NBS TECHNICAL NOTE 736

Carrier Lifetime Measurement

by the Photoconductive

Decay Method
NATIONAL BUREAU OF STANDARDS

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wl z':~~'" cr sTAssAnas

Carrier Lifetime Measurement by the

Photoconductive Decay Method

Richard L. Mattis and A. James Baroody, Jr.

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

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U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acting Director,

Issued September 1972
National Bureau of Standards Technical Note 736

Nat. Bur. Stand. (U.S.), Tech. Note 736, 52 pages (Sept. 1972) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. 03.46:736). Price 50cents.
PREFACE

The research reported herein was carried out as part of the Joint

Program on Methods of Measurement for Semiconductor Materials, Process

Control, and Devices. This program was undertaken in 1968 under joint

sponsorship by the National Bureau of Standards (NBS) and other government agencies. The program aims to enhance the performance, interchangeability, and reliability of discrete semiconductor devices and integrated

circuits through improvements in methods of measurement for use in specifying materials and devices and in control of device fabrication processes. In particular, this report is intended to assist in the understanding and use of the measurement of carrier lifetime by the photoconductive

decay (PCD) method.

The authors are indebted to many people at NBS for assistance in

carrying out this research. W. E. Phillips and W. M. Bullis provided

helpful suggestions throughout the course of the work. The lifetime

versus temperature data were taken by F. R. Kelly. The specimen temperature versus specimen current data were taken by F'. H. Brewer. Fabrication assistance was provided by A. W. Stallings. The manuscript was

typed at various stages by T. A. Schultz, R. E. Joel, M. L. Stream, and

K. E. Dodson.

The authors are also indebted to Dr. H. Benda for supplying a preprint of his publication which is referenced herein.

111

TABLE OF CONTENTS

Page

1. INTRODUCTION 2

2. DEFINITION OF LIFETIME 2

3. THE PCD METHOD 2

4. BULK DECAY TIME CALCULATION 3

5. BASIC LIMITATIONS

5.1. Excess Carrier Density 6

5.2. Light Source 10

5.3. Inhomogeneities 11

5.4. Filter Thickness 14

5.5. Temperature 21

6. OTHER CONSIDERATIONS

6.1. Light Turnoff Time 21

6.2. Series Resistance 23

6.3. Specimen Current, Illumination Pattern and

Sweep-Out 25

6.4. Specimen Current and Ohmic Heating 30

6.5. Specimen End Contacts 32

7. TRAPPING 33

8. SUMMARY 34

9. REFERENCES 36

APPENDIX 40
LIST OF FIGURES

Page

1. Schematic diagram of apparatus used in the PCD method 4

2. Bulk decay time Xg in microseconds as a function of relative

excess carrier density An/pQ for six specimens, where xg has

been multiplied by (1 + An/pQ) so that the plot may be com- pared with the linear behavior described by eq (4) 8

3. Cross-section of a 10 fi'cm, n-type silicon crystal showing

the original locations of ten cut specimen 12

4. Illustration of the illumination pattern used to study

inhomogeneities in specimen SS13 19

5. Bulk decay time in microseconds as a function of temperature

in degrees Celsius for four specimens 22

6. Photoconductive decay time xp^j) as a function of turnoff time

t ff for five specimens where both xpQ) and t Q£f have been

normalized with respect to the average xpcD which was measured

before turnoff affected the measurement TpQ) 24

7. Photoconductive decay time xp^p, signal level Vs ±o> and percent

standard deviation s as a function of series resistance Rg for

four specimens 26

vi
LIST OF TABLES

PAGE

1. Signal Level at Which a Relative Sample Standard Deviation

of 4 Percent Was Observed in TpQ) Measurements on Six

Specimens 9

2. Comparison of Photoconductive Decay Times Measured with

Chopped Light and Pulsed Light Excitation 9

3. Decay Times of Specimens Cut from a 10 ft •cm, n-Type

Silicon Crystal 13

4. Decay Times of a Specimen Cut from a 4 fi*cm, p-Type

Silicon Crystal as a Function of Specimen Size 15

5. The Effect of Filters of Different Thicknesses on the

Photoconductive Decay Time TpQ^ Measured with Chopped

Light Excitation 16

6. The Effect of Filters of Different Thicknesses on the

Photoconductive Decay Time Tp^p Measured with Pulsed

Light Excitation 17

7. Photoconductive Decay Time of Specimen SS13 Measured with

the Illumination Incident at Several Locations on Side A . . . 20

8. Photoconductive Decay Time of Specimen SS13 Measured

with the Illumination Incident on Sides B and D for

Various Filter Thicknesses 20

9. Number of Drift Lengths from Each End Contact at

Which Sweep-out First Appeared for a Group of

Specimens 29

10. Power Dissipations at Which Specimen Temperature

Increased 0.25°C for a Group of Twelve Specimens 31

11. Specimen Characteristics 40

vii
LIST OF SYMBOLS

Unless otherwise noted in the text, physical quantities described in

this paper are given in the units defined by the International System of

Units (SI units) as defined by the General Conference on Weights and Measures in 1960. The SI base units encountered in this report are the

metre, the second, and the ampere. Other SI derived units are the volt

and the ohm. Where SI base units are not used in favor of centimetre,

millimetre, microsecond or degree Celsius, the units are given in the

text.

In some instances the strict adherence to SI units may represent a departure from the common parlance of the semiconductor industry. Examples of this are carrier concentrations in atoms per cubic metre and

the use of square metres per second for diffusion coefficient. In most

of these cases, however, the equations in which these quantities occur are such that the units cancel, thereby making it possible to substitute

cgs units for SI units.

Following is a list of symbols used in the report along with the

appropriate units.

D ambipolar diffusion coefficient, square metres per second

D diffusion coefficient for electrons, square metres per second

D diffusion coefficient for holes, square metres per second

P d drift length, metres

E electric field intensity, volts per metre

e base of natural logarithms

i specimen current, amperes

L specimen length, metres

L distance between illumination boundary and nearest end contact,

metres

L ambipolar diffusion length, metres

L. length of illuminated region, metres

n„ equilibrium electron density, electrons per cubic metre

An excess electron density, electrons per cubic metre

p. equilibrium hole density, holes per cubic metre

Ap excess hole density, holes per cubic metre

viii
R specimen bulk resistance, ohms

R contact resistance, ohms

c R series resistance, ohms

s

r specimen radius, metres

s relative sample standard deviation, percent

T specimen thickness, metres

t ff light turnoff time, seconds

AV change in specimen voltage corresponding to an excess carrier

density An = Ap, volts

Vft dc voltage across illuminated portion of the specimen, volts

V . peak value of PCD signal, volts sig

V . * value of V . measured for the case R /R = 20, volts

sxg sig s W specimen width, metres

x position coordinate for illumination of specimen SS13, millimetres

y ambipolar mobility, square metres per volt-second

U mobility of majority carriers, square metres per volt-second

maj

y . mobility of minority carriers, square metres per volt-second

y mobility of electrons, square metres per volt-second

y mobility of holes, square metres per volt-second

p specimen resistivity, ohm-metres

x carrier lifetime, seconds

t bulk decay time, seconds

t photoconductive decay time, seconds

t * value of t „ for the case R /R = 20, seconds

~PCD

Value °f T PCD

When fc off

<K TPCD»

seconds

t q

carrier lifetime when An = Ap = 0, seconds

t^ carrier lifetime when An = Ap >> n

n

, pn

, seconds

ix

Carrier Lifetime Measurement by the

Photo conductive Decay Method

Richard L. Mattis

and

A. James Baroody, Jr.

ABSTRACT

The photoconductive decay (PCD) method of carrier lifetime measurement is discussed with emphasis on experimental and analytical work done

at NBS. The relationship between photoconductive decay time Tpgn, bulk

decay time x , and lifetime is described briefly and the PCD method is

summarized. The determination of x from x and the influence of higher modes of recombination are discussed.

Experimental data, supported by theoretical considerations, are presented to demonstrate the dependence of xpqq on excess carrier density,

the type of light source, specimen homogeneity, filter thickness, and

temperature. The dependences of xp^rj on excess carrier density and temperature are consequences of the statistics of the recombination process.

Measurements made with chopped light excitation are shown to be less in error due to higher modes of recombination than are measurements made

with pulsed light excitation. The presence of inhomogeneities is verified in two crystals. Use of a filter is also shown to reduce the influence of higher modes. An unexpected reduction in x with increasing

filter thickness is shown to be caused by an inhomogeneity

Other experimental conditions are discussed as they affect the measurement of XpQj). It is shown that the light turnoff must be sufficiently fast and the series resistance sufficiently large that they do not

interfere with the measurement. Equations are developed whereby the

specimen current and illumination pattern can be chosen such that carrier

sweep-out at the ends of the specimen and ohmic heating are avoided. The

end contacts must be sufficiently ohmic that excessive contact resistance

does not interfere with the measurement.

Trapping is defined and the means for identifying it are discussed

briefly. The PCD method is inappropriate for determining minority carrier lifetime when trapping is present or under other circumstances when

the hole and electron lifetimes are unequal.

Key Words : Carrier lifetime; germanium; photoconductive decay; silicon.
1 . INTRODUCTION

In 1965, the National Bureau of Standards (NBS) initiated a study of

methods for measuring carrier lifetime in semiconductor crystals . Prior

to the present report an annotated bibliography of lifetime measurement

was compiled [1], and a preliminary report that described several procedures for the measurement was prepared [2], A principal phase of the

study involved a detailed investigation of the photoconductive decay

(PCD) method. This paper summarizes the experimental and analytical work

relevant to the PCD method which has been done since the publication of

the earlier report.

