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Theoretical investigations of initial growth process on GaAs(001) surfaces
surface science ELSEVIER
Surface Science 386 (1997) 241-244
Theoretical investigations of initial growth process on GaAs (001 ) surfaces T o m o n o r i Ito a.,, K e n j i Shiraishi b a N T T System Electronics Laboratories, 3-1, Morinosato Wakamiya, Atsugi-shi 243-01, Japan b N T T Basic Research Laboratories, 3-1, Morinosato Wakamiya, A tsugi-shi 243-01, Japan Received 5 November 1996; accepted for publication 26 February 1997
Abstract
This paper briefly reviews our latest achievements in theoretically approaching the initial growth process including adatom migration and changes in the atomistic structure on the GaAs(001)-(2 x4) surface. The calculations are performed using the ab initio pseudopotential method, empirical interatomic potential and Monte Carlo (MC) simulation. On the (2 x 4)ill surface, we found that Ga adatom migration strongly depends on the Ga adatom coverage during molecular-beam-epitaxy growth. This can be interpreted by the electron counting model. Based on these findings, migration potentials near the steps on the (2 x 4)fl2 surface can be successfully calculated using a simple energy formula. Using this energy formula, the newly developed electron-counting MC simulation results imply that the GaAs(001) surface changes its atomic arrangement from an initial (2 x4)f12 to (2 x4)fll via (2 x 4)ct. Further Ga and As adsorptions fill up the lattice sites in the missing dimer region continuing layer-by-layer growth. © 1997 Elsevier Science B.V. Keywords: Adatom kinetics; Computer simulations; Epitaxy; Gallium arsenide; Growth; Surface structure
I. Introduction
GaAs(001 ) surfaces are very interesting not only in terms of surface physics but also in terms of the semiconductor technology of thin-film growth. The GaAs(001) surface exhibits a sequence of reconstructions dependent on the surface stoichiometry, ranging from the As-rich c ( 4 x 4 ) structure to the Ga-rich c(8 x 2) reconstruction. Among these, the As-rich (2 x 4) surface is the most technologically important because molecular-beam-epitaxy (MBE) growth under As-rich conditions usually begins and ends with this surface. The atomic * Corresponding author. Tel: (+ 81 ) 462 40.2884; fax: (+ 81 ) 462 40.4351; e-mail: [email protected] 0039-6028/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0039-6028 (97)00320-8
structure of the (2 x 4) surface has therefore been intensively investigated from both experimental and theoretical viewpoints [1-6]. However, there have been very few theoretical studies on the initial MBE growth process that incorporate surface reconstructions. This paper briefly reviews our latest achievements in theoretically approaching the initial growth process including adatom migration and changes in the atomistic structure on the GaAs(001)-(2 x 4) surface. Ga adatom migration on the (2x4)fll surface is investigated using stochastic Monte Carlo (MC) simulation based on migration potentials obtained by ab initio calculations. Furthermore, migration potentials near steps on the (2 x 4)fl2 surface are evaluated
~ Ito, K. Shiraishi / Surface Science 386 (1997) 241-244
242
by a simple energy formula using empirical interatomic potential and an energy term extracted from the ab initio pseudopotential calculations. Based on successful applications of the simple energy formula, a newly developed electron-counting MC (ECMC) simulation procedure is performed to investigate changes in the atomistic structure of the (2 x 4) surface during MBE growth.
2.
Adatom
migration
on the surface
During MBE growth, adatom migration on a reconstructed semiconductor surface is crucial in controlling atomic arrangements. In this section, the migration of Ga adatoms on the (2 x 4)ill surface (see Fig. 3c) is theoretically investigated using the stochastic MC approach based on the migration potentials obtained by our ab initio total energy calculations [7,8]. Calculated migration potentials indicate that a stable adsorption site strongly depends on Ga adatom coverage and changes from an As dimer region to a missing dimer region as the number of Ga adatoms increases. Based on this, MC simulation of 20 x 20 square sublattices was performed at 600°C and a growth rate of 2 ML s -1 [7-10].
Fig. 1 shows the ratio n/N of the number of Ga adatoms n in the dimer region (closed squares) and missing dimer region (open squares) to the total number of surface lattice sites N as a function of surface coverage 0. This figure implies that Ga adatoms favorably exist in the dimer region at the initial stage of growth, that is, 0 < 0.1. The number of Ga adatoms in the missing dimer region is found to linearly increase with increasing coverage and to approach that in the dimer region in the 0.1<0<0.3 range. At higher adatom coverage 0>0.3, again, the number of Ga adatoms on As dimers linearly increases, whereas the number of Ga adatoms in the missing dimer region stays nearly constant. This is because anisotropic migration is suppressed at higher adatom coverage resulting from the migration potential with lower activation barriers. Similar qualitative trends were also found in Alo.sGao.sAs [9,10]. This migration behavior reflects the coverage dependence of the migration potentials. This suggests that atomic arrangements resulting from adatom migration can be obtained by considering stable lattice sites in migration potentials, because effective activation barriers are sufficiently low at typical growth temperatures such as 600°C.
3. 0.5
....
0.4
I ....
•
, ....
I ....
