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Pulsed laser annealing of Si–Ge superlattices
Materials Science and Engineering C 23 (2003) 19 – 22 www.elsevier.com/locate/msec
Pulsed laser annealing of Si–Ge superlattices N.A. Sobolev a,b,*, G.D. Ivlev c, E.I. Gatskevich c, J.P. Leita˜o a, A. Fonseca a, M.C. Carmo a, A.B. Lopes d, D.N. Sharaev c, H. Kibbel e, H. Presting e a Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal Institute of Solid State and Semiconductor Physics, 220072 Minsk, Belarus c Institute of Electronics, 220090 Minsk, Belarus d Department of Ceramics and Glass Engineering, University of Aveiro, 3810-193 Aveiro, Portugal e Daimler Chrysler Research Center, 89081 Ulm, Germany b
Abstract Si5Ge5 superlattices (SL) were treated by 80-ns pulses of a ruby laser in a wide range of energy densities. The induced structural and electronic changes were monitored in situ by time-resolved reflectivity (TRR) and ex situ by scanning electron microscopy (SEM), Raman scattering and atomic force microscopy (AFM). The SL starts to melt at energy densities typical of bulk Ge (less than 0.4 J/cm2). At R 0.7 J/ cm2, a self-organization phenomenon is observed: a system of quasiregular rectangular grains with linear dimensions of about 100 nm is developed on the sample surface. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Silicon; Germanium; Superlattice; Laser annealing; Recrystallization
1. Introduction The details of the melting and solidification processes are far from being completely understood, even if the phase transformation occurs nearly in the thermodynamic equilibrium. In a nonequilibrium situation, the variety of interesting physical effects is even wider. The melting of materials due to short laser pulses is an extremely nonequilibrium phenomenon. In a heterogeneous system, such processes as intermixing, interdiffusion and segregation are added. This makes the situation quite unpredictable and lets expect novel phenomena. In this paper, we report an investigation of pulsed laser annealing of ultrathin-layer Si5Ge5 superlattices (SL). When the energy density exceeded a certain threshold, a quasiregular grain structure with a characteristic grain dimension of ca. 100 nm appears on the sample surface.
2. Experimental A symmetrically strained Si5Ge5 superlattice (the lower indices designate the number of atomic monolayers in a SL * Corresponding author. Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal. Tel.: +351-234-370356; fax: +351-234-424965. E-mail address: [email protected] (N.A. Sobolev).
period) containing 360 periods with an entire thickness of f 500 nm was grown by MBE at 500 jC on a (001) Si substrate on top of a thin relaxed Si0.4Ge0.6 buffer. Prior to the growth of the buffer, one monolayer (ML) of Sb has been deposited [1,2] to act as a surfactant. This ML is refilled during growth by co-evaporation from an effusion cell to guarantee a complete ML Sb coverage of the surface during growth. The residual incorporated Sb is overcompensated by the boron doping in the p-part of the sample. Finally, a 10nm-thick Si capping layer terminates the structure. A schematic diagram of the sample and the growth temperatures are shown in Fig. 1. The wafer was irradiated by single pulses of a ruby laser upon normal incidence. The pulse was of a nearly gaussian temporal shape with full width at half maximum (FWHM) of 80 ns. The probing light of a Ndglass laser (k = 1.064 Am) and its second harmonics (0.532 Am) were focussed into a spot with a diameter of 1 mm in the centre of the zone treated by the ruby laser. The incidence angle was 45j. The reflected probing beams, separated by a frequency sensitive mirror, were detected by two photomultiplier tubes (PMT) equipped with interference filters and the output signals was registered by a two-beam oscilloscope. The experimental setup was described in detail elsewhere [3]. The Raman spectra were measured with a room temperature micro-Raman setup (Jobin Yvon Spex T 64000) with a triple grating monochromator and a cooled CCD as a
0928-4931/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 8 - 4 9 3 1 ( 0 2 ) 0 0 2 2 2 - 9
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N.A. Sobolev et al. / Materials Science and Engineering C 23 (2003) 19–22
At 0.37 – 0.39 J/cm2, the changes of the TRR become stronger and its behaviour gets nonmonotonous. (This behaviour is then observed till 0.67 J/cm2, see Fig. 3.) More pronounced cracks are observed in the SEM. The FAP is strongly reduced in the Raman spectrum.
