Donor equilibria in the Germanium-oxygen system

J. Pkys. Ckem. Solids

DONOR

Pergamon

Press 1961. Vol. 17, Nos. 314, pp. 301-307.

EQUILIBRIA

Printed in Great Britain.

IN THE GERMANIUM-OXYGEN SYSTEM*

C. S. FULLER, Bell Telephone

W. KAISER

Laboratories,

and C. D. THURMOND

Incorporated,

Murray

Hill, New Jersey

(Received 6 July 1960) Abetract-Donor equilibria involving the reaction of oxygen have been determined in a series of oxygen-doped Ge crystals of known oxygen concentrations. The intrinsic electron concentration is shown to be an important factor in determining the equilibrium. The results confirm that four oxygen atoms are involved in the formation of one donor. The standard enthalpy change (71 kcal, 3.1 eV) for the donor formation is somewhat greater than that expected for a GeO4 structure. The entropy (48 e.u.), however, appears to be much too large for a simple rearrangement model.

I. INTBODUCTION

THE REACTIONSof oxygen leading to donor formation in silicon have been the subject of a considerable number of investigations over the past five years.(l) lnvestigation of the kinetics of the donor formation indicated that an aggregation of oxygen atoms takes place upon annealing and, in particular, that a structure consisting of four oxygen atoms is formed which has donor properties.(als) More recently ELLIOTT@) found, in germanium, that donors attributable to oxygen are formed upon annealing. A more detailed study of the donor formation in oxygen-doped germanium has been reported by BLOEM et al. (5) who described their results qualitatively in terms of temperature dependent equilibria between neutral oxygen atoms and a donor consisting of four oxygen atoms. 4Nefi

(1)

where N represents the neutral oxygen atom and D represents the donor. We have investigated the formation of donors over a wide temperature range in germanium single crystals having welldefined oxygen concentrations. It is shown that the concentrations of donors formed can be accounted for quite well if each donor is assumed to contain four oxygen atoms. However, in order to obtain * A preliminary account of this work has appeared in J. Pkys. Ckem. Solids 16, 161 (1960). 301

satisfactory agreement with experiment, we have found it necessary to introduce the intrinsic carrier concentration into the equilibrium equation (l), which then may be written

4NzDz?D++ee-

(2)

since ionization of the donor is essentially complete in these experiments. In equation (2) the donor ion, D+, is assumed to be composed of four oxygen atoms surrounding a Ge atom of the crystal and may be designated Ge04. In the later discussion, we take up some subsidiary factors affecting the equilibrium as well as a comparison of the results with similar data for silicon containing oxygen. II. EXPERIMENTAL

A. Materials and measurement The crystals, containing oxygen in various concentrations, were prepared by growing from melts under different partial pressures of oxygen in argon. Infra-red absorption measurements, made at 11.7 microns, showed the crystals employed to be uniform in oxygen concentration to within about 5 per cent. The absorption measurements themselves in this range are precise to a few per cent. The infra-red determinations were standardized by means of gas analysis on a separate series of oxygen-doped Ge crystals.(as7) Specimens for the resistivity and Hall effect measurements

302

C. S. FULLER,

W.

KAISER

and C. D. THURMOND

Table 1. Equilibrium donor concentrations in 1Ols cme3 for various oxygen contents and temperatures. Oxygen cont. cm-s x lo-l6 9” 19 25 d 40 39 44 49 60 120

b 7.6 17.3 20.8 25.2 38.4 40.4 44-O

51.2 59.2 129.2 n* x 10-16

Reaction Temperature, “C 350

385

1 *go 4.34 5.20 6.3 9.6 10.1 11-o

l-22 3 *47 4.50 5.7 8.2 9.2 1”2.:

12.8 14.8 32.3 20

14.1 30.0 30

435

7

470

500

None c O-25 0.71 1.66 4.10 4.77 5.30 7.3 8.5 23 *4 100

None ,, ,,

517

527

0.14 0.59 o-45 2.05 3 -00 18.8 150

None

560

_.