The PCD method was studied in detail because of its wide acceptance

and its adoption as a standard by both the Institute of Electrical and

Electronics Engineers (IEEE) [3] and the American Society for Testing and

Materials (ASTM) [4], The present report provides the technical basis

for changes which are being proposed for incorporation into a revision of

the ASTM standard.

The relative two-sigma precision [5] for the measurement is quoted

in the ASTM standard as ±50 percent for germanium and ±135 percent for

silicon. One objective of the lifetime study was to identify the causes

of this poor precision and to develop the technology necessary to improve

the precision of the measurement. A multi-laboratory round-robin experiment to test the proposed changes is being planned by ASTM Committee F-l

on Electronics.

2. DEFINITION OF LIFETIME

Minority-carrier lifetime is defined as "the average time interval

between the generation and recombination of minority carriers in a homogeneous semiconductor" [6] . Rather than attempting to evaluate the lifetime as defined, the emphasis in this report is on the time constant of

carrier decay (photoconductive decay time, Tp^D

) and the bulk decay time,

t . Whereas t is influenced by recombination at the surface as well

as in the bulk, x is derived from Tj>qj) and is a time constant of bulk

recombination. In the case of simple bulk recombination through a single

center, the carrier decay is exponential and the bulk decay time is equal

to the bulk minority carrier lifetime. In general, however, they may be

different [7].

3. THE PCD METHOD

In the PCD method [2-4, 8-11] a semiconductor specimen through which

a small current is passed is illuminated with radiation of energy near

the band gap energy. The excess carriers created increase the conductivity of the specimen which decreases the voltage across the specimen.

Under small-signal conditions, the specimen voltage change and excess carrier density are inversely proportional. The time constant of the in- crease of the specimen voltage when the light is abruptly removed is the

photoconductive decay time, t .
The experimental apparatus is shown schematically in figure 1. The

light source may be either a pulsed light source, such as a xenon flash

tube or other spark source, or a mechanically chopped, steady light

source, such as a tungsten filament lamp or other suitable lamp. Light

from the source is directed to the specimen by a system of lenses or mirrors. The filter, of the same material as the specimen, absorbs non- penetrating light so that the carriers are generated more uniformly

throughout the specimen volume. The mask limits the illumination to the

desired region of the specimen. Current is passed through the specimen

by means of ohmic contacts at each end. The specimen voltage is amplified and displayed on an oscilloscope.

Two methods of measuring the photoconductive decay time were studied. In the first method, the PCD curve is matched to an exponential

curve inscribed on the oscilloscope graticule by adjusting the sweep rate

of the oscilloscope. A time mark generator is used to measure the time

constant of the inscribed curve and hence to determine ^ . In the second method, a differential oscilloscope input is used to match the PCD

curve with an electronically generated exponential curve with adjustable

time constant. When the time constants of the two curves are equal, a null in the form of a straight line is formed.*

Additional details of the apparatus may be found in the literature

[2-4, 8-11].

4. BULK DECAY TIME CALCULATION

Specimens measured by the PCD method are usually as-grown crystals

or rectangular parallelepipeds cut from these crystals. Cut specimens

are usually lapped on each surface to produce surfaces with high surface

recombination velocity. If the surface recombination velocity is assumed

to be infinite, then carriers recombine immediately upon reaching the

surface. The surface recombination is then limited only by the rate of

diffusion of carriers to the surface. Under this condition, the relation

between x and tb is given by:

-[w-^+^r

for the case of a rectangular parallelepiped [12] , and by:

=

|_ TPCD ' - ^ifp" J

-1

tb

= I rnr, n - tt z D -dh^r (2)

Preliminary results indicate that although TpQ) values measured by the

time mark method are slightly longer than Tp^p values measured by the

null method the two methods agree to within two sample standard deviations of the measurement. However, to avoid any discrepancies resulting

from the use of two techniques, intercomparative measurements should be

made using just one technique.
o

UJ

UJ 42 e> 4J * 6 cr< PM 5 <u UJ

43

4J H

(U

(0

CO

4J

co

S-i copu

exO

00

ccj •H

CO

43O

CO

cu

00

•H
for the case of a right circular cylinder [8] . In these expressions W

is the specimen width, T is the specimen thickness, r is the specimen

radius, and D is the ambipolar diffusion coefficient given by [13]

D D (n n + p ) D = _2L_E 0_ (3) D n. + D p„ ' ^ n p^O

where D and Dn are the diffusion coefficients of electrons and holes, n " and nQ and pq are the equilibrium electron and hole concentrations . For

extrinsic materials, D reduces to the minority carrier diffusion coefficient.

Several assumptions are made in deriving eqs (1) and (2). First, it

is assumed that the specimen can be characterized by a single bulk decay

time. The process of crystal growth often produces an inhomogeneous distribution of flaws and impurity centers which causes x to vary with position in the crystal. This can result in poor measurement reproducibility unless the same portion of the specimen is illuminated consistently.

This variability is discussed further in section 5.3.

A second assumption is that the surface recombination velocity is

very large over the entire specimen surface. As already indicated this

condition can be approximated if a lapped surface is used.

A third assumption is that higher modes or recombination [14] can be

neglected. In a manner resembling the Fourier analysis of a waveform,

the carrier recombination can be assumed to consist of a series of modes

of recombination. In this series each mode is characterized by a time

constant and an initial amplitude. As decay proceeds, the modes representing surface decay contribute less and less to the total recombination. Because of the higher rate of recombination at a lapped surface,

and the resulting depletion, the contribution of surface recombination to

the total recombination process changes as recombination progresses. For

example, if decay begins from a uniform excess carrier distribution,

those carriers within a diffusion length of the surface dominate the initial stages of decay. In the later stages of decay a smaller fraction of

the total recombination takes place at the surface. The influence of

higher modes is affected by such experimental parameters as the type of

light source and filter thickness as discussed elsewhere in this report.

The significance of higher modes can be reduced to a negligible effect by

an appropriate choice of these experimental conditions.

A fourth assumption is that of small-signal conditions such that

conductivity modulation is not significant [2]. This condition can be

met by an appropriate choice of signal level.

A fifth assumption is that photoinjected carriers do not diffuse or drift to the end contacts. If recombination occurs at the end contacts,

eqs (1) and (2) must be modified to include a term involving the specimen

length or a term involving the applied electric field or both. This
assumption and the conditions under which it is valid are discussed in

section 6.3.

A sixth assumption is that trapping is not significant so that the

electron and hole lifetimes are equal. The effects of trapping and un- equal hole and electron lifetime are discussed in section 7.

When these six assumptions are valid x can be calculated from xp^D

using eqs (1) and (2). However, in instances where surface recombination

is dominant such that x > 3x , t may be imprecise since it is calculated from the difference between two large numbers . A possible inaccuracy also occurs since x is then sensitive to D, the assumed value of

which may be in error.

5. BASIC LIMITATIONS

Carrier lifetime is dependent upon a number of quantities and con- ditions which are inherent in the nature of semiconductor materials and

the recombination process. These quantities and conditions include excess carrier density, the type of light source, specimen homogeneity,

filter thickness, and temperature. The effect of these quantities and

conditions upon the measurement of xpcj) is discussed in this section.

Specimens for which data are recorded in support of the discussion are identified in the Appendix.

5.1. Excess Carrier Density

Recombination in silicon and germanium occurs primarily through re- combination centers with energy states in the forbidden gap. These

energy states result from the presence of foreign impurity atoms or other

defects in the material. If the characteristics of these energy states

are known, it is possible to predict theoretically the dependence of the

lifetime on excess carrier density and temperature in a given specimen.

Correction factors could then be determined to deduce the lifetime at some reference excess carrier density and temperature from the lifetime

measured at an arbitrary excess carrier density and temperature.

In practice it is very difficult to characterize the recombination

centers in a given specimen. Mathematical models have been developed

which describe the recombination process under certain idealized conditions . One such model was developed independently by Shockley and Read

[15] and by Hall [16]. According to the Shockley-Read-Hall (SRH) re- combination model the lifetime x is related to the excess carrier density

An (assumed equal to Ap) by

L

n

o + po J ° L

n

o + po J

where x n is the lifetime in the limit as An approaches zero, and x^ is

the lifetime in the limit as An approaches infinity.
Data indicating that t may be a function of excess carrier density has been reported by many authors [2, 10, 17-20]. The observed dependence was usually greatest in p-type silicon. Although the linear

relationship of eq (4) is sometimes observed [18] , experimental data of

TPCD as a function of An more often give a non-linear plot [10, 17, 19,

20] . This indicates that the recombination process of most specimens is

too complex to be described by the relatively simple SRH model. An ex- tensive discussion of the SRH model is given by Blakemore [21] . The same work provides an introduction to more complicated recombination

models

Under small-signal conditions, the excess carrier density An is proportional to the change in voltage across the specimen AV. Since TpQ)

depends on the excess carrier density, and since AV depends on the illumination intensity, a specimen may exhibit a dependence of t r on illumination intensity.

In order to verify the extent of the excess carrier density dependence, the bulk decay time of several specimens was measured as a function

of PCD signal amplitude. The relative excess carrier density was then

calculated from [2]

*£. AV M

p . , *0 " " V

"n + %

where \i and u are the mobilities of electrons and holes, Vn is the dc n p voltage across the illuminated portion of the specimen and AV is the signal level at which t was measured. Equation (5) is valid for p-type

material; an analogous expression is applicable to n-type material. In

these measurements t was evalauted after 75 percent of the carriers

had decayed; therefore AV was one-fourth the total PCD signal amplitude.

