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National Bureau of Standards

Library, E-01 Admin. Bldg.

MAR 18 1971

NBS TECHNICAL NOTE 570

Determination of Deep Impurities

in Silicon and Germanium

by Infrared Photoconductivity

INAL BUREAU OF STANOA*ES

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

NBS TECHNICAL NOTE 570

ISSUED MARCH 1971

Nat. Bur. Stand. (U.S.), Tech. Note 570, 13 pages (Mar. 1971)

CODEN: NBTNA

Determination of Deep Impurities

in Silicon and Germanium

by Infrared Photoconductivity

W. Robert Thurber

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

**«MU Of **

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Determination of Deep Impurities in Silicon and Germanium

by Infrared Photoconductivity

W. Robert Thurber

The feasibility of using infrared photoresponse and photoconductivity measurements to study deep impurities in germanium

and silicon is examined by reviewing the literature. It is

concluded that photoconductivity is useful in detecting the

presence of specific impurities because each impurity has a long wavelength cut off in response associated with its ionization energy. However, when there are several deep impurities in the same specimen, it is difficult to be certain

of detecting each one because some have broad cut offs and

many have nearly the same ionization energies. Photoconductivity as a general technique has serious limitations for

determining the total concentration of deep impurities . The

equations for determining impurity concentration from the

magnitude of the photoconductivity signal depend on the relative influence of deep and shallow centers . Equations are derived for several situations and experimental results from the

literature are discussed for each one. Only uncompensated centers are available for photoionization and therefore the total

concentration can not be obtained directly. In some situations the response due to a deep center is independent of

its concentration. Other techniques for studying deep impurities are discussed briefly.

Key words: Deep impurities; germanium; infrared; photoconductivity; photoresponse; semiconductors; silicon.

1. Introduction

This report discusses the following two questions: (l) Can a specific impurity in germanium or silicon be identified from photoconductivity? (2) Does the photoconductivity vary with impurity concentration in a systematic way?

Before proceeding to answer the questions, some experimental aspects

will be discussed. The electrical circuit for photoconductivity measurements is very simple. The specimen and a load resistor are connected in

series with a voltage source. Chopped, monochromatic radiation is incident on the specimen and the resulting change in specimen conductivity

gives rise to a voltage change which is detected by a phase-sensitive
amplifier. A more detailed treatment of the experimental method can be

found in Ryvkin [l]. For most measurements, specimens must be cooled

to 77 K or below to eliminate thermal ionization of the impurity under

study. Since a small change in conductivity resulting from photoionization is most easily detected in a high resistance specimen, the lowest

readily available temperature is often used to freeze-out uncompensated

shallow impurities. However, since the lifetime and mobility of the

photoionized carriers are functions of temperature , there is usually a maximum in the response at some particular temperature.

A deep impurity is one that has an energy level near the middle of

the band gap. To obtain quantitative information on a deep impurity it

is necessary to know the optical absorption and capture cross sections

of the impurity at the temperature used for the photoconductivity measurements . These values may be available in the literature , but if they

are not, it is necessary to determine them experimentally. For some impurities there are large discrepancies in the published data, and

additional measurements are needed to obtain reliable values.

The most direct method for determining the optical absorption cross section of a particular impurity is measurement of the transmission of a specimen containing a known concentration of the impurity. Emmons [2]

gives a discussion of the procedure with specific application to gallium

in silicon at 20 K. Data are usually obtained as a function of wavelength and at the temperature used for the photoconductivity measurements

as the cross sections are generally wavelength and temperature dependent.

Ryvkin [3] has discussed the determination of the absorption cross section from the initial slopes of the photoconductivity rise and decay

curves. Putley [4] has compiled absorption cross sections of some deep

impurities in germanium.

The most common method of obtaining data on capture cross sections

is carrier lifetime measurements. Blakemore [5] has discussed in detail

the relation between lifetime and capture cross section.

Capture cross sections can also be determined from measurements of

the generation-recombination noise as a function of frequency. This technique is discussed by Schibli and Milnes [6] and by Neuringer and Bernard

[7] who determined the cross sections of free holes in p-type gold-doped

germanium.

