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MOVPE of high quality ZnSe: Role of mismatch on reflectivity and photoconductivity
204
Journal of Crystal Growth 101 (1990) 204—207 North-Holland
MOVPE OF HIGH QUALITY ZnSe: ROLE OF MISMATCH ON REFLECTIVITY ANI~PHOTOCONDUCTIVITY R.L. AULOMBARD, M. AVEROUS, 0. BRIOT J. CALAS, D. COQUILLAT, F. HAMDANI, J.P. LASCARAY, N. MOULIN and N. TEMPIER “,
Groupe d’Etudes des Semiconducteurs, UA 357, Université des Sciences ci Techniques dii Languedoc, P/ace E. Batai//on, F-34060 Montpellier Cedex, France
Metalorganic vapor phase epitaxy was used to grow high quality ZnSe. Two procedures were employed involving growth both at 300 and 500°C.To achieve epitaxy of ZnSe at temperatures as low as 300°Cfrom alkyls, it was necessary to use a special double zone reactor. Reflectivity spectra show the lattice deformation due to mismatch for layers thinner than 1 ~tm. Photoconductivity responses related to the layer thickness are also reported.
I. Introduction Zinc selenide has a large direct band gap corresponding to the blue part of the visible spectrum (EG = 2.7 eV at room temperature) and is extensively investigated in view of its application to optoelectronic devices. In order to obtain high quality materials, and afterwards high performance p—n junction devices, there has been considerable interest in developing the techniques of molecular beam epitaxy (MBE) and metalorganic vapor phase epitaxy (MOVPE) for growing ZnSe films. In these epitaxial techniques gallium arsenide has been mostly used as substrate material. However, the lattice mismatch of 0.27% and the thermal expansion coefficient difference of about 33% between ZnSe and GaAs induce lattice distortions which have a significant influence on the optical properties of the heteroepitaxial ZnSe layers. The effect of the lattice mismatch on the optical properties of the epitaxial ZnSe films grown on GaAs substrates by MBE, atomic layer epitaxy and MOVPE have been previously investigated by reflectivity [1,2] and/or photoluminescence [1,3,4] photoreflectivity, and piezomodulation [5]. Coherent growth is found for
*
ASM France, 74 Route de St. Georges-d’Orques, F-34990 Juvignac, France.
0022-0248/90/$03.50 © 1990
—
ZnSe films with a thickness less than 0.15 /.Lm and is accommodated by a two-dimensional contraction in the ZnSe epilayer. For thicker films, misfit dislocations are generated and the strain is progressively reduced. After about 1 ~tm of growth, the lattice parameter of the ZnSe matches the bulk material, and the strain is fully relieved. For films thicker than 1 ~tm, the ZnSe epilayer suffers two dimensional tensile stress, due to the difference in the differential thermal contraction between the ZnSe epilayer and the GaAs as the sample is cooled [1,2]. In this paper, the effects of lattice deformation due to the lattice misfit are investigated by means of a reflectivity study on low pressure MOVPE ZnSe/GaAs layers. Many growth conditions and ZnSe film thicknesses were investigated. The influence of the heteroepitaxial layer thickness on the photoconductivity response was examined.
2. Crystal growth In recent years, many workers have developed ZnSe using the MOVPE technique. Two kinds of source combination were usually used as initial reactants. When zinc alkyls and H2Se were used as source materials, the large reactivity between the components permits the use of very low growth
Elsevier Science Publishers B.V. (North-Holland)
LI
R.L Aulo,nbard et a!.
