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SiGe type-II quantum wells on Si(100)
Solid-State Electronics Vol. 37. Nos 4-6,
pp. 933-936. 1994 Copyright © 1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0038-1101/94 $6.00+0.00
~ ) Pergamon
BAND-EDGE PHOTOLUMINESCENCE OF SiGe/STRAINED-Si/SiGe TYPE-II QUANTUM WELLS ON Si(100) D. K. NAYAK,N. USAMI,H. SUNAMURA,S. FUKATSUand Y. SH1RAKI Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, 4-6-I Komaba, Meguro-ku, Tokyo 153, Japan Abstract--High-quality completely relaxed SiGe buffer layer is grown on Si(100) by gas source molecular beam epitaxy. Pseudomorphic Si layer is grown on this relaxed SiGe buffer to form SiGe/strained-Si/SiGe type-II (staggered) quantum wells. Intense band-edge photoluminescence is observed from these quantum wells for the first time. Quantum confinement effect in SiGe/strained-Si/SiGe type-II quantum wells is demonstrated from the systematic shift of photoluminescence energy peaks with the width of the quantum well. Transitions from the strained-Si quantum well are identified as radiative recombination of excitons, which are confined into the quantum well.
Epitaxial Sij_xGex layers on Si are being studied extensively for potential use in Si-based optoelectronic device technology. In particular, strained-layer (Si),,/(Ge)n superlattices (SLS) are important for possible efficient light emitting applications in the near-infrared region. (Si)J(Ge)n SLS show enhanced photoluminescence (PL) properties compared to indirect bandgap Ge and Si. Also, the possibility of artificially producing quasidirect bandgap in SLS has generated much interest in (Si)m/(Ge)n SLS[I-12]. In such SLS, Si layer must be under lateral tensile strain, which is produced by growing alternating layers of pure Si and pure Ge on a relaxed SiGe buffer layer. In this case, Si and Ge layers are strained, and radiative interband recombination occurs between minibands of conduction and valence bands. Earlier report on the photoluminescence study of (Si),,/(Ge L SLS was controversial because of the poor quality of SiGe buffer[9,10]. With the recent development in SiGe buffer layer technology, however, enhanced luminescence from (Si)~,/(Ge)n SLS grown on graded SiGe buffer has been obtained[12]. The luminescence is described in terms of recombination of excitons localized at random potential fluctuations in SLS. However, no study on the properties of relaxedSiGe/strained-Si/relaxed-SiGe quantum well, which forms type-II (staggered) heterostructure and acts as the basic block for many optical devices, has been reported. In this letter, we report for the first time a systematic study of band-edge photoluminescence characteristics of SiGe/strained-Si/SiGe quantum wells, which are grown on a thick relaxed Si0.82Ge0.~8 buffer layer on Si(100). Quantum confinement effects and photoluminescence properties of excitons in this quantum well are presented. Basic requirement for the growth of strained-Si layer is to obtain a good quality relaxed SiGe buffer layer on Si substrates. Recently, it has been shown ssE 37~,--AA
933
that a high-quality buffer layer can be grown by grading Ge concentration in the buffer layer[13-15]. In this study, we use step-graded buffer layer, which is grown by gas source MBE (Daido Sanso VCE$2020) at 800°C[16]. The starting material consists of Y', p-type, 5-10f~-cm, Si(100) wafer, 3000/~ Si buffer, 3.8/~m step-graded SiGe buffer (0 to 18°/. Ge in 9 steps), and 2.5/am Si0.82Ge0.~8 buffer cap layer. Five quantum wells with equal well width were grown on this buffer layer at 700°C. The barrier between adjacent wells was 350/~ Si0.82Ge0.J8, which eliminates any coupling between the quantum wells. All epitaxial layers were undoped. PL spectra were recorded using a standard lock-in technique. A multi-line argon laser was used for excitation. Signal was monochromatized using a l-m dispersive monochromator, and was detected by a liquid-nitrogen cooled Ge photodetector. Temperature control was achieved by a closed-cycle refrigerator. Figure l(a) shows PL spectra from a thick (6.3 pm) step-graded relaxed Ge0.~sSi0.82 buffer layer at 4.2 K. A peak at 1.093 eV, denoted as SUB x°, is due to TO assisted excitonic recombination in Si substrate. A sharp peak at 1.072 eV corresponds to NP transition from the relaxed buffer layer. Transitions from buffer (barrier) layer are denoted by "B". Full-width at half-maximum of this peak is 4 meV at 4.2 K, which shows that the top region of the buffer is of good quality. Phonon-assisted momentum-conserving transverse-acoustical (TA) and transverse-optical (TO) replicas are found at lower energies, TA at 16meV, TO(Ge-Ge) at 36meV, TO(Ge-Si) at 51 meV, and TO(Si-Si) at 58 meV. Locations of these energy peaks agree well with PL measurement results on SiGe buffer layers by others[17]. Complete relaxation of the buffer layer was confirmed by X-ray diffraction measurements. PL peaks at 0.880, 0.906
934
D.K. NAYAKet al.
