Slow conductivity relaxation in bulk germanium containing oxygen

f. Phys. Chem. Solids

Pergamon

Press 1967. Vol. 28, pp. 1821-1829.

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Printed in Great Britain.

RELAXATION IN BULK

GERMANIUM CONTAINING OXYGEN EIICI-II ADACI-II Central Research Laboratory,

Hitachi Ltd.,

Kokubunji,

Tokyo, Japan

(Receiued 7 April 1967)

Ah&net-In oxygen-doped n-germanium, heat-treated at 300°C, slow conductivity relaxations have been observed over the temperaturn range about ZlO-300°K; they occur after not only photoexcitation but also thermal excitation, namely the excitation by rapidly cooling or heating a sample. Their time constants range between a fraction of a second and two hours. The time constant of the conductivity relaxation for cooling and the time constant for heating agree well with the time constant of the photoconductivity relaxation, and, therefore, it is suggested that there is a common rate-limiting process among these relaxation processes. It is concluded that the slow relaxation phenomena occur in bulk germanium and are associated with oxygen-complex (probably Ge*Oa). 1. INTROI3UCTION

IN oxvom-doped

and heat-treated n-germanium, slow conductivity relaxation@ have been observed in the tempem~e range about 190-210°K. FULLER and DOLEIIHIN(~~have suggested that the slow conductivity relaxation can be attributed to the relaxation of the donor, which is formed by a heat-treatment at about 3OO”C,contains less than four oxygen atoms and has ionization energies of 0.2 eV and/or 0.04 eV. It is well known, on the other hand, that there appear slow trapping phenomena at room temperature in bulk silicon containing oxygen.(2*3) KAISER, FRISCH and REISS'~'have suggested that these trapping centres would correspond to the electrically active complexes containing two or three oxygen atoms in silicon. Considering close similarity between the behaviour of oxygen in silicon and the one in germanium, it seems most probable that the trapping phenomena appear also in oxygen-doped germanium. The measurement on the photoconductivity, therefore, was made in oxygen-doped and heattreated n-germanium(6) in order to ascertain the validity of the Fuller and Doleiden’s model with an expectation that both the slow trapping and the slow conductivity relaxation(l) have the same origin. Cur results indicate that the oxygencomplex related to the O-2 eV level acts as a trap 1821

of a minority carrier, and the time constant of the photoconductivity relaxation due to the trap agrees well with the one of the “donor relaxation”, namely, there are close relations between both relaxations, Results also suggest that there exists a relation between the O-2 eV donor and the 044 eV donor. This relation is not fully taken into account in the Fuller and Doleiden’s model. The relation is, therefore, investigated further by the measurement on the slow conductivity relaxation by not only rapidly cooling, but also rapidly heating the sample. Some results are obtained which are inconsistent with the Fuller and Doleiden’s model. Some possible models, therefore, are discussed.

The specimens employed in this experiment were prepared as follows.@*‘) Germanium single crystals were pulled from the melt under an ambient argon gas containing about l/100 partial pressure of oxygen. The cut specimens were quenched after a short heating close to the melting point of germanium. In this way the annealing effects which occurred during the normal cooling of the pulled crystal were eliminated, and the oxygen atoms were kept in a supersaturated solution in the germanium lattice.

1822

EIICHI

The oxygen concentrations were determined by the measurements on the infrared oxygen absorption band at 11 a7 p using a Perkin-Elmer model 21 double beam infrared spectrophotometer.(4) The oxygen concentrations of the specimens used in this experiment were about 3 x 101’ atoms/cm”. The specimens were heat-treated at 300°C for given times in ambient Ns gas in order to form the oxygen-complexes, which contained less than four oxygen atoms(g) and had the ionization energies of O-2 eV and/or 0.04 eV.(l)

ADACHI

Table 1. Heat-treatment at 300°C

Sample

GO3-13 G03-14 G03-15 G03-17 GO3-18

Heattreatment time (min.) 5 30 1:: 2340

Sample

FIG. 1. A typical photoconductivity

+ n,

3 x 1015 8 x lOle 1.5~10’~ 2.9 x 10le

Nt at 230°K (cm-“)

PIat 230°K (cm - 3,

2.2 x 1014 6.0 x 1Ol4 1.2~10~~

3.1 x 10’4 5.5 x lOI4 7.2~10~~ 1.17 x 10’6

GO3 -15 232’K

recorder trace of the decay in the at 232°K for the sample GO3-15.

