- Email: [email protected]
In situ observation of macrostep formation on misoriented GaAs(111)B by molecular beam epitaxy
,. . . . . . . .
CRYSTAL G R O W T H
ELSEVIER
Journal of Crystal Growth 166 (1996) 217-221
In situ observation of macrostep formation on misoriented GaAs(111) B by molecular beam epitaxy Hong-Wen Ren *, Xu-Qiang Shen, Tatau Nishinaga Department of Electronic Engineering, Faculty of Engineering, The Universi~ of Tokyo, 7-3-l Hongo, Bunkyo-ku. Tokyo 113, Japan
Abstract
This paper reports, for the first time, the formation of straight macrosteps during the growth of GaAs on misoriented GaAs(Ill)B substrates inclined toward the [110] direction, and their in situ observation in a microprobe-reflection high-energy-electron-diffraction/scanning-electron-microscope molecular-beam-epitaxy system. It was found that step bunching usually occurs at a lower A s 4 flUXunder a Vt~ × ~ surface reconstruction, while smooth surfaces are obtained at higher A s 4 flux. In situ observation showed that macrosteps are formed gradually during the growth and finally develop into giant macrosteps consisting of flat terraces and rough risers with straight step edges along the [110] direction. Atomicforce-microscopy studies revealed that these macrosteps are composed of near-(111)B terraces and near-(110) risers.
1. Introduction
Recently, the study of "step bunching" in both metalorganic vapor phase epitaxy (MOVPE) [1,2] and molecular beam epitaxy (MBE) [3,4] has been stimulated by the prospect of potential applications of such structures for fabricating quantum wires. The formation of macrosteps by step bunching occurs under limited growth conditions and depends strongly on surface misorientation. So far, a few GaAs surfaces have been found to generate macrosteps by MBE, such as misoriented GaAs(111)A inclined toward the [ll0] direction [3], GaAs(ll0) inclined toward the [111]A direction [4], and (331)A, (311)A, (210) high-index surfaces [5,6]. Epitaxial layers grown on GaAs(111)B substrates have many advantages because of their interesting properties, such as a large piezoelectric effect in strained heterostruc* Corresponding author. E-mail: [email protected].
tures [7] and reduction in the threshold current density in quantum-well (QW) lasers [8]. Previous studies of MBE growth on GaAs(l 11)B substrates have focused on obtaining smooth surfaces [8-12] and showed that only under very limited growth conditions can they be obtained. Morphological studies were mainly limited to those misoriented ( l l l ) B inclined 0.5 ° [8,9], 1° [8,11], 1.5 ° [10], or 3° [12] toward the [001] direction. While macrostep formation on misoriented GaAs(111)B substrates inclined toward the [110] direction has been studied by MOVPE using reevaporation-enhancement effects
[2]. The present paper reports, for the first time, the in situ observation of the formation of straight macrosteps during the MBE growth of GaAs on the same kind of substrates. The formation and evolution of straight macrosteps on such surfaces were observed in situ in a microprobe-reflection high-energy-electron-diffraction/ scanning-electron-micro-
0022-0248/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved SSDI0022-0248(95)00528-5
H.-W. Ren et al. /Journal of Crystal Growth 166 (1996) 217-221
218
scope molecular-beam-epitaxy (p~-RHEED/SEM MBE) system and the resultant morphologies were studied by atomic force microscopy (AFM). These ordered macrostep surfaces may have potential applications for fabricating one-dimensional quantum wire structures.
