NAT'L INST. OF STAND & TECH

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Reference

Publications NBSIR 83-2792

Measurement Techniques for

High-Resistivity Detector-Grade

Silicon: Progress Report,

July 1, 1982 to June 30, 1983

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Semiconductor Materials and Processes Division

Washington, DC 20234

December 1983

-QC

100

. U56

83-2792

1933

Prepared for Electronics Technology and Devices Laboratory

Fort Monmouth, New Jersey 07703

v

MEASUREMENT TECHNIQUES FOR

HIGH-RESISTIVITY DETECTOR-GRADE

SILICON: PROGRESS REPORT.

JULY 1, 1982 TO JUNE 30, 1983

NBSIR 83-2792

-Rf/.

GC

i Oo

• US G

<V5-3-7^Z

13* i

R. D. Larrabee and J. R. Lowney

US. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Semiconductor Materials and Processes Division

Washington, DC 20234

December 1 983

This is a progress report. The work is incomplete and is continuing.

Results and conclusions are not necessarily those that will be included in the final report.

Prepared for: Electronics Technology and Devices Laboratory

Fort Monmouth, New Jersey 07703

«• o

<t

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

Abstract 1

I* Introduction 1

II. , Measurement of Average Ingot Resistivity 3

III. Profiling Excess-Carrier Recombination Lifetime . 6

IV. Profiling Radial Resistivity Variations ..... 13

V. Conclusions 15

VI. Acknowledgment 15

VII. References 15

LIST OF FIGURES

Page

1 . Schematic and pictorial views of a cylindrical ingot specimen

provided with four van der Pauw contacts 4

2. Schematic diagram of the optical portion of the apparatus for

profiling excess-carrier recombination lifetime 7

3. End view of a cylindrical ingot specimen showing the relationship

between the scanning diameter and the four van der Pauw contacts . 8

4. Schematic diagram of the electrical portion of the apparatus for

profiling excess-carrier recombination lifetime .. 10

5. Results of a feasibility experiment to demonstrate the lifetime

measurement technique ....... 11

iii
PREFACE

This work was conducted as part of the Semiconductor Technology Program at

the National Bureau of Standards (NBS). This program serves to focus NBS

research in areas that enhance the performance and reliability of discrete

semiconductor devices and integrated circuits through improvements in

measurement technology for use in specifying materials and devices. These

research programs are designed to produce carefully evaluated and welldocumented test procedures and associated technology. The resulting improved

measurement technology leads to greater economy in government and industrial

procurement by providing a common basis for purchase specifications. This

program is conducted in collaboration with industrial and governmental users

and suppliers of semiconductor materials and devices and with standardization

groups such as the American Society for Testing Materials (ASTM).

The segment of the Semiconductor Technology Program described in this report

was partially supported by the Electronics Technology and Devices Laboratory

(ET&DL) at Fort Monmouth, New Jersey under their Project No. 82-JAK-06 and

NBS Task No. 725-2310. The contract was monitored by Dr. R. L. Ross and R.

Savage of ET&DL. The NBS point of contact for information about the

technical elements of this project is R. D. Larrabee of the Semiconductor

Materials and Processes Division at the National Bureau of Standards.

IV
Measurement Techniques for High-Resistivity Detector-Grade Silicon:

Progress Report, July 1 , 1982 to June 30, 1983

R. D. Larrabee and J. R. Lowney

Semiconductor Materials and Processes Division

National Bureau of Standards

Washington, DC 20234

ABSTRACT

Techniques for nondestructi vely characterizing the resistivity and

excess-carrier recombination lifetime in ingots of highresistivity, long-lifetime detector-grade silicon are being evaluated. In particular, three interrelated techniques for nondestructi vely 1 ) measuring an average resistivity, 2) profiling the lowlevel excess-carrier lifetime, and 3) profiling the resistivity of

cylindrical ingot specimens are proposed and are in the process of

being evaluated. All three techniques treat the ingot under test

as a large van der Pauw specimen and require removable silver-paste

contacts or pressed-on capacitive contacts. The profiling measurements utilize a highly penetrating 1 . 1 5-pm He-Ne laser beam as an optical probe. The conceptual and theoretical background for these

measurements and the results of feasibility experiments obtained to

date are presented. These results show the expected behavior and

produce reasonable results, but additional work is required to

complete the feasibility experiments and to confirm the results on

a few specimens by some independent technique.

Key words: detector-grade silicon; lifetime profiling; resistivity

profiling; van der Pauw measurements.

