Electron mobilities and photoluminescence of solution grown indiumphosphide single crystals

J. Phys. Chem. Solids

Pergamon Press 1970. Vol. 3 I, pp. 2625-2634.

Printed in Great Britain.

ELECTRON MOBILITIES AND PHOTOLUMINESCENCE OF SOLUTION GROWN INDIUMPHOSPHIDE SINGLE CRYSTALS 0. RijDER, U. HEIM and M. H. PILKUHN Physikalisches Institut, UniversitSt Frankfurt/M., Germany (Received

8 December

1969; in revisedform

9 February

1970)

Abstract-InP single crystals were grown from an indium solution. They show a typical dendrite structure. The electron concentration ranges from 1Or6to 10*9cm-3. The dependence of the room temperature Hall mobility on the electron concentration is compared with the theoretical curves of Moore and Brooks-Herring. Photoluminescence spectra of relatively pure undoped samples show two major emission bands at low temperatures, one near 1.416 eV (containing four emission lines) and a band near 1.38 eV. Time resolved spectroscopy shows that the 1.38 eV band is due to donor-acceptor pair recombination. At high doping levels the luminescence spectra show a pronounced BursteinMoss shift to higher energies, the band-acceptor transition gains in relative intensity and broadens considerably. Above lOI*crnm3it is the only remaining emission band at low temperatures. The shift of the Fermi level with carrier concentration is compared with the theory assuming a parabolic conduction band. It is found, that the experimental shift does not follow quantitatively the expected Burstein-Moss shift, presumably due to band tailing and gap shrinkage effects. 1. INTRODUCTION

InP HAS A DIRECT bandgap of 1.42 eV at low temperature, i.e. only O-1 eV below that of GaAs. The effective electron mass is presumably of similar magnitude for both materials, namely about 0.07 mo[ 11. In contrast to GaAs not much information has been reported either on crystal growth, mobilities or on the luminescent properties of InP. Turner et al. [2] and Leite[3] investigated the optical absorption and emission of not intentionally doped InP in the electron concentration range from 9 X 1015to 4 X 1017cmm3. Their spectra show a near edge emission at about 1.416eV and a second emission band near 1.36 eV[2] or 1.38 eV[3]. The 1.416 eV emission has been ascribed to the free exciton decay[2] and the 1.38 eV emission to a donor-acceptor transition [3]. Recently, Heim [4,27] demonstrated by time resolved spectroscopy that the 1.38 eV emission can be indeed described by a donor-acceptor pair mechanism. The intensity dependence on excitation intensity of several emission lines near the fundamental gap between 1.40 and 1.42 eV was investigated by

Heim et al. [5,27]. No photoluminescence data have been published till now for highly doped InP. A reason, why InP is much less investigated than GaAs is the difficulty to grow single crystalline material. Recently Mullin et al. [6] described an encapsulation method to grow single crystalline InP at high pressure. We used a method in which InP is grown from a dilute In-InP solution. The corresponding method, growth from a gallium solution, has been successfully applied to GaP[7]. The photoluminescence of these solution grown crystals was investigated, in particular its dependence on doping level, temperature and excitation intensity. 2. EXPERIMENTAL

2.1. Preparation of crystals InP melts at 1065°C under a phosphorus dissociation pressure of more than 15 atm. [8]. In our experiments the high phosphorus pressure was avoided by using a solution growth method first reported by Wolff et al. [9]. Polycrystalline InP (purchased by Monsanto