2. Experimental procedure The p~-RHEED/SEM MBE system used in this experiment has been described in detail elsewhere [13]. The substrates were a silicon-doped n +GaAs(II1)B (doping concentration is 2 X 1018 cm -3) inclined 3° toward the [110] direction and a
a
0 min
5p'ml
semi-insulating GaAs nominally exact (001) for reference. Before the growth, the substrates were cleaned in organic solvents and etched in an H2SO 4 : H 2 0 z : H 2 0 (8 : 1 : 1) solution at 40°C for 1.5 min to remove surface damage. The native oxides on the substrate surfaces were removed by heating the sample to 580°C under arsenic over pressure followed by 5 min heating at 620°C. All the GaAs growth experiments were performed under 1 ~ x 1 ~ reconstruction on the ( l l l ) B surface, which has been known to be important for producing a smooth GaAs surface morphology free of pyramidal defects [14]. The growth temperature was 560°C, the growth rate was 0.31 p~m/h for the in situ
b
60 min
5~m
!i,
c 120 min
lOpml
d 180 min
20p,m,
Fig. 1. In situ SEM images of macrostep formation during MBE growth of GaAs on a misoriented GaAs(l 11)B surface inclined 3° toward the [110] direction at an A s / G a flux ratio of 2.
H.-W. Ren et aL/ Journal of Crystal Growth 166 (1996) 217-221
studies. To investigate the influence of A s 4 flUX on the macrostep formation, the input A s / G a flux ratio was varied from 2 to 7. Observation of the growth in situ was made with an 25 keV electron beam incident at a glancing angle of 10° along the [110] azimuth perpendicular to the step-flow direction. Secondary electron SEM images were obtained in real time without interrupting the growth. The samples were examined ex situ using both a Nomarski phase-contrast optical microscope and a Nanoscope II atomic force microscope (AFM) (Digital Instrument).
3. Results and discussion 3.1. In situ observation of the macrostep formation
The A s / G a flux ratio was set at 2 at first for in situ observation of the macrostep formation. Before starting the growth, the misoriented G a A s ( l l l ) B surface was mirror-like and featureless as shown in the in situ SEM image (Fig. la). After depositing 0.3 v~m of GaAs, the surface was observed to be covered with many long " m o u n d s " , as shown in Fig. lb. It seems that these mounds are formed by bunching of
219
monolayer steps during the growth. After 0.6 Ixm of material had been deposited, bunched steps, or socalled macrosteps, with dimensions of about 0.5 ~ m in width and several micrometers in length along the [110] direction were clearly observed as shown in Fig. l c. In some areas, because of further step bunching, very large macrosteps were also formed (hereafter referred to as giant macrosteps) together with macrosteps. After growing to a thickness of 1 txm, the macrosteps were observed to have similar step widths and lengths varying from several tens of micrometers to a few millimeters as observed in Fig. ld. The terrace areas of the giant macrosteps (white areas in Figs. lc and ld) were observed to expand rapidly in the [110] direction. All these macrosteps are coherently aligned with straight step edges in the [110] direction. By measuring the distance between neighboring macrosteps resolved in Fig. 1 and taking into account the misorientation angle of the substrate, it is estimated that these macrosteps are formed by the bunching of 40 to 80 monolayer steps. 3.2. AFM study of the macrostep morphology
Surface morphologies were examined by optical microscopy and AFM. Although the macrosteps can
Fig. 2. Tilt-compensatedtopographic AFM image of the macrostepstructure on a misoriented GaAs(l11)B surface inclined 3° toward the [110] direction.
220
H.-W. Ren et al. /Journal of Crystal Growth 166 (1996) 217-221
be resolved by phase-contrast optical microscopy, the actual step heights are very small. Because AFM has sufficient height resolution to observe monoatomic steps, it was employed to quantitatively study the macrostep structures and surface morphologies. Fig. 2 shows the tilt-compensated topographic AFM image of representative macrosteps. The figure clearly shows that the macrosteps are formed by step bunching. The terrace surfaces of the macrosteps are smooth while the risers are relatively rough and unfaceted. The terrace widths vary from 0.25 to 0.80 p~m, which is in good agreement with those widths observed in situ. From the average slope, it is clear that the terraces are still misoriented 1.5 ° toward the ( l l l ) B face, hence we call them near-(lll)B terraces; the rough step risers along the [110] direction are inclined toward the (110) face and are hereafter called near-(l 10) risers.