The data from this experiment, shown in figure 2, illustrate the extent

of the variation in tg with excess carrier density. These results are comparible with similar experiments which have been reported [10, 17-20],

Because no relationship is known for predicting the excess carrier

dependence of a particular specimen, it is necessary that the measurement

be made at a specified signal level. An experiment was set up to determine what signal levels might be appropriate. Six specimens were selected on which Tp^-Q was measured three times for each specimen current

polarity at each of several signal levels . Three percent standard deviations of the measurement at each signal level were calculated: for the

three measurements taken at each current polarity and for all six measurements combined. For each specimen a plot was made of these percent

standard deviations as a function of signal level. For each plot, the

point distribution suggested an envelope below which 90 percent of the

points were located. The signal level at which this envelope gave a standard deviation of 4 percent was judged to be suitable for PCD measurements. The six specimens and the corresponding signal levels at

which a standard deviation of 4 percent was observed are given in table

1. For smaller signal levels a larger percent standard deviation was observed.
80

SSI2 oSS7

*~o

40

20

~o

» —SS6

.002 .004 .006

An/Pj

.008 .010 .012

Figure 2. Bulk decay time xg in microseconds as a function of relative

excess carrier density An/p

Q

for six specimens, where t b has

been multiplied by (1 + An/p

Q

) so that the plot may be compared with the linear behavior described by eq (4).
Table 1 - Signal Level at Which a Relative

Sample Standard Deviation of 4 Percent

Was Observed in xpQ) Measurements

on Six Specimens.

Specimen Signal Level, mV

SS8 8.8

SS18 0.36

452D 1.68

678c/l 0.6

16444/2 3.0

12-620-3 2.8

Table 2 - Comparison of Photoconductive

Decay Times Measured with Chopped

Light and Pulsed Light Excitation

Specimen TPCD'

ys

Chopped L ight Pul sed Li

SS8 73.6 67.6

SS11 83.2 71.4

SS14 84.4 77.2

NBS-13 174. 155.

777E 91.6 84.0

Percent Difference

8.2

14.2

8.5

10.9

8.3
The variability of the signal levels recorded in table 1 made it

difficult to determine a signal level which would be suitable for all

specimens. One approach is to combine this information with the results

of sections 6.3. and 6.4. concerning choice of specimen current and to

calculate a suitable signal level based on a selected value of relative

excess carrier density. For example, for a relative excess carrier density of 0.001, the signal level Vsig would then be calculated from the

following relationship based on eq (5)

:

v. = 4 av = (4)(o.ooi) -s*s-—£§i_i i R , (6) Slg ymaj L S

where L is the specimen length, L^ is the length of the illuminated portion of the specimen, and R is the bulk (excluding contact) resistance

of the specimen and is is the specimen current. The factor of 4 accounts

for the convention that the decay constant is measured after threefourths of the carriers have decayed. To reduce the time required to

calculate Vs ±g from eq (6), it is convenient to define a quantity

^(^min + ^mai'/^maj as ^y an(* tabulate Gy for each material and type for

ready reference. A two-probe resistivity measurement has been found

suitable for measurement of R. This is discussed further in section 6.4.

It should be recognized that in some specimens having low resistivity or large cross-sectional area, the signal level given by eq (6) for a particular choice of An/p„ may not be attainable because of limitations of

the light source, and a lower signal level would have to be used.

5.2. Light Source

There is presently no specification in the standards [3, 4] as to

whether a chopped or pulsed light source is to be used (although pulsed

light is given some preference) . Both types are in use at various places

in the industry. An experiment was set up to determine the degree of

agreement between TpQ) measurements made with chopped and pulsed light

systems. The chopped light system employed a 6-V, 8-A tungsten ribbon

filament lamp as a light source. Light from this source was chopped me- chanically at either 14, 45 or 77 Hz. The pulsed light source was a xenon flash tube with an associated 0.05-yF capacitor. The capacitor was typically charged to 500 to 1500 V before the discharge was triggered.

The triggering rate was approximately 2 Hz.

Experimental data taken with the two light sources are shown in

table 2. For each individual specimen all experimental conditions except

the light source were unchanged. A 1-mm thick filter (see sec. 5.4.) was

used, and all data were taken by the same operator. Each value is an average of three measurements. The amount by which the pulsed light measurement is less than the chopped light measurement is given as a percent

of the average value obtained with chopped light in the fourth column.

The sample standard deviation based on each set of three measurements

varies from 0.24 to 0.90 percent of the average value for the chopped

light measurements and from 0.82 to 2.74 percent for the pulsed light

measurements.

10
The difference between chopped light and pulsed light measurements

is related to the carrier distribution at the beginning of the decay. If

light is applied to the specimen for a time equivalent to many lifetimes,

as in the case of chopped light, a steady-state excess carrier distribution is established. This does not occur under pulsed light excitation.

A theoretical comparison of chopped and pulsed light was presented by

Blakemore and Nomura [14] as part of a more general discussion of higher

modes of recombination. They showed that the error in xp^-p caused by

higher modes is greater for pulsed light excitation than for chopped

light excitation under a variety of measurement conditions . An effect of

higher modes is thus to produce erroneously short photoconductive decay

time measurements under normal experimental conditions when using pulsed

light. This conclusion is also supported by a theoretical treatment re- ported by Ridley [22]. Because of this, it appears that a truer value

for Tpcj) is obtained if chopped light rather than pulsed light is used.

Also, for the particular apparatus which was used in these investigations, the chopped light measurement was more reproducible than the

pulsed light measurement.

5.3. Inhomogeneities

Most specimens have dopants and unwanted impurities distributed nonuniformly throughout their volume; this may result in variability of both

resistivity and t . Inhomogeneities in tp^p can be detected by making

individual measurements with the light incident on different portions of

the specimen. This technique is time-consuming and has a spatial resolution limited by the diffusion length or the illumination pattern or both. Schemes have been suggested for detecting longitudinal lifetime

inhomogeneities in a filament but these have not gained wide recognition

[23-27].

To evaluate the extent of the inhomogeneity of Tp^jj, a section of a right circular cylindrical crystal (10 ft* cm, n-type silicon) was cut

longitudinally into ten specimens each with an approximately square

cross-section and a length equal to the length of the original section.

The location of the ten specimens within the cross-section of the original crystal is shown in figure 3. (Specimen 1 in fig. 3 is identical

with specimen SS13 discussed in sec. 5.4.). The photoconductive decay

times of the ten specimens are given in table 3. These data suggest that

Tg varied by a factor of ten with position in the original crystal and

that tg was lowest at the crystal center and increased near the crystal

surface. Unfortunately the side surfaces of the ten specimens cannot be

identified relative to their position in the original crystal section.

If this could be done, the inhomogeneity in specimen 1 discussed in section 5.4. might be shown to be consistent with the overall inhomogeneity

within the crystal.

In another experiment designed to detect inhomogeneities, a specimen

(4 Q*cm, p-type silicon) in the form of a rectangular parallelepiped was

cut from the center of a right circular cylindrical crystal. The cross- section of the parallelepiped was reduced several times in succession by

lapping. Following each size reduction, a Tp^jj measurement was made on

11
8 I 10

9

Figure 3. Cross-section of a 10 ft* cm, n-type silicon crystal showing

the original locations of ten cut specimens.

12
Table 3 - Decay Times of Specimens

Cut from a 10 ft* cm, n-Type

Silicon Crystal

Specimen Cross--section,

(see fig. 3) cm by cm

I 1.002 by 0.998

2 0.499 by 0.497

3 0.251 by 0.249

4 0.246 by 0.248

5 0.498 by 0.503

6 0.246 by 0.247

7 0.249 by G.254

8 0.498 by 0.503

9 0.502 by 0.502

10 0.248 by 0.246

TPCD' yS V ys

132 137

84 91

65 86

233 2500

494 947

208 1110

240 2500

193 237

518 1030

231 2330

13
the specimen. The data from this experiment are shown in table 4. The

decrease in Tg which was measured for successively smaller specimen

cross-sections suggests that the bulk decay time of the original crystal

increased with distance from the center. The increase in t between the

sixth and seventh readings resulted from changes in recombination characteristics caused by accidental heating during a drift mobility measurement rather than any change in cross-section. Presumably the heating an- nealed out some of the recombination centers causing an increase in the

lifetime.

In interpreting a PCD measurement, it must be understood (1) that

the Tg value represents an average over the illuminated region, and (2)

that different Tg values might be measured on different portions of the

specimen.

5.4. Filter Thickness

It is desirable that the incident light penetrate deeply into the

specimen so that carriers are generated as uniformly as possible within

the bulk. Completely uniform generation is not physically realizable but

may be approached by filtering the incident light. A filter is a slice

of the specimen material with two parallel polished surfaces. It is

placed close to the specimen and oriented so that the polished surfaces

are perpendicular to the incident light path. The present standards

specify that a filter be used; the IEEE standard [3] specifies that the

filter thickness be comparable with specimen thickness , while the ASTM

standard [4] specifies that the filter be about 1 mm thick.

Blakemore and Nomura [14] report the computer synthesis of two decay

curves, one of which proceeds from uniform generation (approximating the use of a thick filter) and one of which proceeds from non-uniform generation (approximating the use of no filter) . The error in the Tp^ measurement due to the influence of higher modes is shown to be greater in

the case of non-uniform generation.

Other work done specifically on the effects of filters has also been

reported. Blakemore [17] suggests the use of the thickest possible filter, yet his data show a difference of only a few percent between photoconductive decay times measured with 0.5-mm thick and 5-mm thick filters

and a pulsed light source. Sim [28] recommends the use of a filter 3 to

7 mm thick and calculates that for a pulsed light source the measurement

error which results from not using a filter is between 25 and 50 percent.