References to other techniques such as the pulsed field effect and

frequency-dependent capacitance methods are given by Schibli and Milnes

[6] who have also compiled capture cross section data for impurities in

silicon. Bonch-Bruevich and Landsberg [8] have published a review article on recombination mechanisms which includes tables of cross sections

for impurities in both silicon and germanium.
2. Identification of Specific Impurities

That photoconductivity as a function of wavelength for each impurity in a given material is unique makes possible the identification of

an unknown impurity from its photoconductivity spectrum. The most significant feature for each impurity is the long wavelength cut off of the

response. At this wavelength the energy of the radiation is equal to the

ionization energy of the impurity. For longer wavelength radiation,

photoionization is not possible and photoconductivity ceases. Some impurities in a given material have a sharp long wavelength cut off whereas

other impurities have a broad and irregular one. This variation can be

an advantage when identifying impurities with nearly the same ionization

energies. However, when two or more impurities with about the same ionization energy are present in the same specimen, broad long wavelength

cut offs are a definite disadvantage.

A further complication is that the thermal ionization energies of

various impurities, as determined by Hall effect measurements for example,

do not correspond to the same relative position on the photoconductivity

curves. Thus if unknown impurities are to be identified from photoconductivity measurements , it is important to have photoconductivity spectra

for the likely impurities. Several impurities in the same specimen can

be identified by photoconductivity if each is present in sufficient con- centration to give a sharp drop in response at its respective long wavelength cut off. If two or more of the impurities have about the same ionization energies, then photoconductivity may be attributed to fewer

impurity species than are actually present. Graphs of photoconductivity

spectra for many deep impurities in germanium and silicon have been collected in data sheets prepared by the Electronic Properties Information

Center [9].

3. Dependence of Photoconductivity on Impurity Concentration

3.1 Concentration of Deep Impurities Exceeds that of Shallow Impurities

First the basic equations will be reviewed. Putley [4] has derived

the expression

*° ^r w

where Aa is the change in conductivity,

I is the intensity of radiation falling normally on the surface,

q is the electronic charge,

u is the mobility of the generated carriers

,

x is the lifetime of the free carriers

,

r\ is the fraction of incident photons absorbed by the impurity

centers

,
V is the specimen volume,

h is Plank's constant, and

v is the frequency of the radiation.

With the assumption that each quantum absorbed liberates one free

carrier, n is determined by the fractional amount of energy absorbed.

For a specimen with polished, parallel sides

n

* <l-R)(l-e-"*)

( 2 ) 1-Re~ ax

where R is the reflectivity, a is the impurity absorption coefficient,

and x is the specimen thickness. Further manipulation will relate the

change in conductivity to impurity density for p-type material containing

a single deep acceptor whose concentration exceeds that of the shallow

donors. The quantity ax is usually less than one and an approximation for

n good to 20 % for ax between 0.1 and 0.7 and R = 0.3 (appropriate for

silicon) can be obtained by neglecting Re~ax in the denominator and ex- panding the numerator to give

n = (1-R)(ax) = (1-R) a_ (N.-N„)x (3) a A a where a a is the photoionization (absorption) cross section of an un- occupied center, N is the density of deep (capital subscript) acceptors,

and N, is the density of shallow donors available for compensating the

deep acceptors

.

In general free carrier recombination occurs by the capture of car- riers by ionized impurities . At temperatures low enough so that thermal

ionization is unimportant, the number of recombination centers in material for which the deep impurity concentration exceeds that of the shallow impurities is determined by the concentration of compensating impurities . The carrier lifetime is

T = (n-type samples) (4)

and

t =

vN a

n a n

vN„a

d p

(p-type samples) (5)

where v is the thermal velocity of the charge carriers , a^ is the capture

cross section for an electron by a positively charged (before capture)

deep center, and o~ is the capture cross section for a hole by a negatively charged deep center. Deep impurities such as copper or gold are usu- ally very effective recombination centers if they are charged.