3.3. Dependence of macrostep formation
on As 4 flux
During the in situ observation by SEM and also ex situ observations by phase-contrast optical microscopy, it was found that at a lower A s 4 f l u x , nearly the whole surface was covered by macrosteps, while at a higher A s 4 f l u x , nearly the whole surface tended to become smooth. Fig. 3 shows a representative SEM image taken in situ on such a smooth surface. Marks indicated by the arrows have been selected for the dynamic focus of the surface. The epitaxial layer was 1 ixm thick and was grown at an A s / G a flux ratio of 4 (the A s 4 flux was tWO times as much as that used for growth in Fig. 1). AFM profiles of the surface morphologies grown at higher A s 4 flUX showed that the bunched steps are also present, but they are composed of only a few atomic layers. The edges of the bunched steps are wavy. When a lower A s 4 flux is employed during the growth, however, the step-edges tend to straighten along the [110] direction. There are several possible mechanisms for the step bunches. For instance, according to the Schwoebel effect [15,16], when the sticking coefficient of Ga atoms to the step edges from the upper terrace is larger than that from the lower terrace during growth, the terrace widths tend to be unstable, and step bunching occurs. Simulation of this kind of
Fig. 3. In situ SEM image of a misoriented GaAs(l I I)B surface inclined 3° toward the [110] direction after MBE growth of 1 txm GaAs at an A s / G a flux ratio of 4.
morphological instability shows the formation of smooth terraces with a steady state of moving atomic step arrays with a wider separation and sharp risers of bunched steps [17]. Our AFM study shows that the macrostep terraces are always smooth but still have some misorientation toward the nominally exact (111)B face, this means steady-state atomic-step arrays with a wider and uniform separation are stable on the terraces, while the risers are formed by step bunching. If we assume that the Schwoebel effect govems the present case, the difference between the sticking coefficients of Ga atoms to the step edge from the upper terrace should be much larger than that from the lower terrace when the A s 4 flUX is lower, so that step bunching occurs easily. On the contrary, if the increase of A s 4 flux makes the sticking coefficients to the step edges from the upper terrace smaller than that from the lower terrace, step bunching is hindered except for small-scale accidental bunching. Therefore, the surface looks smooth by macroscopic observation.
H.-W. Ren et al. /Journal of Crystal Growth 166 (1996) 217-221
4. Conclusions We have succeeded in observing, in situ, the formation of ordered macrostep arrays during the growth of GaAs on misoriented GaAs(lll)B inclined toward the [110] direction using txRHEED/SEM MBE. These macrosteps are formed gradually during growth and are finally developed into very straight and long macrosteps at a relatively lower A s 4 flux under ~ X~ surface reconstruction. They are coherently aligned and are composed of near-(l 11)B terraces and near-(110) risers. The step-edges are straight along the [170] direction. When a higher As 4 flux is introduced, step bunching is suppressed and smooth surfaces are obtained.
Acknowledgements The authors would like to thank Professor H. Komatsu and Dr. T. Nakada of the Institute for Materials Research, Tohoku University for helping with the AFM observation. They would also like to thank associate Professor M. Tanaka and Ms. M. Washiyama of the University of Tokyo for their help in carrying out this work. One of the authors (H.W.R.) would like to thank the Japan Society for the Promotion of Science (JSPS) for a post-doctoral fellowship at the University of Tokyo. This research was supported by Grants-in-Aid for Scientific Research on Priority Areas "Crystal Growth Mechanism in Atomic Scale" Nos. 03243102 and 04227101
221
from the Ministry of Education, Science and Culture, Japan.
