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InP heterostructures
Materials Science and Engineering, B13 (1992) L 5 - L 8
L5
Letter
Determination of lattice coherency by X-ray synergetic techniques in InGaPAs/InP heterostructures Jongwon Lee and Thomas Tsakalakos Department of Materials Science, PO Box 909, Rutgers University, Piscataway, NJ 08855 (USA) (Received November 18, 1991; accepted December 6, 1991)
Abstract InGaPAs/InP heterostructures grown by organometallic vapor phase epitaxy (OMVPE) were systematically examined. The coherency state of the interface was assessed by comparison of normal and parallel lattice parameters and by X-ray topography. Based on these results, the metastable limit of critical thickness was computed. Dependence of X-ray full-width at half maximum (FWHM) on the lattice mismatch and on the tetragonality of the epilayer was observed. These results demonstrate that the coherency state of the hetero-interface is of primary importance in influencing the crystal quality of the InGaPAs active layer.
I. Introduction
There has been intensive interest in Ifl~_xGa xsystems that can be used for fabrication of optoelectronic devices such as laser diodes, light emitting diodes and photo diodes. One of the main requirements in the fabrication of heterostructures is lattice matching between epilayer and substrate because the misfit strain has been shown to have significant influence on various properties (lattice parameters, photoluminescence, electrical properties) [1]. In particular, several investigations [1-4] have been made of the effects of lattice mismatch on the physical properties of InGaPAs/InP heterostructures grown by liquid phase epitaxy (LPE). In this letter, we demonstrate the effect of the elastic strain and plastic deformation on the crystal quality as represented by the X-ray line-width of an Inl_xGaxPl_yAsy epilayer grown on (001) InP substrate by organometallic vapor phase epitaxy (OMVPE).
consisting of three layers: a p-InP clad layer (about 0.6 /,m, p = 1 x 10 t8 cm- 3), a quaternary In l_xGaxP1 _yAsy active layer (about 1/~m), and an n-InP buffer layer (about 2 ktm, n =- 1 x 1018 cm -3) on a (001) InP substrate (about 380/~m). The reactants for the growth were triethylgallium, trimethylindium, arsine, and phosphine at low pressure and a temperature of 565 °C. The dopant was zinc for the p-clad layer and silicon for the n-buffer layer. The alloy composition was varied such that the lattice mismatch between the epilayer and substrate ranged from -3.88 x 10 -3 t o 7.29x10 -3. The composition variation in e a c h sample was computed by the relationship between the strain-free lattice parameter of the epilayer obtained by X-ray diffraction and the band-gap energy determined from the position of peak of photoluminescence (PL) spectra that were obtained at room temperature with broad area excitation at 1064 nm (Nd:YAG) using a filtered infrared microscope [5]. In order to study the coherency state of the interfaces, the X-ray measurements were performed by a double crystal diffractometer (DCD) using Cu Kal radiation (2=0.154056 nm). The (200) reflection of a LiF monochromator was used to provide a highly parallel incident beam.
P1 _ymSy/InP
2. Experimental details
The specimens examined for this investigation were OMVPE grown double-heterostructure (DH) wafers 0921-5107/92/S5.00
3. Results and discussion
Mismatch measurements were performed to examine the coherency state of the hetero-interface. As shown in Table 1, the normal mismatch Aaql/ab T A B L E 1. Normal and parallel lattice mismatch between the InGaPAs epilayer and the InP substrate Sample
Epilayer thickness
Aaq±/ab
Aaqll/ab
-
-
(~m) 1 2 3 4 5 6 7 8 9 10
0.99 0.97 0.99 1.01 0.98 0.96 0.97 0.99 1.06 0.75
3.88E-3 1.47E-3 9.92E-4 7.76E-4 2.72E-4 1.29E-3 2.18E-3 2.99E-3 4.71E-3 7.29E-3
1.99E-4 4.23E-5 2.89E-5 1.15E-5 1.02E-5 6.99E-5 1.74E-4 8.28E-5 3.69E-3 5.98E-3
© 1992 - Elsevier Sequoia. All rights reserved
Letter
L6 TABLE 2. X-rayfull-width at half maximum (FWHM), tetragonality factor and the existence of misfit dislocation at hetero-interface Sample
X-ray FWHM on epilayer (s)
Tetragonality Misfitdislocation factor by X-ray ( x 10- 2) topography
1 2 3 4 5 6 7 8 9 10
86 61 55 47 69 58 55 77 130 354
- 0.368 -0.143 - 0.096 - 0.076 - 0.035 0.122 0.2 0.3 ---
(Aaq±=aq±-ah) and (Aaqll=aqll-at,) were