I. INTRODUCTION

This project was designed to explore the feasibility and practicality of new

or improved measurement techniques for the characterization of highresistivity, long-lifetime detector-grade silicon. The project is part of

the NBS Semiconductor Technology Program and is intended to improve the characterization of detector-grade silicon for applications such as PIN photodiode detectors and CCD imaging arrays. Characterization of this material by

conventional techniques provides some measure of material quality, but this

may not prove to be the best possible measure for any given device application. The establishment of a series of well-documented characterization

techniques specifically designed to suit the intended application and adapted

to high-resistivity, long-lifetime material should lead to better control of

the significant properties of the starting material and the possibility of

higher yield and performance of completed devices. The emphasis of the present work has been on the development of techniques for nondestructi vely

characterizing ingot sections of as-received (as-shipped) silicon prior to

any processing except grinding to a cylindrical shape and polishing the ends

to facilitate optical probing measurements.

1
Dark current due to leakage or thermal-generation mechanisms is of prime

importance to CCD imaging and signal processing devices and, if large enough,

is of interest in PIN photodiode detectors. There are several potential

mechanisms of dark-current generation: thermal generation within the depletion region of an MOS capacitor, Schottky barrier device, or p-n junction;

diffusion of minority carriers, which were generated elsewhere within the

device structure, to this depletion region; and surface-related mechanisms.

Therefore, it is inappropriate to characterize even the bulk contributions to

dark current by a single parameter. However, the excess-carrier recombination lifetime is sometimes used for this purpose. But insofar as it only

characterizes the diffusion of minority carriers to the depletion region (and

not thermal generation within the depletion region), it is inadequate. The

thermal-generation lifetime within the depletion region [1] is more difficult

to measure [2,3], is fundamentally different from the excess-carrier recombination lifetime [1,3-5] and is a necessary parameter for the characterization

of the net thermal generation within a device containing a depletion region.

Characterization of surface-related leakage mechanisms can be important for

fully fabricated devices, but is not apropos to the characterization of as- received ingots. This report will discuss a way to profile nondes tructively

an axial-average excess-carrier low-level recombination lifetime over the cross section of cylindrical ingots of high-resistivity silicon. At the

present time, the authors are not aware of any technique for nondes tructively

profiling the corresponding axial-average thermal-generation lifetime over

the cross section of cylindrical ingots.

The resistivity of as-received ingots can be of prime importance for applications in which the active portion of the device is the depletion region. For

a given fixed value of reverse-bias operating voltage, the width of the depletion region is a function of the net doping density. For the high-purity

detector-grade silicon of present interest, the room-temperature carrier

mobilities are determined by lattice scattering and are virtually independent

of the doping density. Under these conditions, the net doping density can be

characterized by resistivity measurements.

Although various techniques have been developed for measuring the resistivity

of silicon, they are not all applicable to nondestructive measurements on high-resistivity ingot specimens. Probe techniques are commonly used at

lower resistivities [6,7] and find extensive application in measuring the

axial dependence of the resistivity of as-grown ingots. The four-point probe

technique is also used to profile the radial dependence of silicon wafers

[6,7]. However, these techniques may become unreliable and unstable at high

resistivities due to surface and probe-contact effects and, at best, require

extreme care and attention to details. Therefore, alternative approaches

have been studied as a replacement for probe techniques or as a means of

confirming the results of probe measurements. Contactless magnetic coupling

(eddy current) techniques become increasingly insensitive at high resistivities due to the small values of induced current. Increasing the frequency of

operation helps in this respect, but is limited by the resulting increases in

displacement current. This limits the frequency of operation to a few megahertz for resistivities in the tens of kilohm-cm region, if the silicon specimen is to be modeled as a "pure" resistance. The present experiments with

high-resistivity detector-grade silicon have shown greater coupling using

capacitive contacting techniques (e.g., ingot specimens placed inside coils

2
interacted through capacitive coupling to the wires of the coil instead of

through the coil's ac magnetic field), thus indicating that this is the

preferred approach.

This report will discuss resistivity measurements using an ac version of the van der Pauw technique [8,9] with removable silver-paste contacts or with

pressed-on capacitive contacts to the lateral surface of cylindrical ingot

specimens. This report will also discuss resistivity and lifetime profiling

techniques which are extensions of this basic van der Pauw technique and

which use the same van der Pauw specimen.

The basic van der Pauw technique assumes a homogeneous specimen resistivity.