References [I] M. Kasu and T. Fukui, Jpn. J. Appl. Phys. 31 (1992) L864. [2] K. Okamoto, O. Ito and K. Yamaguchi, Jpn. J. Appl. Phys. 31 (1992) L820. [3] T. Yamamoto, M. lnai, T. Takebe, M. Fujii and K. Kobayashi, J. Crystal Growth 127 (1993) 865. [4] K. lnoue, K. Kimura, K. Maehashi, S. Hasegawa and H. Nakashima, J. Crystal Growth 127 (1993) 1041. [5] R. Notzel, L. Daweritz and K. Ploog, J. Crystal Growth 127 (1993) 858. [6] R. Notzel, N.N. Ledentsov, L. Daweritz and K. PIoog, Phys. Rev. B 45 (1992) 3507. [7] D.L. Smith, Solid State Commun. 57 (1986) 919. [8] T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto and T. Hijikata, Jpn. J. Appl. Phys. 26 (1987) L302. [9] T. Hayakawa, M. Kondo, T. Morita, K. Takahashi, T. Suyama, S. Yamamoto and T. Hijikata, Appl. Phys. Lett. 51 (1987) 1705. [10] K. Tsutuis, H. Mizakami, O. Ishiyama, S. Nakamura and S. Furukawa, Jpn. J. Appl. Phys. 29 (1990) 468. [11] A. Chin, P. Martin, P. Ho, J. Ballingall, T. Yu and J. Mazurowski, Appl. Phys. Lett. 59 (1991) 1899. [12] K. Elcess, J.-L. Lievin and C.G. Fonstad, J. Vac. Sci. Technol. B 6 (1988) 638. [13] T. Suzuki and T. Nishinaga, J. Crystal Growth 142 (1994) 49. [14] P. Chert, K.C. Rajkumar and A. Madhukar, Appl. Phys. Lett. 58 (1991) 1771. [15] R.L. Schwoebel, J. Appl. Phys. 40 (1969) 614. [16] R.L. Schwoebel and E.J. Shipsey, J. Appl. Phys. 37 (1966) 3682. [17] M. Sato and M. Uwaha, Phys. Rev. B 51 (1995) 11172.
CRYSTAL G R O W T H
ELSEVIER
Journal of Crystal Growth 166 (1996) 217-221
In situ observation of macrostep formation on misoriented GaAs(111) B by molecular beam epitaxy Hong-Wen Ren *, Xu-Qiang Shen, Tatau Nishinaga Department of Electronic Engineering, Faculty of Engineering, The Universi~ of Tokyo, 7-3-l Hongo, Bunkyo-ku. Tokyo 113, Japan
Abstract
This paper reports, for the first time, the formation of straight macrosteps during the growth of GaAs on misoriented GaAs(Ill)B substrates inclined toward the [110] direction, and their in situ observation in a microprobe-reflection high-energy-electron-diffraction/scanning-electron-microscope molecular-beam-epitaxy system. It was found that step bunching usually occurs at a lower A s 4 flUXunder a Vt~ × ~ surface reconstruction, while smooth surfaces are obtained at higher A s 4 flux. In situ observation showed that macrosteps are formed gradually during the growth and finally develop into giant macrosteps consisting of flat terraces and rough risers with straight step edges along the [110] direction. Atomicforce-microscopy studies revealed that these macrosteps are composed of near-(111)B terraces and near-(110) risers.
1. Introduction
Recently, the study of "step bunching" in both metalorganic vapor phase epitaxy (MOVPE) [1,2] and molecular beam epitaxy (MBE) [3,4] has been stimulated by the prospect of potential applications of such structures for fabricating quantum wires. The formation of macrosteps by step bunching occurs under limited growth conditions and depends strongly on surface misorientation. So far, a few GaAs surfaces have been found to generate macrosteps by MBE, such as misoriented GaAs(111)A inclined toward the [ll0] direction [3], GaAs(ll0) inclined toward the [111]A direction [4], and (331)A, (311)A, (210) high-index surfaces [5,6]. Epitaxial layers grown on GaAs(111)B substrates have many advantages because of their interesting properties, such as a large piezoelectric effect in strained heterostruc* Corresponding author. E-mail: [email protected].