No No No No No No No No Yes Yes
the parallel mismatch Aaqll/at, calculated using (004) and ( 115 )/(2 24) reflections, respectively, where aq±and a qll are the lattice constants of the InGaPAs quaternary layer normal and parallel to the wafer surface, respectively, and a b is the lattice constant of the InP substrate. A calculation to examine the X-ray penetration depth into the sample yields a penetration depth of about 10/~m [6]. This reveals that X-ray information is reliable since it was obtained from the region including the quaternary layer and both interfaces. Table 2 includes the X-ray full-width at half maximum (FWHM), the tetragonality factor ((aqi-aqll)/ab) and the existence of interfacial misfit dislocation examined by X-ray translation topography. These results indicate that among ten samples investigated in this study, samples 1-8 did not have dislocations and samples 9 and 10 had dislocations. Figure 1 shows, for example, two translation X-ray topographs obtained from sample 5 (Fig. l(a)) and sample 10 (Fig. l(b)). It can be seen in sample 5 that the dislocations are practically absent. The bright lines in the middle of both topographic images are owing to the presence of lattice curvature (approximately 10 m) observed in these samples. Even though the diffraction angle was set at the Bragg's angle of the epilayer, part of the substrate was also brought into the reflecting position because of the curvature as the sample translated. Superimposition of substrate image on epilayer image is shown as the bright line in the topographic image. In sample 10, however, many dislocations are present. These dislocations give rise to reflecting power differences, which in turn lead to contrast differences in photographic image. The approximate dislocation density of 1 x 10 s cm -2 for sample 10 and 2.5 x 107 cm -2 for sample 9 respectively, was calculated by both parallel mismatch and relation between X-ray F W H M and dislocations
Fig. 1. Translation X-ray topographs obtained by modified Lang camera. Topographs were taken at the Bragg's angle of InGaPAs active layer for 5 min at 30 kV and 30 mA. Translation distance was 1.5 cm. (a) Sample 5 (coherent interface); (b) sample 10 (incoherent interface).
density [7]. These results suggest that the misfit dislocations are generated if the parallel mismatch is in the range of about 10 -3 for this particular system. For further investigation of the coherency state of the interfaces, the critical thickness calculation was made using the force-balancing model by Matthews and Blakeslee
N:
b(1-vc°s20) (ln~+ l) hc = 2ztf(1 + v) cos 2 where b is the Burgers vector of the dislocation (all2), v is the Poisson ratio (~), 0 is the angle between the dislocation line and its Burgers vector (60°), A is the angle between the slip direction and the direction in epilayer normal to the intersection line of slip plane and interface (60°). Figure 2 shows the equilibrium critical thickness (thick line) based on the above equation and the metastable limit of critical thickness (thin line) obtained for this particular system. The lattice misfit f is assumed to be equivalent to one half (approximately equal to ( 1 - v)/(1 + v)) of Aaq±/ab [9]. The samples with coherent interfaces are represented by open circles and samples with incoherent interfaces by solid circles. Note that the three samples (indicated by arrows) that are supposed to be incoherent according to the force-balancing model are still coherent. From this result, it is suggested that the metastable limit of critical thickness in this particular case is about nine times larger than that expected by Matthews and Blakeslee. A similar coherency limit was observed by
Letter 105
10 4
103.
E_
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102,
o 10 1
.
.
.
.
.
.
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.
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.
.
.
.
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.
.
.
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I
0.1
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.
.
.
.
.
.
.
10
100
LATTICEMISRTf (xE-3) Fig. 2. Equilibrium critical thickness of InGaPAs epilayer calculated by force balancing model ( ) and the metastable limit of critical thickness ( ). o, the samples which have coherent hetero-interfaces; e, the incoherent.