Fig. 1. Schematic diagram of the strained layer Si5Ge5 superlattice (SLS) sample. The growth temperatures of the individual layers are indicated.
detector. The scattering was excited by a 200-mW Ar-ion laser operating at 514.5 nm. The employed scattering geometry was z(xV,xV)z¯, with zzh001i and xVzh011i. Scanning electron microscopy (SEM) was performed by a Hitachi S4100 microscope and atomic force microscopy (AFM) images were measured by a Digital Instruments AFM Nanoscope IIIa apparatus.
3. Results and discussion Prior to laser irradiation, the sample has a mirror-like surface. The Raman spectrum (Fig. 2) reveals features typical of a SimGen SL [4,5]: the Si – Si vibration centred at 499 cm 1, the Si –Ge mode at 410 cm 1, the Ge –Ge mode at 305 cm 1, and the folded acoustical phonon (FAP) at 150 cm 1. The first three modes also appear in the Raman spectra of a SiGe alloy, though at slightly different frequencies [6]. The FAP band is a fingerprint of the SL. Besides, a weak peak centred at 511 cm 1 is observed, which we ascribe to the Si –Si vibrations in the capping layer. Its frequency is shifted down from the Raman frequency of bulk Si (520 cm 1) due to the tensile strain. After the laser treatment with energy densities lower than 0.3 J/cm2, neither a visual change of the surface colour nor changes of the surface morphology are observed. The FAP mode preserves its intensity relatively to the other major spectral features. At 0.31 – 0.34 J/cm2, a transient change of the reflectivity is observed. It should be emphasized that the changes observed at the wavelengths of 0.532 and 1.064 Am have opposite signs (Fig. 3). On the sample surface, the lasertreated spot becomes clearly visible. In the SEM, one observes some cracks (like those for 0.39 J/cm2, see Fig. 4, but less pronounced). In the Raman spectrum, the FAP peak gets weaker relatively to the other bands and the Si– Ge mode grows as compared to the Si –Si and the Ge – Ge peaks. Three weak features appear at 428, 446, and 468 cm 1 at the low-energy side of the Si– Si peak, which were previously attributed to localized Si – Si optical modes whose frequencies are lowered because of the larger mass of neighbouring Ge atoms [5].
Fig. 2. Raman spectra of the Si5Ge5 superlattice, as grown and laser annealed with the energy densities indicated.
N.A. Sobolev et al. / Materials Science and Engineering C 23 (2003) 19–22
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almost simultaneously because of the very small thickness. It is interesting to note that upon ion implantation the Si and Ge layers in similar SL samples undergo a simultaneous crystalline-to-amorphous phase transition at a dose that is very close to that of the amorphization of bulk single-crystalline Ge although the amorphization doses of bulk Si and Ge differ by more than one order of magnitude [8]. The diffusion coefficient of Ge in liquid Si lies in the range from 1.5 10 4 to 6 10 4 cm2/s [9]. This means that the intermixing of the 5 ML thick Si and Ge layers in the liquid phase is a matter of several ps. The dissolution of the still solid 5 ML thick Si layers in liquid Ge may take somewhat more time but should occur very rapidly, too. In addition, there may be the same type of the instability of very thin crystalline Si layers intercalated by disordered Ge ones as observed in the ion implantation experiments. Thus, the melting and subsequent intermixing of a part of the SL situated close to the surface (and thus contributing most strongly to the Raman
Fig. 3. Time-resolved reflectivity at two wavelengths (1064 and 532 nm) of the Si5Ge5 superlattice during pulsed laser annealing with the energy densities indicated.
In the range from 0.46 to 0.64 J/cm2, the FAP almost entirely disappears from the Raman spectrum and the relative intensity of the Si – Ge peak further increases. However, the Si– Si peak from the capping layer still can be observed. In the 0.67 – 0.79 J/cm2 range, dramatic changes occur in the characteristics of the sample. At 0.67 J/cm2, the SL Si – Si peak increases again and the Si –Si peak deriving from the cap disappears from the Raman spectrum. At 0.71 J/cm2, the TRR behaviour gets much simpler than at lower energy densities. At both probing wavelengths, the reflectivity first rises, reaches a plateau, and then returns to the initial level. With increasing energy density, only the temporal duration of the plateau becomes longer. However, the most surprising change occurs in the surface morphology as observed by SEM: instead of chaotic cracks, a system of quasiregular rectangular ‘‘cells’’ with linear dimensions of about 100 nm emerges (Fig. 4). A preliminary AFM study shows that the elementary building blocks of this new structure are rather crystallites or grains than concave cells (Fig. 5). This almost regular relieve is strikingly different from the chaotic relieve observed at lower laser energy densities (not shown). We propose the following explanation of the observed behaviour. In the range 0.31– 0.37 J/cm2, melting of the SL starts in the Ge layers because Ge has a lower melting temperature than Si (1211 and 1687 K, respectively) [7]. Nevertheless, the Ge and Si layers in the SL probably melt
Fig. 4. SEM images of the surface of the Si5Ge5 superlattice subjected to pulsed laser annealing with the energy densities 0.39 and 0.79 J/cm2.