/ MO VPE of high quality
ZnSe
205
Table 1 Experimental conditions for MOVPE growth of ZnSe Sample
Growth temperature T (°C)
Reactants
Flow rates through reactants 3/min) (cm DMZn DESe H 2Se
Gas phase ratio VI/Il
Thickness (tim)
Experimental measurements
1 2 3 4 5 6 7
300 300 500 500 500 500 320
DMZn+DESe DMZn+DESe DMZn+DESe DMZn+DESe DMZn+DESe DMZn + DESe DMZn+H2Se
6.6 6.6 2.2 2.2 2.2 2.2 2
5 5 5 5 5 5 5
0.14 0.15 0.19 0.67 0.78 0.70 2.38
Reflectivity Reflectivity Reflectivity Reflectivity Reflectivity Photoconductivity Photoconductivity
160 160 54 54 54 54 —
temperatures (-.- 300°C),but limits the uniformity of growth. When zinc and selenide alkyls were used as source materials, the prereactions were limited and uniform crystals were obtained easier. However, temperatures of almost 500°C were needed, reflecting the thermal stability of the selenium alkyls. In order to obtain good homogeneous samples using only alkyls as source materials at temperatures as low as 300°C, the double zone reactor MOVPE technique described previously [6] was also used. The studied samples are listed in table 1 in which growth parameters are reported. The MOVPE equipment employed is an ASM France OMR 12. The substrates were Undoped semi-insulating (100) GaAs wafers. The starting metallorganics were dimethyizinc (DMZn) and diethylselenium (DESe) (supplied by SMI, Marseille, France). H2Se was employed as selenium source when the combination hydride— organometallic was used. The obtained layers were monocrystalline. The thickness of the ZnSe layers were determined using interferometric measurements
— — — — — —
18
split twofold degenerate T’7 state lying an energy z10 below F8. For the case of internal biaxial stress parallel to the [100] and [010] directions, the hydrostatic component of the stress shifts the center of gravity of F8 and F7 states relative to the bottom of the lowest conduction band. The tetragonal distortion splits the fourfold multiplet into a twofold-degenerate m = ±~ and a twofold degenerate m = ±~ state. The calculated shifts with respect to its zero stress value for intraband transition associated with F6 and I’8 band extrema are given, for example, in refs. [1,5].
____________________
0 157.
I
I
I
I
3. Reflectivity
Reflectivity measurements were performed on epilayers 1 to 5 of table 1 using a standard set-up at T= 1.8 K or 4.2 K. Light from the tungsten lamp was focused perpendicularly to the epilayer surface. For a zinc-blende type material, the valence bands at k = 0 consist of a fourfold-degenerate F8 valence band maximum and a spin—orbit
2.775
2.800
2.825
ENERGY leVi . . Fig. 1. Reflectivity spectrum of a ZnSe/GaAs epilayer (0.15 tim) at T = 4.2 K and the numerically calculated derivative curve.
206
R.L. Aulombard et al. / MO VPE of high quality ZnSe
Using the values of isotropic and shear deformation potential constants given in ref. [7], we obtain the following results: —1.668 (eV),
(1)
~E2= —6.952~(eV),
(2)
z~=E2—E1=5.284 (eV),
(3)
=
~,
~,
~,
—
—
L~
=
E1
—
E0,
—
LIE2
________________________
w 10
where is the magnitude of the biaxial strain. Fig. 1 shows the reflectivity spectrum of a 0.15 ~tm thick ZnSe (see table 1). The spectrum is of a quality comparable to the best MBE-grown films described in the literature, even for growth at 300 °C. It is characterized by two main reflection features. In order to determine more easily the transition energy, we have numencally calculated the derivative curve of the reflectivity spectrum. Following Yao et al. [1] and Lee et a!. [5], we identify the stronger feature at 2.8004 eV as the excitomc transition associated with the heavy hole valence band ±~), whereas the weaker feature at 2.8106 eV is attributed to the light hole valence band I ±~). Confirmation of this interpretation follows from the fact that the spectrum clearly shows that the feature associated with I ±~) state is about three times stronger than the one at the higher energy position [8], and these two features are observed for the thinner films of table 1 for temperatures up to 200 K [9]. Based on these observations, the feature at the higher energy cannot be attributed to the n = 2 free exciton, as has already been discussed in ref. [5]. Fig. 2 shows the shifts of heavy hole valence band L~E~and light hole valence band L~E2 with respect to the stress-free bulk crystal. In order to determine L’oE1 and z.X E2 experimentally, an evaluation of the free exciton E0 of bulk ZnSe is obtained by using eqs. (1), (2) and (3), and E0 E1 z~ E~,E0 = E2 i.\ E2. The deduced value E0 obtained from both excitonic transitions for the five studied epilayers is E0 = 2.796 eV, in good agreement with values obtained from reflectivity measurements at low temperature on bulk ZnSe [10]. The shifts of the heavy hole and light hole valence bands are given by: —
20
=
E2
—
E0.
