotation frequency.

K. BENSON : Fred, have you been able to correlate the magnitude of the microinhomogeneity in

the radial direction versus the magnitude of microinhomogeneity in the longitudinal direction.!

F. VOLTMER : Well, they should certainly correlate. We have not quantified it but the same variations occur in both directions

K. BENSON : Have you been able to correlate the magnitude of one versus the other?

F. VOLTMER : We have not yet done that. We will report on it when it is done.

B. MORRIS : If I am properly interpreting o^e of the last profiles shown_|_by Dr. Assour, more

gold was accumulating in the region of a p diffusion than that of an n , is that correct?

J. ASSOUR : No, more gold accumulates in the n region than the p"*". The fact that the p"*" junction seems to have been raised in resistivity is the fact that you have more gold that

accumulated right at the junction and In the n region.

F. VIEWEG-GUTBERLET ; The explanation you derived from your results in oxygen distribution

may lead to the conclusion that oxygen is distributed nonuniformly into the crystal. But I do disagree from our experiments and there may be an explanation that your experiments were

done with p-type material. That means that acceptors are distributed in the silicon crystal

nonuniformly in the form of striations. If you raise the level of oxygen related donors by

the heat treatment at 450° C, you will get compensation at some points and you will increase

the compensation rate so the residual resistivity will go up. But this is not due to non- uniform oxygen distribution. It is more due to the nonuniform distribution of acceptors

that came out from our experiments when we tried to find out oxygen striations on p-type

material but this explanation gave a good agreement of the other measurements on n-type

material.

J. ASSOUR : According to your point of view I fail to explain the fact that infrared measurements on wafers before heat treatment do show different oxygen concentrations across the

wafer

268
7. VIEWEG-GUTBERLET : This may be due to swirls because in crucible pulled material the

;5wirl complexes and distributed very nonunif ormly

; ic. BENSON : I did have one coiranent I would like to make to F. Vieweg-Gutberlet . You may

jiave only looked at one oxygen concentration. The problem with all techniques is dependence

I pn the concentration of oxygen in the crystal. If you look at an oxygen concentration of

jlO^^ and then at one of 10^ you may see completely different reactions. So whether you

jiave seen inhomogeneity or not, I think, depends on what the original oxygen concentration

jyas in the crystal.

j l''. MAYER : I would suggest that Ken's explanation may be close to the truth. I think the

iiiuestion of time which it takes to develop oxygen donors during the heat treatment comes

rLnto it. It takes a long time at 450° C to develop donor dependent resistivity changes

jissoclated with striations. I suggest you might try to determine this experimentally.

[S. SCACE : The papers were very .interesting, both Fritz's paper and the paper that was just

^iven, and we can get into an argument that would last for a week about what is going on

j.nside the silicon but the point is that we have an extremely powerful tool here now for

Exploring just this kind of thing so let us not get off onto what is happening in the silicon,

jjjet us look at what is happening with the measurement.

s. PRUSSIN : We have been referring to the spreading resistance probe tests as being nonjlestructive. However, there is no question in the earlier discussion that part of an

jiffective probe measurement is that it leaves a footprint, an area full of little cracks,

which act as very nice nucleation sites for dislocation generation if there is any kind of

jihermal stress. I know that we have tried to remove generation of slip dislocations by the

iieans by which we prepared our wafers . We make sure that we have developed polishing techniques that leave no mechanical damage and so forth and I know that a great many of the

jitudies that have been made in the past have shown a very direct correlation between the

uresence of mechanical damage and slip associated with thermal shock. I am just wondering

lias anyone looked into the spread of, or the generation of dislocations or slip from some

jpf these "nondestructive" spreading resistance probe measurements that we have made.

|[. MURRMANN : We have not done it until now but we just started experiments and I personally

jim not afraid of getting dangerous slip damage from that probe tip damaged region especially

i'or (100) material.

'. VIEWEG-GUTBERLET : In answer to the last question, you can see from the slides I showed

A-2] we found spreading resistance traces after heat treatment, and again in the wafer when

i-e etched the wafer after repolishing them. So we have deep damage from the spreading resisijtance probes and heat treatment at 1100° C.

MURRMANN : That is a question of the heat treatment you apply to the wafers, and what you

tonsider to be dangerous damage.

l

'. VIEWEG-GUTBERLET : May I ask a question of Dr. Murrmann? How does the accuracy of your

l^pi thickness measurement depend on the dopant distribution in your epi layer? Is it true

hat the assumption is made that the epi layer is uniform in resistivity?

MUREIMANN : You are right, the method that we have proposed has to be calibrated for eaoh

ipeoific epitaxial process that you apply. For instance, you would get slight differences

ietween silicon tetrochloride epi and silane epi. In addition, the buried layer diffusion

^'rocess has some influence on this. But whenever you take a certain buried layer and epiaxial process you can well determine the effective epi layer thickness by this method. We

jiave checked it in addition by comparison with breakdown voltage measurements and these

'Values agreed very well too.

i. GOLDSMITH : The only region we have checked for thickness correlation between IR and

preading resistance was a series of samples at around 100 micron epi thickness and here we

ound that the error was really in point count: you have to choose where you place the

i.nterface. For the samples I looked at we agreed to ±1 point count. For the step size and

mgle we used this was ±1 micron out of 100. The accuracy is also limited by knowing where

i 269
you start from which adds to the error of where you place the interface. Our interface

position is selected by our computer program which calculates the substrate resistivity and

then looks for the point where the substrate resistivity breaks and assigns that as the

thickness

F . MAYER ; I would like to add here that the subcommittee 6 of F-1 has just undertaken the

evaluation of this method as a standard method and I think Fred Voltmer has volunteered to draft it. Do you want to comment on this, Fred?