To obtain additional data on the influence of a filter, the photoconductive decay time was measured on several specimens. Three different

filter thicknesses and either chopped or pulsed light excitation or both

were used. The light intensity was adjusted to maintain a constant signal level for each specimen. These data, shown in tables 5 and 6, indicate that Tp£D usually is longer when a filter is used, and that a 1-mm

thick filter usually gives almost the same result as a thicker filter.

The data of tables 5 and 6 also show the effect of the filter to be

greater with pulsed light than with chopped light excitation. This is

14
Table 4 - Decay Times of a Specimen Cut from

a 4 ft* cm, p-Type Silicon Crystal as a Function of Specimen Size

Reading

1

2

3

4

5

6

7

8

Cross-section,

cm by cm

1.003 by 1.002

0.999 by 0.875

0.995 by 0.751

0.874 by 0.750

0.753 by 0.750

0.633 by 0.750

0.633 by 0.750

0.500 by 0.749

TPCD'

ys

83,

79,.5

75,.5

73,,5

70,.0

68,,0

88.,1

74.,0

V US

87.7

84.6

81.0

79.3

76.0

74.9

100.

85.5

15
Table 5 - The Effect of Filters of Different

Thicknesses on the Photoconductive

Decay Time Tp^p Measured with

Chopped Light Excitation

Specimen

DOFL

NBS-13

SS8

SS10

SS11

SS14

777E

13069/3

14787/5

15705/5

16444/2

52792A

Filter

572.

185.

73.3

274.

88.0

81.6

99.2

1210.

127.

134.

2150.

1520.

TPCD'

ys

im Filter 5mm Filter

573. 573.

187. 186.

73.6 74.1

277. 278.

90.1 88.7

84.4 85.5

98.2 98.7

1210. 1220.

126. 122.

130. 125.

2200. 2160.

1510. 1500.

10mm Filter

569.

183.

73.6

276.

87.7

98.9

1240.

121.

123.

2200.

1500.

16
Table 6 - The Effect of Filters of Different

Thicknesses on the Photoconductive

Decay Time Tp^p Measured with

Pulsed Light Excitation

Specimen TPCD'

yS

No Filter 1mm Filter 5mm Filter 10mm Fi

NBS-13 150. 155.

SS4 21. 25. 25. 24.

SS5 20. 23. 22. 23.

SS6 19.5 23.7 22.6 23.4

SS8 45.2 67.6 67.6 66.8

SS9 28.7 35.2 34.9 34.8

SS11 70.3 71.4

SS14 58.3 77.2 78.4

777E 65.3 84.0

15710/3b 20.5 16.5 15.0 13.0

17
because the decay process for the chopped light cases does not involve

higher modes to the same extent as for pulsed light (see sec. 5.2.)

thereby decreasing the extent to which a filter can further reduce higher

mode decay. For most specimens listed in table 5, the measured dependence of t-pCD on fil ter thickness is less than the relative sample standard deviation of chopped light measurements reported in section 5.2. For

most specimens listed in table 6, the percent change in Tp^p which is observed when comparing measurements made with no filter ana measurements

made with a 1 mm filter is greater than the relative sample standard deviation of pulsed light measurements reported in section 5.2. Further

increases in filter thickness cause changes in tp^p which are small com- pared with the relative sample standard deviation for pulsed light measurements, however.

Those instances in tables 5 and 6 in which use of a filter resulted

in a decreased value of TpQ) might be caused by the presence of an inhomogeneity. Since the filter thickness determines the distribution of ex- cess carriers within the specimen and so determines the depth at which

the typical carrier is generated, an inhomogeneity can cause tp^-p to be

shorter when measured with a thicker filter. Increasing the filter

thickness causes the typical excess carrier to be generated closer to the

center of the specimen cross-section. If the lifetime of the material

decreases with distance into the specimen from the surface, a measurement

with a thick filter can give a shorter TpQj) value than does a measurement

with a thinner filter or with no filter. Conversely, if the lifetime of

the material increases with distance into the specimen from the surface,

a measurement with a thick filter can give a longer Tppp value than does

a measurement with a thinner filter or with no filter.

An example of the effect of a filter on an inhomogeneous specimen

was observed in specimen SS13. One of the specimen sides, side A, was illuminated with a rectangle of light 1.25 cm long and 0.6 cm wide, as shown in figure 4. The left edge of the lighted region initially touched

the AB edge of the specimen. The distance x from the AB edge to the illumination boundary was then increased in 0.5-mm increments until the

right edge of the lighted region touched the AD edge. A measurement of

T PCD was maae at each step. The data, shown in table 7, indicate an in- crease in Tp£j) in going from the AB edge to the AD edge, verifying that

lifetime is inhomogeneous in this specimen. Specimen SS13 was then measured with filters of different thicknesses with light incident on sides

B and D. The data, shown in table 8, illustrate the effect of a filter

in the presence of an inhomogeneity. With the light incident on side D,

the measurement with the filter was less than the measurement without a filter, while with the light incident on side B the opposite was true.

This specimen thus illustrates the behavior described in the previous

paragraph.

The data discussed in this section indicate that the effect of a filter on a chopped light PCD measurement is very small if the specimen

is homogeneous. Nevertheless, if a 1 mm filter is used to enhance the

uniformity of the excess carrier generation within the illuminated region

a larger volume of the specimen is influential in the measurement.

18
ILLUMINATION

Figure 4. Illustration of the illumination pattern used to study

inhomogeneities in specimen SS13.

19
Table 7 — Photoconductive Decay Time of Specimen SS13 Measured

with the Illumination Incident at Several Locations on Side A

x,mm

TPCD'

ys

0.0 99

0.5 100

1.0 103

1.5 108

2.0 118

2.5 127

3.0 143

3.5 151

4.0 162

Notes

Light adjacent to AB edge

Light centered on specimen

Light adjacent to AD edge

Table 8 — Photoconductive Decay Time of Specimen SS13 Measured with the

Illumination Incident on Sides B and D for Various Filter Thicknesses

Incident

Surface

No Filter

TPCD'yS

1mm Filter 5mm Filter

side B 102. 113. 121.

side D 164. 154. 144.

20
However, when measuring specimens of low resistivity material with large

cross-sectional area, the PCD signal level may be too low to permit the use of a filter. Attainment of the signal level given by eq (6) appears

to be more important than the use of a filter.

5.5. Temperature

In most specimens, TpQ) is a function of temperature. This is con- sistent with the SRH recombination model [15, 16] as well as more complex

models and is discussed by Blakemore [21] and by Susila and Suryan [29].

The temperature dependence is caused by the movement of the Fermi level

with respect to the recombination center energy levels. Data of lifetime

as a function of temperature have been reported by many authors [18, 19,

30-33].

The photoconductive decay time of several specimens was measured as

a function of temperature in order to evaluate the dependence near room

temperature. In figure 5 the bulk decay time of these specimens is plotted as a function of temperature near room temperature. The bulk decay

time change with temperature ranges from 1 to 5 percent per degree Celsius.

Because a few degrees difference in temperature may cause a significant change in Tg, the precision of the measurement is reduced if the

temperature is not maintained constant at a known value or is not cor- rected for. In theory lifetime- temperature correction factors could be

determined from knowledge of the energy level or levels of the recombination centers in a particular specimen. In practice this is difficult to

do and temperature correction factors for lifetime cannot generally be

given. It is therefore necessary to make intercomparative measurements

of TpQ) at the same temperature.

6. OTHER CONSIDERATIONS

Whereas the previous section dealt with phenomena which are inherent

in the nature of semiconductor materials and of the recombination process, this section discusses effects which result from tehcnological problems related to instrumentation and specimen preparation. Light turnoff

time, series resistance, specimen current, illumination pattern, and

specimen end contacts are discussed as they affect the measurement of

TPCD6.1. Light Turnoff Time

The light turnoff time must be sufficiently short that it does not

interfere with the measurement of Tppp. In the case of linear light

turnoff, such as would be encountered using chopped light, there is no

error in the Tp^D measurement if it is made any time after the light is

completely extinguished [34, 35].

For the idealized case of purely linear light turnoff, the turnoff

time, t Q ££, is defined as the minimum time between the conditions of

21
440

360-

^ 280

0*

SSIO

Figure 5.

10 20 30 40 50 60

TEMPERATURE °C

Bulk decay time in microseconds as a' function of temperature

in degrees Celsius for four specimens.

22
light fully on and light fully off. To determine the effect of turnoff

time on the T-prn measurement, decay curves for various values of

t ff/ T pcD were synthesized. This analysis revealed that when TpcD is

measured after 75 percent of the excess carriers have recombined, the

TPCD measurement is unaffected by light turnoff if ^ ff/ T -prr) is less than

about 4.

An experiment was set up to observe the effect of varying the turnoff time and to compare these observations with the theoretical prediction just discussed. By driving the chopper motor with an audio oscillator through a power amplifier, the chopper speed could be controlled by

the oscillator frequency. Measurements were made on five specimens in

which the t ff/ T PCD rat i° was varied from approximately 1 to 4. The

light turnoff characteristic typically consisted of a linear portion preceded and followed by rounded portions at the initial and final stages of

turnoff. The linear portion generally occupied the center half of the

turnoff characteristic. In these measurements, t Q ff was determined by

extrapolating the linear portion until it intersected the levels corre- sponding to light fully on and light fully off and measuring the time between these two intersections. The results, shown in figure 6, indicate

that for values of t ff/xpcD between 2 and 3, the measured_decay time

T PCD begins to increase from its short-turnoff-time value fp^-p. The deviation from the prediction for the idealized case is attributed to the

rounding of the initial and final portions of the turnoff charactristic.