~
5
0
________________________ 0.00
0.10
0.20
0.30
STRAIN El 1%) Fig. 2. Data points are shifts ~ E~+ ÷~ and ~ E2(~)for the heavy hole valence band and light hole valence band, respectively, as a function of strain at T = 4.2 K for samples 5, 4, 3, 1 and 2 as the strain c increases. Solid lines represent the variations given by eqs. (3) and (4).
The elastic strain corresponding to a given thickness is obtained from experimental values of L~ and eq. (3). For thinner films, this calculation yields an elastic strain smaller than the ZnSe/GaAs misfit strain (~= 0.27%). The data for 300 and 500°C grown films follow the predicted dependence of the energy transition on strain given by eqs. (1) and (2) quite well. 4.
Photoconductivity
Photoconductivity spectra were obtained at 300 K. Samples were illuminated by the chopped output light from the monochromator. The chopper frequency was about 60 Hz. The wavelength range investigated was 4000—8000 A. In fig. 3 spectral photoresponses are reported. For sample 7, the photoconductivity increases from about 2.5 eV up to a maximum value corresponding to the gap energy value 2.6 eV. Then the photoconductivity slowly decreases to zero at 3.8 eV. This behaviour is analogous to the usual one in the Il—VI cornpounds. The decrease of the photoconductivity encountered in the bulk resulting from the above band gap results from recombination near the surface. The rather surprising lack of GaAs substrate effect on the photoconductivity response has not yet been explained. For sample 6 a large
R.L Au!ombard etal.
a
/ MO VPE of high quality ZnSe
207
source materials at growth temperatures of both 300 and 500°C. Extensive characterization of reflectivity properties shows that the distortion due to the lattice misfit between ZnSe and the GaAs substrate induces the displacement and the splitting of the excitonic lines associated with the heavy hole and light hole valence bands.
b
.5 I-
Li
z D
Li 0 0
Acknowledgements
0~
1.0
1.5
2.0
2.5
3.0
3.5
ENERGY leVi
The present work was supported by funds from the “Conseil Regional Languedoc—Roussillon” under a scientific program on materials (PREMAT).
Fig. 3. Photoconductivity spectra at room temperature for epilayers of 0.7 jim (a) and 2.38 jim (b) thickness.
References plateau-like spectrum is observed in the range 1.35—2.7 eV. Elsewhere photoconductivity is weak or vanishes. These data can be explained by taking into account the GaAs substrate as indicated ~ ref. [11]. The lower part of the spectrum (E> 2 eV) where the ZnSe layer is transparent corresponds to the absorption of the light in the substrate. Photocarriers are collected in the conducting ZnSe layer. When the energy increases up to the band gap, photoconductivity slowly decreases. For higher energies a sharp decrease is initially observed and is then followed by another monotonic one up to 3.3 eV. The ZnSe layer overcomes the effects of the surface recombination of the GaAs substrate, so that important photoconductivity is observed near the band gap of ZnSe. Better control of the layer thickness ought to allow optimization of the system for the manufacture of a wide range of detectors.