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Fig. 5. AFM image of the surface of the Si5Ge5 superlattice subjected to pulsed laser annealing with the energy density 0.79 J/cm2.
spectrum) causes a diminution of the FAP band intensity and a growth of the Si –Ge mode intensity in the Raman spectra. However, as can be concluded from the same spectra, the much thicker (10 nm) Si cap layer does not melt below an energy density of 0.7 J/cm2. This value is lower than the melting threshold of bulk Si (1 J/cm2) [10], but we believe that there is some dissolution of the capping layer in the molten SiGe alloy. Below 0.7 J/cm2, the Si cap suffers strong deformations caused by the melting of the subjacent layer, which is manifested by the cracks seen in the SEM and disordered relieve seen in the AFM. The recrystallization at these relatively low energy densities starts from both interfaces Si cap/melt and melt/solid SL (or buffer or substrate), so that the existence of a solid surface layer with the thickness varying over the time causes interferences of the probing beams and thus the complicated behaviour of the TRR observed in the experiment. The interference conditions are different for both the wavelengths used by us, which qualitatively explains the differing behaviour of the TRR at 0.532 and 1.062 Am. However, at the moment we have not yet a quantitative model describing the TRR curves. When the Si cap melts at 0.7 J/cm2 too, it experiences an intermixing but the surface layer remains enriched by Si after solidification, as evidenced by the vanishing of the weak Si– Si peak at 511 cm 1 and by the growth of the intensity of the main Si– Si peak. The interference phenomena in the TRR curves disappear because of the disappearance of a solid layer on top of the structure and we observe a behaviour typical of the laser-induced melting of bulk Si, namely, a rise of the reflectivity at the moment of the melting, a plateau lasting for the time of the existence of the melt and a drop of the reflectivity to its initial value as soon as the melt solidifies. An intriguing question is that of the driving force causing the formation of the ‘‘cells’’ or nanocrystallites observed in
the SEM and AFM. It is well known that segregation of components occurs in the course of laser melting and solidification of Si– Ge alloys [9], with segregation effects quite dramatic in some case. Another origin of the selforganization may be strain caused by the discrepancy of the lattice constant of the Si substrate and the solidifying Si –Ge alloy. Further experiments and calculations to clarify the problem are underway.
Acknowledgements The authors would like to thank V.V. Shvartsman for the help in the AFM measurements. A.F. acknowledges the financial support by the University of Aveiro.
References [1] M. Copel, M.C. Reuter, M. Horn v. Hoegen, R.M. Tromp, Phys. Rev., B 42 (1990) 11682. [2] E.T. Croke, T.C. McGill, R.J. Hauenstein, R.H. Miles, Appl. Phys. Lett. 56 (1989) 367. [3] E.I. Gatskevich, G.D. Ivlev, A.M. Chaplanov, Quantum Electron. (UK) 25 (1995) 774. [4] R. Schorer, G. Abstreiter, S. de Gironcoli, E. Molinari, H. Kibbel, H. Presting, Phys. Rev., B 49 (1994) 5406. [5] M.I. Alonso, K. Winer, Phys. Rev., B 39 (1989) 10056. [6] S. de Gironcoli, E. Molinari, R. Schorer, G. Abstreiter, Phys. Rev., B 48 (1993) 8959. [7] C. Kittel, Introduction to Solid State Physics, 6th ed., Wiley, New York, 1986. [8] N.A. Sobolev, K. Ga¨rtner, U. Kaiser, U. Ko¨nig, H. Presting, B. Weber, E. Wendler, W. Wesch, Mat. Sci. Forum, 248 – 249 (1997) 289. [9] D.P. Brunco, M. Thompson, D.E. Hoglund, M.J. Aziz, H.-J. Gossmann, J. Appl. Phys. 78 (1995) 1575 (and references therein). [10] G.D. Ivlev, E.I. Gatskevitch, Semiconductors 30 (1996) 1093.
