Investigation of strain effects in selectively grown GaAs on Si

CRYSTAL GROWTH ELSEVIER

Journal of Crystal Growth 145 (1994) 345—352

_____________________

Investigation of strain effects in selectively grown GaAs on Si K. Zieger

a G. Frankowsky a~A. Hangleiter a F. Scholz a,* J• Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany b Max-Planck-Institut für Festkorperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany

a,

P. Stauss

Spitzer

b

a~

Abstract In this paper we describe the investigation of strain effects in GaAs layers which were selectively grown on Si substrates by metalorganic vapor phase epitaxy (MOVPE). The experimental strain determined by high resolution X-ray diffraction, Raman and photoluminescence measurements were compared to an analytical thermal strain model and showed very good agreement. The strain relaxation observed in selectively grown GaAs layers depends on the square dimensions and the layer thickness of the GaAs squares. By cathodoluminescence measurements, an inhomogeneous strain distribution inside the GaAs layers as predicted by our thermal strain model could be verified. Differences in the experimentally and theoretically evaluated thermal strain are explained by the dislocation movement during the high temperature part of the cooling process after growth.

1. Introduction The epitaxial combination of GaAs and Si has attracted a lot of interest in the recent years due to its potential for the integration of GaAs based photonic devices with advanced Si electronic devices [1]. However, the growth of GaAs on Si is accompanied by a high density of dislocations in the GaAs layer due to the large lattice mismatch (4.1%). Several techniques have been developed, such as post-growth annealing [2], in situ thermal annealing [3], thermal cyclic growth [4] and specially designed strained buffer layers [5], to reduce the dislocation density. Moreover, the large difference in thermal expansion coefficients results in a biaxial tensile strain in the GaAs layer.

*

Corresponding author.

This causes the formation of microcracks for GaAs layer thicknesses exceeding 3 ~tm which might be a major problem for device processing. It has been demonstrated that the selective area growth of GaAs on Si has effectively reduced the dislocation density leading to a better crystalline quality [6] and the internal biaxial strain [71.Moreover, strain variations and strain relief occurred with decreasing lateral dimensions of selectively grown GaAs on Si [8] and selectively etched GaAs on Si after planar growth [9]. These methods make it possible to adjust precisely the geometrical dimensions of the GaAs layers and to obtain quantitative data of the strain distribution inside the layers, which is necessary for device engineering. Whereas selective area etching after planar GaAs/Si growth certainly does not reduce the dislocation density, the selective area growth enables studies for a fundamental understanding

0022-0248/94/$07.00 © 1994 Elsevier Science By. All rights reserved SSDI 0022-0248(94)00324-F

a

a a a a a a a a a 346

K Zieger er al. /Journal of C~sta1Growth 145 (1994) 345—352

of strain-dependent dislocation generation and therefore for further dislocation reduction processes. Although several studies have been performed on theoretical modeling of strain distribution in structured GaAs layers on Si [10—12],few work has been done on a detailed comparison of theoretical and experimental results. In this paper, we report about a systematic study on strain in GaAs layers selectively grown on Si substrates by metalorganic vapor phase epitaxy (MOVPE) with respect to the variations of the lateral dimensions

cooling down to 700°C,a 50 nm thick GaAs layer was grown. The procedure of 50 nm GaAs growth at 400°C, annealing to 900°Cand 50 nm GaAs growth at 700°Cwas repeated again. After this, an in-situ thermal annealing procedure was performed containing cooling down to 200°C, heating to 900°C, again cooling down to 200°C, and raising the temperature to 700°C.The growth of the GaAs layer was continued to total layer thicknesses of 1.5—8 j.tm. We obtained mirrorlike surfaces of the GaAs layers and only little polycrystalline GaAs nucleation on the Si02 mask.

and the thickness of the GaAs layers. The experimental results were compared to an analytical thermal strain model.

High resolution X-ray diffraction measurements (HRXRD) were carried out on a Philips five crystal diffractometer using CU~Ka radiation. On large unmasked growth regions, we measured a full width at half maximum (FWHM) of the (004) peak of about 100 arc sec, demonstrating the high quality of our GaAs layers grown by the TCG process. Moreover, the symmetric (004) reflections give the lattice distortion perpendicular to the (001) surface, while asymmetrically performed (115) andboth (115) reflections measure the lattice distortion perpendicular and parallel to the (001) surface of the sample. The spot diameter of the X-ray beam was 1 X 1 mm2.