Electrical measurements Conductivity measurements were made on specimens of 1 x 2.3 x 10 mm3 placed in a cryostat, in which temperature was controlled to within 0.4”C; for photoconductivity measurements a tungsten filament lamp and a germanium filter of thickness 0.7 mm were used; latter was able to eliminate surface effects practically. Estimation of the conduction electron density was made from conductivity measurement using the MORIN and MAITA’S mobility data.‘lO) Donor concentrations Nd were determined using the equation Nd = (2n2/N,)exp((Ec - E,)/kT)

(cmN”-3,

(1)

where N,, n, EC, Ed, k, and T were the density of the states in the conduction band, the conduction electron density in thermal equilibrium, the energy at the conduction band edge, the energy of the O-2 eV donor, the Boltzmann’s constant, and absolute temperature, respectively.(ll) Values of

Nd and n are shown in Table 1. The experiment on the conductivity relaxation was made rapidly changing the sample temperature from one temperature to another and tracing the conductivity change by a recorder.

3. EXPERIMENTAL

RESULTS

A. Photoconductivity relaxation relaxation slow photoconductivity The phenomena were investigated as a function of the temperature, illuminating light intensity, and the concentration of the O-2 eV donors using the specimens which were heat-treated for different times at 300°C. Experimental results are summarized as follows. 1. Photoconductivity decay is closely exponential except under strong illumination as shown in Figs. 1 and 2. 2. The slow relaxation phenomena appeared after a short heating at 300°C and disappeared after

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close to the melting point of germanium. These procedures correspond to the appearance and the disappearance of the O-2 eV levels.~l’ 3, They were insensitive to surface treatments such as etching and lapping, and also to ambient gas in the measurement. a short heating

GBBMANrUM

CONTAINING

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1823

8. The trap density varied with the temperature of the sample, It decreased as the temperature was raised aa shown in Fig* 4. 9. The trap density increased nearly proportional to the concentration of the O-2 eV levels. This tendency appears in Fig. 4 and Table 1.

It is known that the “donor relaxation” process follows first order kinetics.(i) In order to measure the time constant of this process by rapidly heating or cooling the sample, the following condition must be satisfied: the sample temperature can be rapidly changed from a temperature to another with a time constant much smaller

tq

I

.

.

’

‘S

,

’

t

IXiO'

TIME IN SECONDS

4. Light of l-5 p (its photon energy > &) can induce the slow relaxation, but light of 2 p (its photon energy < E#) cannot. The photoconductivity is, therefore, considered ta be due to intrinsic excitation. 5. The temperature dependence of the photoconductivity relaxation time constant can be described well by the relation TP = 5.2 X IO-l6 exp(0.75 eV/W),

(2)

as abown in Fig. 3. The time constant 7P was independent of the concentration of the O-2eV donor in the range of our experiment. 6. The photoconductivity increased linearly with increasing illuminating light intensity, and saturated under strong ilhnnination where the trapping centres were considered to be occupied entirely. 7. The trap density (NJ is estimated from the saturation value of the photoconductiviry and it is shown in Table 1 together with heat-treatment time. 7

tiG. 3. Temperature dependence of the photoctmductiv&y rehzation time constant. &an the time constant of the process. In our experiment the time constant of the “donor relaxation” process (i.e. conductivity relaxatian) could be measured in the range longer than about 100 sec. A recorder trace of the conductivity decay by rapidly cooling the sample from room temperature to 213*X, is shown in Fig. 5. In the range

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ADACHI

,oJ-----3G

3s

40

IO3

41

/ T

42

A

003-17

0

003-15

0

603-14

43

44

43

5

(‘K-l]