F. VOLTMER : Yes, I think that the thickness depends very much on the angle which you are probing and the precision or the range of thicknesses you are looking at. For example, for

very shallow angles or very thin epitaxial layers the critical factors are quite often the

alignment of the probe and the precision with which you can form a bevel. We feel at TI at least that when we are careful and when we are talking about lapping on 17 minute blocks we can determine the thickness of an epitaxial layer, and that is a defined thickness, let me point out, to about 400 angstroms. We define the thickness as the intercept of the

slope in the change in epitaxial resistivity with the extension of the substrate. When one has p/n junctions it becomes quite a bit more difficult because there is quite often a depletion region which makes it difficult to define exactly the point where the junction

occurs. For thicker epitaxial layers, it is a matter of how many steps you want to take

and how shallow a bevel you want to use for probing. In other words, if you have a thick

epitaxial layer and are willing to probe almost forever you can get these same kind of precisions. If you take larger steps the step size becomes a limitation on the precision.

G. GRUBER : Fred and I had a bit of discussion about this same thing at the committee meeting

As he says the thickness measurement is dependent certainly on the ability to measure the ang

and also on the ability to determine the position of a p/n junction or what you would call

the interface between an n and region. In most cases, I would say in the majority of cases, the picking of the p/n junction is a matter of extrapolating the two sides of the

junction to the point of maximum inflection on the curve and calling this point the p/n

junction. If there is a broad high resistance region where the spreading resistance is off

scale then you do have a problem in choosing the junction. This however, is not the normal

case. For determining the thickness of a layer, such as an n/n'^ or p/p''', most people do

exactly as Fred has said and pick the point where you get maximum inflection in the transitioi

region from n to n . In the normal situation we find that you can determine this thickness

to within several percent, or better.

W. SCHROEN : I would like to make a comment on epitaxial layer thickness and concentration.

We have seen data this morning which showed that there can be a distinct out diffusion from

the substrate at the interface of the substrate and the epi layer. The same sort of out diffusion or autodoping can happen at the interface of the epi layer and the buried layer.

From a modeling standpoint this effect has been well explained by researchers at Fairchild

such as Grove and Deal and others. Now the question is how do we distinguish between this

experimental fact and the multilayer analysis which can pretend such an effect as we have

seen yesterday. The answer is that when there is a real out diffusion the original spreading

resistance data will show it. The original spreading resistance data can be corroborated

by the results of the C-V technique and thus distinguish a true out diffusion effect from

the artifact of the multilayer analysis.

2

E

51 J

[i

ii

11

§. PRUSSIN : The point was made that by using a very shallow bevels we can increase our precision in measuring shallow diffusions or thin epi layers. By doing that we raise

another problem. That is the greater difficulty in determining where to start the probes

because the bevel's junction with top surface then becomes less sharp. I think that the end

of the layer is one of definition and is not really a problem, but I think there is a major

problem with exactly getting your probes to start at the surface-bevel intercept. I was wondering whether there were some suggestions in terms of practical techniques which would

enable the operator to start more precisely at this junction.

F . VOLTMER : I would like to address that point. We have established a technique whereby

we grow a reactor deposited nitride on the surface of the slice as Walter Schroen pointed

out in one of the earlier talks. That nitride is hardness-adjusted to equal that of silicon

so that we can get a very distinct intercept between the lapped part and the nitride, so distinct that it is quite apparent in the microscope. The subsequent probing across that

270

•til
lows then a very drastic change in the spreading resistance when you go off the nitride onto

le silicon layer and that then allows you to identify very precisely the position of the

2ginning of the bevel. The problem is that if you are using, for example, the 17 minute

igle beveling block; a 5 micron error in the position of where you put the bevel will give

3u a 500 angstroms error in depth and I feel that doing much better than that with the 5 Lcron probe point is quite difficult, but we use the nitride to define very precisely the

jsition at which the bevel occurs. This allows you to see if the bevel is straight, which

m be another source of error.

GRUBER : We have seen the same thing with an oxide layer on the surface. You can use the

ime technique.

SCHROEN ; In answer to your question, I feel as Fred Voltmer stated, that the intercept

E the bevel and the surface is no longer much of a problem. It is much more of a problem

,\3 determine where the junction is with the substrate or with the buried layer, since we may

^ve to deal with the effects of out diffusion or the artifacts of the multilayer analysis,

ijwever, anyone skilled in the art can extrapolate where the intersection of the epitaxial

layer and the substrate is. This extrapolation is usually precise enough, even for very

pin epi layers. I feel confident that we can determine the thickness of the epi layer at

iie interface with the substrate.

PRUSSIN : One of the techniques that we have tried was to examine the bevel surface after

i completed the spreading resistance analysis and tried to find out where the first footint appeared using interference microscopy. Possibly in this way one can determine very

:curately the relationship of the first footprint with the theoretical bevel-surface inter-

»pt. What I want to know is whether techniques like this have been tried by anybody.

GRUBER : I would like to make the comment that we have been talking about very shallow

)w angles for measuring very thin layers. We have found in some of the work that we have me that you do not really have to go to as shallow an angle as you might expect to use for

very thin layer. If you go to smaller increments, for example, across a less shallow

vel, say 1 degree, many people worry about the overlap of the probe imprints and so forth.

have been able to determine experimentally that even down to a 1 micron step increment

; have been able to repeat and reproduce the results without any problem due to overlap.

MORRIS: As to that, I would like to ask what surface preparation technique you use.