In the case of a pulsed source such as a spark gap or xenon flash

tube, the decay of light is often irregular. Later stages of the light

decay are approximately exponential, and considerable time may be re- quired for the light to extinguish entirely. The extent to which pulsed

light turnoff interferes with the measurement is difficult to analyze due

to the irregular nature of the light decay. For the apparatus used in

this study, the full-width-at-half-maximum (FWHM) pulse width varied from

1.3 ys at a discharge voltage of 500 V to 0.45 ys at 1500 V. The corre- sponding times between initiation of the pulsed light flash and the decay

to 5 percent of peak intensity were 7.5 and 5 ys . This was considered to

be the lower limit of measurable photoconductive decay time using this source.

6.2. Series Resistance

In the ideal case, a constant current is supplied to the specimen.

When this is so and when small-signal conditions prevail, the PCD signal

amplitude AV is directly proportional to the excess carrier density An

(see eq (5)). The present standards [3, 4] suggest as adequate a con- stant voltage power supply in series with a resistance R which is at

least twenty times the specimen resistance R. The principal effect of

using a constant voltage supply and series resistor Rs is to reduce the

amplitude of the PCD signal for a given excess carrier density to the

fraction R /(Rs + R) of the value it would have under constant current

conditions. If contact resistance Rc is present the above fraction must

be modified such that R becomes R + Rc

.

23
1.35

30 —

1.25

8 1-20

"q 1.15 O

.10 —

1.00 —

0.95

-

1

1 ' I ' l ' I ' — o —

O SSII • SS 8 A

- + SS 5 — 777E •

- A SS 14

u — a —

—

O

o A

- O

+c*

—

o o#

D — or &

i

+

I i l i

1 2 3

t off / ^PCO

Figure 6. Photoconductive decay time x PCD as a function of turnoff time

t ff for five specimens where both TpQ) and t ff have been

normalized with respect to the average TpcD which was measured

before turnoff affected the measurement x*p CD .

24
An experiment was performed to verify the predicted behavior of the

signal level for various values of series resistance Rs , and to observe

any changes in Tp^p resulting from changes in Rg

. The experiment was

performed on four specimens for which the ratio Rg /R was varied between

20 and 0.1. All measurements on a given specimen were made with the same

light intensity. Measured values of T-prj) and Vs jo were normalized with

respect to the respective values measured at Rs /R = 20, denoted Tp^^* and

Vgj*. The data, summarized in figure 7, indicate that (1) the standard

deviation of the measurement was essentially independent of the ratio

Rg/R despite the lower signal-to-noise ratio at low Rg/R ratios, (2) the

signal level decreased as Rs /R decreased in good agreement with the re- lationship mentioned above, and (3) the i-prr) values were not significantly affected by changes in Rs /R for Rs /R _> 1. These results suggest that

suitable measurements can be made when Rs

>_ R. The effect of series re- sistance on the signal level should be taken into account in eq (6) , however, when the reduction in signal level is significant. The desired

value of Vg£„ would then be obtained by multiplying the right-hand side

of eq (6) by Rg/CRg + R)

.

6.3. Specimen Current, Illumination Pattern and Sweep-Out

In order for xg and Tp^p to be related in the manner stated in eqs

(1) and (2) it is necessary that photoinjected carriers neither diffuse

nor drift to the end contacts. Recombination occurs almost immediately

at the end contacts, and such diffusion or drift would result in an er- roneously short tpQ) measurement.

Stevenson and Keyes [8] studied the case of uniform excess carrier

generation throughout an entire specimen in the form of a rectangular

parallelepiped. They derived an equation which, expressed in the notation of this report, can be written as:

T, [w1 -*2j>(e^ +

^)

(pE)

B I

L PCD " "I L

2- ' W

z ' Tz

/ 4D

-1

(7)

where E is the applied electric field and y is the ambipolar mobility

given by [3] :

V \i In. - pi

m np I 0_|_

m Vn + P yp

In extrinsic material, u reduces to the minority-carrier mobility. A

similar expression could be written for a right circular cylindrical

specimen.

Note the similarity between eqs (1) and (7) . The term tt z D/L2 in

eq (7) represents excess carrier recombination resulting from diffusion

to the end contacts. The term (yE) z /4D in eq (7) represents excess carrier recombination resulting from drift to the end contacts under the applied field E.

25
CO —

o

10'

8

6

4

2

rry

1.2

0.8

> 0.4-

1

8 1-2t

a

o

1-°- 1.0 -

o

0.8 *

1

1 °"

o

/V

+ SSI4

o SS 5 • 16444/2

a 12-620-3 ^v

{*:

i ± _L

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 50.0 100.0

Rs /R

Figure 7. Photoconductive decay time Tpcp, signal level Vs £g, and percent

standard deviation s as a function of series resistance Rs for

four specimens. (Values of Rs have been normalized with respect

to the specimen resistance R. Values of tpcd and Vs ^„ have been

normalized with respect to the values of Tp^n and Vs ^„ measured

for Rs /R equal to 20, t pcd* and V

sl * plot of Von

- as a function of R

respectively. In the

, each specimen followed the sig same pattern. In the interest of clarity only one set of data

is plotted. In the plot of Vs ±o as a function of Rs , each specimen followed the same pattern. In the interest of clarity only

one set of data is plotted.)

26
For the case of uniform generation in the entire specimen, Stevenson

and Keyes [8] suggest that the electric field E be such that

(yE) 2 l 2 fi l l 1

(9)

B

This expression forms the basis for the specification in the standards

[3, 4] that E be such that

_300_ ; (1Q)

(UT) 1 /

2

where E is in volts per centimetre, y is in square centimetres per voltsecond, and t is the lifetime in microseconds.

In practice it is preferable not to illuminate the entire specimen.

In the first place, photovoltages which interfere with the measurement

are often generated at metal-semiconductor end contacts. In the second

place, the calculation of Tg from Tp^jj is simplified if the regions near

the specimen ends are masked from the incident light and the electric

field is selected such that photogenerated carriers do not diffuse or drift to the end contacts. To assure this it is necessary that the distance Lc between the illumination boundary and the nearest end contact

be large compared to both the drift length d and the ambipolar diffusion

length Lp. The quantities d and Lq are defined by:

d - pETpCD (11)

S~ (DTPCD

)1/2

• < 12 >

Carrier recombination at the end contacts caused by drift under applied

electric field is called sweep-out. The problem of sweep-out is discussed in the IEEE standard [3] and by several authors [2, 9, 36-38].

Based on the definitions of TpcD and d, one expects that if a steady-state excess carrier density An is established in an illuminated

region, in a time Tpcj) the excess carrier distribution drifts under the

applied field a distance d. At a distance d from the illumination boundary, in the direction of carrier drift, the excess carrier density is re- duced from An to An/e where e is the Naperian base. At a distance 4d

from the illumination boundary one expects an excess carrier density of

An/e4

Z 0.02 An. Presumably, an end contact at a distance 4d from the

illumination boundary would result in sweep-out of only a small fraction

of the total number of excess carriers , and thereby would have an insignificant effect on the measurement of Tpp^.

An experiment was performed to test this hypothesis. The photoconductive decay time was not measured directly, rather changes in Tp£D were

detected by measuring steady-state photoconductivity. The steady-state

photoconductivity of a specimen is approximately directly proportional to

27
the lifetime. Several specimens were scanned with a narrow light beam

and their photoconductivity (PC) profiles were plotted on an x-y recorder. The specimen current was normally chosen to give a drift length of

1 mm. The diffusion lengths of the six specimens ranged from 0.30 mm to

1.68 mm, but all specimens except specimen 678c/l had a diffusion length

of 0.67 mm or less. In most instances therefore, Lp was small compared

to d. The PC profiles were relatively flat in the center but showed a decrease in photoconductivity near the end contacts. This decrease in

photoconductivity was interpreted as a decrease in TpQj caused by sweepout. The distance from the end contacts Lc at which sweep-out first became noticeable was recorded in . terms of the number of drift lengths,

that is, in terms of the ratio Lc /d. The specimens profiled and the Lc /d

ratios obtained are shown in table 9.

In interpreting the data in table 9, two considerations need to be

kept in mind. In the first place the diffusion length was not subtracted

from the drift lengths. This may account for some of the variation between specimens. In the second place, in a PCD measurement a broader

band of illumination is used than was used in the PC scans. Illuminating

a larger portion of the specimen tends to keep the decay time at its

average value even though a few excess carriers at the edge of the illumination might be swept out. It is therefore not necessary to interpret

the data of table 9 too conservatively. Based on these considerations it

appears that if the illumination is restricted from the regions within

four drift lengths of each end contact sweep-out effects would not be ex- pected to interfere with the measurement. Under these conditions, Lc would be chosen to be greater than or equal to four times d as given by

eq (11).

Assuming that the experimental conditions can be selected to prevent

sweep-out, it is then necessary to verify that diffusion (as opposed to

drift) to the end contacts is not present. The present standards [3, 4]

recommend that specimens for PCD measurements be cut to one of three preferred sizes. The largest of these sizes, which for a given Tg would

have the largest TpQ) and consequently the largest LD , is 1.0 by 1.0 by

2.5 cm. For the case in which the center half of such a specimen is illuminated such that regions within 0.625 cm of each end contact are

masked, it can be shown that L is equal to approximately 3.5 diffusion

lengths when Tg = 3tt>qt)- When tr

> 3xp^p Lc will be less than 3.5 in

terms of diffusion lengths, but under these conditions a Tp^n measurement

is considered inadvisable for other reasons (see sec. 4). Because the excess carrier density is reduced by 97 percent in 3.5 diffusion lengths,

diffusion to the end contacts can be made insignificant by illuminating

only the center half of the specimen in the specimen geometries preferred

in the standards. In as-grown crystals it would also be possible to ren- der negligible diffusion to the end contacts in specimens sufficiently

long.