0.17 2.07 2.80 3.7 6.3 7.3 7.7 11.9, 28.7 62

l’.i 5 2.17 2.63 4.00 5.80 20.2 140

,> 0::s 1.79

15.4

I 160

~ 20:.5

a. As determined by infra-red absorption. b. 4D+ at 35O’C. c. “None” corresponds to < 1014cm-s. d. Not determined. were taken immediately adjacent to the specimens used for oxygen analysis. The oxygen contents of the crystals used in this work ranged from O-9 to 12.0 x 1017 atoms cm-s* (Table 1). Hall measurements were made on standard bridges,(*) using a field of 1600 Oe. Resistivity measurements were made upon rectangular bars (2 x 2 x 15 rnms) by means of a four-point probe device.(4) The accuracy in the resistivity measurements was better than 1 per cent. B. Armealing procedure Since the crystals undergo reactions as a consequence of heating during crystal growth, it is essential before each run to heat each specimen to near the melting point of Ge and to quench rapidly from this temperature. Because contamination by copper nearly always occurs when Ge is heated to high temperatures, the following procedure was followed: The resistivity specimens were cleaned by means of a light etch in mixed HF and HNOs, rinsed in pure water, plated lightly in a .gold cyanide plating bath and finally given a rinse in pure water. The dry specimens were sealed under about 10 mm air pressure in quartz. tubes, heated for la min at 915”C, and quenched in water to near room temperature in * All o&en

contents are in atoms &n-s.

less than 5 sec. In this way the starting resistivities (after removal of the surface plating by grinding off several mils) were always above 2 ohm cm for the crystals containing 6.0 x 1017 cm-s oxygen or less. Anneals were carried out in furnaces controlled to + 1°C. All resistivity measurements were made after quenching to 25 & 1°C. The rates of cooling to room temperature were less than 3 see and in no case were they found to affect the results. No reaction was observed at room temperature for long times. Annealing temperatures ranged from 329 to 560°C for times (in some cases as long as 1000 hours which were sufficient to attain near-equilibrium concentrations as discussed below. The pertinent data are given in Table 1. Tests at 325°C for over 1000 hr showed the same equilibrium value as obtained after a long time at 350°C. The concentrations of donors formed in Ge are much greater under comparable conditions than in Si.(s) Most important, the rates of donor formation in Ge are at least 500 times greater than in Si for similar temperatures and oxygen concentrations. C. Calculation of donor concentrati43ns In order to convert the resistivity changes observed upon annealing into donor concentrations,

DONOR

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it is necessary to know the electron mobilities as a function of donor concentration. The mobility values employed are shown in Fig. 1 and represent an average of our determinations, those of DEBYE

ELECTRON

MOBILITY IN CM’/VOLT-SEC

FIG. 1. Relation between resistivity (25T) and mobility used to calculate electron (donor) concentrations.

and CONWELL and of PRINCE. The maximum error in mobility is about 5 per cent. No attempt has been made to correct Hall mobilities to drift mobilities since, for low fields ,LLJJ/~ is very nearly unity. The Hall coeflicients of a number of samples have been measured as a function of temperature. It is found that the donors formed after annealing to equilibrium are essentially fully ionized at room temperature. A detailed account of this work will be given in a separate article. D. Determination of equilibrium donor concentrations In order to be sure that true equilibrium values for the donors are measured, it is necessary to follow the changes in donor concentration with time of annealing. It has been found that the