If the specimen has a small inhomogeneity, the method yields an average value

that, in general, does not represent equal contributions from every volume

element within the ingot. This "average" ingot resistivity may not be an adequate characterization for those applications that require uniformity for

different devices fabricated on the same wafer (e.g. , uniformity of

depletion-layer depth at a given voltage). For these cases, it would be

desirable to profile nondes tructi vely the resistivity of the ingot in order

to select those ingots with resistivity variations which are not considered

excessive for the intended application. Small resistivity gradients along

the ingot length can be measured by cutting the cylindrical ingot into

smaller length pieces and measuring the "average" resistivity of each piece

by the ac van der Pauw method to be discussed in this report. This report

will also discuss an optical-profiling technique that can be applied to these

van der Pauw pieces for nondes tructi vely profiling their radial variations in

resistivity. Therefore, the combination of cutting into smaller length

pieces and of optical profiling allows one to characterize the resistivity

variations in three dimensions and thus determine if the variations throughout the entire ingot are acceptable for the intended application. These

techniques are based on the assumption that, to a first approximation, the

specimens are homogeneous in resistivity and then, as a second approximation,

the inhomogeneity is measured against this uniform background.

The three basic characterization techniques to be discussed in this report

(i.e., measurement of average ingot resistivity, profiling ingot resistivity,

and profiling radial variations of excess-carrier recombination lifetime) can all be performed on the same cylindrical van der Pauw specimen (ingot section) provided with removable silver-paste or pressed-on capacitive contacts.

The procedures for these nondestructive measurements and the interpretation

of the data obtained are relatively simple and the necessary equipment is not

prohibitively expensive. Therefore, it is anticipated that they may find

applications for the routine inspection of incoming (or outgoing) material to

assure compliance with specifications.

II. MEASUREMENT OF AVERAGE INGOT RESISTIVITY

Figure 1 shows a cylindrical ingot section that has been provided with four

linear contacts on its lateral surface to effectively make the entire ingot

section into one large van der Pauw specimen [8-10]. In this way, a current

I can be passed through two adjacent contacts (labeled 1 and 2 in fig. 1) and

the resulting voltage V observed at the remaining two contacts (labeled 3 and

3
CO P30p CO P p U P It •H P s c0

XJ o

a; X!

p

•H c > CD o P P P

a, 3O e

a) P e 0

•H

p

Oa 0

-C

p CO 0

tr> CO c It *H

T3

rH a)

(0 CO o 3 HP X)

x> c c (t

•ri rH XJ

S»I & V P

<u <d E P 3 0 C

CO CD

s* P

CD It •H> CO p

rH o

10 ct •H P P c 0 0 P u o

CD 04 £

Eh X!C

it •

CO o p

•HO • P it CO

ct P CD E C P

CD o 0

JO o P o 04

CO s3 CD

it 3> • P4 ct t— P P rH

ID CD 0 P X! > 3

Cn c n

•H <t c

fcr > id 4
4 in fig. 1). The ingot resistivity p is then computed from the well-known

van der Pauw relationship [7,10] for this geometry:

(V/I) 7T L

P £n ( 2

)

(1 )

where L is the length of the ingot specimen.

The use of this technique on ingot sections instead of wafers not only de- creases the potential problems with surfaces (because of the smaller

surface/volume ratio), but also permits evaluation of ingot sections before

they are cut up into wafers. This technique has been used successfully with

dc current and removable silver-paste contacts to an as-ground lateral surface on a 2-in. diameter, 1-in. long silicon ingot with a resistivity of

about 50,000 52 »cm. The slope of the current-voltage characteristic at the

origin between any two of the 1 -mm wide van der Pauw contacts was about

100,000 52 . The use of dc techniques with removable silver-paste contacts on

an as-ground-and-e tched lateral surface remains to be explored.

Pressed-on capacitive contacts offer an attractive possibility but necessitate the use of ac instead of dc. In this case, the reactance of the capacitive contacts must not be so large as to prevent the required current flow

and must be small compared to the impedance of the voltage sensing device (to

validate the assumption of ignoring the voltage drop across the voltagesensing contacts). Increasing the frequency of operation lowers the reactance of the contact capacitance, but if the silicon material is to be modeled as a pure resistance, the frequency of operation cannot be so high as to

give rise to a significant amount of displacement current. The charge and

displacement currents in silicon are equal when a/toe = 1, where a is the

conductivity of the silicon (reciprocal resistivity, p), w is the radian

frequency of operation, and e is the dielectric constant of silicon (1.06 x 1O~10 farads/meter). This occurs at a frequency of 15 MHz for 10,000 ft»cm

silicon. Thus, to avoid the necessity of modeling the silicon as a complex

impedance, the frequency of operation should be well below this value.