2625

2626

0. RGDER. U. HEIM and M. H. PILKUHN

or Minig and Chemical Products) was regrown from a dilute In-InP solution. This method has the advantage of a relatively low growth temperature and therefore the possibility of contaminating the crystals by the container material is decreased. Many of the impurities introduced with the InP charge are diluted or extracted by the large excess of the indium solvent. N- and p-type doping was achieved by addition of metallic tellurium or zinc to the solution. The In-InP mixture was placed into a cleaned and vacuum heated quartz container tube of about 100 cm3 volume, which was then evacuated to 5 X 10e5 Torr and sealed. A typical charge was 6 g In and 1 g InP corresponding to a phosphorus content of 10 at %. The sealed tube was supported in a vertical tube furnace (length 1 m, #J 30 mm) at a temperature 40-50°C above the saturation solubility temperature for some hours to ensure complete solution of the InP. It was then lowered through the built-in temperature gradient at an average cooling rate of lO”C/h. The excess indium was dissolved in cold cont. HNO,. 2.2. measurement tech~~4~es The samples were characterized by Halland resistivity measurements. Contacts were provided by alloying tin into n- and indiumzinc into p-material. The n-contacts had a series resistance of a few ohms. Major difficulties were encounted making ohmic contacts to p-material. The luminescence was measured by a conventional apparatus involving a lock-in amplifier technique. We used an immersion Dewar vessel, a 30 mW He-Ne-laser for ~lumination and a Spex- 1700-III-sting spectrometer with a resolution of better than O-2 meV whenever necessary. The excitation intensity was varied by insertion of neutral density filters. The spectrograph was calibrated by means of the laser lines. The signal was detected by a cooled photom~tiplier with Slcharacteristic. The experimental setup for the time resolved measurements was described

earlier[4]. Careful etching of the crystal surface was found to be necessary in order to eliminate erroneous luminescence bands, which are caused by surface effects, 3. RESULTS AND DISCUSSION

3.1, Crystal morphology Solution grown InP single crystals show the characteristic dendrite structure typical for almost all crystals of elemental and compound semiconductors grown from a metallic solution, A great diversity of these dendrites was found. In Fig. l(a), (b) and (c) typical dendrites which are frequently observed are examplifIed. The common characteristic of all the crystals investigated is the twinned stmcture, with twinning taking place invariably between the flat (1, 1, 1) and (1, i, 7) surfaces of the platelets. An illustration of the twin structure is given in Fig. l(d). It shows the tip of a dendrite crystal, terminated by ( 1, 1, 1 )planes. The intersection of two (1, 1, 1Iterminal planes coincides with the twin plane in the crystal. In the case of Fig. l(d) these twin planes are perpendicular to the plane of view. In general, we obtained nearly the same results as Foster et al. [73 reported earlier for solution grown GaP. A more detailed discussion involving the twinning problems in polar semiconductors is found in the review articles by Sangster[ 10) and Faust and Lindbergh [ 11 I. No faculties were encountered in doping the crystals n- and p-type. The largest crystals were obtained for high tellurium doping. The maximum crystal sizes reached were 10 X 4 X 2 mm3. 3.2. Electron mo~ili~ The electron mobility was measured in the doping range (Te-doping) between 1016 and 2 x 10lg crnw3, Room temperature mobilities are depicted in Fig. 2 as a function of the electron concentration. Samples with a carrier concentration smaller than IO” cmm3 are not intentionally doped. The mobility decreases monotonically with increasing carrier concen-

Fig. l(a). Typical solution grown InP crystals. (b) Hat (1, 1, I)-In surface of a standard type cry&d used for photoluminescence measurements. (c) Facetted long dendrite crystals. (d) Tip of a crystal containing three twin planes. [Facing page 26261

ELECTRON

MOBILITIES

t

IN

$S 3

,“n. $2 I

IO"

IO”

”

2621

AND PHOTOLUMINESCENCE

[cnq ‘O’”

Fig. 2. Room temperature Hall mobility as a function of the electron concentration (Te-dopant)-Squares indicate copper contaminated samples. Theoretical values are calculated after Moore [ 131 and Brooks-Herring [ 141 using Ehrenreich’s[lS] mobility limit of 4 700 cm2/Vsec.