The approximate dependence of the photoresponse, Aa/I, on impurity

concentration for initially n-type material which has been doped with
a deep level impurity to become p-type is found by substituting Eqs. (5)

and (3) into (l). That is

Ao qP(l-R>°

a

(N

A

-N

d

)x

j

• (6)

vVhvN ,o~ d p

The equation for n-type material is found by substituting N

D for N^,

Na for N^, and using the electron mobility and appropriate cross sections.

The photoresponse has the disadvantage that the concentration of deep

impurities can not be found unless the density of compensating impurities

is known or can be determined by an independent experiment.

Quist [10] has shown that the relative photoresponse at a given

temperature for three copper-doped germanium detectors , each with the

same copper concentration (7 x 10 15 atoms/cm3 ), but with different donor

concentrations is proportional to the reciprocal of the donor density as predicted by Eq. (6).

Newman and Tyler [11] prepared a series of p-type germanium specimens by diffusing nickel at 850°C into crystals with predetermined con- centrations of donors (arsenic). The photoconductivity spectra at 77 K

had a threshold at 0.23 eV corresponding to the energy of the lower nickel level. The dependence of the photoresponse on the ratio of arsenic to

nickel concentrations was in excellent agreement with Eq. (6). Thus

compensation plays a dominant role in photoresponse measurements.

Sidorov and Lifshits [12] have studied the dependence of the photoresponse on the impurity concentration and degree of compensation in the

systems Ge:Au:Sb and Ge:Zn:Sb. Gold concentrations varied from 0.3 to

i+ x 10 15 atoms /cm 3

, while zinc concentrations ranged from 0.2 to 5 x 10 15

atoms/cm3

. The amount of antimony in the germanium was chosen to give

specimens with different degrees of compensation — from nearly empty

levels for Au (0.15 eV) or Zn (0.09 eV) (the 0.03 eV Zn level was com- pletely filled) to complete occupation of these electron levels. For the

gold system hole recombination occurs at Au~ ions whereas for the zincdoped specimens hole capture is by Zn ions. The photoresponse of both

sets of specimens showed the expected dependence on compensation as given

by Eq. (6).

To calculate the photoconductivity, Aa/al, for p-type material we need to divide Eq. (6) by the conductivity pqy where p at low temperatures

is given by

VN

d

p = g

Nve^ep[-(E i-Ev

)/kT]. (7)

d
Eq. (7) holds for partially compensated material where N v is the density

of states in the valence band and E^ - E

y

is the ionization energy of the

deep impurity. The photoconductivity is

Aa (l-R)a xeajp[(E

i

-Ev

)/kT]

_= _ • (8)

vVhva N

Thus if the dark conductivity and the light induced change in conductivity are determined by impurity atoms of one species , the photoconductivity is independent of the concentration of active centers and their

compensation and is determined only by the ratio of the cross sections of

these centers for light absorption and charge carrier recombination.

This type of behavior has been observed for copper-doped germanium by

Adams, Beyen, and Petritz [13]. For copper concentrations from 1.7 to

14.0 x lCr 5 atoms/cm 3

, the photoconductivity they observed at 5 K was independent of copper concentration.

It is interesting to note that when the photoconductivity is given

by Eq. (8), cross section data can be obtained without measuring the

impurity concentration. Thus from photoconductivity data and knowledge

of one cross section, the value of the other cross section can be calculated.

3.2 Concentration of Shallow Impurities Exceeds that of Deep Impurities

If the shallow impurities outnumber the deep ones, then the recom- bination center density depends on the characteristics of the specific

impurities. For example, gold has both donor and acceptor levels in

silicon, and in n-type material the Au~ ions are effective capture centers whereas in p-type material the Au+ ions have large capture cross sections. Thus for either n- or p-type silicon the number of recombination centers is equal to the gold concentration.