Therefore:

f <<

q

2ire

1 2irep

( 2 )

Some preliminary experiments with capacitive contacts to as-ground surfaces

have indicated that a porous deformable conducting material (such as the foam

plastic material used to short-circuit the pins of sensitive integrated circuits during shipment or storage) can be cut to the desired shape and pressed

against the ingot surface to provide a capacitive contact with a very small

external spacing. However, the total dielectric thickness of the contact

capacitance also includes any surface depletion layer in the silicon, and it

may be necessary to pre treat the surface to a weak accumulation condition to

minimize the total effective spacing and thus maximize the effective contact

capacitance. In addition, the ac drive should not be so larqe in amplitude

as to produce an appreciable depletion layer at the peak of the voltage

cycle. If this occurs, the contact capacitance could become a significant

nonlinear element in the circuit. These conditions have been satisfied for

capacitive contacts with larger areas than shown in figure 1 for this 50,000

5
ft»cm specimen, but the thin linear capacitive contacts of the van der Pauw

structure of figure 1 have not yet been studied.

The average resistivity obtained by this van der Pauw technique is not the

simple numerical average of the resistivity over the circular cross section

because different regions of the circular cross section contribute differently to the "average." However, if the variations in resistivity over the cross section are not large, this "weighted average" can be compared for

specimens cut from different positions along the length of the parent ingot

and thus give information about any axial variation of resistivity. If the

axial variations of resistivity of a single ingot section are significant,

each of the four van der Pauw contacts can be broken up into equal length

segments and van der Pauw measurements performed on each set of four segments

(which then define a smaller length of the ingot specimen). In this case,

the same ac (or dc) voltage needs to be applied to each corresponding pair of

segmented van der Pauw current contacts to prevent current from flowing axially and thus permit the measurement of the van der Pauw voltage over the

uncut portion of the ingot length as if it had been cut out. These axial

profiling techniques assume that, to a first approximation, the specimen is

homogeneous and that axial variations are measured against this background.

The following sections of this report discuss extensions of this basic scheme

to resistivity and lifetime profiling. These profiling techniques use the same van der Pauw ingot section specimen as the present average resistivity

technique, and the previous discussion about contacts and frequency of operation also pertains to these profiling measurements.

III. PROFILING EXCESS-CARRIER RECOMBINATION LIFETIME

A chopped 1.15-pm infrared He-Ne laser beam can be passed axially through the

ingot specimen of figure 2 to generate electron-hole pairs in the illuminated

region. An infrared-transmitting filter is included in the system of figure

2 to remove any visible light from the beam; a neutral-density filter is also

included to provide for adjusting the intensity of the beam. The beam is

mechanically chopped with a short on-period and a long off-period compared to

the excess-carrier recombination time being measured. The laser beam is

incident on one of the polished ends of the ingot specimen, and either the

specimen or the laser beam is movable so the laser beam can be scanned along

a specimen diameter oriented 45 deg with respect to the diameters joining

opposite contacts as shown in figure 3. The coordinate x is used to

designate the position of the laser beam along this diameter relative to the

center of the ingot face. The optical absorption depth of 1.15-ym infrared

light is several inches in high-purity silicon, and if the ingot is not too

long, laser light can be detected passing out the far end of the ingot as indicated in figure 2. Detection of this light is not necessary for the

present purposes, but the transmitted beam should be terminated properly as a safety precaution and to assure that it does not reflect off something and

return to the specimen.

The basic physics and geometrical aspects of a circular column of light scanning along a diameter of a much larger cylindrical specimen of semiconductor

material have been studied previously by Larrabee and Blackburn [10]. If the

quantity p in the denominator of eq (8) of that paper is replaced by the

6
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LU

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•H

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fd -P p a> <p

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+j

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OU

a; • p

CM P

a) a)

S' P

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<DC

0) p

0) Sia

•HX

cocoHP

(0 iH

d)P

a> 5

O'c

•HO£

CO •

CO

C •P

<u o E 03 H -P o C

a) 0

a, o a ? p 3 0 03 O' a* c

•p

p

a)

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03

p >

T3C P

•H 3 H O

ip

O

0)