If it is valid to assume that excess carriers do not diffuse to the

end contacts and that sweep-out is the limiting factor in determing the

maximum allowable specimen current, then the maximum specimen current can

28
Table 9 - Number of Drift Lengths from

Each End Contact at Which Sweep-out

First Appeared for a Group of

Specimens

.

Specimen

R818A

SS14

SS11

678c/l

SS5

SS8

Distance from End Contact in

Drift Lengths at Which Sweepout Was First Observed

Left End

4.3

2.6

4.4

4.6

Right End

4.0

3.7

3.0

2.9

3.8

4.8

29
be derived from eq (11) for the case Lc = 4d:

TWL

i =

7 — , (13)

S 4pyTPCD

where p is the specimen resistivity. If the center half of the specimen

is illuminated such that Lc = L/4, then eq (13) can be replaced by:

TWL ,-..

1 = TZ • (14)

s 16 P yTpCD

Whereas in the standards [3, 4] the maximum acceptable electric

field is determined by eq (10) , a different approach is represented in

eqs (13) and (14). This latter approach is also suggested by Benda, et

al [38].

6.4. Specimen Current and Ohmic Heating

If the specimen current and resulting power dissipation are sufficiently large, the specimen temperature increases, resulting in a possible increase in TpQ) (see sec. 5.5.). An experiment was set up to establish a criterion for identifying a maximum specimen current beyond which

ohmic heating might occur. Twelve silicon specimens were selected, each

of which was approximately the size of one of the three sizes preferred

in the standards [3, 4].* Each specimen was mounted in the PCD specimen

holder and a sequence of specimen currents was applied to it. At each

current level, 15 minutes was allowed for thermal stabilization. The

temperature increase was determined from the resistivity as measured by

a two-probe method [39] and the temperature coefficient of resistivity

for each specimen [40]. The specimen current which caused a 0.25°C temperature increase was determined by interpolating between the selected

currents. From this current, the power dissipated, the power dissipated

per unit specimen surface area, and the power dissipated per unit specimen volume were all calculated. These power dissipations were calculated

in two ways: (1) total power dissipated based on a measurement of the

specimen resistance which included contact resistance, and (2) bulk power

dissipated based on bulk resistance (calculated from the measured resistivity and the specimen geometry) which did not include contact resistance. The resulting six quantities are tabulated in table 10 for each

specimen. From these data it can be shown that (1) the power dissipated

(total or bulk) at which the specimen temperature increased by 0.25°C for

the twelve specimens had a lesser variability in terms of percent standard deviation than did either the power dissipated per unit surface area

or power dissipated per unit volume, (2) the total power dissipated at

which the specimen temperature increased by 0.25°C for the twelve specimens had a lesser variability in terms of percent standard deviation and

overall range than did the bulk power dissipated, and (3) the total power

*In place of the 1.5 cm length suggested by the standards for the size A

geometry, the specimens were all approximately 2.5 cm in length.

30
c

CU ao

a)a co CO

rl 42 O

CJ M-l CO •H C

JS CJ CU 2 om

rt • o

COC TJ

01 CO •H CO >

•u co rH

co a> cu ex ^ js •h o H

co

a

01

H IH

•H

•HO

CJ co

u

0)o

P-.I

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•H

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31
dissipated at which the specimen temperature increased by 0.25°C did not

appear to depend to an appreciable extent on the specimen geometry.

Since the total power dissipated is the least variable of the six

quantities calculated, it appears to be the most suitable parameter upon

which to base a specification for the maximum specimen current with re- spect to ohmic heating. However, calculations are more easily based on the bulk power dissipated since p has already been measured. The total

power dissipated can then be limited by specifying that contact resist- ance not exceed a fixed percentage of the bulk specimen resistance. For

example if it were determined that total power dissipation in preferred

size silicon specimens should not exceed 5 mW and that Rc

<_ 0.25 R, then

the maximum bulk power dissipated would be 4 mW and the maximum specimen

current would be given by:

[

0.004 TW i/ 2 — , 1CN Tl~ J

' (15)

where eq (15) is of the form current = y power/resistance.

In practice it is usually necessary to calculate a maximum specimen

current for both the power dissipation and the sweep-out limitations.

The lesser of these two currents should then be used in the PCD measurement. When measuring specimens larger than the largest of the three preferred geometries the total power dissipation limit may be different from

the limit established for the geometries preferred in the standards. In

such instances it must also be verified that diffusion of excess carriers

to the end contacts is not significant (see sec. 6.3.).

6.5. Specimen End Contacts

Ohmic contact must be made to the specimen. This is usually a twostep process involving first the formation of a soldered, alloyed or evaporated metal-to-semiconductor contact at each end of the specimen and

second the electrical connection of a wire to each contact. A variety of

procedures has been developed for both silicon and germanium [3, 4, 9,

19, 30, 41, 42], In the present experiments, ohmic contacts were formed

by lapping the specimen ends with 12 um alumina and then evaporating a 300-nm thick layer of gold or aluminum onto the specimen ends. Electrical connection was then made either by thin copper sheets or by goldplated copper screens with foam rubber backing pressed against the contacts .

Regardless of the care which is taken in making ohmic contact to the

specimen, contact resistance is often present which is a significant

fraction of the bulk specimen resistance. The bulk specimen resistance

or resistivity, required in eqs (6), (13), (14) and (15) can be measured

by the two-probe method [39]. From the results of this measurement, the

contact resistance can be determined and the quality of the end contacts

evaluated

.

32
7 . TRAPPING

Recombination in silicon and germanium takes place primarily through

energy states or recombination centers within the forbidden gap caused by

lattice defects or impurity atoms. For instance, a conduction band electron might fall into a recombination center. If a valence band hole then

falls into the same center, a hole-electron pair has been annihilated and

recombination has occured. Sometimes, however, centers exist for which a captured electron is more likely to be emitted to the conduction band

than to recombine with a hole. The electron is said to be trapped and

the center is called a trap. If recombination does not occur, the electron remains trapped until it is excited to the conduction band. Such

excitation may require much more time than recombination through ordinary

recombination centers. The trapping of holes is analogous to that of

electrons. If minority carriers are trapped, photoconductive decay is

governed by the release of minority carriers from the traps and the result is an erroneously long t-prj) measurement. Experimental studies of

the phenomenon of trapping [43-46] and mathematical models to describe

the behavior of excess carriers in the presence of trapping [31, 44] are reported in the literature.

Trapping is sometimes present in silicon at room temperature and in

germanium at lower temperatures. It is most easily identified by a PCD

curve which has an initial short-time-constant portion followed by a long-time-constant tail. The tail can usually be eliminated by flooding

the specimen with a steady background light [3, 4, 46, 47]. Such a procedure produces a decay curve which is more nearly exponential. However,

the background light also acts to increase the specimen temperature and

create a steady-state carrier density larger than the equilibrium carrier

density, so that the measurement is no longer a low level measurement.

Unless specifications are made regarding the background light, PCD measurements made under these conditions may have poor reproducibility.

In some applications, the PCD method is used to detect trapping.

Only relatively large trap concentrations can be detected as tailing,

however. It is possible that trapping might also be detected by noting

a decrease in t-prr\ with increasing temperature [9].

In the presence of trapping the hole and electron lifetimes differ.

The hole and electron lifetimes can also differ when the density of re- combination centers is not small in comparison with the majority carrier

density. Transient recombination in the presence of an arbitrary density

of recombination centers is very difficult to analyze. Blakemore [21]

gives approximate analytical expressions for the initial and final portions of the decay and presents computer drawn decay curves for holes and

electrons under a variety of special conditions. Because the PCD method

measures changes in conductivity, it is unable to separate hole and electron lifetimes where they differ and yields instead a weighted average of

the two.

33
The present standards [3, 4] specify that the measurement should not

be made when the trapping tail constitutes more than five percent of the

total amplitude of the curve. The surface photovoltage (SPV) method [48]

and the photomagnetoelectric effect method [49] are more suitable for

measuring carrier lifetime in the presence of trapping.

8. SUMMARY

An investigation of the photoconductive decay method for measuring

carrier lifetime has been completed. Analytical and experimental studies

were conducted to determine suitable conditions under which the measurement could be made. Suitable conditions are those such that (1) the as- sumptions underlying the equations by which the measured decay time Tp^jj

and the bulk decay time tg are related are valid, (2) the predicted percent standard deviation is acceptable, (3) the measurement is made under

low-level conditions, and (4) the experimental apparatus is not overly

complex. In order to define the suitable measurement conditions, the

following parameters were studied: (1) the excess carrier density, (2)

the type of light source, (3) specimen inhomogeneities , (4) filter thickness, (5) specimen temperature, (6) chopped light turn-off time, (7)

resistance in series with the specimen, (8) specimen current and its relation' to sweep-out , illumination pattern and ohmic heating, (9) end contact quality, and (10) trapping in the specimen.

The dependence of xpQ) on excess carrier density and therefore on PCD signal level was verified in several specimens. Because correction

factors by which XpQ) measurement made at an arbitrary excess carrier

density could be corrected to a reference excess carrier density are not

generally known, it is necessary to measure Tp^pj at a selected value of excess carrier density or signal level. An experiment was performed to

determine a minimum acceptable signal level in terms of measurement re- producibility. It was found, however, that the behavior of the measurement reproducibility as a function of signal level showed considerable

variation among the specimens tested. A generally applicable signal

level was therefore not found. An expression was developed, however, for

signal level in terms of other specimen parameters.

Measurements of t-prj) using chopped and pulsed light sources were

compared. The chopped light source was found to give a Tp^p value which

for the five specimens measured averaged about 10 percent longer than the

value measured with the pulsed light source. The chopped light measurements also had a smaller sample percent standard deviation than did the

pulsed light measurements.