2. Experimental procedure For these studies, (001) Si substrates, misoriented 2°off towards [110] direction, have been masked with 200 nm Si02 by e-beam evaporation.2 We mask patterns consisting of 2>< 2 wideused square regions (subsequently denoted mm as growth regions) which were further subdivided into open squares ranging from 20 x 20 j~m2to 2000 x 2000 ~ The patterning of the Si0 2 masked substrates was done by standard photolithography and the squares with edges parallel to the [110] and [110] directions were opened in a buffered HF solution. Immediately after the substrate preparation, the masked Si substrates were loaded into the reactor and subsequently heated up to 950°C.By this treatment, we were able to desorb the natural oxide from the uncovered Si surface without destroying the SiO2 mask. The MOVPE growth was performed at low pressure (20 hPa) in a horizontal reactor (Aixtron AIX 200). We used trimethylgallium (TMGa) and arsine (AsH 3) as palladium-diffused H source materials and 2 as carrier gas. The conventional 2-step growth procedure [131 and the thermal cyclic growth (TCG) [4] were applied according to the following procedure: After a 20 nm nucleation layer at 400°Cand 1 ~m conventional growth of GaAs at 700°C, a 50 nm low temperature GaAs layer at 400°Cwas deposited. The sample was annealed at 900°Cand then after

Therefore the results have to be interpreted as integral information over many squares of the same size in one growth region. For both, Raman measurements performed in backscattering geometry at 77 K and photoluminescence at 2 K, the samples were excited by the 514.4 nm line of an ~ laser. The Raman signal was dispersed with a 2.12 m SOPRA double monochromator and detected in the 10th order with a photomultiplier in order to obtain a high resolution and reproducibility, whereas the PL light was dispersed by a 1 m grating monochromator and detected with a liquid-N2-cooled Ge2, detector. Owing to the laser spot of about 1 mm we obtained integral information over many squares of the same size. The lateral strain distribution was evaluated by spatially resolved cathodoluminescence (CL) with an electron beam energy of 20 kV at 7 K. The spatial resolution was in the range of 4 ~.tm, limited by the carrier diffusion. The thickness of the selectively grown GaAs squares was measured by a Dektak pro-

K Zieger et aL/Journal of Crystal Growth 145 (1994) 345—352

filometer taking the masked areas as a reference line. Thus the local growth rate and growth uniformity across the mask pattern could easily be determined.

3. Analytical strain model

=

(a11

—

1

0

y y y y

~

The difference in thermal expansion coefficients of GaAs and Si causes a biaxial tensile strain inside planar grown GaAs layers which results in a tetragonal lattice distortion. The relative strain components parallel and perpendicular to the heterointerface are defined as: a0)/a0,

347

0

\. — — — — =

‘

I .0O•h O.75~h 0.50.h 0.25•h

L/2h

=

10

(a) ____________________________________ I I I 2

4

•

6

8

10

0.8

1.0

x/h 1

(la) (ib)

where a0 is the lattice constant of the unstrained GaAs (a0 0.565325 nm [14]), and a11 and a are the lattice constants of the strained GaAs. Assuming GaAs stripes with rectangular cross section grown selectively on Si, the strain distribution within this stripes can be evaluated following an analytical thermal strain model proposed by Aleck [15]. For simplicity, the second lateral square dimension of our mask pattern is neglected by considering stripes of infinite length. In this model, the strain distribution in a rectangle of height h and width L (see Fig. 1)is computed under the assumption of shear forces along the interface of GaAs and Si. The absolute value of these shear forces is taken into account by a fitting parameter Eth which can be interpreted directly as the thermally induced strain. The material properties are considered by the elastic constants C11 of GaAs. The ratio L/2h

y y

=

y

GaAs Si substrate

—

2

=

0

=

h

~

+

T

y

—2

y

—

(b) 0.0

•

—

O.75•h 0.50.h

— —

0.25•h 0.00~h

—

•

0.2

•

0.4

•

0.6

x/h Fig. 2. Lateral and horizontal strain distribution of e~(normalized to the thermal strain ~ due to the thermal strain model for different L/2h ratios: (a) L /2h = 10; (b) L/2h = 1. Since the structure has symmetry with respect to the center line (see Fig. 1), only one half is shown.