03

Xp

ip0 TJC s 03

a) •H P > a> -p T3C

a)E W 03 •H

03 • co O'C

a) •H p C 3 c

O' 03 •H O

Cp CO 8
local resistivity at the light-spot position p(x), eq (11) of that paper

becomes: _

AV34 4a2b2p

ave (Ap) 1 AR — _ — / ( 3

)

12 7T L ( 2p ( x ) + Ap ) ( b*+ + x

1* )

where the voltage and current subscripts have been changed to the present

notation, p ave is the average resistivity of the ingot specimen (e.g. , measured by the technique discussed in sec. II, above), a is the radius of the

laser beam, b is the radius of the ingot specimen, L is the length of the

ingot specimen, and Ap is the change in resistivity caused by photoexcitation

of electron-hole pairs by the laser beam. The quantity p ave eq (3) is

not taken to be a function of x because this term arose in an expression for

an electric field which was integrated to give the voltage distribution over

the wafer surface (i.e., eq (3) in ref. 10). Therefore, this resistivity is

representative of the whole wafer, whereas the resistivity presently called

p(x) arose from solving the boundary condition at the light spot position and

is therefore characteristic of this particular region of the wafer. AV

31+ is

the change in van der Pauw voltage at contacts 3 and 4 due to the existence

of a Ap (i.e., due to chopping the laser beam). If Ap/pave

i s then

Aa = -Ap/(p (x) )2, where Ao is the change in conductivity due to the photoexcited carriers. If this expression for Aa is substituted into the above

equation and the resulting equation solved for the product (a2 Aa)/ one obtains:

a2

4t> = r.L. l .-AR)— (b1* + x*-) . (4)

2b2 P aveP (x)

Consequently, at any given position of the laser beam (i.e. , any given value

of x), AR = AV^/I is directly proportional to A a* Thus, the variation of

the van der Pauw voltage AV31+ for a fixed current I 12 can be used to monitor

directly the changes in Aa as the excess photogenerated carriers recombine.

Therefore, the transient return of AV^ to steady-state conditions can be

used to measure directly the excess-carrier recombination lifetime at any

position x on the scanning diameter in a manner completely analogous to a conventional decay of photoconductivity measurement [11].

Several conditions must be satisfied for this scheme to produce a valid measurement of excess-carrier recombination lifetime. The observed transient

return to steady state after the laser light has been chopped off should be

exponential. Nonexponentiality could arise from too large a laser light

intensity (lifetime varying with excess-carrier density), unequal electron

and hole lifetimes (due to selective trapping of one carrier), or multiple

recombination centers (giving rise to several distinct mechanisms of recombination with different lifetimes). Since this is essentially a decay of photoconductivity experiment, all the conventional caveats about that technique [11] apply equally well to the present situation. The assumption was made in the derivation of eq (4) that Ap/p ave was sma H» Therefore, it is

necessary to vary the laser light intensity (by using the various neutral

density filters) to assure that it is low enough to satisfy this constraint

(i.e., measured lifetime does not depend on the light intensity used) and not

9
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d)ox

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03

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4-> OV

03 x:

4->

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03 4J P 03 U1 <P

03 -P

•H »H

T!

C o o

•H *H 4-> 4-1 03 03 E C

d) *P

x: -Qp

d) d3 P *rt SS•P 03 t O

10
CO CM OO CO ID CO

3SN0dS3d 3AI1V13U

CM

00

,Z_ 03

TO

11

Figure

5.

Results

of

a

feasibility

experiment

to

demonstrate

the

lifetime

measurement

technique

Insert

shows

the

modulation

envelope

of

the

ac

van

der

Pauw

voltage

during

the

light-chopping

cycle.

The

graph

shows

plotted

points

measured

from

the

modulation

envelope

and

a

fitted

leastsquares

line

indicating

that

the

decay

is

exponential

and

that

the

lifetime

is

4.8

ms.
so high as to produce nonexponentiali ty. When these conditions are satisfied, the measured lifetime will be the low-injection-lavel excess-carrier

recombination lifetime [4,5].

In addition, it is necessary to use a constant ac current drive (i.e., not

dc) to assure that there is no drift of the photoexcited minority carriers

out of the region where they were excited (i.e., the laser beam) towards the

appropriately biased current contact. The use of ac causes the photoexcited

carriers to oscillate about their point of generation without a dc component

of drift. The amplitude of the ac drive cannot be so large as to produce a significant amplitude of oscillation compared to the laser-beam radius.