Consider the response of a deep acceptor level in a specimen where

the shallow donor concentration exceeds the deep acceptor density. The

light absorption and carrier lifetime are both proportional to the deep

impurity concentration so the photoresponse is

qy(l-R)a x |2.= ^ ' (9)

vVhva

p

At low temperatures the conductivity is

(N -N ) a = qy

2 Nceap[-(E -E.)/kT], (10)

jn a
where N is the density of states in the conduction band and E - E- is

c c the ionization energy of the shallow donor. Then the photoconductivity

due to the deep acceptor is given by

. (l-R)a xN.eccp[(E -E.)/kT]

Aa a A

r c 1

^ , , al vVhva"(Nd-NA

)N

(

The shallow donor will also give rise to photoconductivity and may mask

the contribution of the deep acceptor. For this case there is no reason

to measure the photoconductivity as the equation for the dark conductivity gives the dependence on impurity concentration. To obtain N from

the conductivity it is necessary to know N , . Hall effect measurements as

a function of temperature can be used to get both N, and N. , but considerable effort is required.

Small concentrations of deep impurities have been detected in sili-

' con by photoconductivity measurements made by Plotnikov and co-workers

[14], They observed shoulders in the spectra at wavelengths corresponding to the energy levels of copper and gold. Concentrations were estimated to be 10 10 to 10 11 atoms/cm 3 using literature values for the capture cross sections, but the equations used were not given. For these

low densities the dependence of photoconductivity on impurity concentration may be approximately linear. The absorption of light by a particular deep impurity is proportional to its uncompensated concentration

whereas the carrier lifetime is determined by other centers when there

are so few deep ones. In addition the deep impurities may have very

little influence on the specimen conductivity so in very pure material it

may be appropriate to replace Eq. (7), which holds only for partially

compensated material, with an equation involving only the majority impurity concentration. Silicon crystals intentionally doped with gold and

copper to 5 x 10 15 atoms/cm 3 were also investigated. The results supported the conclusion that the photoconductivity structure observed in

the undoped material was due to gold and copper.

The previous equations and experimental results indicate the

complexities of determining deep impurity concentrations from photoresponse and photoconductivity measurements. There is no circumstance

in which the deep impurity concentration can be obtained without knowing

the density of compensating impurities. Since the applicable equations

depend on the situation, it is necessary to know whether the deep impurity acts as an acceptor, donor, or both, and to know its concentration

relative to that of the shallow impurity. The equations were written for

a single deep impurity in the presence of a single shallow impurity. The

influence of additional impurities can be readily included, but there remains the practical problem of estimating the concentrations of these impurities so that their effect on the impurity under study can be determined.
4. Summary of Other Methods for Determining Deep Impurities

Since photoconductivity spectra generally do not yield directly the

needed information on impurity density, it seems worthwhile to briefly

examine other techniques which may be more useful or which can supplement

or confirm information obtained by photoconductivity.

Deep impurities introduce recombination centers which reduce the

carrier lifetime. For example gold acts as a recombination center in

silicon with an observable room temperature effect on lifetime in both

n- and p-type silicon at the 10 12 atoms/cm 3 level [15]. At low temperatures even fewer impurity atoms may influence the lifetime in pure single

crystals. Experimental data show the expected inverse linear relation

between lifetime and recombination center density for center densities

covering many orders of magnitude. Thus, for a single impurity, if the

capture cross section is known, the center density can be calculated.

From lifetime measurements at one temperature it is not possible to identify the specific impurity involved. However, when measurements are made

as a function of temperature, it is possible to obtain the position of

the recombination level in the band gap from the slope of the lifetime

vs. temperature plot as discussed by Streetman [16]. Since ionization

energies of most deep impurities in silicon and germanium are well known,

it is often possible to correlate an observed energy with a specific

impurity. The photoconductive decay (PCD) method is commonly used for

lifetime measurements on bulk specimens . Two ohmic contacts are generally

used to pass current through the specimen, but contactless techniques can also be used. Ryvkin [3] has discussed the determination of the impurity

concentration from the initial slope of the photoconductivity rise curve.

The diode recovery method has been popular for measuring lifetime in

p-n junction structures. In this method, a diode which is forward biased

is abruptly reverse biased. The time before the onset of the normal re- verse current is called the recovery time and can be related to the lifetime. There is an inverse linear relation between reverse recovery time

and deep impurity concentration in many systems. A good example is golddoped silicon [17].