will be called aspect ratio in the further investigations. We have evaluated the strain distribution of such stripes for aspect ratios L/2h 10 and L/2h = 1 (Fig. 2) with the elastic parameters C11 = 118.4 GPa and C12 = 53.7 GPa of GaAs [14]. For L/2h = 10 (Fig. 2a), the GaAs stripe is nearly homogeneously tensile strained, almost independent of the x- and y-positions. Only near the edges (at x/h L/2h) some strain relax=

ation occurs. Obviously, the relaxation near the h

2

Fig. 1. Schematic diagram of the thermal strain model for selectively grown GaAs on Si.

interface(y(y= =0)h).is For surface stronger an aspect thanratio at the of L/2h GaAs/Si = 1 (Fig. 2b), a strong vertical dependence of the strain can be seen throughout the whole stripe. In consequence, the GaAs layer can no longer be regarded as homogeneously strained. At the sur-

348

K. Zieger et al. /Journal of Crystal Growth 145 (1994) 345—352

face, the values of e11(x, y) even become negative, indicating compressive strain. Although spectroscopic methods such as HRXRD, Raman and PL measurements can be used to determine the strain in planar grown GaAs on Si, it is difficult to measure directly the spatial strain distributions in narrow stripes. As mentioned earlier, the detected signal only gives integral information of the strain distribution over many squares of the same dimension. Therefore, we have extended Aleck’s model in order to determine the average strain of selectively grown GaAs/Si stripes by integrating over the spatial directions x and y: y) e~ dy dx Ii’

=

f L/2 f h

I

I

A

I

A AAA

A

~‘

1~0 .

/ —

strain model

A A

0.0

:

A

F

i

i

i

1

1

I

I

100

1000

A A

•_

A AA

~

.

I

I~

GaAs/Si (TCG) I = 300K

(2)

AA A

e~’~dydx

~x=0’y=0 0.1

The absorption of the incident light probing the strain distribution is taken into account by the exponential factor e”~’,where a is the absorption coefficient and depends on the wavelength of the incident light. The resulting values of and ~ depend on the aspect ratio L/2h. They will be compared to experimental strain values of selectively grown GaAs squares on Si substrates determined by HRXRD, Rarnan and PL measurements in the following sections.

4. Experimental results Using various mask patterns (see Section 2), we have grown selectively GaAs on Si in order to analyze the strain distribution along the abovementioned model. The width L is given very precisely by the patterning of the SiO2 mask, whereas the height h can be controlled by the GaAs growth rate. Both dimensions have been checked after growth by optical microscopy and surface profilometry, respectively, Both experimental strain components Eli and determined by HRXRD at 300 K, showed a lattice relaxation with decreasing aspect ratio L/2h (Fig. 3). The curves of and ~ calculated from the strain model using Eq. (2) with neglect~,

1

10

L/2h Fig. 3. Strain components e~and e ~ determined by HRXRD

(T = 300 K) versus the aspect ratio L/2h of the GaAs layers. A comparison with the thermal strain model shows an excellent agreement.

ing absorption (a = 0) have been fitted to the experimental data by adjusting ~th accordingly. We obtained a best fit for a parameter of Eth 1.40 x i0~ at 300 K. The value of the fitting parameters will be discussed in the next sections. Raman measurements were performed on selectively grown GaAs/Si samples and on a GaAs/ GaAs reference sample at 77 K (Fig. 4). The peak of the reference sample at 294.3 cm~ is attributed to the scattering by the longitudinal optical (LU) phonon of GaAs, which is Raman active, while the TO mode is not expected in near backscattering geometryThe fromLO a (001)-faced crys1’d symmetry. phonon peak is tal withto 293.5 cm~ in planar GaAs/Si owing shifted to the built-in tensile strain. With decreasing square dimensions we observed a back shift to the LU phonon frequency of the unstrained GaAs/GaAs reference sample. The phonon shift to higher frequencies can be attributed to the strain relaxation [16,17].

K Zieger et al. /Journal of Crystal Growth 145 (1994) 345—352

Similarly, PL spectra recorded at T= 2 K showed the well-known shift of the excitonic lines of GaAs/Si to lower energies and a shift back to higher energies for decreasing square dimensions (Fig. 5). Moreover, two excitonic lines (m~ ±~,± can be detected in our larger GaAs squares owing to the strain-induced lifting of the valence band degeneracy [18]. In both sets of data (Raman and PL), the spectral line shift can be attributed to a strain relaxation within the GaAs squares of decreasing size. For homogeneously

Wavelength [.s~m] 0.86

4Em

±1/2

(inmeV), I.lEmj= ±3/2

0.85

•

.