However, this is easily checked experimentally by measuring the lifetime as a function of ac drive and the frequency of operation and requiring that it be

independent of both.

Thermal diffusion of photoexcited carriers out of their region of photogeneration is certainly a problem if they reach the surface of the cylindrical

ingot. However, if the laser beam is kept at least a few diffusion lengths

away from the ingot surface, then as the carriers diffuse, the effective size

of the region containing the photoexcited carriers increases (i.e., it is no longer equal to the laser radius a). However, if this situation is modeled

as an expanding cylindrical region of constant Aa/ then the product a 2 Aa of

eq (4) is not changed by this radial expansion if a is taken as the radius of

the expanded region containing the photoexcited carriers. Therefore, the van der Pauw voltage a v still serves the purpose of measuring the recombination

lifetime, but over a volume defined by the sum of the laser light radius and

the diffusion length.

The laser light is attenuated as it propagates axially through the specimen.

This is not a serious limitation in the low-injection regime of interest

where the lifetime is not a function of the photoexcited carrier density.

However, it does limit the length of ingot that can be measured, and it may

be necessary to measure long ingots a second time with the laser light incident from the opposite end. In fact, it may be desirable to do this with the

shorter ingots as a check on the validity of the results.

Figure 4 shows the circuit used to test the feasibility of this approach

using the 50,000 ft* cm specimen of silicon discussed in Section II above. The

two 150,000 ft series resistors in the current-drive circuit comprise about 80

percent of the ac circuit resistance and thus effectively give a constant ac current drive characteristic. The voltage-sensing probes are high impedance

probes (compared to the specimen impedance between the voltage contacts) so

they accurately sense the voltage at the ingot surface at the contact position. The removable silver-paste contacts to an as-ground surface discussed

in Section II above were used in this feasibility test, and similar tests

with silver-paste contacts to etched surfaces and pressed-on capacitive contacts are planned for future experiments. The results to be presented were not sensitive to the frequency of operation over the range from 200 to 500

KHz, and 300 KHz was used for the results to be reported. The oscilloscope

display of the top portion of the modulation envelope of the 300-KHz signal,

V^ t+ , is shown in the insert of figure 5. The lifetime can be directly observed as the time constant of the exponential decay following the 1 -ms illumination period (i.e., on-time of the chopping wheel). The transient was

12
measured at the indicated points and plotted as shown in figure 5 to give a measured lifetime of 4.8 ms. This measurement was performed at the center of

the ingot face (i.e. , x = 0) and at a low enough ac drive and light intensity

(«10 pW) to give results that were independent of drive and light intensity.

It was also observed that the lifetime did not vary significantly over the

scanning diameter until the light spot was within a few mm from the as-ground

ingot surface and then decreased as that surface was approached. Independent

measurements using the same ingot with a commercially available instrument

that floods the whole specimen with infrared light and uses a 30-MHz operating frequency and capacitive coupling to sense the resulting conductivity

changes gave a lifetime of about 7 ms. A possible explanation for the difference between this value and the presently obtained value of 4.8 ms is the

non-negligible displacement current at 30 MHz in a 50,000 ft«cm specimen

(i.e., inequality 2 is not satisfied). The resulting effect of this added

capacitive component of specimen impedance on this measurement is currently

under investigation. Note, however, that this is not a problem at the 300-

KHz operating frequency used with the present laser-scan technique.

Therefore, it has been demonstrated that this laser-scan technique can be

used to profile an axially averaged low-level excess-carrier recombination

lifetime over a scanning diameter to within a few diffusion lengths of the

ingot surface. By rotating the specimen by 90 deg in figure 4 and renumbering the contacts accordingly, a second diameter, perpendicular to the first, can also be scanned without otherwise changing the system or specimen in any

way. Only standard laboratory equipment (a low power He-Ne laser, a signal

generator, and an oscilloscope) are needed and the procedure and data reduction are relatively simple and straightforward. This technique has the potential of providing a practical way to profile the radial variations of

excess-carrier recombination lifetime in ingots of high-resistivity silicon.

Axial profiling could, in principle, be done by using the techniques discussed in Section II above (e.g., by segmenting the four van der Pauw contacts), but this has not been explored.

One additional advantage of this technique is discussed in the following

section where it is shown that this identical measurement can also produce a profile of the relative resistivity (i.e., p(x)/p(o)) over the scanned diameter. Since these two measurements use the same specimen and the same basic

technique, all of the above discussion about ac drive, laser light intensity,

validity of eq (4), etc. will also pertain to the following discussion of

radial resistivity profiling.