tration. A qualitatively similar curve has been found in solution grown GaAs]12]. The samples designated by squares in Fig. 2 have usually low mobilities. These samples were contaminated with copper, as revealed by a spectrographic analysis of the indium solvent. These particular samples also exhibit a very strong luminescence band at 1.2 eV (compare Fig. 7 of Section 3.4), which is most likely caused by deep impurity levels due to copper. We have compared our experimental data with the theoretical dependence of the mobility on donor concentration. The solid line in Fig. 2 refers to Moore’s theory [ 131, the dotted line to the Brooks-Herring formula[l4]. Ehrenreich’s [ 151 room temperature value of 4 700 cm2/Vsec for the mobility limit due to polar lattice scattering was assumed. Lattice scattering was combined with ionized impurity scattering by summation of reciprocal mobilities. For the electron effective mass and for the dielectric constant the same values as for GaAs were used (m, = 0.07 m, [l] and k = 13.5 [ 161). Good agreement between experimental data and Moore’s theory is found in the high doping range. Experimental mobilities are somewhat lower than predicted in the concentration range between 10la and 1018 cmT3. Since Moore’s treatment is confined to degenerate material, this disagreement is not surprising. The Brooks-Herring expression

with Ehrenreich’s mobility limit does not fit our experimental data. Recently Hilsum and co-workers [ 171 published electron mobility data of InP crystals with a low electron concentration. From their data as well as from their theoretical considerations a mobility limit higher than Ehrenreich’s value results, namely 5 800 cm2/Vsec. So far, we have not sufficient experimental data in the low concentration range to decide, which mobility limit is correct. 3.3. The Luminescence at low electron concentrations and low temperatures The luminescence data in this section refer to not intentionally doped crystals and to the temperature range between 1.8 and 20°K. Different samples with electron concentrations between 9 X 1015cm-3 and 1 X 10” cme3 were used. A spectrum typical for low electron concentration is shown in Fig. 3. It contains a band A at l-416 eV, which is the unresolved near edge emission. Its fine structure depends on the illumination intensity and will be discussed below in more detail. Furthermore, a band B at about 1.375 eV is observed; which can be attributed to a donor-acceptor pair recombination as mentioned earlier[4,27].

A[%3 lO,OOO

3

95co

T=tB=‘K

n(30WKI=3xld6cni3

B-2L0

hv

[eV]

Fig. 3. Typical photoluminescence spectrum of a not intentionally doped sample at 1g”K. Line A is unresolved donor valence band/exciton recombination, line B a donor acceptor pair recombination with three phonon satellites. The linewidths are given in meV.

2628

0. RODER,

U. HEIM and M. H. PILKUHN

Phonon cooperation. We observe three additional lines, designated as B-LO, B-2L0 and B-3L0 in Fig. 3. These lines are apparently phonon satellites of the pair recombination line B. The phonon replicas yield a phonon energy of (42*5&0*5) meV as an average value derived from data of 8 samples. This result agrees well with the corresponding infrared reflectivity (43 meV, 28, 18) and Raman data (42.8 meV, 17). In Table 1, data concerning the phonon cooperation are listed for InP and GaAs[20] samples containing acceptors with different binding energies E,. The donor binding energy is assumed to be constant and small (- 8 meV). From Table 1 it can be seen that larger values of E, are associated with stronger phonon cooperation. No significant change of the intensity ratio Z,/Z,_LO with temperature has been found for InP in the range between 1.8 and 20°K.

The donor-acceptor recombination band B. As was confirmed recently by time resolved spectroscopy[4,27], band B should be assigned to a donor-acceptor pair transition. A peak shift to lower energies and a steepening of the high energy shoulder of the band were observed for spectra at increasing times after excitation. The time decay of the integrated emission of band B could be described using a decay model of Thomas et al. [22]. The fit of the theoretical curves to the experimental data yielded an effective Bohr-radius of 90- 100 A for the donor and a transition probability W,,, = 7 X IO’ set-‘. Qualitatively similar results have been reported for the case of GaAs[l9]. Figure 4 demonstrates the influence of excitation intensity on band B, when excited with the d.c. He-Ne-laser (maximum photon