5. Conclusion Growth of high quality ZnSe/GaAs films has been carried out by low pressure metalorga.nic vapor phase epitaxy using dimethy]zinc diethylselenium or dimethyizinc-hydrogen selenide as
[1] T. Yao, Y. Okada, S. Matsui, K. Ishida and I. Fujimoto, J. Crystal Growth 81 (1987) 518. [2] T. Matsumoto, T. lijina and T. Ishida, Japan. J. Appi. Phys. 27 (1988) L892. [3] J.E. Potts, H. Cheng, S. Mohaprata and T.L. Smith, J. Appl. Phys. 61 (1987) 333. [4] R.L. Gunshor, L.A. Kolodziejski, M.R. Mellock, M. Vaziri, C. Choi and N. Otsuka, Appi. Phys. Letters 50 (1987) 200. [5] Y.R. Lee, A.K. Ramdas, L.A. Kolodziejski and R.L. Gunshor, Phys. Rev. B38 (1988) 13143. [6] 0. Briot, R. Delinas, N. Tempier, R. Sauvezon and R.L. Aulombard, J. Crystal Growth 98 (1989) 857. [7] We have used the deformation-potential constants a and b ofZnSe given by A. Blacha, H. Presting and M. Cardona, Phys. Status Solidi (b) 126 (1984) 11 and the elastic stiffness constants C 11 and C12 of ZnSe given by L.C. Hodgins and J.C. Irwin, Phys. Status Solidi (a) 28 (1975) 647. [8] L.D. Laude, M. Cardona and F.H. Pollak, Phys. Rev. Bi (1970) 1436. [9] D. Coquillat, F. Hamdani, J.P. Lascaray, 0. Briot, N. Tempier and R.L. Aulombard, to be published. [10] M. Aven and J.S. Prener, Eds., Physics and Chemistry of Il—VI Compounds (North-Holland, Amsterdam, 1967); G.E. Hite, D.T.F. Marple, M. Aven and B. Segall, Phys. Rev. 156 (1967) 850; D.W. Langer, R.N. Eurvema, K. Era and T. Koda, Phys. Rev. B2 (1970) 4005. [11] H.J. Hovel, in: Semiconductors and Semimetals, Vol. 11, Eds. R.K. Willardson and AC. Beer (Academic Press, New York, 1975) ch. 2.
Journal of Crystal Growth 101 (1990) 204—207 North-Holland
MOVPE OF HIGH QUALITY ZnSe: ROLE OF MISMATCH ON REFLECTIVITY ANI~PHOTOCONDUCTIVITY R.L. AULOMBARD, M. AVEROUS, 0. BRIOT J. CALAS, D. COQUILLAT, F. HAMDANI, J.P. LASCARAY, N. MOULIN and N. TEMPIER “,
Groupe d’Etudes des Semiconducteurs, UA 357, Université des Sciences ci Techniques dii Languedoc, P/ace E. Batai//on, F-34060 Montpellier Cedex, France
Metalorganic vapor phase epitaxy was used to grow high quality ZnSe. Two procedures were employed involving growth both at 300 and 500°C.To achieve epitaxy of ZnSe at temperatures as low as 300°Cfrom alkyls, it was necessary to use a special double zone reactor. Reflectivity spectra show the lattice deformation due to mismatch for layers thinner than 1 ~tm. Photoconductivity responses related to the layer thickness are also reported.
I. Introduction Zinc selenide has a large direct band gap corresponding to the blue part of the visible spectrum (EG = 2.7 eV at room temperature) and is extensively investigated in view of its application to optoelectronic devices. In order to obtain high quality materials, and afterwards high performance p—n junction devices, there has been considerable interest in developing the techniques of molecular beam epitaxy (MBE) and metalorganic vapor phase epitaxy (MOVPE) for growing ZnSe films. In these epitaxial techniques gallium arsenide has been mostly used as substrate material. However, the lattice mismatch of 0.27% and the thermal expansion coefficient difference of about 33% between ZnSe and GaAs induce lattice distortions which have a significant influence on the optical properties of the heteroepitaxial ZnSe layers. The effect of the lattice mismatch on the optical properties of the epitaxial ZnSe films grown on GaAs substrates by MBE, atomic layer epitaxy and MOVPE have been previously investigated by reflectivity [1,2] and/or photoluminescence [1,3,4] photoreflectivity, and piezomodulation [5]. Coherent growth is found for
*
ASM France, 74 Route de St. Georges-d’Orques, F-34990 Juvignac, France.