Sah and co-workers [18] have described capacitance-voltage and transient capacitance experiments with and without light which give information on deep impurities. Concentrations as low as 10 L1 atoms /cm 3 were

said to be detectable. The C-V measurements allow the determination of

impurity concentration as a function of position if data are obtained on

a control specimen with no impurities and on a specimen with a known

impurity density.

Armantrout [19] has explored an infrared photoresponse technique

for determining impurity ionization energies and concentrations in a
lithium compensated germanium detector. From a plot of photoresponse as

a function of incident radiation energy, it may be possible to identify

various impurities and defects because of their characteristic spectra.

No quantitative relations are given between the photoresponse signal and

the concentration of defects and impurities.

Another method for determining deep centers is thermally stimulated

conductivity measurements. In this technique excess carriers are excited

into the traps of a reverse biased p-n junction diode, either by light

or by a small forward bias. By heating the specimen, the thermally stimulated current is obtained as a function of temperature. Peaks in the

spectrum are due to the release of charge carriers from a particular

trapping level. The integrated area between the current peak and the

dark conductivity is proportional to the trap concentration. This method

has detected nickel, silver, copper, and iron in silicon with concentrations of 0.4 to 3 x 10 12 atoms/cm3 [20].

Hall effect measurements as a function of temperature are another

source of information about deep impurities. Concentrations of ionized

impurities as low as 10 11 atoms/cm3 can be detected providing the shallow

impurity density does not exceed 10 13 atoms/cm 3. It is possible to identify a specific deep impurity from a measured ionization energy. However,

since several impurities have about the same energy levels , other information may be necessary for the positive identification of a specific

impurity.

Electron spin resonance combined with infrared absorption has been

used by Kravitz [21] to study deep impurities. Ionization and trapping

processes which change the impurity population are detected by monitoring

the spin resonance signal of an impurity while simultaneously illuminating

the specimen with monochromatic infrared radiation.

Neutron activation analysis is a widely used technique for determination of many elements simultaneously in a specimen. The total

chemical concentration is obtained in contrast to the other techniques

discussed which determine only the electrically active atoms. Activation analysis is generally non-destructive, but the electrical properties

of semiconductors may be affected by the irradiation. Annealing will

usually restore the original properties. Activation analysis is very sen- sitive for many deep impurities. For example, as few as 1 * 10 12 gold

atoms/cm can be detected in a one gram specimen of silicon.

5. Conclusions and Recommendations

Infrared photoresponse and photoconductivity are useful techniques

for identifying specific impurities because the response due to each

impurity has a long wavelength cut off associated with the ionization

energy of the impurity. When a single species is present in sufficient
concentration to give a strong signal, the technique gives a result

which is easily interpreted. However, if two or more species are present

in the same specimen, then identification is more difficult since long

wavelength cut offs are frequently not sharp and a number of impurities

have about the same ionization energies. For determining impurity con- centrations, the techniques are limited to well-characterized situations

as the applicable equations depend on the combination of impurities

present. Only neutral impurities can be photoionized so information

about compensation is necessary if the total deep impurity concentration

is desired.

In specimens used for most applications, the deep impurity concen- tration is several orders of magnitude smaller than the shallow impurity

density. If both impurities are acceptors with comparable absorption

and capture cross sections, then the signal due to the deep impurity will

generally be masked by that due to the shallow impurity. It is assumed

that the temperature of the specimen is low enough so neither impurity

is thermally ionized. If the shallow impurity is thermally ionized, then

the specimen conductivity is high and the fractional change due to photoionization of the deep impurity may be difficult to detect. Likewise,

a deep acceptor level compensated by a large concentration of shallow

donors would contribute little to the photoconductivity since photoexcitation of the donors would predominate at all wavelengths.

Photoconductivity measurements may be helpful in a research situation

as one of several techniques for determining the concentration of deep

impurities. As a single technique, photoconductivity appears to have no advantages over several other methods.

The support of the AEC Division of Biology and Medicine for portions

of this work is gratefully acknowledged.

10
References

1. S. M. Ryvkin, Photoelectric Effects in Semiconductors3 pp. 19-34,

Consultants Bureau, New York, 1964.