Table 1. Intensity ratios of line B (peak energy Es) and its first phonon satellite (line B-LO) for three diRerent acceptor binding energies E, (E, = Egap- EB - 8 mev) in InP and GaAs [20]. InP I%, meV ItJIB--LO GaAs J% meV IBIIR-I.0

(&?[3]) 1.5-23

(this3iork) 15-20

(Re?[2]) 4.5

19.5

28

35

48

33

22

We have compared our results with theoretical data derived from Hopfield’s ‘shallow trap model’ [2 l] which, however, is confined to trap energies larger than the LO-phonon energy. Experimentally we find the following intensity for subsequent phonon replicas: ratios 1 : 0 -055 : 0.0027 : [email protected] theoretical coupling factor turns out to be much too large (by about two orders of magnitude), and a Poisson distribution would lead to a somewhat more rapid decrease of the intensity of subsequent phonon satellites.

.

, I 370

I

I 375

hv[eVl

Fig. 4. Emission in band B (sample 38,, n = 9.7 X 10” cm-s) at 1.8”K for three different excitation levels. The lowest excitation intensity I0 corresponds to 10” photons/ cm2 . sec.

ELECTRON

MOBILITIES

AND PHOTOLUMINESCENCE

flux 1021 photons/cm2 . set). The sample 382R used for this measurement has a carrier concentration of n = 9.7 x lOl5 cme3. As may be seen from Fig. 4, band B shifts slightly to higher energies and broadens on the high energy side, when the excitation intensity is increased. Very similar behaviour was reported recently for a pair band in weakly doped GaAs[23]. The near edge emission band A. At high resolution the emission band A was found to consist of several narrow lines when weakly doped samples and low excitation levels were used. In Table 2 peak energies, linewidths and tentative assignment of the lines are given. The influence of excitation intensity and the nature of these emission lines have been briefly discussed in preceeding communications [5,27]. The discrepancy between earlier published data for the energetic position of the near edge emission (l-4165 eV Turner et al. [2], 1.413 eV Leite[3]) can now be explained as resulting from different excitation levels in the experiments.

2629

tegrated emission in band A increases linearly in the whole range of the He-Ne-laser excitation. The spectra at elevated temperatures show a different behaviour (Fig. 5(b)). The narrow line at 1.4143 eV, which was ascribed to a bound exciton[5] vanishes at temperatures above 14°K. Contrary to the intensity effect, the l-4165 eV line remains the dominant line in the whole temperature range considered. It shifts only slightly to lower energies as the temperature is raised. The results of Fig. 5(b) are consistent with the interpretation of the 1.4143 eV line as a bound exciton line and the l-4165 eV line as the free exciton line. The difference of the two energies, i.e. 2.2 meV, is the binding energy of the exciton to the localized center. When the temperature is raised, we would indeed expect, that less excitons are bound to this center. The assignments of the excitation lines (Table 2) are not unambigous in view of the following discussion of the 1.418 eV shoulder on the high energy side of band A: It may be

Table 2. Peak energies and halfwidths of the emission lines of weakly doped samples at low excitation levels (1~8°K). Accuracy of the peak energies is O-2 meV Peak energy eV

Halfwidth meV

Comments

l-418 1.4165 1.4143 1.4126 1.375-1.385

shoulder 0+8 0.6 1.5 3-8

free exciton or excited level free or bound exciton bound exciton donor-valence band transition donor-acceptor pair transition