0022-0248/90/$03.50 © 1990
—
ZnSe films with a thickness less than 0.15 /.Lm and is accommodated by a two-dimensional contraction in the ZnSe epilayer. For thicker films, misfit dislocations are generated and the strain is progressively reduced. After about 1 ~tm of growth, the lattice parameter of the ZnSe matches the bulk material, and the strain is fully relieved. For films thicker than 1 ~tm, the ZnSe epilayer suffers two dimensional tensile stress, due to the difference in the differential thermal contraction between the ZnSe epilayer and the GaAs as the sample is cooled [1,2]. In this paper, the effects of lattice deformation due to the lattice misfit are investigated by means of a reflectivity study on low pressure MOVPE ZnSe/GaAs layers. Many growth conditions and ZnSe film thicknesses were investigated. The influence of the heteroepitaxial layer thickness on the photoconductivity response was examined.
2. Crystal growth In recent years, many workers have developed ZnSe using the MOVPE technique. Two kinds of source combination were usually used as initial reactants. When zinc alkyls and H2Se were used as source materials, the large reactivity between the components permits the use of very low growth
Elsevier Science Publishers B.V. (North-Holland)
LI
R.L Aulo,nbard et a!.
/ MO VPE of high quality
ZnSe
205
Table 1 Experimental conditions for MOVPE growth of ZnSe Sample
Growth temperature T (°C)
Reactants
Flow rates through reactants 3/min) (cm DMZn DESe H 2Se
Gas phase ratio VI/Il
Thickness (tim)
Experimental measurements
1 2 3 4 5 6 7
300 300 500 500 500 500 320
DMZn+DESe DMZn+DESe DMZn+DESe DMZn+DESe DMZn+DESe DMZn + DESe DMZn+H2Se
6.6 6.6 2.2 2.2 2.2 2.2 2
5 5 5 5 5 5 5
0.14 0.15 0.19 0.67 0.78 0.70 2.38
Reflectivity Reflectivity Reflectivity Reflectivity Reflectivity Photoconductivity Photoconductivity
160 160 54 54 54 54 —
temperatures (-.- 300°C),but limits the uniformity of growth. When zinc and selenide alkyls were used as source materials, the prereactions were limited and uniform crystals were obtained easier. However, temperatures of almost 500°C were needed, reflecting the thermal stability of the selenium alkyls. In order to obtain good homogeneous samples using only alkyls as source materials at temperatures as low as 300°C, the double zone reactor MOVPE technique described previously [6] was also used. The studied samples are listed in table 1 in which growth parameters are reported. The MOVPE equipment employed is an ASM France OMR 12. The substrates were Undoped semi-insulating (100) GaAs wafers. The starting metallorganics were dimethyizinc (DMZn) and diethylselenium (DESe) (supplied by SMI, Marseille, France). H2Se was employed as selenium source when the combination hydride— organometallic was used. The obtained layers were monocrystalline. The thickness of the ZnSe layers were determined using interferometric measurements
— — — — — —
18
split twofold degenerate T’7 state lying an energy z10 below F8. For the case of internal biaxial stress parallel to the [100] and [010] directions, the hydrostatic component of the stress shifts the center of gravity of F8 and F7 states relative to the bottom of the lowest conduction band. The tetragonal distortion splits the fourfold multiplet into a twofold-degenerate m = ±~ and a twofold degenerate m = ±~ state. The calculated shifts with respect to its zero stress value for intraband transition associated with F6 and I’8 band extrema are given, for example, in refs. [1,5].
____________________
0 157.