2. R. B. Emmons, "Extrinsic Photoconductivity in Silicon," Semiannual Technical Summary Report, ARPA Contract No. 00014-68-C-0421,

September 30, 1968, AD-68486.

3. S. M. Ryvkin, Op. Cit. 3 pp. 194-198.

4. E. H. Putley, "Far Infra-red Photoconductivity," Phys. Stat. Sol.

6, 571-614 (1964).

5. J. S. Blakemore, "The Relation Between Carrier Lifetime and Capture

Cross-Section in an Extrinsic Photoconductor , Exemplified by

Indium-Doped Silicon," Proceedings of the 9th Inter. Conf. on

the Physics of Semiconductors > pp. 486-491, Moscow, 1968.

6. E. Schibli and A. G. Milnes , "Deep Impurities in Silicon," Mater.

Sci. Eng. 2, 173-180 (1967).

7. L. G. Neuringer and W. Bernard, "Generation-Recombination Noise

in p-type Gold-Doped Germanium," Phys. Rev. Letters 6_, 455-457 (1961),

8. V. L. Bonch-Bruevich and E. G. Landsberg, "Recombination Mechanisms,"

Phys. Stat. Sol. 29, 9-43 (1968).

9. M. Neuberger, "Germanium Data Sheets," February, 1965; M. Neuberger

and S. J. Welles, "Silicon Data Sheets," October, 1969, Electronic

Properties Information Center, Hughes Aircraft Co. (sponsored by

Air Force Materials Laboratory), AD-610828 and AD-698342, respectively.

10. T. M. Quist, "Copper-Doped Germanium Detectors," Proc. IEEE 56_,

1212-1213 (1968).

11. R. Newman and W. W. Tyler, "Photoconductivity in Germanium,"

Solid State Physicss Volume 8, pp. 49-107, F. Seitz and D. Turnbull,

Eds. (Academic Press, New York, 1959).

12. V. I. Sidorov and T. M. Lifshits, "Photoelectric Properties of

Germanium Alloyed with Gold and Zinc," Radio Engin. & Electronic

Phys. (USSR) ]_, 1927-1935 (1962).

13. H. D. Adams, W. J. Beyen, and R. L. Petritz, "Photoconductivity

Research on Cu-Ge," J. Phys. Chem. Solids 22, 167-172 (1961).

11
14. A. F. Plotnikov, V. D. Tkachev, and V. S. Vavilov, "Remanent

Impurity Photoconductivity Spectra of Silicon Single Crystals,"

Soviet Physios - Solid State 4-, 2616-2617 (1963).

15. C. B. Collins, R. 0. Carlson, and C. J. Gallagher, "Properties

of Gold-Doped Silicon," Phys. Rev. 105 , 1168-1173 (1957).

16. B. G. Streetman, "Carrier Recombination and Trapping Effects in

Transient Photoconductive Decay Measurements," J. Appl. Phys.

37, 3137-3144 (1966).

17. A. E. Bakanowski and J. H. Forster, "Electrical Properties of GoldDoped Diffused Silicon Computer Diodes," Bell Syst. Teoh. J.

39_, 87-104 (1960).

18. C. T. Sah, L. Forbes, L. L. Rosier, and A. F. Tasch, Jr., "Thermal

and Optical Emission and Capture Rates and Cross Sections of

Electrons and Holes at Imperfection Centers in Semiconductors from

Photo and Dark Junction Current and Capacitance Experiments,"

Solid-State Electronics 13_, 759-788 (1970).

19. G. A. Armantrout, "Defect Study and Identification in Ge(Li) P-N

Junction Radiation Detectors," Metallurgical Trans. 1, 659-665 (1970)

20. H. Schade and D. Herrick. "Determination of Deep Centers in Silicon

by Thermally Stimulated Conductivity Measurements," Solid-State

Electronics 12, 857-860 (1969).

21. L. C. Kravitz, "ESR and Optical Experiments on Deep-Lying Impurities

in Germanium and Silicon," Harvard University, Technical Report No.

HP-9, June 14, 1963, AD-423329.

12
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WASHINGTON, D.C. 20230

OFFICIAL BUSINESS POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE

PENALTY FOR PRIVATE USE, $300