The presence of inhomogeneities was verified in two crystals.

The photoductive decay time of a group of specimens was measured using filters of different thicknesses. The effect of the filter was greater with pulsed light than with chopped light. With either light

source, increasing the filter thickness beyond 1 mm produced no significant change in Xp^p in most specimens. Anomalous dependence of t-pQ-Q on

34
filter thickness was shown to be caused by an inhomogeneity in one specimen.

The dependence of Tp^n on temperature around room temperature was measured on four specimens. Because correction factors by which Tp^Q

values measured at an arbitrary temperature could be corrected to a ref- erence temperature are not generally known, only Tp^p measurements made

at the same temperature may be compared.

The effect of chopped light turnoff time was observed on five specimens. Although ideally, linear light turnoff should not affect the Tpcj)

measurement unless t Q ff :> 4 TpQp, due to rounding of the initial and

final portions of the turnoff characteristic, the measurement was in fact

affected for t Q ff £ 2 TpCD .

It was demonstrated that the series resistance Rg need not be many

times larger than the specimen bulk resistance R. The tj>rT) value and its

reproducibility are not appreciably affected provided that Rs

_> R. It is

necessary, however, to consider the effect of the reduced PCD signal

level which results when Rg is not large compared to R.

The selection of suitable specimen currents was shown to be governed

by sweep-out, carrier diffusion to the end contacts, and ohmic heating.

The sweep-out limitation on the specimen current was considered in terms

of the drift length d. The distance from the illumination boundary to

the end contact Lc at which sweep-out was first observed was measured for

several specimens by a steady-state photoconductivity technique and was expressed in terms of Lc /d. It was determined by analysis that carrier

diffusion to the end contacts does not influence the measurement when

specimens having one of the three geometries preferred in the standards

are illuminated in their center half.

An experiment was performed on twelve silicon specimens to determine

a suitable limitation on the specimen current with respect to ohmic heating. The total power dissipated was the parameter which was least variable and therefore it appears to form the most suitable basis for a specification on the specimen current with regard to ohmic heating.

Specimen end contacts need to be sufficiently ohmic that excessive

contact resistance does not interfere with the measurement. Many of the

problems associated with excessive contact resistance can be avoided by

making a two-probe resistivity measurement on the specimen, calculating

the actual contact resistance, and correcting for it in the seperate

equations. Where appropriate in this report, contact resistance was

either explicitly accounted for (such as by defining R as bulk resistance

to be determined by a two-probe measurement) or discussed in the text.

The PCD method is not applicable in the presence of trapping. Tailing which results from trapping can be reduced by applying steady background light to the specimen. This is done at the expense of increasing

the excess carrier density, however. Other methods are suggested for

measuring lifetime in the presence of trapping.

35
9 . REFERENCES

[I] Bullis, W. M. , Measurement of Carrier Lifetime in Semiconductors —

An Annotated Bibliography Covering the Period 1949-1967, NBS Tech.

Note 465, June, 1968.

[2] Mattis, R. L., Phillips, W. E. , and Bullis, W. M. , Measurement and

Interpretation of Carrier Lifetime in Silicon and Germanium, May,

1968; AFML-TR-68-81 . Available from the National Technical Information Service, Springfield, Virginia 22151, Accession No.

AD 671552.

[3] IRE Standards on Solid-State Devices: Measurement of MinorityCarrier Lifetime in Germanium and Silicon by the Method of Photoconductive Decay (IEEE Standard 225) , Proc. IRE U9_, 1293-1299

(1961)

.

[4] Standard Method for Measuring Minority-Carrier Lifetime in Bulk

Germanium and Silicon, ASTM Designation F28-66, Annual Book of ASTM

Standardsj Part 8 (American Society for Testing and Materials,

Philadelphia, 1971)

.

[5] Use of the Terms Precision and Accuracy as Applied to Measurement

of a Property of a Material, ASTM Designation E177-71, Annual Book

of ASTM Standards^ Part SO (American Society for Testing and Materials, Philadelphia, 1971).

[6] IRE Standards on Solid-State Devices: Definition of Semiconductor

Terms, 1960 (IEEE Standard 216), Proo. IRE 48, 1772-1775 (1960).

[7] Ryvkin, S . M. , Photoelectric Effects in Semiconductors3 pp. 237-245

(Consultants Bureau, New York, 1964).

[8] Stevenson, D. T. , and Keyes , R. J., Measurement of Carrier Lifetimes in Germanium and Silicon, J. Appl. Phys. 26^, 190-195 (1955).

[9] Watters , R. L. , and Ludwig, G. W. , Measurement of Minority Carrier

Lifetime in Silicon, J. Appl. Phys. 27_, 489-496 (1956).

[10] Dale, E. B., Beck, R. , Peet, C. S., and Beer, A. C, Scientific Report No. 2, Measurements of Bulk Lifetime in Silicon, May 15, 1957,

Contract No. AF19 (604) -1852, (Available from the National Technical

Information Service, Springfield, Virginia 22151, Accession No.

AD 117072.

[II] Gutberlet-Vieweg, F., Verbesserungen am Gleichstrom-PhotodecayVerfahren zur Ermittlung des Minoritatstrager-Lebensdauer in

Silicium-Einkristallen, Archiv. Techn. Messen 366 , 151-154 (1966).

[12] Shockley, W. , Electrons and Holes in Semiconductors (Princeton, New

Jersey: D. Van Nostrand Company, Inc., 1950), pp. 318-325.

36
van Roosbroeck, W. , The Transport of Added Current Carriers in a Homogeneous Semiconductor, Phys. Rev. 91, 282-289 (1953).

Blakemore, J. S., and Nomura, K. C, Influence of Transverse Modes

on Photoconductive Decay in Filaments, J. Appl. Phys. 31_, 753-761

(1960)

.

Shockley, W. , and Read, W. T. , Jr., Statistics of the Recombinations of Holes and Electrons, Phys. Rev. 87^ 835-842 (1952).

Hall, R. N. , Electron-Hole Recombination in Germanium, Phys. Rev.

87, 387 (1952).

Blakemore, J. S., Lifetime in p-Type Silicon, Phys. Rev. 110 , 1301-1308 (1958).

Okada, J., Recombination Centers in Germanium, J. Phys. Soc. Japan

13, 793-800 (1958).

Ivanov, V. G. , Recombination in High-Resistivity Silicon, Soviet

Phys. -Solid State _8, 1306-1307 (1966).

Okada, J., Effect of External Illumination on Carrier Lifetime in

Semiconductors, J. Phys. Soo. Japan 14, 1550-1557 (1959).

Blakemore, J. S., Semiconductor Statistics (New York: Pergamon

Press, 1962).

Ridley, B. K. , Measurement of Lifetime by the Photoconductive Decay Method, J. Electronics Control 5_, 549-558 (1958).

Buimistrov, V. M. , Theory of the Photodif fusion Effect Caused by a Non-uniform Distribution of Recombination Centers, Soviet Phys.-

Solid State 5_, 351-356 (1963)

.

Kovtonyuk, N. F., Recombination-Gradient Photo-emf in Semiconductors, Soviet Phys. -Solid State 7_, 1243-1244 (1965).

Suleiman, G. I., Kovtonyuk, N. F., and Kokorev, D. T. , Automatic

Apparatus for Recording the Lifetime Distribution of Nonequilibrium Charge Carriers in Semiconductors, Instrum. Exper. Tech. 8_, 203-205 (1965).

Esposito, R. M. , Loferski, J. J., and Flicker, H. , Concerning the

Possibility of Observing Lifetime-Gradient and Dember Photovoltages

in Semiconductors, J. Appl. Phys. 38., 825-831 (1967).

Shachar, G. , The Generation of Lifetime-Gradient Photovoltages in

Photoconductors, J. Appl. Phys. 38, 5412-5413 (1967).

37
[28] Sim, A. C. , A Note on the Use of Filters in Photo-conductive Decay

Measurements, Proa. IEE3 Paper 2885E, May 1959, vol. 106B, Suppl.

#15, 308-310.

[29] Susila, G. , and Suryan, G., Temperature Dependence of Recombination

and Trapping in Germanium, Indian J. Pure Appl. Phys. 2^, 125-129

(1964).

[30] Sandiford, D. J., Temperature Dependence of Carrier Lifetime in

Silicon, Proa. Phys. Soa. 71, 1002-1006 (1958).

[31] Streetman, B. G. , Carrier Recombination and Trapping Effects in

Transient Photoconductive Decay Measurements, J. Appl. Phys. 37 , 3137-3144 (1966).

[32] Okada, J., Recombination of Excess Carriers in Semiconductors, J.

Phys. Soa. Japan 12 , 1338-1344 (1957).

[33] Leadon, R. , and Naber, J. A., Recombination Lifetimes in HighPurity Silicon at Low Temperatures, J. Appl. Phys. 40, 2633-2638

(1969).

[34] Susila, G., A Method for the Determination of Short Lifetime of

Carriers in a Photoconductor from the Transient Photoresponse,

Indian J. Pure Appl. Phys. 2, 44-47 (1964). I

[35] Penchina, C. M. , and Levinstein, H. , Measurement of Lifetimes in

Photoconductors by Means of Optical Beating, Infrared Phys. 6^ 173-

182 (1966).

[36] McCormick, J. R. , and Henisch, H. K. , Simple Equipment for Lifetime

Measurements on Semiconductors, Amer. J. Phys. 33 , 965-967 (1965).

[37] Ridley, B. K. , The Effect of an Electric Field on the Decay of Excess Carriers in Semiconductors, Proa. Phys. Soa. _75, 157-161

(1960).