In Fig. 5(a) and 5(b) the effects of excitation intensity at constant temperature and of temperature at constant excitation intensity are compared. More photons are emitted in the lower energy lines, when the excitation intensity is increased at constant temperature [5] (Fig. 5(a)). We have also studied the intensity of the isolated l-4165 eV line as a function of the excitation level and found, that it saturates at high excitation intensities. On the other hand it was observed, that the in-

noticed in Fig. 5(b) that this shoulder increases in relative intensity as the temperature is raised. Assuming a value of 1.4205 eV for the bandgap[2], this shoulder cannot be interpreted as a hycrogenic excited state of a free exciton at l-4165 eV. Possibly the shoulder might be due to the free exciton itself. A comparison of the curves in Fig. 5(a) and 5(b), which exhibit quite different behaviour, leads to the conclusion, that sample heating and excitation level influence the spectra in a

0. ReDER,

2630

U. HEIM and M. H. PILKUHN

AK1

A[%1 8750

8800

loo

8750 1

7’ InP

InP

Sample M,,

Sample

T = I.8OK

IO=const.

I415

M,,

----

1.80~

-

14,1°K

I415

hv[eV]

I 420

hvkV1

Fig. 5. Photoluminescence spectra (band A) of InP (n = 9,7x 1Ol5cm-3) (a) at 1.8”K for three different excitation levels (He-Ne laser). The lowest excitation intensity lo corresponds to 3 x IO**photons/cm*. sec. (b) At constant excitation level for three different temperatures. Different arbitrary intensity scales have been used.

different manner. This means in particular, that a genuine effect of excitation level is present besides sample heating. In Fig. 6 the emission for the case of very high excitation intensities (N,-pulse laser) is shown. Besides band A a new emission line emerges at about 1.407 eV, which dominates the spectrum at highest excitation levels. This line narrows and shifts continuously to lower energy when the excitation intensity is increased. The luminescence intensity of this new line increases stronger than quadratically with excitation intensity. At highest excitation levels the decay time of this line shortens beyond our resolution limit of about 3 nsec. These observations are interpreted in terms of manybody interaction effects and stimulated emission [5]. 3.4. Temperature

dependence

of the lumine-

scence

Luminescence

spectra

at three

different

temperatures are shown in Fig. 7 for a sample with a donor density of 2 x 1017cmW3 and in addition containing deep impurity levels. The spectrum at 4°K shows line A and B together with phonon satellites and a deep impurity line C, which is discussed in detail below. As the temperature is raised, the fine structure of the near edge emission line A first changes and finally disappears completely. The temperature dependence of this fine structure has already been discussed in Section 3.3. At 77°K band A contains no detectable substructure and it should be now interpreted as band-to-band recombination [3]. Line B has been interpreted as donoracceptor-pair transition at the lowest temperature. At elevated temperatures it should become the conduction band-acceptor transition, as was recently investigated for Ge-Gepairs in GaAs [23]. Phonon satellites have not been detected above 77°K. Notice that line A is weaker in intensity than

ELECTRON ssooA [%I 8850 I

1 MO4

,

MOBILITIES

8750 I

2631

AND PHOTOLUMINESCENCE

I

InP 20,3=‘K

I

I3

I.2

I4

hvb’l

Fig. 7. The emission spectrum for three different temperatures, n = 2 X 10” cm-s.

At low energy an additional emission line is observed near 1.2 eV in the sample of Fig. 7. This emission line was particularly intense in samples, which were contaminated with copper. We therefore attribute the 1.2 eV line to a transition to a deep acceptor level introduced by copper. It should be mentioned, that the I.40 I41 1 42 I 43 samples showing a very intense 1.2 eV line, hub/l had a low electron mobility, as indicated by Fig. 6. Photoluminescence spectra of InP (n = 9.5 X 1Ol6 the squares in Fig. 2.

cm-s) at 20°K for several excitation levels with the Nzpulse laser. The lowest excitation intensity I corresponds to 2 x lo*” photons/cm*. sec.

line B by a factor of about 40 at 4°K. At 77”K, line A dominates and exceeds the intensity of line B by a factor of 4. At room temperature only one considerably broadened emission band is observed, which is presumably the band-to-band transition. This effect of temperature on the relative intensities of line A and B may be explained in the following way: at higher temperatures it will become more difficult to trap a hole at an acceptor level, hence the band-to-band transition will prevail. Line A shifts to lower energies as the temperature is raised. This shift coincides with the energy gap variation as reported by Turner [2].