and 0.923 eV can be attributed to dislocation- and point defect-related transitions D2, D3 and D4[18,19]. The origin of these peaks (D2-D4) is not clear at this point. This is because these peaks (D2-D4) in PL spectra could also be explained by the presence of a very broad peak (0.8--0.95eV) combined with absorption "dips" due to quartz glass and air. "Quartz-dip" due to the absorption in quartz glass at about 0.9 eV is shown in Fig. l(b). Dislocation-related transition at 0.81 eV, D1, appears only for thin buffer layers, but it disappears as the buffer layer thickness exceeds 3 pm. These dislocation-related PL, D l - D 4 , have been also reported for fully relaxed SiGe buffer layers grown by solid source MBE[15,19]. Five quantum wells with equal well width were grown on the above buffer layer at a lower temperature (700°C) in order to avoid thermal relaxation of strain and Ge/Si interdiffusion in the quantum well. PL spectra from the multiple quantum wells are shown in Fig. l(b). All transitions from the strainedSi quantum well are denoted by "X". Well and barrier widths were l0 and 350 A, respectively. Figure l(b) looks identical to Fig. l(a) except that two new peaks (as a pair) appear at 0.985 and 1.043 eV in 1
I
B Ne
4.2K
en To
B --] Ge
ISi-.~
[-,
D4
Z to D2
I
,d
700
800
900
PHOTON i
1
ENERGY i
1000
1100
(mcV) i
4.2K
F-,
"Quartz-dip"
Z to
(b) t.. 700
800
900
PHOTON
ENERGY
1000
11 O0
(meV)
Fig. 1. (a) PL spectra at 4.2 K from a fully relaxed thick (6.3#m) step-graded SiGe buffer layer. D2, D3 and D4 correspond to defect-related transitions. Buffer layer is grown at 800C by gas-source MBE: (b) PL spectra at 4.2 K from 10 A strained-Si quantum wells grown on this buffer layer at 700C.
A(4) CB
t
A(6)
A(2)
GeSi
Si
GeSi
c
~'i.hh
VB lh i i
i
hh Fig. 2. Schematic type-II band alignment at relaxedSiGe/strained-Si/relaxed-SiGeheterointerfaces.