Pulsed laser annealing of Si–Ge superlattices N.A. Sobolev a,b,*, G.D. Ivlev c, E.I. Gatskevich c, J.P. Leita˜o a, A. Fonseca a, M.C. Carmo a, A.B. Lopes d, D.N. Sharaev c, H. Kibbel e, H. Presting e a Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal Institute of Solid State and Semiconductor Physics, 220072 Minsk, Belarus c Institute of Electronics, 220090 Minsk, Belarus d Department of Ceramics and Glass Engineering, University of Aveiro, 3810-193 Aveiro, Portugal e Daimler Chrysler Research Center, 89081 Ulm, Germany b
Abstract Si5Ge5 superlattices (SL) were treated by 80-ns pulses of a ruby laser in a wide range of energy densities. The induced structural and electronic changes were monitored in situ by time-resolved reflectivity (TRR) and ex situ by scanning electron microscopy (SEM), Raman scattering and atomic force microscopy (AFM). The SL starts to melt at energy densities typical of bulk Ge (less than 0.4 J/cm2). At R 0.7 J/ cm2, a self-organization phenomenon is observed: a system of quasiregular rectangular grains with linear dimensions of about 100 nm is developed on the sample surface. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Silicon; Germanium; Superlattice; Laser annealing; Recrystallization
1. Introduction The details of the melting and solidification processes are far from being completely understood, even if the phase transformation occurs nearly in the thermodynamic equilibrium. In a nonequilibrium situation, the variety of interesting physical effects is even wider. The melting of materials due to short laser pulses is an extremely nonequilibrium phenomenon. In a heterogeneous system, such processes as intermixing, interdiffusion and segregation are added. This makes the situation quite unpredictable and lets expect novel phenomena. In this paper, we report an investigation of pulsed laser annealing of ultrathin-layer Si5Ge5 superlattices (SL). When the energy density exceeded a certain threshold, a quasiregular grain structure with a characteristic grain dimension of ca. 100 nm appears on the sample surface.
2. Experimental A symmetrically strained Si5Ge5 superlattice (the lower indices designate the number of atomic monolayers in a SL * Corresponding author. Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal. Tel.: +351-234-370356; fax: +351-234-424965. E-mail address: [email protected] (N.A. Sobolev).
period) containing 360 periods with an entire thickness of f 500 nm was grown by MBE at 500 jC on a (001) Si substrate on top of a thin relaxed Si0.4Ge0.6 buffer. Prior to the growth of the buffer, one monolayer (ML) of Sb has been deposited [1,2] to act as a surfactant. This ML is refilled during growth by co-evaporation from an effusion cell to guarantee a complete ML Sb coverage of the surface during growth. The residual incorporated Sb is overcompensated by the boron doping in the p-part of the sample. Finally, a 10nm-thick Si capping layer terminates the structure. A schematic diagram of the sample and the growth temperatures are shown in Fig. 1. The wafer was irradiated by single pulses of a ruby laser upon normal incidence. The pulse was of a nearly gaussian temporal shape with full width at half maximum (FWHM) of 80 ns. The probing light of a Ndglass laser (k = 1.064 Am) and its second harmonics (0.532 Am) were focussed into a spot with a diameter of 1 mm in the centre of the zone treated by the ruby laser. The incidence angle was 45j. The reflected probing beams, separated by a frequency sensitive mirror, were detected by two photomultiplier tubes (PMT) equipped with interference filters and the output signals was registered by a two-beam oscilloscope. The experimental setup was described in detail elsewhere [3]. The Raman spectra were measured with a room temperature micro-Raman setup (Jobin Yvon Spex T 64000) with a triple grating monochromator and a cooled CCD as a
0928-4931/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 8 - 4 9 3 1 ( 0 2 ) 0 0 2 2 2 - 9
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N.A. Sobolev et al. / Materials Science and Engineering C 23 (2003) 19–22
At 0.37 – 0.39 J/cm2, the changes of the TRR become stronger and its behaviour gets nonmonotonous. (This behaviour is then observed till 0.67 J/cm2, see Fig. 3.) More pronounced cracks are observed in the SEM. The FAP is strongly reduced in the Raman spectrum.