~

•

I

0.82

0.81

I

pIonar~

2000wn

_____________

1O00~m

___________

________

.~ 4)

___________

200am

C

.

_____________

10

_____

~

—13.1 x i03~—0.16 x 10~~

=

•

GaAs/Si (ICC) I = 2K

I

.~‘

strained been applied material, for our the quantitative following equations strain evaluahave tion [16]: (3a) ~iWLO= —0.488X103~~(incmt),

349

(3b) —6.4 x i03e~

=

1 (in meV).

(3c)

I_______________________________

1.44 to the LU phonon shift with respect to the unstrained GaAs/GaAs and

1.46

1.48

1.50

1.52

Energy [eV]

L~WLO corresponds

Fig. 5. PL spectra (T

=

2 K) of selectively grown GaAs squares

on Si of various dimensions. For comparison a PL spectrum of GaAs/GaAs is shown.

GaAs/Si (TCG) T = ~

~iEm =

±

1/2,± 3/2

are the energy shifts due to the

straifi induced variation of the band gap. The planar 2000~sm

~

___._—~“~“~---_._____~

l000um

d >~

500~sm 200~sm

~

1 OOsm

~

Cl)

~

50~arn 20~sm

~

tion depth of the exciting Ar laser line. Therefore, we obtained compressive strain contributions in the calculations for aspect ratios below 1 (see Fig. 2b). Now, best fits have been obtained with parameters of ~th = 1.50 X i0~ for Raman measurements (77 K) and ~th = 2.25 X i0~ for PL experiments (2 K). We obtained very good agreement between the experiments and the predictions of the thermal strain model. CL linescans were performed to get better spatial information about the local strain distribu+

_~/‘~‘\~~

GaAs/GaM~

_______________________________ I .1 .1. .1... I. 288 290 292 294 296 Raman shift [cm~] •

experimental data are plotted in Fig. 6 and reflect the mean strain of our squares. We observed in both methods a significant strain relaxation with decreasing aspect ratio. Consequently, they have been compared to ~ according to our model 4 cm’ has been ascalculations coefficient ofdescribed a = 7.6 above. x i0 Here, an absorption sumed, taking into account the limited penetra-

•

Fig. 4. Raman measurements (T = 77 K) of selectively grown GaAs squares on Si of various dimensions. The Raman spectrum of the GaAs/GaAs reference sample is also shown,

350

K Zieger et a!. /Journal of Crystal Growth 145 (1994) 345—352 2

.

I

1

1

1~I~

GaAs/Si (TCG) 1

tion. The electron beam is scanned over the GaAs squares parallel to the [110] direction (centered in the [110] direction). At each point a complete CL spectrum is recorded and the energetic position of the CL peak extracted. Near the edges of all squares a shift to higher energies can be seen, indicating strain relaxation (Fig. 7). In the center of the 1000 X 1000 j~m2GaAs square the strain almost reaches values of planar grown GaAs/Si. In the 100 x 100 ~tm2 GaAs square, we found qualitatively the same behavior. However, the GaAs square of 50 x 50 ~m2 clearly shows the strain relaxation not only at the edges, but also in the middle of the square, in very good agreement with our model calculations. The experiments are clearly demonstrating the presence of a nonuniform strain distribution inside the GaAs squares.

.

A A

77K

AA

(a) ‘I 1

2K

‘I

I I

I

A A1

II

0.1

1

1

10

I

100

I

5. Discussion

1000

L/2h We notice excellent agreement of our data obtained by three different methods of strain evaluation with results of our model calculations. This can be very well explained by the strain relaxation in squares with decreasing aspect ratio L/2h as described above (see Fig. 2), starting at

Fig. 6. Strain component ~ versus the aspect ratio L/2h determined by (a) Raman measurements (T = 77 K) from the GaAs LO phonon peak position of selectively grown GaAs/Si squares and (b) PL measurements (T = 2 K) from the cxcitonic peak positions of selectively grown GaAs/Si squares. The solid curve shows the results of the thermal strain model for an absorption coefficient of a = 7.6X io~cm’.

1.505 1.500. >..

~ 1.495

GaAs/Si (TOG) 1=7K

\j

square size •

.

~

w

~ 0

1.490

50gm ioo~am

~JO1000~m~0~m

-J

0

1.485

planar

•.