GRUBER

This is a Syton polished surface using a Plexiglas plate.

MORRIS: I have never found that to be true. I wish it were.

GRUBER: You have to be sure that when you calibrate, you use the same step increment

bring the calibration as is used when running a specimen.

MORRIS: I still find that with less than 2 1/2 micron steps we have a very large signal

} noise degradation and the whole curve shifts. I have one other comm.ent to make as to

ae surface definition. We do an anodic oxidation, growing about 400 or 500 angstroms which

wves you a definite darkening of the surface. This involves no heat so you are not going

p change any of the profiles.

i MAZUR: I have a comment on that, I have made this comment to a number of individuals

[ad perhaps should make it publicly to all, that the business of sample preparation and

'irticularly beveling with small anges is in part a matter of skill. At lunch, I pointed

ft the similarity to the situation involved if someone buys a transmission electron micropope and just goes in that afternoon and starts to prepare samples. There is a certain

Qount of skill involved in the preparation of samples! The other point to this is that

^sically what Gil Gruber has said has merits. What we are suggesting to you is that you

onsider the possibility of actually being able to use one micron steps despite what Bernie

orris said and thereby achieve greater precision in the measurement of thicknesses on such

,iyers. Along with that I will make a suggestion that I have made to a number of people

'aat I have talked to in the past and that is that the contacts we use are 5-6 microns

-ameter and as someone pointed out when you are taking one micron steps and you go back to

ook at it afterwards you of course find it hard to see where that first one was because it

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'j 565-448 0 - 75 - 19
is covered over by subsequent probe marks. I would like to suggest here that at the time

you begin the run you set up to center the first contact on the bevel edge and initially set the probe to take a single measurement point. Then when it stops you shift the stage laterally by 5 - 10 microns and continue running. This causes a displacement of the rest of the

points in the run from the first point and allows you to go back later with an interference

microscope or a scanning electron microscope if you like and locate exactly where that first

point was relative to the bevel edge. Perhaps parenthetically, I guess, the point would

have to be made that the interference microscope is not going to do you much good beyond

about a quarter micron as far as determining where you are in depth.

M. POPONIAK : Just a comment on this overlapping. We have done a considerable amount of

study and it is a function of the actual resistivity. What I am saying is that there are ranges of resistivity that you can apparently overlap and that is predominantly the high

concentration regions. As you go to lower concentration regions it is very sensitive to this and you cannot overlap.

G . GRUBER : What do you mean by "you cannot overlap"?

M. POPONIAK : You get an increase in apparent spreading resistance, an error due to the

overlapping.

G . GRUBER : As I said, it is required that you calibrate using this same step increment as when running the specimen. If you do this you can eliminate any effect of overlap.

M. POPONIAK : All right j that is your comment, but that has to be proven because now you are trying to probe into a mechanical damage area, yet everybody is trying to get a good polish

to start with.

G. GRUBER : All I know is that I can use a step increment that results in overlap of suc- cessive contacts and if I calibrate with that overlap I can get the same resistivity as for

the case where I have used a larger, nonoverlapping step increment for both calibration and

sampling.

D. DICKEY : I would like to comment on Goldsmith's paper. The errors that you found in your

diffused layers no doubt result from the fact that you do not have uniform resistivity in

those layers. The so called Dickey correction assumes that you have uniform resistivity

throughout the layer. That assumption is certainly not valid for shallow diffusions. This

points up the need for an improved correction scheme and that is the subject of my second

comment. The problem of correcting spreading resistance measurements in a layer having

depth dependent resistivity is something that needs working on. I indicated on my last

slide yesterday that the imaginary superposition of a number of layers of uniform resistivity could be a useful approach. It occurred to be last night that that approach is really

just the spreading resistance equivalent of the incremental sheet resistivity experiment

that people have used for years with a four point probe. I suggest that you could derive

corrected spreading resistance measurements from an incremental approach using the same mathematics that are used with incremental sheet resistivity. The calculations that would

be required would be rather trivial and I think it is a very logical thing to try.

N. GOLDSMITH : I will comment on your first point. In the interest of time I did not

choose to read our introduction which clearly said that your formula was derived from uniform

samples and was hardly expected to provide adequate corrections for a diffused layer.

^ W. SCHROEN : Let me question you with regard to your suggestion of another approach to cor- rection factors. I did not fully understand your suggestion of using a procedure with over- - lapping steps in order to get to an analogous, situation of the four point probe. Would you

please repeat your suggestion?

D. DICKEY : I am just suggesting that you should go through the mathematics of using the

superposition principle and find out what the difference between successive spreading re- sistance measurement should be at slightly different depths. The difference in the measured

resistance that you see at two microns down, and at 2.1 microns down, for instance, should be

characteristic of the resistivity in that (1/10) micron increment just as it is in an incremental sheet resistivity.

272
'. MAYER : Perhaps I could throw another question at you as it seems like an opportune

loment. Listening to what we had this morning there has been an excellent correlation

etween patterns of resistivity established by other methods and by spreading resistance

:easurements , which says that the spreading resistance probe has arrived as a tool that is

ccepted. Not only is it accepted, by and large the data seem to fit the models we have of

reduction processes. Having gotten to this point I think it is pertinent to ask where we

0 from here. Obviously we are moving into an era where we can begin to standardize

preading resistance probe measurements and I think that is underway now. My opinion is

hat we have not got the speed yet or the facility to use it as an on-line production control

nstrument or even as a routine instrument in a development laboratory situation. It would

e interesting to hear what the panel and perhaps what Bob Mazur would have to say on this

ubject

'. SCHROEN : Your comment is well taken with regard to the actual probes. In addition, I ould like to suggest that 'maybe the National Bureau of Standards should start to standardize

he multilayer analysis. This standardization should consider what needs to be done analytically, what are reasonable mathematical assumptions, what are reasonable calculation proedures, what are the best computer programs and so on to make sure that all users can unijormly use spreading resistance data.