400
i
300 200 100' 0 -8
.'6
-',
(a)
.'2
LATTICE MISFIT f (xE-3)
100 9O
i ,° 7O
n-
60 50
40 -0.5
|
-0.3
|
-0.1
|
0.1
•
L7
other investigators [9]. For example, in the InGaPAs/ InP LPE system, a seven-fold increase of the coherency limit has been reported. It is well known that the X-ray F W H M of an epilayer is a function of the crystal quality and the thickness [4]. F W H M dependence of our samples on thickness is excluded because the thickness of the InGaPAs active layer is kept constant (about 1/~m). It can therefore be said that the X-ray F W H M in this investigation depends only on the crystal quality of the active layer. X-ray F W H M of the InGaPAs active layer was measured and correlated with the lattice misfit (Fig. 3(a)) and also with the tetragonality factor (Fig. 3(b)). As can be seen in Fig. 3(a), the lower F W H M is obtained for samples with the smaller mismatch of lattice parameter. This low F W H M corresponds to the homogeneous elastic lattice deformation. The pronounced increase in F W H M of two samples at the far right indicates that the plastic deformation was caused by misfit dislocations, relaxing the supercritical strain at the hetero-interfaces. A similar trend can be seen in Fig. 3(b) where the effect of elastic strain, as represented by the tetragonality factor, is revealed. This figure shows that the smaller tetragonality factor corresponding to lower tetragonal distortion leads to the smaller X-ray FWHM. This dependence of X-ray linewidth on elastic strain may be attributed to the wafer curvature observed in the InGaPAs active layer. Note that samples 9 and 10 are excluded in constructing Fig. 3(b), since these samples are relaxed from the tetragonally distorted state owing to the dislocations. This correlates favorably with the prediction that the elastic strain and the relaxation of strain by generation of misfit dislocations can cause deterioration of the crystal quality [10]. In an attempt to establish the empirical relation between optoelectronic property and X-ray property, PL tests were performed and PL intensity was related to X-ray FWHM. It was observed, as expected, that substantially low PL intensities were obtained for samples 9 and 10. It should be noted that these low values of PL intensities can be attributed to the dislocations that are probable sites for non-radiative recombinations due to the dangling bonds around the dislocation cores [11]. This demonstrates that the plastic deformation (dislocation) can affect the optoelectronic property (PL intensity) as well as the crystal quality (X-ray FWHM).
i
0.3
0.5
(b) TETRAGONALITY FACTOR (xE-2) Fig. 3. (a) X-ray full-width at half maximum (FWHM) as a function of lattice misfit f, showing lower X-ray FWHM occurring at smaller lattice misfit; (b) X-ray FWHM as a function of the tetragonality of the InGaPAs active layer.
4. Concluding remarks InGaPAs/InP D H wafers (1 ~ 1.27 /~m) grown by OMVPE were systematically examined by X-ray DCD. Misfit dislocations owing to loss of coherency at
L8
Letter
hetero-interfaces can be detected by X-ray topography. T h e critical thickness of InGaPAs was calculated using the force-balancing model (theoretical) and X-ray topographs (experimental). T h e metastable limit of critical thickness in these samples was shown to be about nine times larger than the equilibrium critical thickness expected by theory. A fairly low X-ray F W H M was obtained for the samples which were elastically strained and a pronounced F W H M for the samples which were plastically deformed, hence, relaxed by formation of dislocations at hetero-interfaces. This indicates that the coherency state at interface between InGaPAs and InP has a major influence on the crystal quality of the InGaPAs active layer.
Acknowledgments T h e authors wish to thank M. Ferreira of Lytel Incorporated for performing the PL measurements. They are grateful to Dr. E. Imhoff and Dr. R. Wilson, also of Lytel, for their helpful discussions. Furthermore,
they are also grateful to Dr. E Dugan of Bell Core for valuable suggestions and discussions.
References 1 K. Ozasa, M. Yuri, S. Tanaka and H. Matsunami, J. Appl. Phys, 68(1)(1990)1. 2 V. Strakhov, N. Yaremenko, A. Telegin and V. Ogandzhanyan, Soy. Phys. Semicond., 19 (4) (1985) 373. 3 T. Yagi, Y. Fujiwara, T. Nishino and Y. Hamakawa, Jpn. J. Appl. Phys., 22 (1983) L467. 4 C. Bocchi, C. Ferrari and P. Franzosi, J. Elec. Mat., 16 (4) (1987)245. 5 R. E. Nahory, M. A. Pollack and W. D. Johnston, Jr., Appl. Phys. Lett., 33 (1978) 659. 6 J. Chaudhuri, S. Shah and J. P. Harbison, J. Appl. Phys., 66 (1989) 5373. 7 E B. Hirsch, Progress in Metal Physics, Pergamon, New York (1956), Chapter 6. 8 J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth, 27 (1974) 118. 9 K. Oe, Y. Shinoda and Y. Sugiyama, Appl. Phys. Lett., 33 (1978)962. 10 W. D. Johnston, Jr., Mat. Res. Soc. Symp. Proc., 14 (1983) 453. 11 J. Matsui, Mat. Res. Soc. A~vmp. Proc., 14 (1983) 477.