Fig. 1. Schematic diagram of the strained layer Si5Ge5 superlattice (SLS) sample. The growth temperatures of the individual layers are indicated.
detector. The scattering was excited by a 200-mW Ar-ion laser operating at 514.5 nm. The employed scattering geometry was z(xV,xV)z¯, with zzh001i and xVzh011i. Scanning electron microscopy (SEM) was performed by a Hitachi S4100 microscope and atomic force microscopy (AFM) images were measured by a Digital Instruments AFM Nanoscope IIIa apparatus.
3. Results and discussion Prior to laser irradiation, the sample has a mirror-like surface. The Raman spectrum (Fig. 2) reveals features typical of a SimGen SL [4,5]: the Si – Si vibration centred at 499 cm 1, the Si –Ge mode at 410 cm 1, the Ge –Ge mode at 305 cm 1, and the folded acoustical phonon (FAP) at 150 cm 1. The first three modes also appear in the Raman spectra of a SiGe alloy, though at slightly different frequencies [6]. The FAP band is a fingerprint of the SL. Besides, a weak peak centred at 511 cm 1 is observed, which we ascribe to the Si –Si vibrations in the capping layer. Its frequency is shifted down from the Raman frequency of bulk Si (520 cm 1) due to the tensile strain. After the laser treatment with energy densities lower than 0.3 J/cm2, neither a visual change of the surface colour nor changes of the surface morphology are observed. The FAP mode preserves its intensity relatively to the other major spectral features. At 0.31 – 0.34 J/cm2, a transient change of the reflectivity is observed. It should be emphasized that the changes observed at the wavelengths of 0.532 and 1.064 Am have opposite signs (Fig. 3). On the sample surface, the lasertreated spot becomes clearly visible. In the SEM, one observes some cracks (like those for 0.39 J/cm2, see Fig. 4, but less pronounced). In the Raman spectrum, the FAP peak gets weaker relatively to the other bands and the Si– Ge mode grows as compared to the Si –Si and the Ge – Ge peaks. Three weak features appear at 428, 446, and 468 cm 1 at the low-energy side of the Si– Si peak, which were previously attributed to localized Si – Si optical modes whose frequencies are lowered because of the larger mass of neighbouring Ge atoms [5].
Fig. 2. Raman spectra of the Si5Ge5 superlattice, as grown and laser annealed with the energy densities indicated.
N.A. Sobolev et al. / Materials Science and Engineering C 23 (2003) 19–22
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almost simultaneously because of the very small thickness. It is interesting to note that upon ion implantation the Si and Ge layers in similar SL samples undergo a simultaneous crystalline-to-amorphous phase transition at a dose that is very close to that of the amorphization of bulk single-crystalline Ge although the amorphization doses of bulk Si and Ge differ by more than one order of magnitude [8]. The diffusion coefficient of Ge in liquid Si lies in the range from 1.5 10 4 to 6 10 4 cm2/s [9]. This means that the intermixing of the 5 ML thick Si and Ge layers in the liquid phase is a matter of several ps. The dissolution of the still solid 5 ML thick Si layers in liquid Ge may take somewhat more time but should occur very rapidly, too. In addition, there may be the same type of the instability of very thin crystalline Si layers intercalated by disordered Ge ones as observed in the ion implantation experiments. Thus, the melting and subsequent intermixing of a part of the SL situated close to the surface (and thus contributing most strongly to the Raman
Fig. 3. Time-resolved reflectivity at two wavelengths (1064 and 532 nm) of the Si5Ge5 superlattice during pulsed laser annealing with the energy densities indicated.
In the range from 0.46 to 0.64 J/cm2, the FAP almost entirely disappears from the Raman spectrum and the relative intensity of the Si – Ge peak further increases. However, the Si– Si peak from the capping layer still can be observed. In the 0.67 – 0.79 J/cm2 range, dramatic changes occur in the characteristics of the sample. At 0.67 J/cm2, the SL Si – Si peak increases again and the Si –Si peak deriving from the cap disappears from the Raman spectrum. At 0.71 J/cm2, the TRR behaviour gets much simpler than at lower energy densities. At both probing wavelengths, the reflectivity first rises, reaches a plateau, and then returns to the initial level. With increasing energy density, only the temporal duration of the plateau becomes longer. However, the most surprising change occurs in the surface morphology as observed by SEM: instead of chaotic cracks, a system of quasiregular rectangular ‘‘cells’’ with linear dimensions of about 100 nm emerges (Fig. 4). A preliminary AFM study shows that the elementary building blocks of this new structure are rather crystallites or grains than concave cells (Fig. 5). This almost regular relieve is strikingly different from the chaotic relieve observed at lower laser energy densities (not shown). We propose the following explanation of the observed behaviour. In the range 0.31– 0.37 J/cm2, melting of the SL starts in the Ge layers because Ge has a lower melting temperature than Si (1211 and 1687 K, respectively) [7]. Nevertheless, the Ge and Si layers in the SL probably melt
Fig. 4. SEM images of the surface of the Si5Ge5 superlattice subjected to pulsed laser annealing with the energy densities 0.39 and 0.79 J/cm2.