IV. PROFILING RADIAL RESISTIVITY VARIATIONS

The technique for profiling excess-carrier recombination lifetime discussed

in Section III above can also be used to profile radial variations of resistivity. The basic equation describing that lifetime measurement was eq (4).

If this equation is solved for p(x), one obtains:

p

( x ) =

71

tr**) (b^ + X*M , (5)

2b2 P aVe (a2Aa)

13
where AR = AV /I

34 12 (i.e., any given value of x),

Consequently, at any given position of the laser beam

is a measure of pfxj/tb4 + x

1* ) if Ao could

34

be made independent of x. If the on-time of the chopped laser beam Tonis

short compared to the excess-carrier recombination lifetime in the silicon

ingot, there will be negligible recombination during the interval that the

laser is on, and Ao at the end of this interval will be given by:

Ao = (p + + M_)egT

on

( 6 )

where y + and p_ are the carrier mobilities, e is the electronic charge, and

g is the photoexcitation rate of electrons and holes per unit volume. Clearly, g depends on the intensity of light in the laser beam, but it is virtually independent of all ingot-related variables such as dopant or deep-level

density in the high-purity, detector-grade silicon of interest. Nothing in

the above equation for Ao is a function of x, and Ao can be taken as a con- stant in eq (5) for any given experimental situation. If A is the amplitude

of the change in the van der Pauw voltage at the end of the Ton period (see

insert to fig. 5), then the relative resistivity at any position x is given

by:

p (x) _ A(x

)

p ( o ) A(o) (7)

where A(x) and A(o) are the measured amplitudes at positions x and o, re- spectively.

In eq (6), it is assumed that the excess electron and hole densities at the

end of the laser on-period were both equal to gTon » Although excess electrons and holes will be generated equally for photoexcitation across the

bandgap during the light-on period, it is possible for traps to capture one carrier preferentially and thus invalidate eq (6). This would have no adverse effects if that trap were uniformly distributed in the ingot specimen

so that Ao would still be independent of x, but there are potential problems

if the traps are inhomogeneous ly distributed and Aa varies with x. At the

present time, the authors are unaware of any nondestructive measurement that can be made on these van der Pauw specimens to distinguish between inhomogeneous distributions of such traps and inhomogeneity of resistivity. Therefore, in any practical use of the laser-scan technique, it may be necessary

to determine that the material in question has sufficiently low trap density

or that the traps are sufficiently uniformly distributed to validate the

assumption that Aa is independent of x.

This technique was tested on the 50,000 u*cm ingot specimen with removable

silver-paste contacts that was used in the previous tests discussed above.

The on-period of the laser beam was shortened from the 1-ys value of figure 5 to 0.4 ys, and amplitude A was measured at regular intervals along the

scanning diameter. A value of p(x)/p(o) was then calculated from eq (6) for

each measurement position x. No significant variations of resistivity could

be seen over the central 2/3 of the scanning diameter (i.e., p(x) was con- stant to within about ±20 percent). It was concluded that the sensitivity of

the system needed to be improved in order to measure accurately resistivity

variations this small. However, p(x) was observed to fall off to about 50 to

14
60 percent of its value at x = 0 near the ends of the scanning diameter. At

the present time, there is no facility at the National Bureau of Standards

for confirming these results. Therefore, plans are being made to develop a confirmation technique based on capaci ti ve-voltage measurements of guarded

Schottky barrier contacts spaced along the scanning diameter to measure the

dopant density profile along the same diameter used in the laser-scan measurement. In addition, plans are being made to test this laser-scan technique with removable silver-paste contacts to an etched surface on the ingot

specimen and with pressed-on capacitive contacts. It is felt that this additional work is necessary before this basic laser-scan technique can be recom- mended for routine use.

V. CONCLUSIONS

Three coupled techniques for nondes tructively 1) measuring an average resistivity, 2) profiling the low-level excess-carrier lifetime, and 3) profiling

the resistivity of cylindrical ingot specimens of high-resistivity detectorgrade silicon have been proposed and are in the process of being evaluated.