L5
Letter
Determination of lattice coherency by X-ray synergetic techniques in InGaPAs/InP heterostructures Jongwon Lee and Thomas Tsakalakos Department of Materials Science, PO Box 909, Rutgers University, Piscataway, NJ 08855 (USA) (Received November 18, 1991; accepted December 6, 1991)
Abstract InGaPAs/InP heterostructures grown by organometallic vapor phase epitaxy (OMVPE) were systematically examined. The coherency state of the interface was assessed by comparison of normal and parallel lattice parameters and by X-ray topography. Based on these results, the metastable limit of critical thickness was computed. Dependence of X-ray full-width at half maximum (FWHM) on the lattice mismatch and on the tetragonality of the epilayer was observed. These results demonstrate that the coherency state of the hetero-interface is of primary importance in influencing the crystal quality of the InGaPAs active layer.
I. Introduction
There has been intensive interest in Ifl~_xGa xsystems that can be used for fabrication of optoelectronic devices such as laser diodes, light emitting diodes and photo diodes. One of the main requirements in the fabrication of heterostructures is lattice matching between epilayer and substrate because the misfit strain has been shown to have significant influence on various properties (lattice parameters, photoluminescence, electrical properties) [1]. In particular, several investigations [1-4] have been made of the effects of lattice mismatch on the physical properties of InGaPAs/InP heterostructures grown by liquid phase epitaxy (LPE). In this letter, we demonstrate the effect of the elastic strain and plastic deformation on the crystal quality as represented by the X-ray line-width of an Inl_xGaxPl_yAsy epilayer grown on (001) InP substrate by organometallic vapor phase epitaxy (OMVPE).
consisting of three layers: a p-InP clad layer (about 0.6 /,m, p = 1 x 10 t8 cm- 3), a quaternary In l_xGaxP1 _yAsy active layer (about 1/~m), and an n-InP buffer layer (about 2 ktm, n =- 1 x 1018 cm -3) on a (001) InP substrate (about 380/~m). The reactants for the growth were triethylgallium, trimethylindium, arsine, and phosphine at low pressure and a temperature of 565 °C. The dopant was zinc for the p-clad layer and silicon for the n-buffer layer. The alloy composition was varied such that the lattice mismatch between the epilayer and substrate ranged from -3.88 x 10 -3 t o 7.29x10 -3. The composition variation in e a c h sample was computed by the relationship between the strain-free lattice parameter of the epilayer obtained by X-ray diffraction and the band-gap energy determined from the position of peak of photoluminescence (PL) spectra that were obtained at room temperature with broad area excitation at 1064 nm (Nd:YAG) using a filtered infrared microscope [5]. In order to study the coherency state of the interfaces, the X-ray measurements were performed by a double crystal diffractometer (DCD) using Cu Kal radiation (2=0.154056 nm). The (200) reflection of a LiF monochromator was used to provide a highly parallel incident beam.
P1 _ymSy/InP
2. Experimental details
The specimens examined for this investigation were OMVPE grown double-heterostructure (DH) wafers 0921-5107/92/S5.00
3. Results and discussion
Mismatch measurements were performed to examine the coherency state of the hetero-interface. As shown in Table 1, the normal mismatch Aaql/ab T A B L E 1. Normal and parallel lattice mismatch between the InGaPAs epilayer and the InP substrate Sample
Epilayer thickness
Aaq±/ab
Aaqll/ab
-
-
(~m) 1 2 3 4 5 6 7 8 9 10
0.99 0.97 0.99 1.01 0.98 0.96 0.97 0.99 1.06 0.75
3.88E-3 1.47E-3 9.92E-4 7.76E-4 2.72E-4 1.29E-3 2.18E-3 2.99E-3 4.71E-3 7.29E-3
1.99E-4 4.23E-5 2.89E-5 1.15E-5 1.02E-5 6.99E-5 1.74E-4 8.28E-5 3.69E-3 5.98E-3
© 1992 - Elsevier Sequoia. All rights reserved
Letter
L6 TABLE 2. X-rayfull-width at half maximum (FWHM), tetragonality factor and the existence of misfit dislocation at hetero-interface Sample
X-ray FWHM on epilayer (s)
Tetragonality Misfitdislocation factor by X-ray ( x 10- 2) topography
1 2 3 4 5 6 7 8 9 10
86 61 55 47 69 58 55 77 130 354