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Fig. 5. AFM image of the surface of the Si5Ge5 superlattice subjected to pulsed laser annealing with the energy density 0.79 J/cm2.
spectrum) causes a diminution of the FAP band intensity and a growth of the Si –Ge mode intensity in the Raman spectra. However, as can be concluded from the same spectra, the much thicker (10 nm) Si cap layer does not melt below an energy density of 0.7 J/cm2. This value is lower than the melting threshold of bulk Si (1 J/cm2) [10], but we believe that there is some dissolution of the capping layer in the molten SiGe alloy. Below 0.7 J/cm2, the Si cap suffers strong deformations caused by the melting of the subjacent layer, which is manifested by the cracks seen in the SEM and disordered relieve seen in the AFM. The recrystallization at these relatively low energy densities starts from both interfaces Si cap/melt and melt/solid SL (or buffer or substrate), so that the existence of a solid surface layer with the thickness varying over the time causes interferences of the probing beams and thus the complicated behaviour of the TRR observed in the experiment. The interference conditions are different for both the wavelengths used by us, which qualitatively explains the differing behaviour of the TRR at 0.532 and 1.062 Am. However, at the moment we have not yet a quantitative model describing the TRR curves. When the Si cap melts at 0.7 J/cm2 too, it experiences an intermixing but the surface layer remains enriched by Si after solidification, as evidenced by the vanishing of the weak Si– Si peak at 511 cm 1 and by the growth of the intensity of the main Si– Si peak. The interference phenomena in the TRR curves disappear because of the disappearance of a solid layer on top of the structure and we observe a behaviour typical of the laser-induced melting of bulk Si, namely, a rise of the reflectivity at the moment of the melting, a plateau lasting for the time of the existence of the melt and a drop of the reflectivity to its initial value as soon as the melt solidifies. An intriguing question is that of the driving force causing the formation of the ‘‘cells’’ or nanocrystallites observed in
the SEM and AFM. It is well known that segregation of components occurs in the course of laser melting and solidification of Si– Ge alloys [9], with segregation effects quite dramatic in some case. Another origin of the selforganization may be strain caused by the discrepancy of the lattice constant of the Si substrate and the solidifying Si –Ge alloy. Further experiments and calculations to clarify the problem are underway.
Acknowledgements The authors would like to thank V.V. Shvartsman for the help in the AFM measurements. A.F. acknowledges the financial support by the University of Aveiro.
References [1] M. Copel, M.C. Reuter, M. Horn v. Hoegen, R.M. Tromp, Phys. Rev., B 42 (1990) 11682. [2] E.T. Croke, T.C. McGill, R.J. Hauenstein, R.H. Miles, Appl. Phys. Lett. 56 (1989) 367. [3] E.I. Gatskevich, G.D. Ivlev, A.M. Chaplanov, Quantum Electron. (UK) 25 (1995) 774. [4] R. Schorer, G. Abstreiter, S. de Gironcoli, E. Molinari, H. Kibbel, H. Presting, Phys. Rev., B 49 (1994) 5406. [5] M.I. Alonso, K. Winer, Phys. Rev., B 39 (1989) 10056. [6] S. de Gironcoli, E. Molinari, R. Schorer, G. Abstreiter, Phys. Rev., B 48 (1993) 8959. [7] C. Kittel, Introduction to Solid State Physics, 6th ed., Wiley, New York, 1986. [8] N.A. Sobolev, K. Ga¨rtner, U. Kaiser, U. Ko¨nig, H. Presting, B. Weber, E. Wendler, W. Wesch, Mat. Sci. Forum, 248 – 249 (1997) 289. [9] D.P. Brunco, M. Thompson, D.E. Hoglund, M.J. Aziz, H.-J. Gossmann, J. Appl. Phys. 78 (1995) 1575 (and references therein). [10] G.D. Ivlev, E.I. Gatskevitch, Semiconductors 30 (1996) 1093.