Fig. l(b). We assign the peak at 0.985 eV to be TO phonon-assisted band-edge transition of confined excitons in strained-Si quantum well. As shown in Fig. 2, type-II band alignment results at the strainedSi/relaxed-SiGe-buffer heterointerface[20]. Therefore, TO-assisted excitonic transition occurs between the confined conduction band state (lowest lying in energy) of strained-Si quantum well and the top of valence band of SiGe buffer layer (Fig. 2). The peak at 1.043eV in Fig. l(b) can be assigned to NP transition from the quantum wells, and always appears as a pair with the TO-assisted transition. These two peaks were separated by 58 meV, which corresponds to TO phonon energy of Si-Si bond. In case of this narrow strained-Si quantum well, the excitonic wave function penetrates considerably into SiGe barriers, where NP transition is allowed due to the randomness of alloying, resulting in NP transition from the confined conduction band state of strainedSi layer (Fig. 2). In order to demonstrate quantum confinement effect in the SiGe/strained-Si/SiGe quantum well, samples with different quantum well width were prepared. In these samples, the buffer layer structure was kept exactly the same. Well width dependent PL peak energy shifts for excitonic phonon-assisted as well as NP transitions are shown in Fig. 3. Figure 3(f) is PL spectrum from the buffer layer without any quantum well. As before, transitions from strained-Si quantum well are marked by "X". For a given well width, the high-energy peak ("X") is NP free excitonic transition from the quantum wells, whereas the low-energy peak is its TO replica. Both these peaks move to lower energy as the quantum well width is increased, Fig. 3(a) and (b). As the well width is increased further, the relative intensity of NP peak becomes weaker with respect to its TO replica, Fig. 3(c), (d) and (e). This is because the penetration
935
SiGe/strained-Si/SiGe type-II quantum wells
IZ ,-4 a_
700
800
900
1000
1100
P H O T O N E N E R O Y (meV)
Fig. 3. PL spectra at 4.2 K from five quantum well structures, which were grown on the buffer layer described in Fig. 1. (a) 10/~, (b) 13fl~, (c) 16J~, (d) 19/~, (e) 21/~, and (f) no quantum well.
of excitonic wave function into SiGe barriers diminishes with increasing well width, and therefore, the N P transition probability becomes smaller. TO-assisted transition for the 10/~-well appears at 0.986 eV, and moves down to 0.947 eV for the 21/~,well. This shift of 39 meV can be used to estimate the conduction band discontinuity at the relaxedSi0.8:Ge0~8/strained-Si heterointerface. Using an envelope function calculation, this is found to be about 86 meV. Temperature dependence of excitonic transitions from strained-Si quantum wells was found to be different from that of SiGe buffer (Fig. 4). With increasing temperature, the N P transition intensity from the buffer layer, B r~P, diminishes rapidly. At 29 K, the N P peak almost disappears, while the transition from the quantum well, X T°, remains unchanged compared to its 16 K value. X r° can be observed until 48 K. This shows that free excitons are effectively confined into the quantum well and that strained-Si layer may have less nonradiative pathway for carrier recombination compared to its SiGe buffer counterpart. In summary, intense band-edge photoluminescence for SiGe/strained-Si/SiGe type-II (staggered) quantum wells is reported for the first time. Quantum confinement effect in this quantum well is clearly demonstrated from the systematic shift of PL energy peaks with the width of the quantum well. Transitions from the strained-Si quantum well are identified as radiative recombination of excitons, which are confined in the quantum well. Acknowledgements--We would like to thank H. Oku, Y. Ohmori, T. Ohnishi and K. Okumura of Daido-Hoxan for their technical help in using gas source MBE. We also like to thank S. Ohtake of RCAST for technical assistance. REFERENCES
LO
.-I ca-
700
800
900
1000
1100
P H O T O N E N E R G Y (meV)
Fig. 4. Temperature dependence of PL spectra at 16, 20, 29, 41 and 48 K.
1. R. People and S. A. Jackson, Phys. Ret,. B 36, 1310 (1987). 2. M. S. Hybertsen and M. Schluter, Phys. Rez,. B 36, 9683 (1987). 3. T. P. Pearsall, J. Bevk, L. C. Feldman, J. M. Bonar, J. P. Mannaerts and A. Ourmazd, Phys. Rez,. Lett. 58, 729 (1987). 4. S. Froyen, D. M. Wood and A. Zunger, Phys. Rez,. B 37, 6893 (1988). 5. S. Satpathy, R. M. Martin and C. G. Van de Walle, Phys. Rez,. B 38, 13237 (1988). 6. E. A. Montie, G. F. A. van de Walle, D. J. Gravesteijn, A. A. van Gorkum and C. W. T. Bulle-Lieuwma, Appl. Phys. Lett. .56, 340 (1990). 7. H. Okumura, K. Miki, S. Misawa, K. Sakamoto, T. Sakamoto and S Yoshida Japan. J. appl. Phys. 28, L1893 (1989). 8. R. Zachai, K. Eberl, G. Abstreiter, E. Kasper and H. Kibbel, Phys. Rer. Lett. 64 1055 (1990). 9. U. Schmid, N. E. Christensen and M. Cardona, Phys. Ret,. Lett. 65, 2610 (1990). 10. R. Zachai, K. Eberl, G. Abstreiter, E. Kasper and H. Kibbel, Phys. Rev. Lett. 65, 2611 (1990). 11. J. Olajos, J. Engvall, H. G. Grimmeiss, U. Menczigar, G. Abstreiter, H. Kibbel, E. Kasper and H. Presting, Phys. Rez,. B 46, 12857 (1992).