FIG. 4. Trap density as a function of temperature. The symbols 0, q and n indicate values for the sample G03-14, GO3-15 and G03-17, respectively.

l-2 of Fig. 5 the sample maintained at room temperature; its temperature began to be decreased at 2; it reached near the desired temperature 213°K at 4; then it was maintained at this temperature. In the range 24 the conductivity decreased at first and then showed a plateau. (In some traces at low temperatures the conductivity showed a hump instead of the plateau.) The conductivity began to show exponential decay at 4 to a new equilibrium value corresponding to 213”K.* Figure 6 shows Ae/e vs. time relation in the range 4-S of Fig. 5. A time constant was determined from Fig. 6; it is designated 7C. Furthermore, a recorder trace of the increase in the conductivity by rapidly heating the sample * This behaviour of the conductivity decay may be understood as follows. In the first part of the range 2-4 of Fig. 5, -(dn/dt)/n was large and (dp/dt)/p was smaller than - (dn/dt)/n, so do/dt showed negative value; with time (d&&)/p possibly increased and then decreased but -(&/&)/a decreased more rapidly to value comparable with (b/&)/c, so do/dt became small value and, therefore, conductivity showed a plateau; when -(dn/dt)/n became smaller than (dp/dt)/p, there appeared a hump in the recorder trace of the conductivity; (&/at) became zero at 4, so the conductivity began to show exponential decay.

from 213°K to 218°K is shown in Fig. 7. In the range l-2 the sample was maintained at 213°K; its temperature began to be raised at 2, it reached the desired temperature 218°K at 4, and then it was maintained at this temperature. The conductivity decreased suddenly at 2, and then turned to increase at 4.t In the range 4-S the conductivity increased very slowly tending to a new thermal equilibrium value correspondiig to 218°K. A time constant was determined from he/o vs. time relation shown in Fig. 8; it is designated Q-,,. Figure 9 shows the conduction electron density vs. l/T for the sample GO3-15. The line 2-3-S shows a path for extremely showly cooling or heating, the thermal equilibrium distribution of electron being established. The lines Z-3+(4’, 4”).5(5’, 5”) show paths for rapidly cooling. The line S-6-7 shows a path for rapidly heating. Figure 10 shows TV, TV, and r,, vs. l/T relations t In contrast to the cooling process (dn/dt)/n was smaller than - (dp/&)/p because of the very large time constant of the increase in the conduction electron density at low temperature, so du/dt showed negative value in the first part of the range 2-4.

SAMPE

503

- I5

-

21%X

30O*K

1

2

3

3

TJfflE

JN

7

8

HOURS

Fro. 5, A typiud nxorder truce of the axmd~r&ity rekx&n by rapidly cooling the semp~e &mpaanre from morn temperature to 213°K for the aampk C%3-15. In tbtsmrige l-2 the temperature wee room c*mpemWre; between 2-4 it was decreased from room &mporacure to 213%, and after 4 it was maintained ac 213%.

for the sample GO3-15. They ham the tame value There are ~veral differences between traps in as a function of temperature, x-germanium snd traps in &licen.~a~ They are To con&n further this fact we measured lP as follows: (1) twu kinds d traps (n-trap and and rc (or T,+) at the same temperature, and p-trap) appear in siiicon, but only one kind of campared one with another. I?igures 11 and 12 show 3 vs. IC, and Tp vs. Tk &ations$ r%?spectivelyS at the same temperature for the sample 603-15.

As a result of the experiment we believe that the oxygen-complex (probably Ce”Oa~) in bulk wa-germanium acts as a trapaplwith which the observed process of the slow phatoconductivity relaxation is associated, because of the following PtZSM3S. 1. The skv ph~~~~ducti~~~ relaxation phenomena appeared and diss~~ed tagether with the 0.2 eV donors. 2. It was insensitive ta surface treatments such aa etching, and lapping, and to ambient gas. 3. The time constant T, or Q agreed well with the time constant of the phetoconductivity relaxation rP; this fact suggesti thst both relaxadcm have a common rate-limiting process. The quantitative relation between the trapping centre density and the concentr&m of the 0.2 eV donors, however, is not explicable as yet.