SYSTEM

303

donors saturate with time and that the saturation (equilibrium) values decrease markedly with temperature.(s) A series of curves of this kind for a crystal containing 36 x 1017 cm-s oxygen is shown in Fig. 2. However, the behavior, depending on the oxygen content and particularly upon the annealing temperature, is often less simple. It is found for example that after sufficiently long reaction times the donors always decrease. This occurs more rapidly at the higher temperatures (above 470°C) especially for the higher oxygen concentrations. Observations of this kind are expected at high temperatures where oxide precipitation occurs. In fact the formation of a precipitated GeOs phase and a corresponding decrease in oxygen in solid solution has been observed by optical means. Of more concern is the formation of a maximum followed by a plateau. Such a behavior has also been noted in Si containing oxygen(sf and is shown for Ge containing oxygen in Fig. 3. A crystal with 6-O x 1017 atoms/cm-s of oxygen was annealed at 500°C. A maximum prior to a lower plateau is clearly shown. Evidence that the plateau is an equilibrium concentration was obtained by annealing a similar sample at 472°C for 2.5 min, at which time a considerably higher donor concentration had been formed than in the crystal annealed at 500°C. When the temperature was raised to 501”C, the donor concentration fell to a value approximately the same as found in the crystal annealed at SOO”C,as shown in Fig. 3. Similar procedures were employed to determine the positions of the equilibria for annealing temperatures above 500°C. Because of the maxima mentioned and the loss of oxygen into precipitate aggregates, which occurs more rapidly as the temperature is increased, the equilibria for the higher temperatures are not as precisely determinable as those for the lower temperatures (below 500°C). IX =UL%X! AND DISCUSSION The results of the determination of the donor equilibrium concentrations at the different temperatures are shown in Table 1 for all of the oxygen doped crystals. If it is assumed that a donor containing 4 oxygen atoms comes to equilibrium with dissolved oxygen atoms, the relationship between the ionized donor concentration, I)+, measured at room temperature, and the equilibrium oxygen concentration, N, can be expected

304

C. S. FULLER,

W.

KAISER

and C. D. THURMOND

AT

12

NOR EQUILIBRIA VARIOUS T’s

3.6 x to” CM-J 0

TIME

IN

MINUTES

OR

HOURS

2. Increase in donor concentration with time of anneal at 35O”C, 47O”C, and 500°C for a crystal of Ge originally containing 4.0 x lOI7cm-3 dissolved oxygen. FIG.

to be given by the following equilibrium expression when the solid solutions are very dilute. D+ N4

= constant

(3)

Equation (3), however, is correct only as long as the concentration of the donor, D+, is much less than the concentration of intrinsic electrons, Q, at the equilibrium temperature. This condition is not met, however, for a number of the samples studied, as can be seen by comparing D+ with na as a function of temperaturecll) in Table 1. From the charge balance relationship and the electron hole equilibrium, a corrected equation is obtained

on the crystals annealed at 350°C indicate that practically all of the oxygen has been converted to a donor ion containing 4 oxygen atoms. Fig. 4 is a plot of the equilibrium donor ion concentration at

.s 7 :

:3 P

85 L

zo4

D+[D+ + (D+2+ 4-GY21 = K (4)

2N4

Since the concentration of oxygen atoms is the difference between the original oxygen concentration, No, and the oxygen contained in the donor ion, Df, equation (4) becomes

x

3

2

1

0 0

D+[D++(D+2+4np] 2(No-4Dt)4

5

10

15

20

TIME

=K

(5)

Equation (5) has been tested in the following manner. It is first noted that the measurements

IN

25 30 MINUTES

35

40

45

50

FIG. 3. Equilibrium position at 500°C for a Ge crystal containing 6.0 x 1017 cm-s oxygen. The upper curve was obtained by reacting initially at 472°C to produce a concentration of donors in excess of the equilibrium concentration at 500°C.

DONOR

EQUILIBRIA

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GERMANIUM-OXYGEN

SYSTEM

305

TabIe 1 gives the corrected values of the oxygen concentration which were used to obtain equilibrium constants. In Fig. 5, the various values of 2K at each temperature have been plotted as a function of l/T. Both the spread and distribution of points are shown. A line given by the following equation has been drawn through the data. 15560 log 2K = -55.38 (6) T An average value of the equilibrium constant has been obtained from equation (6) at each of the TEMPERC;FURE IN DEGREES

so

cl

D~G,NAL4&N

so

1DD

CONCENTRATION,

t2D (CM-?

KELVIN

t4D x 10”

FIG. 4. Plot of equilibrium donor concentration at 350°C vs. original oxygen concentration as determined by infra-red absorption for crystals given in Table 1. The line is drawn to have a slope of l/4.