I . GRUBER : I think it is obvious from this last day and a half that additional work is

'tecessary in the area of layer corrections, i.e. junction corrections and in technique. I Ihink also it is becoming obvious that the technique is becoming more accepted in the in-

|ustry and that applications are being found almost every day, I think in a few years, when

e have the next seminar some of those seats that are empty will be filled.

: .. BENSON : That was a nice leading question to ASTM Subcommittee 6 (of Committee F-1) ; I ade introductory remarks on it the other day. At present we have 3 documents in Subcommittee

on spreading resistance. One is how to make a surface measurement. We have another document looking at how to make profile measurements and we have another document on using it

|s a tool to determine thickness. The documents are in various states of preparation and we

iave only been on this three or four years and every year we do make progress. If anybody

[ants to speed this progress up I suggest that you be with us in Scottsdale, Arizona in

'leptember and by that time we hope to have the first document (on surface measurement) well

j|nderway so that the other two documents can be completed.

|. KORVEMAKER : I would like to add a question and remark to what Walter Schroen was saying

|hat NBS should get us some more idea about the method to follow; so I think what Jim

thrstein was doing in the last half hour of the lecture, in stating that there are certain

jjonditions you have to do to prepare to make the measurements more repeatable could be

, pplicable particularly when you go to a high resistivity area. I wonder if there is not

iinything there but surface layers of moisture that will give you trouble. I personally

ilways had great trouble to measure pico-amps without having some trouble with moisture,

lire the methods that we use for measuring really repeatable and does everyone use the same

iethods? I do not think so.

[ ,. EHRSTEIN : I do not know exactly how to respond. I can say simply that the work I rellorted on this morning was only a beginning of what we intend to do. The difficulty

jys that in terms of any of us with the Bureau of Standards or probably with any government

Ijiigency trying to assess what problem areas need and deserve attention, none of us are really

jjrying to make work. We do need an accurate assessment of what problem areas still remain.

l i. AS SOUR : Now listening here, I really cannot help to feel my frustrations a few years

J|go when we first were introduced to the spreading resistance probe and the first question

lihat came to us is how do you calibrate the probe, and everybody said you use the four probe

jiheet resistance method according to the NBS or the ASTM standards; and naively I said, after

iiorking 10 years with silicon, what calibration sample should I use? I have a wafer here and

' measure 10 fi-cm on my instrument. How do I know it is 10 Q-cm material? Well that is when

think I called Jim and other people and I asked how do I get my hands on something that I

•lan call 10 Q'cm material. But then I thought that for the many years I have been dealing

I'lith silicon we have really never concerned ourselves with this problem and everybody had his wn technique for determining his calibration samples. Accordingly, the semiconductor injustry has progressed very nicely. If we have 10, 10.2, or 10.5 fi-cm does it make a

273
difference? For the past two years a lot of papers have shown that the spreading resistance

technique at least can answer many, many questions that frustrated all of us and I hate to see here that we should get hung up on details about the damage or the microcontact or what

have you. At the National Bureau of Standards here I would like to see very much not only

two samples of known resistivities (SRM 1520) that one can purchase for calibration but a larger number of samples that cover the whole range of resistivity that the semiconductor

industry is actively pursuing.

H . JANUS : I would like to ask if anyone has measured bulk resistivity striations letting

the probe steps going down towards 0, do the striations peaks head toward infinity or is

there an upper limit?

F . VIEWEG-GUTBERLET : We did a lot of measurements especially to build up a spreading resistance topograph of striations and we found that for the rotationals as well as what we call

growth striations, which are autof luctuations , we do not see an advantage to lower the step

width below 10 micrometers. But for very sharp profiles sometimes it seems to be better to switch from the two point probe mode to the one probe mode.

J . EDWARDS : What we found when we were trying to get very good precision was that as we

changed from the 25 micron to the 10 micron step increment, the noise level increased and as we went to the 5 micron step increment the noise level was greater than the resistivity

fluctuations which we were trying to measure.

D. YODER : We have on occasion found we do not know what the conductivity type of the top

layer is when probing devices or multilayer structures. I wonder if anyone has any idea of

how to determine this? Has anyone tried putting a thermal probe in the spreading resistance

probe or something of this order?

B . MAZUR : This is in answer to the previous question about conductivity type. Some years

ago I did make a thermo-electric probe that went on one of the early prototype spreading re- sistance probes. You can do that; it works. We do not have anything like that commercially

available. Obviously with the ingenuity that has been displayed here in the last day and a half, it really is not going to take a whole heck of a lot for people to wrap little pieces

of nichrome wire around one of those probes, and you can do this if you like. I assume that

the question was asked in reference to small areas because obviously if you have a large area exposed on the top surface you could check it with a standard thermo-electric probe. I would suggest the use of chemical stains in conjunction with spreading resistance. I would

definitely not go home and pitch out your staining stuff. We have been using the stains

consistently from the beginning of our measurements as a qualitative indicator of what is

going on overall. Remember that the spreading resistance measurement is a very high spatial

resolution measurement and if you evaluate a epitaxial layer, you may choose to do so at one point rather than all over the wafer or all across the diameter and so you may get a very

detailed picture but it is a very detailed picture of a localized region. It takes only a few seconds after having the sample profiled on the spreading resistance probe to stain it

and get an overall view of whether the junction is uniform and so on. You are not then depending on the stain to indicate a p/n junction or anything. You can simply compare it

back to the spreading resistance profile and use it as an indicator of that point on the

spreading resistance profile where it falls and see whether the layer is uniform and so on. This was found to be quite useful in the power device area for looking at the effect of

rough surfaces on diffusions and the like.