t F&owing F~JLLE@ the asterisk is imp&d to show the feei thst the oxygen-compkx ia aohse and not separate oxide phase.

traps has been found in germanium, (2) the time constant af the photoconductivity decay due to traps does not depend upon majority carrier density and trap density in germanium, but it depends upon them in silicon, (3) in silicon the rate-limiting process of this sfuw plxmixmductivity decsy is in electronic transitirr process, but in Geoff it is nt~t yet clear whether the rate-limiting process is in electronic transition

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EIICHI

ADACHI

SAMPLE 213OK

I

0

TIME

IN

2lS’K

3

*

I

GO3 -15 -

4

HOURS

FIG. 7. A typical recorder trace of the conductivity relaxation by raising the sample temperature from 213°K to 21VK for the. sample GO3-15. In the range l-2 the temperature was 213’K; between 2-4 it was raised from 213°K to 218’K, and after 4 it was maintained at 218°K.

process or in movements of atoms, as mentioned later in Section 4b.

B. Slow conductidy

relaxation Fuller and Doleiden have suggested that the slow conductivity relaxation can be attributed to the “donor relaxation” as follows.(l) The donors, formedby the heat-treatment at 300-35O”C,

Sample

603-15

21S°K

, I

d’l

30

J 35

4.0

I

03/

4s

T

50

55

60

I”K-‘J

FIG. 9. Conduction electron density vs. l/T for the sample G03-15, showing the slow conductivity relsxations. The line 2-3-S shows a path for extremely slowly cooling. The lines 2-3-#(4’, 4”)-5(5’, 5”) show paths for rapidly cooling. The line S-6-7 shows a path for rapidly heating.

1..

1

0

sow TtME

IN

*.

1

*

loaaa

SECONDS

FIG. 8. The growth in the conductivity as a function of time caused by rapidly heating the sample. 7~ = 3.3 X103 set

have two species; one corresponds to the 0.2 eV level and another corresponds to the 0.04 eV level, The latter, moreover, have two forms; the high temperature form (O-04 eV donor) and the low temperature form (neutral or deep-lying donor). All these donors are associated with

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Cie*O,. When a sample is quenched from room temperature to 77°K and then heated to a temperature close to 200% the quenched-in 044eV donors begin to transform into the low temperature form tending to thermal equilibrium with a

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large time constant reqtired for the movements of the oxygen atoms to a new position. According to the Fuller and Do&den’s model, therefore, the rate-limiting process of the slow conductivity relaxation is the transformation process af the O-04 eV donor from the high temperature form to the low tempersture form, and it does not concern with the 0.2 eV donor. In our experiment, however, when a sample being in thermal equilibrium at low temperature is heated to a temperature, not too high, and maintained at this temperature, the change of Sample60345

f L

lb

l-p (secl Pm, 10. rP, TC,and -rhvs. l/T far the aample GO3-15 showing these time constants are nearly same values.

._ Sample GO3- I 5

* J

0 ::

x

u id *

~~/

103 TP

IO’

(sect

I%. il. TV vs. rE for the sample GOi%15, both time constants being measured at the same temperatures.

Fza. 12. 7,, vs. q, for the sample GO3-15, both t&e constants being measured at the same temperatures.

the conduction electron density has been found to increase as follows: it increases not along a 0.2 eV line, but nearly along a O@+eV line at first; then, even at the constant temperature, it increases slowly up to the O-2 eV line. This fact seems to be inconsistent with the Fuller and Doleiden’s model; namely, if the Fuller and Doleiden’s model were right, the conduction electron density should increase along the 0.2 eV line at first as long as the donor transformation is negligible and then might deviate from it as a result of the donor transformation. We have to believe, therefore, that the slow conductivity relaxation could not be explained by the Fuller and Doleiden’s model. A satisfactory explanation for the conductivity relaxation phenomena is very diflkult to pxescnt. Some suggestions, therefore, are presented here.