350°Cas a function of the total oxygen concentration in the crystal as measured by infra-red absorption (calibrated by vacuum fusion gas analysis). The line through the points is of slope l/4. This is the behavior predicted from equation (5) if K is a relativeIy Iarge number. It is not possible to obtain a value of K from the measurements at 35O”C, since the term (No-4D+)4, which is very sensitive to experimental error, occurs in the denominator of equation (5). At each of the other temperatures, however, the experimental measurements can be used to obtain values of K. It is believed that it is possible to obtain a better evaluation of NO by using the electrical measurements on the 350°C annealed samples as a measure of the oxygen concentration rather than the infrared absorption measurements. The absorption measurements were not made on the same samples as those used for electrical measurements, but on samples lying adjacent to these samples in the same crystal. The scatter of points around the line of slope l/4 in Fig. 4 is believed to arise from differences in oxygen concentration arising from small inhomogeneities in the crystal. Column b of 20

5

ro3/ToK

PIG. 5. Semi-log plot of twice the equilibrium constant, 2K, vs. reciprocal of absolute temperature. The vertical lines and points show the range and distribution of values calculated from data of Table 1 using equation The line corresponds to the equation, (5). log 2K = 15560/T55.38.

C.

306

S.

FULLER,

W.

KAISER

experimental anneal temperatures and the relationship between the donor ion concentration and oxygen concentration has been calculated using equation (5). These calculated curves are shown in Fig. 6 where it is seen that a reasonably

FIG. 6. Equilibrium donor concentrations at various temperatures (indicated on the figure) plotted against original oxygen content (see text). The data are taken from Table 1. The curves are calculated (equation 5) using values of K corresponding to each temperature and taken from the line in Fig. 5.

good fit to the data has been obtained. This fit suggests that oxygen atoms dissolved in solid Ge come into equilibrium with a 4 oxygen atom complex which is also in solid solution. The magnitude of the equilibrium constant and its temperature dependence should give additional information about this reaction. The equilibrium constant K is related to a standard heat of reaction, AHQ, and a standard entropy change, ASO, by the following relationship.

logK=

--

AH0

AS’

--2 4.575 T+ 4.575

log NL

(7)

In this expression, NL is the number of germanium atoms per unit volume in pure Ge and is 4.45 x 102s atoms cm-s. It follows that AH0 =

and C. D. THURMOND -71 kcals per 4 oxygen atoms and ASO = - 48 entropy units per 4 oxygen atoms. It may be asked whether these values of AHO and AS0 are reasonable for the reaction being considered. It will now be shown that the magnitudes of these two numbers, especially the value for AS’, are larger than is to be expected for this reaction. This conclusion suggests that we do not as yet have a complete understanding of these solid solutions and additional work will be necessary before this is achieved. The model considered here envisages an oxygen atom bound to two adjacent Ge atoms when it is in the atomic state as in the oxygen-silicon system. When the 4 oxygen atom complex forms, it would be reasonable to suppose that around a particular Ge atom, 4 oxygen atoms disrupt the 4 normal Ge-Ge bonds. Thus, each oxygen atom is bound to one common Ge atom and to one other Ge atom. This reaction requires 4 Ge-0 bonds of one type to be broken and 4 Ge-0 bonds of another type to be made. The value of ASa to be expected for this type of reaction is around zero, rather than the -12 e.u. per oxygen atom we find experimentally. The heat of the reaction, AHa, can be estimated by using the temperature dependence of the solubility of oxygen in germanium, AH*, which is 27.6 kcal or 1.2 eV.(7) If it is assumed that the Ge-0 bond in the GeOa complex is no stronger than the Ge-0 bond in GeOs (glass) it can be shown that - AHs would be expected to be less than 2(1*2) or 2.4 eV. The experimental value of 3.1 eV is appreciably larger than this. IV. COMPARISON WITH Si Because of the much slower rate of reaction in oxygen-doped Si crystals, equilibria of the kind discussed above are difficult to establish except at temperatures so high that only small donor concentrations exist. As has been pointed out(5) donor generation in oxygen-doped Si is much less at the same temperature than in Ge containing the same amount of oxygen. For example at 45O”C, Si containing lOr* cm-s oxygen generates a maximum of about 2 x 101s cm-s donors(s) compared to an estimated 2.5 x 1017 cm-s donors for a similar Ge crystal. In other words, in spite of a much lower intrinsic electron concentration, the generation of donors, as measured at room temperature