I

0

•

I

•

I

•

I

50 100 150 Distance from square edge [j.~mJ

200

Fig. 7. CL peak energy (T = 7 K) as a function of the distance from the square edge for different square sizes.

K Zieger et aL/Journal of Crystal Growth 145 (1994) 345—352

the square edges (at x/h = ±L/2h). It should be noted that for an exact strain analysis of selectively grown GaAs on Si it is important to consider the aspect ratio L/2h as a size controlling parameter. Therefore it is necessary to interpret the strain relaxation obtained from other workers [7] in view of a variation of the aspect ratio and not only of the lateral square dimensions. Moreover, the experimentally observed broadening of the lines in all data can now be attributed to the inhomogeneous strain distribution occurring in horizontal and vertical directions inside the GaAs squares. For planar grown GaAs/Si, the line width is normally interpreted as a measure of the layer quality in terms of the dislocation density. This is no longer applicable for selectively grown GaAs/Si layers. For very small aspect ratios L/2h 2 some differences between model calculations and experimental data appear (see Figs. 3 and 6). This is expected because the calculation using Aleck’s model is only two-dimensional and does not consider the three-dimensional relaxation near the edges in the other lateral dimension and near the corner of the squares. Moreover, the facet form of the GaAs square edges is not rectangular as assumed in the model, but determined by Kill) facet growth. This influences the strain evaluation for very small square dimensions, but was not studied in detail in these investigations, As a main result, has been determined for all data sets (see Table 1). Its physical interpretation is the strain induced at the GaAs/Si interface by the difference of the thermal expansion coefficients. If we assume that the lattice mismatch is relaxed by the generation of misfit dislocations and the GaAs epilayer is grown essenEth

Table 1 Comparison of the experimental fitting parameters and calculated thermal strain values (using Eq. (4)) for different growth temperatures TG Method

Temperature (K) HRXRD 300 Raman 77 PL 2

e~5(fit)

~th

(calculation)

TG = 973 K T0

=

773 K

1.40X103 2.00X103 1.44X103 1.50X 10~ 2.75 X 10~ 2.15 X i0~ 2.25x103 2.76x103 2.17xi03

_____________________________________________

351

tially stress free, then the cooling down after the epitaxial process is responsible for this strain and we can evaluate ~th according to the following equation: T

E~h(T) =

j10 [aGaAs(T)

, —

as1(T

)1 dT~

(4)

T

where aGaAs(T) and as1(T) are the linear thermal expansion coefficients given in Ref. [19], TG is the growth temperature and T the characterization temperature. The data for the calculated thermal strain th using Eq. (4) are also listed in Table 1 for our growth temperature of 700°C(973 K) and different characterization temperatures according to the experiments. Obviously, we obtained significant differences between the experimental and the theoretical strain values The data coincide much better if a lower “growth” temperature of about 500°C(773 K) is assumed (see Table 1). Qualitatively, the same behavior has been found by others [20—22].Surprisingly, the strain in the epitaxial GaAs layers at room temperature is almost the same, no matter which growth method (MBE or MOVPE) or growth temperature was applied. Thus, we have to assume that the thermal strain is only formed during cooling down from about 500°C to ambient temperature, whereas in the first step, when the temperature decreases from the growth temperature to about 500°C,the epitaxial layer remains unstrained. At this stage, the temperature is still high enough to force dislocation movement, resulting in a strain reduction inside the layer [23]. However, when the temperature is approximately 500°C,dislocation movement is frozen in because the dislocation velocity decreases exponentially with decreasing temperature. Thus, in the following cooling process the thermally induced strain is built up inside the GaAs layers. This is in good agreement with observations of Tachikawa and Mon [24,25] that most of the dislocations in hydrideVPE-grown GaAs on Si are formed in the cooling stage, whereas 2) couldonly be detected very fewindislocations situ at the growth (about i0~cm temperature. As shown above, selective area growth of GaAs on Si can be used to adjust the strain inside the Eth.

.

.

...