3.5. Luminescence at higher doping levels The influence of tellurium concentration on the luminescence spectra at 77°K is demonstrated in Fig. 8. At the lowest doping level, one can clearly distinguish between the band to band transition line A, the band to acceptor recombination line B and a phonon satellite to line B as described above for undoped samples. Since these data refer to 77”K, line A is the band to band transition and line B the conduction band to acceptor transition. As the doping level increases, the relative intensity of the impurity band B increases strongly in comparison with that of line A. Simultaneously both bands broaden considerably. In the doping range above 1018cmm3 both bands shift to

0. RODER,

2632

U. HEIM and M. H. PILKUHN

i

IIlP T=20°K

-145-

: : ..’ I.

$ 2 B tl E

I’ -

*

__-a

A ,___‘___L__Lr-.---

_ I’

x g140a

.,,’ -

B . -_______r__._*__.______.-.

KP

n-l 7x10’6ti’

I

I 35

I 40

I 45

I

‘r

’

.

#’

::

.

IO”

nwl

10’8

Fig. 9. Concentration dependence of the peak energy of lines A and B. Samples with an electron concentration below 10” crnd3 are undoped, others tellurium doped.

n=l xl~7cm3 undoped

I

_*‘.

*’

,!

I:

hv [ev!

Fig. 8. Photoluminescence spectra for various doping levels at 77°K. Intensities are plotted in arbitrary linear scale. Line,4 is the band to band transition, line B the conduction band/donor to acceptor recombination line. The linewidths are given in meV.

higher energy. The relative intensity of the phonon satellites to line B decreases as the doping level is raised. Above lOis cm-3 phonon satellites are no longer detectable. At the highest doping level line A disappears completely and the remaining line B broadens and shifts to still higher energies. It may be noticed, that the line is strongly assymmetrical and has a pronounced low energy tail (upper curve). Figure 9 displays the peak energies of line A and B as a function of carrier concentration at 20°K. One can clearly see, that the peak energy of line A remains approximately constant. As shown before in Fig. 8, its intensity decreases considerably with increasing carrier concentration. Line A could not be detected at concentrations higher than 2 X lo’* cm-3. The peak energy of line B begins to rise very

rapidly above lo’* cmV3, just in that range, where line A disappears. In our interpretation, the disappearance of line A at high donor concentrations implies a preference for hole recombination via acceptors instead of direct recombination with electrons. A reasonable interpretation is an increase in the number of compensating acceptors, possibly silicon from the quartz crucible. The peak shift of line A and B to higher energy can be interpreted as the familiar Burstein-Moss shift, i.e. a filling of the conduction band with electrons. We have tried to deduce the shift of the Fermi-level from the luminescence spectra at 20°K as a function of carrier concentration. The high energy cut-off (I(ECUt.,rJ = 0.1 X Ipeak)of the luminescence band can be assumed to be a reasonable measure for the position of the Fermi-level. The experimental shift of the Fermi-level was found to be smaller by a factor of about two than the theoretically expected one, computed on the basis of a constant effective mass (m = 0.07 m,,). The following reasons may be found to explain this behaviour: at high donor concentrations a gap shrinkage with the formation of tail states takes place, reducing the full band filling effect. Simultaneously the acceptor level broadens to an impurity band leading to the same effect. The effective electron mass increases due to nonparabolicity when the

ELECTRON

MOBILITIES

2633

AND PHOTOLUMINESCENCE

Fermi-level moves up in the conduction band as reported earlier for GaAs [24]. Which of the three effects prevails, is not clear, however, they all reduce the expected Burstein-Moss shift. An illustration of the broadening of the emission line I3 as a function of electron concentration is given in Fig. 10. (Halfwidths are plotted vs. electron concentration in double loga~thmic scale). The solid line inserted for comparison represents a AE = n113 relation. At the highest doping levels the experimental points are above this line. The line broadening is a typical high concentration effect which can be attributed to the conduction band tails and a broadening of the acceptor states. The same Q-slope as in Fig. 10 was found for the increase of the linewidth with donor density in the cathodoluminescence of GaAs [25].