DONOR

EQUILIBRIA

IN

THE

is much less in the case of Si. Furthermore, it does not appear possible to explain this difference as being due simply to a difference in the ionization energies of the donors in the two cases. Both infra-red absorptiontrs) measurements and Hall measurements(rs) show levels for the donors in Si which lie in the range 0.03 to 0.06 eV. Likewise the behavior of these donors in p-type Si is such as to suggest that deeper ionization levels are not present. Both the rate of generation of donors and the equilibrium constant are very much smaller for Si than for Ge. Because, however, the position of the equilibria in Si are very difficult to determine, a quantitative comparison over a temperature range is not as yet possible. VI. SUMMARY An investigation of donor equilibria resulting from the reactions of oxygen in Ge crystals of known oxygen concentrations has been made. The oxygen concentrations studied varied from O-9 to 12.0 x 1017 cm-s as determined by infra-red absorption. Reaction temperatures ranged from 325°C to 560°C. Donor concentrations were determined by quenching the reactions to 25°C and measuring resistivity. Hall effect determinations showed that the donors formed are essentially completely ionized at 25°C. The results show that the intrinsic electron concentration is an important factor in the position of the donor equilibrium. A mass-action treatment including the hole-electron equilibrium enables a quantitative expression to be deduced for the equilibrium constant. Calculations based on this expression agree well with the experimental results for temperatures below 5OO”C, giving support to the Ge04 model. At higher temperatures the reactions become more complicated as evidenced by the formation of the maximum in

GERMANIUM-OXYGEN

SYSTEM

307

Fig. 3. As a result the equilibrium concept discussed in equations (1) to (5) should be considered only an approximation (see Fig. 6 for T > 500°C). A comparison of the results with those observed in Si shows a very close similarity suggesting that, although the reactions are about 500 times slower in Si and much lower equilibrium donor concentrations exist at comparable temperatures, nevertheless the reaction mechanisms and donor structures must be essentially the same in the two cases. authors are greatly indebted to the following persons who have contributed valuable assistance in the course of this work: M. KOWALCHIK for help in growing the Ge crystals, F. H. DOLEIDEN and J. P. MAITA for assisting with the Hail and resistivity measurements, KATHWINE WOLFSFIRN for aid with the calculations and drawings and GEORGE WHEATLBY for assistance with the infra-red measurements. Acknowledgements-The

REFERENCES 1. KAISER W., Fnrscri H. L. and REISS H., Phys. Rev. 112,1546 (1958) and references in this paper. 2. KAISHRW., Phys. Reu. 105, 1751 (1957). 3. FULL.ER C. S. and Loorw R. A., J. Appl. Phys. 28, 1427 (1958). 4. ELLIOTT G., Nature, Lond. 180, 1350 (1959). C. and PENNING P., J. Phys. Chem. 5. BLOEM J., m Solids 12, 22 (1959). 6. GULDNER W. G. and BEACH A. L., A.S.T.M.

Spec. Tech. Pub. #222

(1958).

7. KAISERW. and T~JRMOND C. D.. to be oubhshed. E. M., Phys: Rev. 93, 8. DBBYE P. P. and CO-L 693 (1954). 9. VALDES L. B., Proc. Inst. Radio Engrs. N. Y. 42, 420 (1954). PRINCE M. B., Phys. Reu. 92,681 (1953). :;: MORIN F. J. and MAITA J. P., Pkys. Rev. 94, 1525 (1954). 12. HROSTOW~KIH. J. and KAISBR R. H., Pkys. Rew. Letters 1, 199 (1958). 13. MORIN F. J. et al., Pkys. Rev. 96,833 (1954).