936
D . K . NAVAK et al.
12. U. Menczigar, G. Abstreiter, J. Olajos, H. Grimmeiss, H. Kibbel, H. Presting, and E. Kasper, Phys. Ret'. B 47, 4099 (1993). 13. K. H. Jung, Y. M. Kim, and D. L. Kwong, Appl. Phys. Lett. $6, 1775 (1990). 14. F. K. LeGoues, B. S. Meyerson, and J. F. Morar, Phys. Ret,. Lett. 66, 2903 (1991). 15. E. A. Fitzgerald, Y.-H. Xie, M. L. Green, D. Brasen, A. R. Kortan, J. Michel, Y.-J. Mii and B. E. Weir, Appl. Phys. Left. 59, 811 (1991).
16. S. Fukatsu, H. Yoshida, A. Fujiwara, Y. Takahashi, Y. Shiraki and R. Ito, Appl. Phys. Lett. 61, 804 (1992). 17. J. Weber and M. 1. Alonso, Phys. Ret'. B 40, 5683 (1989). 18. R. Sauer, J. Weber, J. Stolz, E. R. Weber, K.-H. Kusters and H. Alexander, Appl. Phys. A 36, 1 (1985). 19. V. Higgs, E. C. Lightowlers. E. A. Fitzgerald, Y. H. Xie and P. J. Silverman, J. appL Phys. 73, 1952 (1993). 20. R. People, IEEE J. Quantum Electron. 22, 1696 (1986).
pp. 933-936. 1994 Copyright © 1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0038-1101/94 $6.00+0.00
~ ) Pergamon
BAND-EDGE PHOTOLUMINESCENCE OF SiGe/STRAINED-Si/SiGe TYPE-II QUANTUM WELLS ON Si(100) D. K. NAYAK,N. USAMI,H. SUNAMURA,S. FUKATSUand Y. SH1RAKI Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, 4-6-I Komaba, Meguro-ku, Tokyo 153, Japan Abstract--High-quality completely relaxed SiGe buffer layer is grown on Si(100) by gas source molecular beam epitaxy. Pseudomorphic Si layer is grown on this relaxed SiGe buffer to form SiGe/strained-Si/SiGe type-II (staggered) quantum wells. Intense band-edge photoluminescence is observed from these quantum wells for the first time. Quantum confinement effect in SiGe/strained-Si/SiGe type-II quantum wells is demonstrated from the systematic shift of photoluminescence energy peaks with the width of the quantum well. Transitions from the strained-Si quantum well are identified as radiative recombination of excitons, which are confined into the quantum well.