I
I
I
I
3. Reflectivity
Reflectivity measurements were performed on epilayers 1 to 5 of table 1 using a standard set-up at T= 1.8 K or 4.2 K. Light from the tungsten lamp was focused perpendicularly to the epilayer surface. For a zinc-blende type material, the valence bands at k = 0 consist of a fourfold-degenerate F8 valence band maximum and a spin—orbit
2.775
2.800
2.825
ENERGY leVi . . Fig. 1. Reflectivity spectrum of a ZnSe/GaAs epilayer (0.15 tim) at T = 4.2 K and the numerically calculated derivative curve.
206
R.L. Aulombard et al. / MO VPE of high quality ZnSe
Using the values of isotropic and shear deformation potential constants given in ref. [7], we obtain the following results: —1.668 (eV),
(1)
~E2= —6.952~(eV),
(2)
z~=E2—E1=5.284 (eV),
(3)
=
~,
~,
~,
—
—
L~
=
E1
—
E0,
—
LIE2
________________________
w 10
where is the magnitude of the biaxial strain. Fig. 1 shows the reflectivity spectrum of a 0.15 ~tm thick ZnSe (see table 1). The spectrum is of a quality comparable to the best MBE-grown films described in the literature, even for growth at 300 °C. It is characterized by two main reflection features. In order to determine more easily the transition energy, we have numencally calculated the derivative curve of the reflectivity spectrum. Following Yao et al. [1] and Lee et a!. [5], we identify the stronger feature at 2.8004 eV as the excitomc transition associated with the heavy hole valence band ±~), whereas the weaker feature at 2.8106 eV is attributed to the light hole valence band I ±~). Confirmation of this interpretation follows from the fact that the spectrum clearly shows that the feature associated with I ±~) state is about three times stronger than the one at the higher energy position [8], and these two features are observed for the thinner films of table 1 for temperatures up to 200 K [9]. Based on these observations, the feature at the higher energy cannot be attributed to the n = 2 free exciton, as has already been discussed in ref. [5]. Fig. 2 shows the shifts of heavy hole valence band L~E~and light hole valence band L~E2 with respect to the stress-free bulk crystal. In order to determine L’oE1 and z.X E2 experimentally, an evaluation of the free exciton E0 of bulk ZnSe is obtained by using eqs. (1), (2) and (3), and E0 E1 z~ E~,E0 = E2 i.\ E2. The deduced value E0 obtained from both excitonic transitions for the five studied epilayers is E0 = 2.796 eV, in good agreement with values obtained from reflectivity measurements at low temperature on bulk ZnSe [10]. The shifts of the heavy hole and light hole valence bands are given by: —
20
=
E2
—
E0.
~
5
0
________________________ 0.00
0.10
0.20
0.30
STRAIN El 1%) Fig. 2. Data points are shifts ~ E~+ ÷~ and ~ E2(~)for the heavy hole valence band and light hole valence band, respectively, as a function of strain at T = 4.2 K for samples 5, 4, 3, 1 and 2 as the strain c increases. Solid lines represent the variations given by eqs. (3) and (4).
The elastic strain corresponding to a given thickness is obtained from experimental values of L~ and eq. (3). For thinner films, this calculation yields an elastic strain smaller than the ZnSe/GaAs misfit strain (~= 0.27%). The data for 300 and 500°C grown films follow the predicted dependence of the energy transition on strain given by eqs. (1) and (2) quite well. 4.
Photoconductivity
Photoconductivity spectra were obtained at 300 K. Samples were illuminated by the chopped output light from the monochromator. The chopper frequency was about 60 Hz. The wavelength range investigated was 4000—8000 A. In fig. 3 spectral photoresponses are reported. For sample 7, the photoconductivity increases from about 2.5 eV up to a maximum value corresponding to the gap energy value 2.6 eV. Then the photoconductivity slowly decreases to zero at 3.8 eV. This behaviour is analogous to the usual one in the Il—VI cornpounds. The decrease of the photoconductivity encountered in the bulk resulting from the above band gap results from recombination near the surface. The rather surprising lack of GaAs substrate effect on the photoconductivity response has not yet been explained. For sample 6 a large
R.L Au!ombard etal.