352

K Zieger et a!. /Journal of Crystal Growth /45 (1994) 345—352

epitaxial layers by the geometrical dimensions. This should be applicable in the future for selectively grown GaAs devices on Si substrates and for a further minimization of the dislocation generation during the cooling process. 6. Conclusions In summary, we have shown that the local strain distribution in selectively grown GaAs layers on Si substrates can be modeled very precisely by an analytical thermal strain model. Experimental strain relaxation determined by HRXRD, Raman and PL measurements showed very good agreement with the theoretical calculations. Important geometrical parameters are the square dimensions L and the thickness h of the GaAs squares. CL measurements showed that the strain distribution inside the GaAs squares is very inhomogeneous, in consistence with predictions of the thermal strain model. The differences between experimentally and theoretically induced thermal strain were interpreted by a strain reducing dislocation movement which is frozen in at about 500°C. This offers the possibility for a strain dependent investigation of dislocation generation and dislocation movement. Acknowledgements We thank A. Fuoss, P. Burkard and H. Gräbeidinger for technical assistance, E. Lux for performing PL measurements, V. Frese (DASA AG, Heilbronn) for mask design and M.H. Pilkuhn for fruitful discussions. The financial support of this work by the Bundesministerium für Forschung und Technologie (BMFT) under Contract No. 0328554C is gratefully acknowledged. References [1] S.F. Fang, K. Adomi, S. Iyer and H. Morkoç, J. Appi. Phys. 68 (1990) R31.

[2] Y. itoh, T. Nishioka, A. Yamamoto and M. Yamaguchi, AppI. Phys. Lett. 52 (1988) 1617. [3] M. Yamaguchi, A. Yamamoto, M. Tachikawa, Y. Itoh and M. Sugo, Appl. Phys. Leit. 53 (1988) 2293. [41R.J. Dieter, F. Goroncy, J.P. Lay, N. Draidia, K. Zieger, w. Kürner, B. Lu, F. Scholz, B. Roos, M. Braun, V. Frese and J. Hilgarth, in: Proc. 11th EC Photovoltaic Solar Energy Conf., Montreux, 1992, p. 225. [51S. Sharan, J. Narayan and J.C.C. Fan, J. Electron. Mater. 20 (1991) 779. [6] M. Yamaguchi, M. Tachikawa, M. Sugo and S. Kondo, AppI. Phys. Lett. 56 (1990) 27. Karam, V. Haven, S.M. Vernon, N. El-Masry, E. Lingunis and N. Haegel, J. Crystal Growth 107 (1991) 129. [8] B.G. Yacobi, C. Jagannath, S. Zemon and P. Sheldon, APPI. Phys. Lett. 52 (1988) 555. [9] N. Tsukamoto, Y. Yazawa, J. Asano and T. Minemura, AppI. Phys. Lett. 61(1992) 810. [101 E. Lingunis, N. Haegel and N.H. Karam, Appi. Phys. Lett. 59 (1991) 3428. [11] E. Lingunis, N. Haegel and N.H. Karam, AppI. Phys.

[71N.H.

Lett. 61(1992) 2202. [12] 5. Sakai, K. Kawasaki and N. Wada, Jap. J. AppI. Phys. 29 (1990) L853. [131 M. Akiyama, Y. Kawarada and K. Kaminishi, J. Crystal Growth 68 (1984) 21. [14] Landolt-Börnstein, Vol. 17a, Physics of the Group IV Elements and Ill-V Compounds, Ed. 0. Madelung (Springer, Berlin, 1982). [15] B.J. Aleck, J. Appi. Mech. 16 (1949) 118. [161 G. Landa, R. Caries, C. Fontaine, E. Bedel and A. Muñoz-Yagüe, J. Appl. Phys. 66 (1989) 196. [171A. Mlayah, R. Caries and A. Leycuras, J. Appi. Phys. 71 (1992) 422. [18] W. Stolz, F.E.G. Guimaraes and K. Ploog, J. Appi. Phys. 63 (1988) 492. [19] Y.S. Touloukian, R.K. Kirby, RE. Taylor and T.Y. Lee, Thermophysical Properties of Matter, TPRC Data Seties, Vol. 13 (Plenum, New York, 1977). [20] N. Lucas, H. Zabei, H. Morkoç and H. Unlu, Appi. Phys. Leit. 52(1988)2117. [21] T. Ueda, S. Onozawa, M. Akiyama and M. Sakuta, Jap. ~. APPI. Phys. 27 (1988) 1815. [22] M. Sugo, N. Uchida, A. Yamamoto, T. Nishioka and M. Yamaguchi, J. Appi. Phys. 65 (1989) 591. [23] I. Yonenaga and K. Sumino, J. AppI. Phys. 62 (1987) 1212. [24] M. Tachikawa and H. Mori, Appi. Phys. Lett. 56 (1990) 2225. [25] M. Tachikawa and H. Mori, Jap. J. AppI. Phys. 30 (1991) 551.