Epitaxial Sij_xGex layers on Si are being studied extensively for potential use in Si-based optoelectronic device technology. In particular, strained-layer (Si),,/(Ge)n superlattices (SLS) are important for possible efficient light emitting applications in the near-infrared region. (Si)J(Ge)n SLS show enhanced photoluminescence (PL) properties compared to indirect bandgap Ge and Si. Also, the possibility of artificially producing quasidirect bandgap in SLS has generated much interest in (Si)m/(Ge)n SLS[I-12]. In such SLS, Si layer must be under lateral tensile strain, which is produced by growing alternating layers of pure Si and pure Ge on a relaxed SiGe buffer layer. In this case, Si and Ge layers are strained, and radiative interband recombination occurs between minibands of conduction and valence bands. Earlier report on the photoluminescence study of (Si),,/(Ge L SLS was controversial because of the poor quality of SiGe buffer[9,10]. With the recent development in SiGe buffer layer technology, however, enhanced luminescence from (Si)~,/(Ge)n SLS grown on graded SiGe buffer has been obtained[12]. The luminescence is described in terms of recombination of excitons localized at random potential fluctuations in SLS. However, no study on the properties of relaxedSiGe/strained-Si/relaxed-SiGe quantum well, which forms type-II (staggered) heterostructure and acts as the basic block for many optical devices, has been reported. In this letter, we report for the first time a systematic study of band-edge photoluminescence characteristics of SiGe/strained-Si/SiGe quantum wells, which are grown on a thick relaxed Si0.82Ge0.~8 buffer layer on Si(100). Quantum confinement effects and photoluminescence properties of excitons in this quantum well are presented. Basic requirement for the growth of strained-Si layer is to obtain a good quality relaxed SiGe buffer layer on Si substrates. Recently, it has been shown ssE 37~,--AA
933
that a high-quality buffer layer can be grown by grading Ge concentration in the buffer layer[13-15]. In this study, we use step-graded buffer layer, which is grown by gas source MBE (Daido Sanso VCE$2020) at 800°C[16]. The starting material consists of Y', p-type, 5-10f~-cm, Si(100) wafer, 3000/~ Si buffer, 3.8/~m step-graded SiGe buffer (0 to 18°/. Ge in 9 steps), and 2.5/am Si0.82Ge0.~8 buffer cap layer. Five quantum wells with equal well width were grown on this buffer layer at 700°C. The barrier between adjacent wells was 350/~ Si0.82Ge0.J8, which eliminates any coupling between the quantum wells. All epitaxial layers were undoped. PL spectra were recorded using a standard lock-in technique. A multi-line argon laser was used for excitation. Signal was monochromatized using a l-m dispersive monochromator, and was detected by a liquid-nitrogen cooled Ge photodetector. Temperature control was achieved by a closed-cycle refrigerator. Figure l(a) shows PL spectra from a thick (6.3 pm) step-graded relaxed Ge0.~sSi0.82 buffer layer at 4.2 K. A peak at 1.093 eV, denoted as SUB x°, is due to TO assisted excitonic recombination in Si substrate. A sharp peak at 1.072 eV corresponds to NP transition from the relaxed buffer layer. Transitions from buffer (barrier) layer are denoted by "B". Full-width at half-maximum of this peak is 4 meV at 4.2 K, which shows that the top region of the buffer is of good quality. Phonon-assisted momentum-conserving transverse-acoustical (TA) and transverse-optical (TO) replicas are found at lower energies, TA at 16meV, TO(Ge-Ge) at 36meV, TO(Ge-Si) at 51 meV, and TO(Si-Si) at 58 meV. Locations of these energy peaks agree well with PL measurement results on SiGe buffer layers by others[17]. Complete relaxation of the buffer layer was confirmed by X-ray diffraction measurements. PL peaks at 0.880, 0.906
934
D.K. NAYAKet al.
and 0.923 eV can be attributed to dislocation- and point defect-related transitions D2, D3 and D4[18,19]. The origin of these peaks (D2-D4) is not clear at this point. This is because these peaks (D2-D4) in PL spectra could also be explained by the presence of a very broad peak (0.8--0.95eV) combined with absorption "dips" due to quartz glass and air. "Quartz-dip" due to the absorption in quartz glass at about 0.9 eV is shown in Fig. l(b). Dislocation-related transition at 0.81 eV, D1, appears only for thin buffer layers, but it disappears as the buffer layer thickness exceeds 3 pm. These dislocation-related PL, D l - D 4 , have been also reported for fully relaxed SiGe buffer layers grown by solid source MBE[15,19]. Five quantum wells with equal well width were grown on the above buffer layer at a lower temperature (700°C) in order to avoid thermal relaxation of strain and Ge/Si interdiffusion in the quantum well. PL spectra from the multiple quantum wells are shown in Fig. l(b). All transitions from the strainedSi quantum well are denoted by "X". Well and barrier widths were l0 and 350 A, respectively. Figure l(b) looks identical to Fig. l(a) except that two new peaks (as a pair) appear at 0.985 and 1.043 eV in 1
I
B Ne
4.2K
en To
B --] Ge
ISi-.~
[-,
D4
Z to D2
I
,d
700
800
900
PHOTON i
1
ENERGY i
1000
1100
(mcV) i
4.2K
F-,
"Quartz-dip"
Z to
(b) t.. 700
800
900
PHOTON
ENERGY
1000
11 O0
(meV)
Fig. 1. (a) PL spectra at 4.2 K from a fully relaxed thick (6.3#m) step-graded SiGe buffer layer. D2, D3 and D4 correspond to defect-related transitions. Buffer layer is grown at 800C by gas-source MBE: (b) PL spectra at 4.2 K from 10 A strained-Si quantum wells grown on this buffer layer at 700C.