- 0.368 -0.143 - 0.096 - 0.076 - 0.035 0.122 0.2 0.3 ---
(Aaq±=aq±-ah) and (Aaqll=aqll-at,) were
No No No No No No No No Yes Yes
the parallel mismatch Aaqll/at, calculated using (004) and ( 115 )/(2 24) reflections, respectively, where aq±and a qll are the lattice constants of the InGaPAs quaternary layer normal and parallel to the wafer surface, respectively, and a b is the lattice constant of the InP substrate. A calculation to examine the X-ray penetration depth into the sample yields a penetration depth of about 10/~m [6]. This reveals that X-ray information is reliable since it was obtained from the region including the quaternary layer and both interfaces. Table 2 includes the X-ray full-width at half maximum (FWHM), the tetragonality factor ((aqi-aqll)/ab) and the existence of interfacial misfit dislocation examined by X-ray translation topography. These results indicate that among ten samples investigated in this study, samples 1-8 did not have dislocations and samples 9 and 10 had dislocations. Figure 1 shows, for example, two translation X-ray topographs obtained from sample 5 (Fig. l(a)) and sample 10 (Fig. l(b)). It can be seen in sample 5 that the dislocations are practically absent. The bright lines in the middle of both topographic images are owing to the presence of lattice curvature (approximately 10 m) observed in these samples. Even though the diffraction angle was set at the Bragg's angle of the epilayer, part of the substrate was also brought into the reflecting position because of the curvature as the sample translated. Superimposition of substrate image on epilayer image is shown as the bright line in the topographic image. In sample 10, however, many dislocations are present. These dislocations give rise to reflecting power differences, which in turn lead to contrast differences in photographic image. The approximate dislocation density of 1 x 10 s cm -2 for sample 10 and 2.5 x 107 cm -2 for sample 9 respectively, was calculated by both parallel mismatch and relation between X-ray F W H M and dislocations
Fig. 1. Translation X-ray topographs obtained by modified Lang camera. Topographs were taken at the Bragg's angle of InGaPAs active layer for 5 min at 30 kV and 30 mA. Translation distance was 1.5 cm. (a) Sample 5 (coherent interface); (b) sample 10 (incoherent interface).
density [7]. These results suggest that the misfit dislocations are generated if the parallel mismatch is in the range of about 10 -3 for this particular system. For further investigation of the coherency state of the interfaces, the critical thickness calculation was made using the force-balancing model by Matthews and Blakeslee
N:
b(1-vc°s20) (ln~+ l) hc = 2ztf(1 + v) cos 2 where b is the Burgers vector of the dislocation (all2), v is the Poisson ratio (~), 0 is the angle between the dislocation line and its Burgers vector (60°), A is the angle between the slip direction and the direction in epilayer normal to the intersection line of slip plane and interface (60°). Figure 2 shows the equilibrium critical thickness (thick line) based on the above equation and the metastable limit of critical thickness (thin line) obtained for this particular system. The lattice misfit f is assumed to be equivalent to one half (approximately equal to ( 1 - v)/(1 + v)) of Aaq±/ab [9]. The samples with coherent interfaces are represented by open circles and samples with incoherent interfaces by solid circles. Note that the three samples (indicated by arrows) that are supposed to be incoherent according to the force-balancing model are still coherent. From this result, it is suggested that the metastable limit of critical thickness in this particular case is about nine times larger than that expected by Matthews and Blakeslee. A similar coherency limit was observed by
Letter 105
10 4
103.
E_
O
102,
o 10 1
.
.
.
.
.
.
.
.
!
.
.
.
.
.
.
.
.
!
I
0.1
.
.
.
.
.
.
.
.
10
100
LATTICEMISRTf (xE-3) Fig. 2. Equilibrium critical thickness of InGaPAs epilayer calculated by force balancing model ( ) and the metastable limit of critical thickness ( ). o, the samples which have coherent hetero-interfaces; e, the incoherent.