All three techniques treat the ingot section under test as a large van der

Pauw specimen and require removable silver-paste contacts or pressed-on ca- pacitive contacts. The profiling measurements require the use of ac current

drive at a frequency low enough so that the displacement current is very much

smaller than the charge current due to the extrinsic carriers. The profiling

measurements use a highly penetrating 1.15-ym He-Ne laser beam as an optical

probe to photoexcite excess carriers to modulate the local extrinsic conductivity for resistivity profiling and to allow observation of their decay for

lifetime profiling. The conceptual and theoretical background for these

measurements and the results of feasibility experiments obtained to date have

been presented. These results show the expected behavior and produce reasonable results, but additional work is required to complete the feasibility

experiments and to confirm the results on a few specimens by some independent

technique.

VI. ACKNOWLEDGMENT

The authors would like to acknowledge W. R. Thurber's assistance in performing the independent measurements of excess-carrier recombination lifetime

discussed in this report.

REFERENCES

1. Schroder, D. K. , The Concept of Generation and Recombination Lifetimes

in Semiconductors, IEEE Trans. Electron Devices ED-29 ,

1 336-1338

(1982).

2. Zerbst, M. , Relaxationseffekte an Halbleiter-Isolator-Grenzflachen, Z.

Angew. Phys. _22, 30-33 ( 1966).

3. Blood, P. , and Orton, J. W. , The Electrical Characterization of Semiconductors, Rep. Prog. Phys. _41_, 1 57-257 ( 1 978).

4. Ghandhi, S. K. , Semiconductor Power Devices (New York, Wiley and Sons,

1977), pp. 1-8.

15
5. Shockley, W. , and Read, w. T. , Statistics of the Recombination of Holes

and Electrons, Phys. Rev. _87, 835-842 (1952).

6. Runyan, W. R. , and Watelski, S. B. , Semiconductor Materials, Handbook of

Materials and Processes for Electronics, C. A. Harper, Ed., Chapter 7 (New York, McGraw-Hill Book Company, 1970).

7. Runyan, W. R. , Resistivity and Carrier-Concentration Measurements,

Semiconductor Measurements and Instrumentation, Chapter 3 (McGraw-Hill

Book Co., New York, 1975).

8. van der Pauw, L. J. , A Method of Measuring the Resistivity and Hall

Coefficient on Lamellae of Arbitrary Shape, Philips Tech. Rep. _20# 220-

224 (1958).

9. van der Pauw, L. J. , A Method of Measuring Specific Resistivity and Hall

Effect of Disks of Arbitrary Shape, Philips Res. Rep. 1

, 1-9 (1958).

10. Larrabee, R. D. , and Blackburn, D. L. , Theory and Application of a Nondestructive Photovoltaic Technique for the Measurement of Resistivity

Variations in Circular Semiconductor Slices, Solid State Electronics 23 , 1059-1068 (1980).

11. 1982 Annual Book of ASTM Standards, Part 43 (American Society for Testing and Materials, Philadelphia, PA, 1982), F 28-75, pp. 195-200.

16
NBS-114A (REV. 2-80) U.S. DEPT. OF COMM. 1 . BIBLIOGRAPHIC DATA

SHEET (See instructions

4. TITLE AND SUBTITLE

PUBLICATION OR 2 REPORT NO.

NBSIR 83-2792

. Performing Organ. Report NoJ 3. Publication Date December 1983

Measurement Techniques for High-Resistivity Detector Grade Silicon: Progress Report

July 1, 1982 to June 30, 1983

5. AUTHOR(S)

Robert D. Larrabee and Jeremiah R. Lowney

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No. 82-JAK-Q6

8. Type of Report & Period Covered

7/1/82 to 6/30/83

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Electronics Technology and Devices Laboratory

Fort Monmouth, NJ 07703

Electronics Technology

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) Techniques for nondestructively characterizing the resistivity and excess-carrier

recombination lifetime in ingots of high-resistivity, long-lifetime detector-grade

silicon are being evaluated. In particular, three interrelated techniques for

nondestructively: 1) measuring an average resistivity, 2) profiling the low-level

excess-carrier lifetime, and 3) profiling the resistivity of cylindrical ingot

specimens are proposed and are in the process of being evaluated. All three

techniques treat the ingot under test as a large van der Pauw specimen and require

removable silver-paste contacts or pressed-on capacitive contacts. The profiling

measurements utilize a highly penetrating 1.15 ym He-Ne laser beam as an optical

probe. The conceptual and theoretical background for these measurements and the

results of feasibility experiments obtained to date are presented. These results

show the expected behavior and produce reasonable results, but additional work is

required to complete the feasibility experiments and to confirm the results on a few specimens by some independent technique.

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and separate key words by semicolon s) detector-grade silicon; lifetime profiling; resistivity profiling; van der Pauw

measurements

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