F. VIEWEG-GUTBERLET : May I comment to that problem? As you remember the paper presented

this morning from RCA with respect to oxygen effects in silicon and silicon striations.

There is a great interest to get information if compensation occurs or if the conductivity

type changes within the limits of striations so the question is does the system you are suggesting have the resolution to find out these changes in conductivity type or compensation

M. POPONIAK : Years ago when we had a three point probe which in reality was a one point

probe, we reversed the current polarity. If you increase the current sufficiently to get

into a non ohmic region you can determine the type down a profile or across the surface by

observing the forward and reverse voltages. It is especially sensitive on high resistivity

material.

274
I. MAZUR : I have comments on both those courses. As far as Fritz's problem goes I do not

lave a quick answer for you on that. You would have to look at the specific situation to

see whether anything could be done. We have generally been able to tell a lot about conluctivity type from the appearance of the profile in conjunction with other knowledge that

.8 available such as the thermo-electric probe conductivity type of the top surface and

)erhaps the substrate region (the regions that are accessible) and we have used that in conunction with the appearance of the profile and with staining techniques to keep track of

conductivity type. Your situation may be a way-out case that is hard to do much with. The

Jther suggestion that Mike was talking about I would caution you about doing that with the

ixisting spreading resistance probes that you are using for making measurements. When you

itart passing large currents through them, you will be heating the material in the region of

:he probe and I do not know what microcontacts there are there but things could change after

rards. I am not speaking from experience, I have not tried to do that, but just be aware.

I. POPONIAK : Just on a comment to Bob's. In essence, you do not have to go up every high

lurrent to look at a very small differential voltage difference between forward and reverse

.urrent so we did not burn our probes out and we did not see deterioration in our older type

irobes. As far as looking at the general profile from a spreading resistance and relating

.t to a conductivity type if you recall that one slide I showed yesterday where within 10

lils I had three complete different profiles and by no means did the spreading resistance

i.ndicate I had a p-type layer all the way up to the top of the epi over my p''' subcollector

Italy the stain showed that up, we did not type it conductivity wise. Right adjacent to that

!'as an epi over p- , adjacent to that was a resistor of the same epi but over an subcol-

'.ector. Spreading resistance profiles can be very difficult to interpret as far as conduc-

! ivity type is concerned.

; .. MAZUR : I think Mike has very well made my earlier point about the valuable usage of the

tain in conjunction with spreading resistance profiles.

i f. MAYER : I have one question that arose out of what Bob said. I would just like to poll

I he panel quickly. There are two ways of doing this, one is constant current and one is

ionstant voltage. I think the majority of the people here are using constant voltage method. How many of you are using the one millivolt or the 10 millivolt respectively?

. EHRSTEIN : NBS tends to run the 10 millivolt constant voltage mode;

|. VIEWEG-GUTBERLET : We use the 10 millivolt mode;

. GRUBER : For higher conductivity material, the opamps in the instrumentation tend to aturate at the 10 millivolt level so we tend to use the one millivolt range;

. EDWARDS : For the work that I did we used the 10 millivolt range;

] . VOLTMER : We use principally 10 millivolts;

GOLDSMITH : All our work was at 10 millivolts;

' |. MURRMANN : We too work with 10 millivolts;

j. ASSOUR: 10 millivolts.

|. MAZUR : We are just in the process of modifying our standard equipment to use 5 millivolt

there is a reason for that. The operational amplifiers that are readily available and most

feadily used have an output current capability of 5 milliamps. When you bias one ohm with

I 10 millivolt signal you have to draw 10 milliamps. The older discrete circuit operational

taplifiers that we used were very nice in going ahead and doing their bit even far beyond

Ihe call of duty. Now those are no longer available and we are using integrated circuit

ijodules that are more tightly designed and will not perform anywhere beyond the specified

I iutput current so we are in the process of shifting to a 5 mV bias. The one millivolt

: Ijrrangement is tricky because drift in the operational amplifiers is such that one or the

Ither of the operational amps may drift in such a direction as to have the offset voltage

jlightly exceed one millivolt in the wrong direction and if so your log Resistance-ratio

Ittiit will malfunction and the output will go off scale up or down. It would then need to

"'ave the offset voltages on the operational amplifiers reset which is a relatively complicated procedure. Anyway, we are switching to 5 millivolts. If you need a standard for the

luture, I would suggest starting there.

V JANUS : I have one thing that has been worrying me. That is when you talk about the

'jccuracy of the measurements at high resistivities, at 5,000 H'cm you have one phosphorous

hltom in one cubic micron. How can you talk about an accuracy of even 10%?

275

I
J. AS SOUR : I guess I should answer this. At least with oxygen and gold you do upgrade the

resistivities. I will not even guess what the accuracy of this resistivity is. Usually

when we reach these kind of resistivity levels we try very hard to get down as fast as possible or be out of business.

D . BARTH : I want to comment on the closely spaced probes and a question. We have done

profiling of thin, one micron and less, epi at one micron stepping distances with a shallow

bevel and we have been able to get, with careful surface preparation (a good plate and good

polish), good flat curves without a lot of noise. Going down to a half micron and quarter

micron steps is very bad. From a noise standpoint, I would consider one micron a lower

limit for the time being. Having been involved in ECL and high power microwave transistor

work where we have a thousand angstrom emitters and 1,000 to 2,000 angstrom base widths,

device performance tells us we are close to that, and we measured that with a spreading re- sistance probe. I have a question. Have any of you gentlemen done any work on very shallow

layers, and I am talking on less than 4,000 angstroms where all the correction factor curves

stop, and have you had any success at making those measurements accurately and do you think

the spreading" resistance technique will be applicable to layers this thin?