400
i
300 200 100' 0 -8
.'6
-',
(a)
.'2
LATTICE MISFIT f (xE-3)
100 9O
i ,° 7O
n-
60 50
40 -0.5
|
-0.3
|
-0.1
|
0.1
•
L7
other investigators [9]. For example, in the InGaPAs/ InP LPE system, a seven-fold increase of the coherency limit has been reported. It is well known that the X-ray F W H M of an epilayer is a function of the crystal quality and the thickness [4]. F W H M dependence of our samples on thickness is excluded because the thickness of the InGaPAs active layer is kept constant (about 1/~m). It can therefore be said that the X-ray F W H M in this investigation depends only on the crystal quality of the active layer. X-ray F W H M of the InGaPAs active layer was measured and correlated with the lattice misfit (Fig. 3(a)) and also with the tetragonality factor (Fig. 3(b)). As can be seen in Fig. 3(a), the lower F W H M is obtained for samples with the smaller mismatch of lattice parameter. This low F W H M corresponds to the homogeneous elastic lattice deformation. The pronounced increase in F W H M of two samples at the far right indicates that the plastic deformation was caused by misfit dislocations, relaxing the supercritical strain at the hetero-interfaces. A similar trend can be seen in Fig. 3(b) where the effect of elastic strain, as represented by the tetragonality factor, is revealed. This figure shows that the smaller tetragonality factor corresponding to lower tetragonal distortion leads to the smaller X-ray FWHM. This dependence of X-ray linewidth on elastic strain may be attributed to the wafer curvature observed in the InGaPAs active layer. Note that samples 9 and 10 are excluded in constructing Fig. 3(b), since these samples are relaxed from the tetragonally distorted state owing to the dislocations. This correlates favorably with the prediction that the elastic strain and the relaxation of strain by generation of misfit dislocations can cause deterioration of the crystal quality [10]. In an attempt to establish the empirical relation between optoelectronic property and X-ray property, PL tests were performed and PL intensity was related to X-ray FWHM. It was observed, as expected, that substantially low PL intensities were obtained for samples 9 and 10. It should be noted that these low values of PL intensities can be attributed to the dislocations that are probable sites for non-radiative recombinations due to the dangling bonds around the dislocation cores [11]. This demonstrates that the plastic deformation (dislocation) can affect the optoelectronic property (PL intensity) as well as the crystal quality (X-ray FWHM).
i
0.3
0.5
(b) TETRAGONALITY FACTOR (xE-2) Fig. 3. (a) X-ray full-width at half maximum (FWHM) as a function of lattice misfit f, showing lower X-ray FWHM occurring at smaller lattice misfit; (b) X-ray FWHM as a function of the tetragonality of the InGaPAs active layer.
4. Concluding remarks InGaPAs/InP D H wafers (1 ~ 1.27 /~m) grown by OMVPE were systematically examined by X-ray DCD. Misfit dislocations owing to loss of coherency at
L8
Letter
hetero-interfaces can be detected by X-ray topography. T h e critical thickness of InGaPAs was calculated using the force-balancing model (theoretical) and X-ray topographs (experimental). T h e metastable limit of critical thickness in these samples was shown to be about nine times larger than the equilibrium critical thickness expected by theory. A fairly low X-ray F W H M was obtained for the samples which were elastically strained and a pronounced F W H M for the samples which were plastically deformed, hence, relaxed by formation of dislocations at hetero-interfaces. This indicates that the coherency state at interface between InGaPAs and InP has a major influence on the crystal quality of the InGaPAs active layer.
Acknowledgments T h e authors wish to thank M. Ferreira of Lytel Incorporated for performing the PL measurements. They are grateful to Dr. E. Imhoff and Dr. R. Wilson, also of Lytel, for their helpful discussions. Furthermore,
they are also grateful to Dr. E Dugan of Bell Core for valuable suggestions and discussions.
References 1 K. Ozasa, M. Yuri, S. Tanaka and H. Matsunami, J. Appl. Phys, 68(1)(1990)1. 2 V. Strakhov, N. Yaremenko, A. Telegin and V. Ogandzhanyan, Soy. Phys. Semicond., 19 (4) (1985) 373. 3 T. Yagi, Y. Fujiwara, T. Nishino and Y. Hamakawa, Jpn. J. Appl. Phys., 22 (1983) L467. 4 C. Bocchi, C. Ferrari and P. Franzosi, J. Elec. Mat., 16 (4) (1987)245. 5 R. E. Nahory, M. A. Pollack and W. D. Johnston, Jr., Appl. Phys. Lett., 33 (1978) 659. 6 J. Chaudhuri, S. Shah and J. P. Harbison, J. Appl. Phys., 66 (1989) 5373. 7 E B. Hirsch, Progress in Metal Physics, Pergamon, New York (1956), Chapter 6. 8 J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth, 27 (1974) 118. 9 K. Oe, Y. Shinoda and Y. Sugiyama, Appl. Phys. Lett., 33 (1978)962. 10 W. D. Johnston, Jr., Mat. Res. Soc. Symp. Proc., 14 (1983) 453. 11 J. Matsui, Mat. Res. Soc. A~vmp. Proc., 14 (1983) 477.