A(4) CB
t
A(6)
A(2)
GeSi
Si
GeSi
c
~'i.hh
VB lh i i
i
hh Fig. 2. Schematic type-II band alignment at relaxedSiGe/strained-Si/relaxed-SiGeheterointerfaces.
Fig. l(b). We assign the peak at 0.985 eV to be TO phonon-assisted band-edge transition of confined excitons in strained-Si quantum well. As shown in Fig. 2, type-II band alignment results at the strainedSi/relaxed-SiGe-buffer heterointerface[20]. Therefore, TO-assisted excitonic transition occurs between the confined conduction band state (lowest lying in energy) of strained-Si quantum well and the top of valence band of SiGe buffer layer (Fig. 2). The peak at 1.043eV in Fig. l(b) can be assigned to NP transition from the quantum wells, and always appears as a pair with the TO-assisted transition. These two peaks were separated by 58 meV, which corresponds to TO phonon energy of Si-Si bond. In case of this narrow strained-Si quantum well, the excitonic wave function penetrates considerably into SiGe barriers, where NP transition is allowed due to the randomness of alloying, resulting in NP transition from the confined conduction band state of strainedSi layer (Fig. 2). In order to demonstrate quantum confinement effect in the SiGe/strained-Si/SiGe quantum well, samples with different quantum well width were prepared. In these samples, the buffer layer structure was kept exactly the same. Well width dependent PL peak energy shifts for excitonic phonon-assisted as well as NP transitions are shown in Fig. 3. Figure 3(f) is PL spectrum from the buffer layer without any quantum well. As before, transitions from strained-Si quantum well are marked by "X". For a given well width, the high-energy peak ("X") is NP free excitonic transition from the quantum wells, whereas the low-energy peak is its TO replica. Both these peaks move to lower energy as the quantum well width is increased, Fig. 3(a) and (b). As the well width is increased further, the relative intensity of NP peak becomes weaker with respect to its TO replica, Fig. 3(c), (d) and (e). This is because the penetration
935
SiGe/strained-Si/SiGe type-II quantum wells
IZ ,-4 a_
700
800
900
1000
1100
P H O T O N E N E R O Y (meV)
Fig. 3. PL spectra at 4.2 K from five quantum well structures, which were grown on the buffer layer described in Fig. 1. (a) 10/~, (b) 13fl~, (c) 16J~, (d) 19/~, (e) 21/~, and (f) no quantum well.