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EIICHI

Our experiment as well as Fuller and Doleiden’s experiment(l) shows the following behaviour: a reversible process with temperature occurs; the thermal equilibrium density of the conduction electrons changes along the 0.2 eV line and the O-2 eV line does not shift during the cooling or heating run; the 0*04 eV level density, however, is affected by the cooling or heating run and shows slow relaxation. The conduction electron density is expressed well by the relation n = N6a exp( - 0.04 eV/kT,), with N6a = Ndl exp( -0.16

(3b)

eV/kT,,,)

where Naa, TL, and Teft* are the 0.04 eV level density, the lattice
kTe,r

= log

-0.16

r

1

-exp

-0.16 +

exp

kTLl

eV

kTLP

eV

-0.16eV - exp

kTLa

There remains a question: whether the 0.16 eV is due to the heat of transformation or the energy difference between the electronic energy levels related to the oxygen-complex, namely, whether the slow conductivity relaxation is attributed mainly to the movements of the oxygen atoms or to the electronic transition process. Our experimental result shows that, if the O-2 eV is the activation energy of the donor, the donor has the large time constant to excite the electron into the conduction band, because, if not so, the path 5-6-7 in Fig. 9 would not appear. Fuller has pointed out that Ge*Os is singly charged. One can have a possible model, therefore, where the 0.2 eV level is the ground level of the oxygen-complex and the 0.04 eV level is its excited level; the large time constant is required for the electronic transition between the 0.2 eV level and the 0.04 eV level of the same oxygen-complex, probably accompanying the internal rearrangement of the oxygencomplex; a 0.04 eV level disappears when a O-2 eV level is occupied by an electron. Another possible model is that the oxygencomplex has two forms, electrically active and inactive; the 0.04 eV level is due to former form; the heat of the transformation is 0.16 eV; the reversible transformation between these forms requires the large time constant. We cannot decide between these two models only from the intrinsic photoconductivity experiment done here, but we may decide from further investigation such as extrinsic photoconductivity experiments.

5. SUMMARY

The oxygen-complex containing less than four oxygen atoms acts as a trap in bulk n-germanium as well as in bulk silicon even at room temperature. Rapidly heating as well as rapidly cooling the sample also resulted in the slow conductivity relaxation, which showed a behaviour, shown in equation (3), different from one expected from the Fuller and Doleiden’s model. The time constant of the conductivity relaxation for cooling 7g and the time constant for heating TVagreed well with the time constant of the photoconductivity T,,, and, therefore, it is suggested Ithat there is common rate-limiting process among these relaxation processes.

exp71, --t

1

ADACHI

where TL1and TLsare the lattice temperature before and after a step-wise temperature change, respectively.

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author wishes to thank Dr. K. SHOGENJIfor many helpful discussions, and S. AKIYAMA for his supplying oxygen-doped germanium crystals. Acknowledgements-The

REFERENCES 1. FULLER C. S. and DOLEIDBN F. H., J. Phys. Chem. Solids 19,251 (1961). 2. HORNBECK J. A. and HAYNBSJ. R., Phys. Rew. 97, 311(1955); HAYNBSJ. R. and HORNBECK J. A., Phys. Rev. 180,609 (1955). 3. OKADAJ. and SUZUKIT., J. phys. Sot. Japan 15, 1709 (1960).

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4. KAISERW., Fnxsc~ H. L. and RBISSH., Phys. Rev. 112,1546 (1958). 5. ADAMI E., J. appl. Phys., 38, 1972 (1967). 6. FULLBR C. S., KAISER W. and -OND C. D., J. Phys. Chem. Solids 16,161 (1960). 7. FIJLL.ERC. S., J. Phys. Chem. Solids 19, 18 (1961). 8. KAISERW. and THBRMOND C. D., J. appl. Phys. 32, 115 (1961). 9. KAISER W., J. Phys. Chm. Solids 23,255 (1962). 10. MORINF. J. and MAITA J. P., Phys. Rew. %, 1525

(1954). 11. WAY N. B., Semiconductors, Hall, London (1959).

p. 30. Chapman and