G . GRUBER : I have looked at some 0.2 and 0.3 micron layers but they were usually n on type with no junction involved. We have also looked at thin ion implants but I do not have

anything more to say about them.

M. POPONIAK : A comment about Westinghouse ' s question. We have done very shallow implants

and they will be reported on and it looks very feasible.

B. MAZUR : In partial answer to that question and also in line with something that Fred

talked about before, obviously, the development of the spreading resistance technique is not

finished. I think it is clear always that anything can be improved. We certainly expect

to do some additional development work in the future. VJe also expect to be able to take advantage of some of the genius at IBM and at various other places in order to obtain

technique improvements similar to the "bent" probes that we now supply to a lot of people.

These are a practical approximation to the IBM closely spaced probes as produced by Ed

Gorey. Perhaps in the future we can get closer to the spacing now used at IBM. Certainly

I think that you would all agree that there is no fundamental limitation in the use of 25

micron radius probes and certainly no fundamental limitation in the lighter load that we use

in normal measurements of 20 grams. Improvements in the mechanical parts, improvements in

the probe tips and vibration isolation and so forth may well may allow us to get down to perhaps 1 micron diameter contacts. It should be interesting to see whether something like

that can be done and perhaps we could then get to a one-tenth micron capability of doing

profiles or something similar for thin layers. One last comment on this and then I will shut

up, Fred. This applies to the Westinghouse question; it also applies to the comments that

TI has made about the junction position, the lack of information about it and so on. You can

of course, use the spreading resistance probe, for instance in the case of samples with base

widths of 2 tenths micron or something. Now, if the spreading resistance profiles in those

structures are not perfect, what else have you got? Or to put it another way, you can con- trol the production of those base widths and the like with spreading resistance profiles

even if you cannot interpret the data to give you absolute impurity concentration profiles.

The same thing goes with respect to junction position location. I would be happier to see raw data used more.

D. WILLIAMS : This afternoon I have heard at least two suggestions on where we go from here.

The first was that we take a simple empirical approach to the measurement. The other, propose

by Dickey, was that we do some more studying of correction factors. It seems to me first of

^ all that spreading resistance is supposed to do something very rapidly, but cheap and dirty

^ to verify something else you have done. NBS, RCA and TI, at least during this meeting, have

claimed that there is a linear relationship between resistivity and spreading resistance. I hope this is true because this implies that the measurement data checks with the simple

model. Now, if we were not interested in going to doping profiles then all you would have

to do is have W samples which you keep the same and as long as you get the same spreading

resistance reading then you do not have to worry about the resistivity of the material, you ! just say that your spreading resistance probe at least on these samples are measuring the same thing. Maybe these are some of the areas that could be investigated. I think that the

study of correction factors is very interesting and make a nice mathematical study. What

276
oes it have to do with actually studying your manufacturing process, if I get a certain

preading resistance characteristic and I know I can get good product on that material and I 0 not if it is some other material, is this the original intention of spreading resistance

easurement?

GOLDSMITH : I would like to add comments to that. There are two aspects to using spreading

esistance for production control. In one case you are interested in reproducing something

nd in our case, as Jacques Assour showed, we have a high resistivity n layer covered over

y a high resistivity p layer and we want to control that high resistivity n layer. Well

hen we simply control on the height of the recorder pen. The higher it goes, the higher

he resistivity and you can sort by the height of the recorder pen without a calibration

raph. That is a practical application; it works and it is in production. However, as alter Schroen pointed out, there are times when you want to go beyond that. You want to redict in advance from the starting material what devices you are going to make. At that

oint you have to have quantification of the data and that is when you have to include corection factors. You also have to know what your calibration curve is and it has to be

ransferable from laboratory to laboratory.

ASSOUR; It is true that with production processes you like control. Good or bad. Of

urse, good control makes good devices, and when you have bad control you try to make it

tter. On the other hand, there are still a lot of device characteristics that we do not

nderstand in solid state devices and there comes a time when you have the structure of the

evice you would like to sit down and think about it and try to correlate it with the

hysics and in this instance you must have some data that you can rely on in order to develp design modeling.

MYLROIE: I think it was alluded to in some of the other answers that there are really

wo areas we are talking about. One is the production control area where the raw data is

jood enough for process control and maintaining a process. The other area where we need

the calibration and correction factors is that of closing the loop back to the device char-

,lcteristics , in order to work v/ith the circuit designer and the device designer. Then when

^ey know the devices they want , through models we can develop and characterize the proesses needed to generate these devices. For this type of work we need to be able to relate

o doping concentrations and the device physics and this area is where we need the accurate

[forrection factors.

WILLIAMS

I perfectly agree, I think that the correction factors are an interesting

tudy and should be done. That is \ssy point. However, there appears to be many chances for

(rror in going from spreading resistance to doping profiles. If I have spreading resistance

?|alues I hope by calibration curves to translate to resistivity values. From there I can

iopefully go to dopant values by using Irvin's curves. Now, many factors, as pointed out by

tjBS and RCA, may cause problems such as surface preparation that gives a high resistivity,

tr maybe you have a damaged surface, but you are also going through at least two translations

nd a correction factor from a spreading resistance to a doping profile before you come up

th any answers. How many other factors there are, I do not know.