tures [7] and reduction in the threshold current density in quantum-well (QW) lasers [8]. Previous studies of MBE growth on GaAs(l 11)B substrates have focused on obtaining smooth surfaces [8-12] and showed that only under very limited growth conditions can they be obtained. Morphological studies were mainly limited to those misoriented ( l l l ) B inclined 0.5 ° [8,9], 1° [8,11], 1.5 ° [10], or 3° [12] toward the [001] direction. While macrostep formation on misoriented GaAs(111)B substrates inclined toward the [110] direction has been studied by MOVPE using reevaporation-enhancement effects
[2]. The present paper reports, for the first time, the in situ observation of the formation of straight macrosteps during the MBE growth of GaAs on the same kind of substrates. The formation and evolution of straight macrosteps on such surfaces were observed in situ in a microprobe-reflection high-energy-electron-diffraction/ scanning-electron-micro-
0022-0248/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved SSDI0022-0248(95)00528-5
H.-W. Ren et al. /Journal of Crystal Growth 166 (1996) 217-221
218
scope molecular-beam-epitaxy (p~-RHEED/SEM MBE) system and the resultant morphologies were studied by atomic force microscopy (AFM). These ordered macrostep surfaces may have potential applications for fabricating one-dimensional quantum wire structures.
2. Experimental procedure The p~-RHEED/SEM MBE system used in this experiment has been described in detail elsewhere [13]. The substrates were a silicon-doped n +GaAs(II1)B (doping concentration is 2 X 1018 cm -3) inclined 3° toward the [110] direction and a
a
0 min
5p'ml
semi-insulating GaAs nominally exact (001) for reference. Before the growth, the substrates were cleaned in organic solvents and etched in an H2SO 4 : H 2 0 z : H 2 0 (8 : 1 : 1) solution at 40°C for 1.5 min to remove surface damage. The native oxides on the substrate surfaces were removed by heating the sample to 580°C under arsenic over pressure followed by 5 min heating at 620°C. All the GaAs growth experiments were performed under 1 ~ x 1 ~ reconstruction on the ( l l l ) B surface, which has been known to be important for producing a smooth GaAs surface morphology free of pyramidal defects [14]. The growth temperature was 560°C, the growth rate was 0.31 p~m/h for the in situ
b
60 min
5~m
!i,
c 120 min
lOpml
d 180 min
20p,m,
Fig. 1. In situ SEM images of macrostep formation during MBE growth of GaAs on a misoriented GaAs(l 11)B surface inclined 3° toward the [110] direction at an A s / G a flux ratio of 2.
H.-W. Ren et aL/ Journal of Crystal Growth 166 (1996) 217-221
studies. To investigate the influence of A s 4 flUX on the macrostep formation, the input A s / G a flux ratio was varied from 2 to 7. Observation of the growth in situ was made with an 25 keV electron beam incident at a glancing angle of 10° along the [110] azimuth perpendicular to the step-flow direction. Secondary electron SEM images were obtained in real time without interrupting the growth. The samples were examined ex situ using both a Nomarski phase-contrast optical microscope and a Nanoscope II atomic force microscope (AFM) (Digital Instrument).