a
/ MO VPE of high quality ZnSe
207
source materials at growth temperatures of both 300 and 500°C. Extensive characterization of reflectivity properties shows that the distortion due to the lattice misfit between ZnSe and the GaAs substrate induces the displacement and the splitting of the excitonic lines associated with the heavy hole and light hole valence bands.
b
.5 I-
Li
z D
Li 0 0
Acknowledgements
0~
1.0
1.5
2.0
2.5
3.0
3.5
ENERGY leVi
The present work was supported by funds from the “Conseil Regional Languedoc—Roussillon” under a scientific program on materials (PREMAT).
Fig. 3. Photoconductivity spectra at room temperature for epilayers of 0.7 jim (a) and 2.38 jim (b) thickness.
References plateau-like spectrum is observed in the range 1.35—2.7 eV. Elsewhere photoconductivity is weak or vanishes. These data can be explained by taking into account the GaAs substrate as indicated ~ ref. [11]. The lower part of the spectrum (E> 2 eV) where the ZnSe layer is transparent corresponds to the absorption of the light in the substrate. Photocarriers are collected in the conducting ZnSe layer. When the energy increases up to the band gap, photoconductivity slowly decreases. For higher energies a sharp decrease is initially observed and is then followed by another monotonic one up to 3.3 eV. The ZnSe layer overcomes the effects of the surface recombination of the GaAs substrate, so that important photoconductivity is observed near the band gap of ZnSe. Better control of the layer thickness ought to allow optimization of the system for the manufacture of a wide range of detectors.
5. Conclusion Growth of high quality ZnSe/GaAs films has been carried out by low pressure metalorga.nic vapor phase epitaxy using dimethy]zinc diethylselenium or dimethyizinc-hydrogen selenide as
[1] T. Yao, Y. Okada, S. Matsui, K. Ishida and I. Fujimoto, J. Crystal Growth 81 (1987) 518. [2] T. Matsumoto, T. lijina and T. Ishida, Japan. J. Appi. Phys. 27 (1988) L892. [3] J.E. Potts, H. Cheng, S. Mohaprata and T.L. Smith, J. Appl. Phys. 61 (1987) 333. [4] R.L. Gunshor, L.A. Kolodziejski, M.R. Mellock, M. Vaziri, C. Choi and N. Otsuka, Appi. Phys. Letters 50 (1987) 200. [5] Y.R. Lee, A.K. Ramdas, L.A. Kolodziejski and R.L. Gunshor, Phys. Rev. B38 (1988) 13143. [6] 0. Briot, R. Delinas, N. Tempier, R. Sauvezon and R.L. Aulombard, J. Crystal Growth 98 (1989) 857. [7] We have used the deformation-potential constants a and b ofZnSe given by A. Blacha, H. Presting and M. Cardona, Phys. Status Solidi (b) 126 (1984) 11 and the elastic stiffness constants C 11 and C12 of ZnSe given by L.C. Hodgins and J.C. Irwin, Phys. Status Solidi (a) 28 (1975) 647. [8] L.D. Laude, M. Cardona and F.H. Pollak, Phys. Rev. Bi (1970) 1436. [9] D. Coquillat, F. Hamdani, J.P. Lascaray, 0. Briot, N. Tempier and R.L. Aulombard, to be published. [10] M. Aven and J.S. Prener, Eds., Physics and Chemistry of Il—VI Compounds (North-Holland, Amsterdam, 1967); G.E. Hite, D.T.F. Marple, M. Aven and B. Segall, Phys. Rev. 156 (1967) 850; D.W. Langer, R.N. Eurvema, K. Era and T. Koda, Phys. Rev. B2 (1970) 4005. [11] H.J. Hovel, in: Semiconductors and Semimetals, Vol. 11, Eds. R.K. Willardson and AC. Beer (Academic Press, New York, 1975) ch. 2.