GRUBER: I would like to comment, I think the fact that this is an NBS and ASTM jointly

iponsored symposium goes a long way in saying that the real need in the industry is for

itandardization of the spreading resistance technique, in fact for standardization of all

lesistivity measurements. This whole week was interesting for me, it was the first time I

j(ad been to an ASTM meeting and I would recommend it to everyone in the industry. It pointed

7!P to me the need for standards in things that I considered pretty well standardized already,

ifuch as wafer thickness. I also sat in on a discussion of the inaccuracies of mobility meaJjurements and the effects on Irvin's curves. Coupled with this I think what we have learned

it this Symposium is the fact that the Spreading Resistance technique can be no better than

:|he standards on which it is based.

277
CONCLUDING REMARKS by Paul Langer

I would like to make a very brief summary. We have heard 22 papers and some last minute re- marks in the last couple of days and I think it points up the direction that spreading re- sistance measurements will probably go in the next few years. There are two areas that

will probably get the bulk of the development effort. The first area is probably the development of more reliable correction factors for all types of structure* specifically very

thin transition regions between either one type or the same type of dopant. I think there

is also a need not only to have very complex correction factor models but also a need for

fast and simple correction factor models so that one will be able to perform these calculations on a calculator or a mini computer. The second area is that of surface preparation

and it is still a big unknown. Most laboratories have standardized more or less on their

own type of sample preparation. Under those constraints good intralab precision has been

obtained but this high level of precision may degrade in interlab studies due to differences

in specimen preparation. So I think surface preparation will get some closer looks over the

next few years. On the positive side, it is very nice to see the wide acceptance that

spreading resistance has had in all areas of the semiconductor industry. Crystal growers

are using it, the people in epi and diffusion are using it, and people modeling devices are using it. Spreading resistance seems to have come of age. It probably does not really have

as far to go as one would think from listening to some of the discussions.

I would like to reemphasize the role of ASTM and NBS in the measurements area. The

American Society for Testing and Materials is your organization as is the Bureau of Standards.

These organizations are here to do the work that people in the semiconductor industry are interested in getting done. The Bureau of Standards does not go off on research projects i, for the sake of research alone as neither does ASTM. It gets its inputs from the industry and

if you have a specific project you think really needs to be pursued or if you would like to help out in pursuing some of the work being done on electrical measurements or other means

of characterization I suggest you attend the next meeting in Scottsdale. It is right after

Labor Day and I think it will be very beneficial since in obtaining intercompany standardization one really needs to exchange material based on spreading resistance measurements.

Finally I would just again like to thank the members of the committee who acted as session

chairmen. Ken Benson and Bernie Morris of Bell Labs, Fred Mayer of RCA, Francois Padovani of

T. I. and Fritz Vieweg-Gutberlet of Wacker Chemitronic; and also to our arrangements man, Jim Ehrstein from the Bureau of Standards. Thank you all for coming and hope to see you all

again soon.

i

278
APPENDIX-BIBLIOGRAPHY

The bibliography which follows is intended for the convenience of users of this

voliime. While not pretending to be an exhaustive list of titles on spreading resistance,

it is nevertheless judged to contain all the major references commonly cited by those

working on spreading resistance measurements. Entries are listed by year of publication

and within each year, by the alphabetic ordering of the primary authors name

1. Kennedy, D. P., Spreading Resistance in Cylindrical Semiconductor Devices, J. Appl,

Phys. 31 #8, 1490-7 (1960).

2. Dickey, D. H. , Diffusion Profiles Using a Spreading Resistance Probe, Extended Abstracts of the Electronics Division, The Electrochemical Society 12 , No. 1, 151 (April

1963).

3. Mazur, R. G. , Dickey, D. H. , The Spreading Resistance Probe - A Semiconductor Resistivity Measurement Technique Extended Abstracts of the Electronics Division, The

Eleotroahemical Society 12_, No. 1, 148 (April 1963).

4. Greenwood, J. A., Constriction Resistance and the Real Area of Contact, Brit. J. Appl.

Phys. 17, 1621-1632 (1966).

5. Mazur, R. G. , Spreading Resistance Resistivity Measurements on Silicon Containing p-n

Junctions, Extended Abstracts of the Electronics Division, The Electrochemical Society

15, No. 1, (1966).

6. Mazur, R. G, , Dickey, D. H. , A Spreading Resistance Technique for Resistivity Measurements on Silicon, J. Eleotrochemiodl Society.. 113 , 255-259 (1966).

7. Dickens, L. E. , Spreading Resistance As a Function of Frequency, IEEE Transactions on Microwave Theory and Technique, MTT-15 No. 2, 101-109 (1967).

8. Greenwood, J. A., The Area of Contact Between Rough Surfaces and Flats, Trans. .ASME, Ser. F. 89, 81-91 (1967).

9. Holm, R. , Electric Contacts, 4th ed. Springer-Verlag, New York, (1967).

10. Mazur, R. G. , Resistivity Inhomogeneities in Silicon Crystals, J. Electrochem. Soc. 114 , 255-259 (1967).

11. Adley, J. M. , Poponiak, M. R. , Schneider, C. P., Schumann, P. J., Tong, A. H. , The

Design of a Probe for the Measurement of the Spreading Resistance of Semiconductors,

Semiconductor Silicon 1969, The Electrochemical Society, 721-736 (1969).

12. Keenan, W. A., Schumann, P. A., Tong, A. H. , Phillips, R. P., A Model for the MetalSemiconductor Contact in the Spreading Resistance Probe, Ohmic Contacts to Semiconductors, The Electrochemical Socity , 263-276 (1969).