3. Results and discussion 3.1. In situ observation of the macrostep formation
The A s / G a flux ratio was set at 2 at first for in situ observation of the macrostep formation. Before starting the growth, the misoriented G a A s ( l l l ) B surface was mirror-like and featureless as shown in the in situ SEM image (Fig. la). After depositing 0.3 v~m of GaAs, the surface was observed to be covered with many long " m o u n d s " , as shown in Fig. lb. It seems that these mounds are formed by bunching of
219
monolayer steps during the growth. After 0.6 Ixm of material had been deposited, bunched steps, or socalled macrosteps, with dimensions of about 0.5 ~ m in width and several micrometers in length along the [110] direction were clearly observed as shown in Fig. l c. In some areas, because of further step bunching, very large macrosteps were also formed (hereafter referred to as giant macrosteps) together with macrosteps. After growing to a thickness of 1 txm, the macrosteps were observed to have similar step widths and lengths varying from several tens of micrometers to a few millimeters as observed in Fig. ld. The terrace areas of the giant macrosteps (white areas in Figs. lc and ld) were observed to expand rapidly in the [110] direction. All these macrosteps are coherently aligned with straight step edges in the [110] direction. By measuring the distance between neighboring macrosteps resolved in Fig. 1 and taking into account the misorientation angle of the substrate, it is estimated that these macrosteps are formed by the bunching of 40 to 80 monolayer steps. 3.2. AFM study of the macrostep morphology
Surface morphologies were examined by optical microscopy and AFM. Although the macrosteps can
Fig. 2. Tilt-compensatedtopographic AFM image of the macrostepstructure on a misoriented GaAs(l11)B surface inclined 3° toward the [110] direction.
220
H.-W. Ren et al. /Journal of Crystal Growth 166 (1996) 217-221
be resolved by phase-contrast optical microscopy, the actual step heights are very small. Because AFM has sufficient height resolution to observe monoatomic steps, it was employed to quantitatively study the macrostep structures and surface morphologies. Fig. 2 shows the tilt-compensated topographic AFM image of representative macrosteps. The figure clearly shows that the macrosteps are formed by step bunching. The terrace surfaces of the macrosteps are smooth while the risers are relatively rough and unfaceted. The terrace widths vary from 0.25 to 0.80 p~m, which is in good agreement with those widths observed in situ. From the average slope, it is clear that the terraces are still misoriented 1.5 ° toward the ( l l l ) B face, hence we call them near-(lll)B terraces; the rough step risers along the [110] direction are inclined toward the (110) face and are hereafter called near-(l 10) risers.
3.3. Dependence of macrostep formation
on As 4 flux
During the in situ observation by SEM and also ex situ observations by phase-contrast optical microscopy, it was found that at a lower A s 4 f l u x , nearly the whole surface was covered by macrosteps, while at a higher A s 4 f l u x , nearly the whole surface tended to become smooth. Fig. 3 shows a representative SEM image taken in situ on such a smooth surface. Marks indicated by the arrows have been selected for the dynamic focus of the surface. The epitaxial layer was 1 ixm thick and was grown at an A s / G a flux ratio of 4 (the A s 4 flux was tWO times as much as that used for growth in Fig. 1). AFM profiles of the surface morphologies grown at higher A s 4 flUX showed that the bunched steps are also present, but they are composed of only a few atomic layers. The edges of the bunched steps are wavy. When a lower A s 4 flux is employed during the growth, however, the step-edges tend to straighten along the [110] direction. There are several possible mechanisms for the step bunches. For instance, according to the Schwoebel effect [15,16], when the sticking coefficient of Ga atoms to the step edges from the upper terrace is larger than that from the lower terrace during growth, the terrace widths tend to be unstable, and step bunching occurs. Simulation of this kind of
Fig. 3. In situ SEM image of a misoriented GaAs(l I I)B surface inclined 3° toward the [110] direction after MBE growth of 1 txm GaAs at an A s / G a flux ratio of 4.
morphological instability shows the formation of smooth terraces with a steady state of moving atomic step arrays with a wider separation and sharp risers of bunched steps [17]. Our AFM study shows that the macrostep terraces are always smooth but still have some misorientation toward the nominally exact (111)B face, this means steady-state atomic-step arrays with a wider and uniform separation are stable on the terraces, while the risers are formed by step bunching. If we assume that the Schwoebel effect govems the present case, the difference between the sticking coefficients of Ga atoms to the step edge from the upper terrace should be much larger than that from the lower terrace when the A s 4 flUX is lower, so that step bunching occurs easily. On the contrary, if the increase of A s 4 flux makes the sticking coefficients to the step edges from the upper terrace smaller than that from the lower terrace, step bunching is hindered except for small-scale accidental bunching. Therefore, the surface looks smooth by macroscopic observation.