of excitonic wave function into SiGe barriers diminishes with increasing well width, and therefore, the N P transition probability becomes smaller. TO-assisted transition for the 10/~-well appears at 0.986 eV, and moves down to 0.947 eV for the 21/~,well. This shift of 39 meV can be used to estimate the conduction band discontinuity at the relaxedSi0.8:Ge0~8/strained-Si heterointerface. Using an envelope function calculation, this is found to be about 86 meV. Temperature dependence of excitonic transitions from strained-Si quantum wells was found to be different from that of SiGe buffer (Fig. 4). With increasing temperature, the N P transition intensity from the buffer layer, B r~P, diminishes rapidly. At 29 K, the N P peak almost disappears, while the transition from the quantum well, X T°, remains unchanged compared to its 16 K value. X r° can be observed until 48 K. This shows that free excitons are effectively confined into the quantum well and that strained-Si layer may have less nonradiative pathway for carrier recombination compared to its SiGe buffer counterpart. In summary, intense band-edge photoluminescence for SiGe/strained-Si/SiGe type-II (staggered) quantum wells is reported for the first time. Quantum confinement effect in this quantum well is clearly demonstrated from the systematic shift of PL energy peaks with the width of the quantum well. Transitions from the strained-Si quantum well are identified as radiative recombination of excitons, which are confined in the quantum well. Acknowledgements--We would like to thank H. Oku, Y. Ohmori, T. Ohnishi and K. Okumura of Daido-Hoxan for their technical help in using gas source MBE. We also like to thank S. Ohtake of RCAST for technical assistance. REFERENCES
LO
.-I ca-
700
800
900
1000
1100
P H O T O N E N E R G Y (meV)
Fig. 4. Temperature dependence of PL spectra at 16, 20, 29, 41 and 48 K.
1. R. People and S. A. Jackson, Phys. Ret,. B 36, 1310 (1987). 2. M. S. Hybertsen and M. Schluter, Phys. Rez,. B 36, 9683 (1987). 3. T. P. Pearsall, J. Bevk, L. C. Feldman, J. M. Bonar, J. P. Mannaerts and A. Ourmazd, Phys. Rez,. Lett. 58, 729 (1987). 4. S. Froyen, D. M. Wood and A. Zunger, Phys. Rez,. B 37, 6893 (1988). 5. S. Satpathy, R. M. Martin and C. G. Van de Walle, Phys. Rez,. B 38, 13237 (1988). 6. E. A. Montie, G. F. A. van de Walle, D. J. Gravesteijn, A. A. van Gorkum and C. W. T. Bulle-Lieuwma, Appl. Phys. Lett. .56, 340 (1990). 7. H. Okumura, K. Miki, S. Misawa, K. Sakamoto, T. Sakamoto and S Yoshida Japan. J. appl. Phys. 28, L1893 (1989). 8. R. Zachai, K. Eberl, G. Abstreiter, E. Kasper and H. Kibbel, Phys. Rer. Lett. 64 1055 (1990). 9. U. Schmid, N. E. Christensen and M. Cardona, Phys. Ret,. Lett. 65, 2610 (1990). 10. R. Zachai, K. Eberl, G. Abstreiter, E. Kasper and H. Kibbel, Phys. Rev. Lett. 65, 2611 (1990). 11. J. Olajos, J. Engvall, H. G. Grimmeiss, U. Menczigar, G. Abstreiter, H. Kibbel, E. Kasper and H. Presting, Phys. Rez,. B 46, 12857 (1992).
936
D . K . NAVAK et al.
12. U. Menczigar, G. Abstreiter, J. Olajos, H. Grimmeiss, H. Kibbel, H. Presting, and E. Kasper, Phys. Ret'. B 47, 4099 (1993). 13. K. H. Jung, Y. M. Kim, and D. L. Kwong, Appl. Phys. Lett. $6, 1775 (1990). 14. F. K. LeGoues, B. S. Meyerson, and J. F. Morar, Phys. Ret,. Lett. 66, 2903 (1991). 15. E. A. Fitzgerald, Y.-H. Xie, M. L. Green, D. Brasen, A. R. Kortan, J. Michel, Y.-J. Mii and B. E. Weir, Appl. Phys. Left. 59, 811 (1991).
16. S. Fukatsu, H. Yoshida, A. Fujiwara, Y. Takahashi, Y. Shiraki and R. Ito, Appl. Phys. Lett. 61, 804 (1992). 17. J. Weber and M. 1. Alonso, Phys. Ret'. B 40, 5683 (1989). 18. R. Sauer, J. Weber, J. Stolz, E. R. Weber, K.-H. Kusters and H. Alexander, Appl. Phys. A 36, 1 (1985). 19. V. Higgs, E. C. Lightowlers. E. A. Fitzgerald, Y. H. Xie and P. J. Silverman, J. appL Phys. 73, 1952 (1993). 20. R. People, IEEE J. Quantum Electron. 22, 1696 (1986).