13. Rymaszewski, R. , Relationship Between the Correction Factor of the Four-Point Probe

Value and the Selection of Potential and Current Electrodes, J. of Sci. Instr. , Series

2 Vol. 2, 170-174 (1969).

14. Schumann, P. A., Gardner, E. E. , Spreading Resistance Correction Factors, SolidState Electronics 12, 371-375 (1969).

15. Schumann, P. A., Gardner, E. E. , Application of Multilayer Potential Distribution to Spreading Resistance Correction Factors, J. Electrochemical Society 116_, 87-91 (1969),

16. Gorey, E. F. , Schneider, C. P., Poponiak, M. R. , Preparation and Evaluation of

Spreading -Resistance Probe Tip, J. Electrochemical Society 117, 721-724 (1970).

279
17. Gupta, D. C. , Chan, J. Y, A Semiautomatic Spreading Resistance Probe, Rev. Sci.

Instrim. 41, 176-179 (1970).

18

19

Gupta, D. C., Chan, J. Y. , Wang, P., Effect of the Surface Quality on the Spreading Resistance Probe Measurements, Rev. Sci. Instrim., 41, 1681-1682 (1970).

Hoppenbrouwers, A. M. H. , Hooge, F. N. , 1/f Noise of Spreading Resistances, Philips

Res. Rep. 25, 69-80 (1970).

20. Mazur, R. G. , Spreading Resistance Measurements on Buried Layers in Silicon Structures,

Silicon Device Processing: Gaithersburg, Maryland, NBS Special Publication 337, 240-

255 (1970).

21. Yeh, T. H. , Khokhani, K. H. , Multilayer Theory of Correction Factors for Spreading

Resistance Measurements, J. Electroohemiaal Society 116 , 1461-1464 (1969).

22. Yeh, T. H, Current Status of the Spreading Resistance Probe and Its Applications,

Silicon Device Processing: NBS Special Publication 337, 111-122 (1970).

23. Brooks, R. D. , Mattes, H. G. , Spreading Resistance Between Constant Potential Surfaces,

Bell System Tech. J. 50, 775 (1971).

24. Chu, T. L. , Ray, R. L. , Resistivity Measurements on Germanium Crystals by the Spreading

Resistance Technique, Solid-State Tech., 37-40 (September 1971).

25. Ting, Chung-Yu, Chen, C. Y., A Study of the Contacts of a Diffused Resistor, SolidState Electronics 14, 433-38 (1971).

26. Hu, S. M. , Calculation of Spreading Resistance Correction Factors, Solid-State ElecElectronics 15, 809-817 (1972).

27. Severin, P. J., Measurement of the Resistivity and Thickness of a Heterotype Epitaxially

Grown Silicon Layer with the Spreading Resistance Method, Philips Res. Rep. 26^, 359-372

(1971).

28. Severin, P. J., Measurement of the Resistivity of Silicon by the Spreading Resistance

Method, Solid-state Electronics 14, 247-255 (1971).

29. Tong, A. H., Gorey, E. F. , Schneider, C. P., Apparatus for the Measurement of Small

Angles, Rev. Sci. Instrwn. 43^, 320-325 (1972).

30. Kraner, P., Van Reuyven, L. , The Influence of Temperature on Spreading Resistance

Measurement, Solid-State Electronics 15, 757-766 (1972).

31. Schumann, P. A., Small Spaced Spreading Resistance Probe, Solid-State Tech., 50-54,

(March 1972).

32. Burtscher, J., Krausse, J., Voss, P., Inhomogeneities of the Resistivity in Silicon:

Two Diagnostic Techniques, Semiconductor Silicon 1973, The Electrochemical Society,

581-589 (1973).

33. Burtscher, J., Dorendorf, H. W. , Krausse, J., Electrical Measurement of Resistivity

Fluctuations Associated with Striations in Silicon Crystals, IEEE Trans, on Elec.

Dev. ED-20 , No. 8, 702-708 (1973).

34. Hu, S., Poponiak, M. R. , Copper Precipitation in Silicon-Observation of Electrical

Effect, Phys. Stat. Sol. (a) 18 no. 1, 5-8 (1973).

35. Witt, A. F. , Lechtensteiger , M. , Gatos, H. C, Experimental Approach to the Quantitative Determination of Dopant Degregat on a Microscale, J. Electrochemical Society

120, 1119-1123 (1973).

280
deKock, A. J. R. , Severin, P. J., Roksnoer, P. J., On the Relation between Growth

Striations and Resistivity Variations in Silicon Crystals, Phys. Stat. Sol. 22a , 163-

166 (1974).

Morris, B. L. , Some Device Applications of Spreading Resistance Measurements on Epitaxial Silicon, J. Eleatrochemiaal Society 121 , 422-426 (1974).

281
NBS-1 14A (REV. 7-73)

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Semioonduotov Measurement Technology : SPREADING RESISTANCE

SYMPOSIUM

PROCEEDINGS OF A SYMPOSIUM HELD AT NATIONAL BUREAU OF STANDARD

June 13-14, 1974

5. Publication Date December 1974

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16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This Proceedings contains the information presented at the Spreading Resistance

Symposium held at the National Bureau of Standards on June 13-14, 1974.

This Symposium covered the state of the art of the theory, practice and applications

of the electrical spreading resistance measurement technique as applied to characterization of dopant density in semiconductor starting materials and semiconductor device

structures. In addition to the presented papers, the transcripts of the discussion

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17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Dopant concentration, dopant profiles, metal-semiconductor contacts, resistivity,

semiconductor surface preparation, silicon, spreading resistance.

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