H.-W. Ren et al. /Journal of Crystal Growth 166 (1996) 217-221
4. Conclusions We have succeeded in observing, in situ, the formation of ordered macrostep arrays during the growth of GaAs on misoriented GaAs(lll)B inclined toward the [110] direction using txRHEED/SEM MBE. These macrosteps are formed gradually during growth and are finally developed into very straight and long macrosteps at a relatively lower A s 4 flux under ~ X~ surface reconstruction. They are coherently aligned and are composed of near-(l 11)B terraces and near-(110) risers. The step-edges are straight along the [170] direction. When a higher As 4 flux is introduced, step bunching is suppressed and smooth surfaces are obtained.
Acknowledgements The authors would like to thank Professor H. Komatsu and Dr. T. Nakada of the Institute for Materials Research, Tohoku University for helping with the AFM observation. They would also like to thank associate Professor M. Tanaka and Ms. M. Washiyama of the University of Tokyo for their help in carrying out this work. One of the authors (H.W.R.) would like to thank the Japan Society for the Promotion of Science (JSPS) for a post-doctoral fellowship at the University of Tokyo. This research was supported by Grants-in-Aid for Scientific Research on Priority Areas "Crystal Growth Mechanism in Atomic Scale" Nos. 03243102 and 04227101
221
from the Ministry of Education, Science and Culture, Japan.
References [I] M. Kasu and T. Fukui, Jpn. J. Appl. Phys. 31 (1992) L864. [2] K. Okamoto, O. Ito and K. Yamaguchi, Jpn. J. Appl. Phys. 31 (1992) L820. [3] T. Yamamoto, M. lnai, T. Takebe, M. Fujii and K. Kobayashi, J. Crystal Growth 127 (1993) 865. [4] K. lnoue, K. Kimura, K. Maehashi, S. Hasegawa and H. Nakashima, J. Crystal Growth 127 (1993) 1041. [5] R. Notzel, L. Daweritz and K. Ploog, J. Crystal Growth 127 (1993) 858. [6] R. Notzel, N.N. Ledentsov, L. Daweritz and K. PIoog, Phys. Rev. B 45 (1992) 3507. [7] D.L. Smith, Solid State Commun. 57 (1986) 919. [8] T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto and T. Hijikata, Jpn. J. Appl. Phys. 26 (1987) L302. [9] T. Hayakawa, M. Kondo, T. Morita, K. Takahashi, T. Suyama, S. Yamamoto and T. Hijikata, Appl. Phys. Lett. 51 (1987) 1705. [10] K. Tsutuis, H. Mizakami, O. Ishiyama, S. Nakamura and S. Furukawa, Jpn. J. Appl. Phys. 29 (1990) 468. [11] A. Chin, P. Martin, P. Ho, J. Ballingall, T. Yu and J. Mazurowski, Appl. Phys. Lett. 59 (1991) 1899. [12] K. Elcess, J.-L. Lievin and C.G. Fonstad, J. Vac. Sci. Technol. B 6 (1988) 638. [13] T. Suzuki and T. Nishinaga, J. Crystal Growth 142 (1994) 49. [14] P. Chert, K.C. Rajkumar and A. Madhukar, Appl. Phys. Lett. 58 (1991) 1771. [15] R.L. Schwoebel, J. Appl. Phys. 40 (1969) 614. [16] R.L. Schwoebel and E.J. Shipsey, J. Appl. Phys. 37 (1966) 3682. [17] M. Sato and M. Uwaha, Phys. Rev. B 51 (1995) 11172.