[38] Benda, H. , Dannhauser, F., and Spenke, E., Die praktische Bedeutung

der sogenannten STEVENSON-KEYES-Bedingung bei der Lichtblitzmethode

zur Bestimmung der Tragerlebensdauer , Siemens Forsahungs- und

Entwicklungs-berichte 3_, to be published in August 1972.

[39] Standard Methods of Test for Resistivity of Semiconductor Materials, ASTM Designation F43-71, Annual Book of ASTM Standards, Part

5, (American Society for Testing and Materials, Philadelphia,

(1971).

[40] Bullis, W. M. , Brewer, F. H. , Kolstad, C. D. , and Swartzendruber,

L. J. , Temperature Coefficient of Resistivity of Silicon and Germanium Near Room Temperature, Solid-State Eleatronias 11, 639-646

(1968).

38
[41] Hogarth, C. A., A Study of Carrier Injecting Properties of Emitter

Contacts and Light Spots at Normal and Moderately Elevated Temperatures, Proe. Phys. Soa. B66, 845-858 (1953).

[42] Iglitsyn, N. I., Kontsevoi, Yu. A., and Kudin, V. D., Measurement

of the Lifetime in Monocrystalline Silicon, Soviet Phys. Teak.

Phys. 2, 1316-1321 (1957).

[43] Hogarth, C. A., On the Measurement of Minority Carrier Lifetimes in

Silicon, Proa. Phys. Soa. B69 , 791-795 (1956).

[44] Hornbeck, J. A., and Haynes, J. R. , Trapping of Minority Carriers

in Silicon I. p-Type Silicon, Phys. Rev. 97, 311-321 (1955).

[45] Haynes, J. R. , and Hornbeck, J. A., Temporary Traps in Silicon and

Germanium, Phys. Rev. 90, 152-153 (1953).

[46] Arthur, J. B. , Bardsley, W. , Gibson, A. F., and Hogarth, C. A., On

the Measurement of Minority Carrier Lifetime in n-Type Silicon,

Proo. Phys. Soa. B68 , 121-129 (1955).

[47] Bemski, G. , Recombination in Semiconductors, Proa. IRE 46, 990-1004

(1958).

[48] Choo, S. C, and Sanderson, A. C. , Bulk Trapping Effect on Carrier

Diffusion Length as Determined by the Surface Photovoltage Method:

Theory, Solid-State Electronics 13, 609-617 (1970).

[49] Zitter, R. N. , Role of Traps in the Photoelectromagnetic and Photoconductive Effects, Phys. Rev. 112 , 852-855 (1958).

39
APPENDIX

In table 11 below the specimens referred to in the report are identified and their type and material, nominal resistivity, and nominal dimensions are given.

Specimen

Table 11 - Specimen Characteristics

Type and

Material

Nominal

Resistivity,

ft* cm

Nominal Dimensions, cm Length Width Thickness

DOFL

NBS-13

SSI

SS2

SS4

SS5

SS6

SS7

SS8

SS9

SS10

SS11

SS12

SS13

SS14

SS15

SS16

SS17

SS18

452D

678c/l

777E

12-620-3

13069/3

14787/5

15705/5

15710/3b

16444/2

52792A

R818

n-Ge

p-Ge

p-Si

p-Si

p-Si

p-Si

p-Si

p-Si

p-Si

p-Si

n-Ge

n-Ge

n-Ge

n-Si

n-Si

n-Si

n-Si

n-Si

n-Si

n-Ge

p-Ge

p-Ge

n-Si

p-Si

p-Si

p-Si

p-Si

p-Si

p-Si

p-Si

30

18

50

50

270

270

270

630

630

630

8

8

8

10

10

10

0.9

0.9

0.9

32

10

33

60

550

650

1400

4500

1550

165

40

2.5

2.15

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

10.5

8.0

7.8

5.1

9.2

5.0

3.5

2.5

1.0 1.0

0.75 0.75

1.0 1.0

0.5 0.5

1.0 1.0

0.5 0.5

0.25 0.25

1.0 1.0

0.5 0.5

0.25 0.25

1.0 1.0

0.5 0.5

0.25 0.25

1.0 1.0

0.5 0.5

0.25 0.25

1.0 1.0

0.5 0.5

0.25 0.25

1.0 1.0

1.0 1.0

0.5 0.5

diam. * 2.5

diam. = 2.04

diam. = 2.4

diam. = 1.95

diam. = 1.94

diam. = 1.99

diam. = 2.36

0.4 0.4

40
foAm NBS-114A (1-71) 2. Gov't Accession No.

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEETS

1. PUBLICATION OR REPORT NO. NBS-TN-736

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Carrier Lifetime Measurement by the Photoconductive Decay

Method

5. Publication Date September 1972

6. Performing Organization Code

7. AUTHOR(S)

Richard L. Mattis and A. James Baroody, Jr.

8. Performing Organization

10. Project/Task/Work Unit No. 4259522 4251126

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

DNA PO 808-70

12. Sponsoring Organization Name and Address National Bureau of Standards

Washington, D. C. 20234

Defense Nuclear Agency

Washington, D. C. 20305

13. Type of Report & Period Covered Interim

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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.) The photoconductive decay (PCD) method of carrier lifetime measurement is discussed

with emphasis on experimental and analytical work done at NBS. The relationship between

photoconductive decay time TpCD , bulk decay time xg, and lifetime is described briefly

and the PCD method is summarized. The determination of Xg from XpCD and the influence

of higher modes of recombination are discussed.

Experimental data, supported by theoretical considerations, are presented to demonstrate the dependence of Tp^p on excess carrier density, the type of light source, specimen homogeneity, filter thickness, and temperature. The dependences of xpQ) on excess carrier density and temperature are consequences of the statistics of the recombination

process. Measurements made with chopped light excitation are shown to be less in error

due to higher modes of recombination than are measurements made with pulsed light excitation. The presence of inhomogeneities is verified in two crystals. Use of a filter

is also shown to reduce the influence of higher modes. An unexpected reduction in xpcj)

with increasing filter thickness is shown to be caused by an inhomogeneity.

Other experimental conditions are discussed as they affect the measurement of xpcDIt is shown that the light turnoff must be sufficiently fast and the series resistance

sufficiently large that they do not interfere with the measurement. Equations are developed whereby the specimen current and illumination pattern can be chosen such that

carrier sweep-out at the ends of the specimen and ohmic heating are avoided. The end contacts must be sufficiently ohmic that excessive contact resistance does not interfere

with the measurement. (Over)

17. KEY WORDS (Alphabetical order, separated by semicolons) Carrier lifetime; germanium; photoconductive decay; silicon.

18. AVAILABILITY STATEMENT

UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

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UNCLASSIFIED

20. SECURITY CLASS

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UNCLASSIFIED

21. NO. OF PAGES

52

22. Price50^

USCOMM-OC 66244-P71
Trapping is defined and the means for identifying it are discussed

briefly. The PCD method is inappropriate for determining minority car- rier lifetime when trapping is present or under other circumstances when

the hole and electron lifetimes are unequal.
.

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The following current-awareness and literature- survey bibliographies are issued periodically by

the Bureau: Cryogenic Data Center Current

Awareness Service (weekly), Liquefied Natural

Gas (quarterly), Superconducting Devices and

Materials (quarterly), and Electromagnetic

Metrology Current Awareness Service (monthly). Available only from NBS Boulder Laboratories. Ordering and cost information may be

obtained from the Program Information Office,

National Bureau of Standards, Boulder, Colorado 80302.

NONPERIODICALS Applied Mathematics Series. Mathematical tables, manuals, and studies. Building Science Series. Research results, test methods, and performance criteria of building materials, components, systems, and structures. Handbooks. Recommended codes of engineering

and industrial practice (including safety codes) de- veloped in cooperation with interested industries,

professional organizations, and regulatory bodies. Special Publications. Proceedings of NBS conferences, bibliographies, annual reports, wall charts,

pamphlets, etc. Monographs. Major contributions to the technical

literature on various subjects related to the Bureau's

scientific and technical activities. National Standard Reference Data Series.

NSRDS provides quantitative data on the physical

and chemical properties of materials, compiled from

the world's literature and critically evaluated. Product Standards. Provide requirements for sizes, types, quality, and methods for testing various industrial products. These standards are developed co- operatively with interested Government and industry

groups and provide the basis for common understanding of product characteristics for both buyers and

sellers. Their use is voluntary.

Technical Notes. This series consists of communications and reports ( covering both other-agency and

NBS-sponsored work) of limited or transitory interest. Federal Information Processing Standards

Publications. This series is the official publication

within the Federal Government for information on

standards adopted and promulgated under the Public

Law 89-306, and Bureau of the Budget Circular A-86

entitled. Standardization of Data Elements and Codes

in Data Systems.

Consumer Information Series. Practical information, based on NBS research and experience, cover- ing areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's tech- nological marketplace.

CATALOGS OF NBS PUBLICATIONS NBS Special Publication 305, Publications of

the NBS. 1966-1967. When ordering, include

Catalog No. CI 3.1 0:305. Price $2.00: 50 cents additional for foreign mailing.

NBS Special Publication 305, Supplement 1, Publications of the NBS, 1968-1969. When ordering, include Catalog No. C13.10: 305/Suppl. 1. Price $4.50: $1.25 additional for foreign mailing.

NBS Special Publication 305, Supplement 2,

Publications of the NBS, 1970. When ordering, include Catalog No. Cl3.10:305/Suppl. 2. Price $3.25: 85 cents additional for foreign mailing.

Order NBS publications (except Bibliographic Subscription Services)

from: Superintendent of Documents. Government Printing Office, Washington, D.C. 20402.
U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. D.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use. $300

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