!I;; -.. Fig. 10. Dependence of the emission iinewidth on electron concentration at 20°K (double logarithmic scale).

3.6. Luminescence of p-type InP Zinc-doped InP crystals were grown in the high doping range only. The luminescence of these samples at 77°K is depicted in Fig. 11. At the lowest acceptor concentration of 1.4 X 1018cm-3 the peak energy lies at 1.366 eV, which falls below the peak energy of line B in n-type samples. As in GaAs[26] the emission peak shifts to lower energy with increasing acceptor concentration and the lines broaden considerably.

x [ai lq3oo

95cm

8%

3cno !

1

/’

I 25

I 30

I 35

140

I 45

[eVl Fig. I 1. Spectra of three p-type samples at various doping levels. hu

The shift to lower energies is usually attributed to a ‘gap shrinkage’ effect. Although we see some structure on the high energy side of the main emission band, it is not clear, whether a band filling effect is present, as reported by Cusano[26] for GaAs. In summary the general appearance of the luminescence of p-type InP is very similar to that of p-GaAs. Acknowledgements-We are grateful to Professor H. J. Queisser for many stimulati-ng discussions. We wish to thank Dr. R. C. C. Leite and Dr. J. B. Gunn for sending us severai InP wafers. We also thank Dr. Pink and Dr. Winstel of the Siemens AG. Miinchen and Dr. Nord of the Wacker-Chemie, Burghausen for carrying out the spectrographic analysis of the indium. Financial support of this work by the Fraunhofer Gesellschaft is gratefully acknowledged.

1. BALKANSKI

2.

3. 4. 5. 6. 7. 8. 9.

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2634

0. RijDER,

10. SANGSTER

R. C., “Prep.

and

Prop.

U. HEIM and M. H. PILKUHN of Ill-V-

(Edited by R. K. Willardson and H. L. Goering) chap. 28. Reinhold Publishing, New York (1962). LINDBERG 0. and FAUST Jr. J. W., ibid., chap. 34. SOLOMON R., Gallium Arsenide, Prac. ofthe 2nd Int. Symp., p. 11. Dallas (1968). GOODWIN A. R., DOBSON C. D. and FRANKS J., ibid. p. 36. MOOREE.J.,Phys.Reo.160,618(1967). BROOKS H., Adv. Electronics Electron Phys. 7.87 Compounds”,

11. 12.

13. 14.

(1955). 15. EHRENREICH

H., J. Phys.

Chem.

Solids 12, 97

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(1969).

YEE J. H. and CONDAS

G. A., J. appl. Phys. 39,

24. PILLER

H., .I. phys.

Sot.

Japan

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21, 206

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C. and ROSE-INNES A. C., Semiconp. 18 1. Pergamon Press, Oxford (1961). _ 17. HILSUM C., FRAY S. and SMITH C., Solid State Commun.

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351 (1968).

(1959). 16. HILSUM ductina

R.,Phys. Rev. 111,1518 (1958). 19. DINGLE R. and RODGERS K. F., Appl. Lett. 14, 183 (1969). DINGLE R., Phys. Rev. 184.788 (1969).

18. NEWMAN

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7, 1057 (1969).

25. PANKOVE J. I.,J. awl. Phys. 39,536s (1968). 26. CUSANO D. A., appl: Phys: Lett. 7,15 1 (1965).

27. HEIM U.. RijDER 0.. OUEISSER H. J. and PILKUHN M. H.,J. Lumb&c. 1,608 (1969). 28. KhHL F., Infrared Reflectiuity of InP.