, ....
dimer region
0.3
0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
O Fig. 1. Calculated results on the (2 x 4)fll surface for the ratio
n/N representing the number of Ga adatoms n to the total number of lattice sites N as a function of coverage in the dimer region (ll) and missing dimer region ([]) on the (2x4)fll surface.
Adatom
migration
potentials
near steps
Farrell et al. [11] proposed a simple criterion for predicting the static surface reconstructions of GaAs(001 ) and growth mechanisms, where all As dangling bonds are kept filled and all Ga dangling bonds are empty. This leads to an electron counting model which can specify the stability of a compound-semiconductor surface based on a simple analysis of the dangling-bond energy levels. According to our ab initio calculations, stable Ga adsorption on the (2 x 4)fll surface can be characterized by considering the strain energy and the electron counting model [7]. Based on this, we proposed a simple energy formula for the system E=Ebond+AEbond [12]. Here Ebond is described in terms of interatomic energies based on the empirical interatomic potential and AEbond is given by the number of electrons AZ remaining in the dangling bonds on the surface.
Z Ito, K. Shiraishi / Surface Science 386 (1997) 241-244
243
It is well-known that adatoms impinging on the surfaces migrate on the growing surface and are finally captured at growth sites such as steps and kinks. However, there have been very few theoretical studies, incorporating surface reconstructions, on stable growth sites of GaAs(001 ) surfaces. To check the versatility of the energy formula, this section discusses stable growth sites on a (2 x 4)/32 surface with steps or kinks. The calculated migration potentials of a Ga adatom near the A- and B-type steps on the (2 x 4)fl2 surface are shown in Fig. 2 [12]. A difference between the A- and B-type steps explicitly appears in the migration potential near the step edges. The A-type edge does not affect the migration potential significantly, whereas
the migration potential energy has the lowest value at the lattice sites on the lower terrace near the B-type step edge as denoted by A in Fig. 2b. This is due to the fact that the Ga adatom located at the A site in the missing dimer row is weakly stretched by an As-dimer and As atom at the regular fcc sublattice and can be dimerized with another Ga atom to reduce the number of electrons in the G a dangling bonds. This suggests that the B-type steps, unlike A-type steps, provide active sites for GaAs growth on the (2 x4)/32 surface. Opposite qualitative trends were found in the calculations on the c(4 × 4) surface [13]. These findings are consistent with previously reported experimental results [ 14,15].
(a)
4. Structural change of the surface
[i~ol [1 10]
(b)
,
To apply the energy formula to MBE growth simulation, we developed a new electron counting MC ( E C M C ) method to investigate the structural change of the GaAs(001) surface during MBE growth [16]. In the calculation procedure, equilibrium atomic arrangements are obtained by lowering the energy E = Ebond+ AEbond according to the Metropolis MC algorithm. Here As adsorption occurs when Ga adatom coverage exceeds 0.25 based on our ab initio calculations of As 2 adsorption energy [17]. A typical adsorption sequence on the GaAs(001)-(2 x 4)fl2 surface obtained by ECMC simulation is shown in Fig. 3. The GaAs(001)
(a)O-o-o.o.o-~ (b)O.*-o-o-o-o~ (c)O-o-o.o-o-o-o-~ 0--o
[1
_
Fig. 2. Calculated migration potentials for a Ga atom on (a) the (2 x4)/32 surface with A-type steps and (b) the 132surface with B-typesteps. Large and small open circlesdenote As atoms on the upper and lower terraces, respectively.The valleyon the contour map corresponds to the missing dimer row. The preferential lattice site in the missing dimer row near a B-type step is labeled A in (b).
0-,,o
,-~[1 ~o]
Fig. 3. Calculated results for the structural change from the GaAs(001 )-(2 x 4)/?2 surface. Shaded and open circles denote Ga and As atoms, respectively.
244
T. [to, K. Shiraishi / Surface Science 386 (1997) 241-244
surface changes its structure from (2 ×4)32 in Fig. 3a to another electronically stable (2 × 4)~ as shown in Fig. 3b. On the (2 ×4)/~1 formed by subsequent As adsorption, shown in Fig. 3c, Ga adatoms occupy the lattice sites on the As-dimers at low Ga adatom coverage in Fig. 3d. As the coverage increases, Ga adatoms tend to reside in the lattice sites in the missing dimer region in Fig. 3e. This coverage dependence of the Ga adsorption site is consistent with the ab initiobased MC simulation presented in the previous section. Further As adsorptions fill up the lattice sites in the missing dimer region, shown in Fig. 3f, continuing layer-by-layer growth restoring the electron counting model. These results imply that the ECMC approach is a feasible method for investigating stable lattice sites for adatoms during MBE growth.
5. Summary Ab initio-based calculations have clarified various elemental processes of MBE growth on the GaAs(001)-(2×4) surfaces, such as the strong dependence of cation migration and anion adsorption on adatom coverage. The complicated initial growth processes on the GaAs(001)-(2 ×4) surfaces can be qualitatively interpreted by simple energy analysis including ECMC simulation based on the empirical interatomic potential and the electron counting model. Our successful applications suggest that ECMC is a feasible approach to simulate MBE growth of compound semiconduc-
tors. We are currently developing an ECMC technique to investigate the dynamic behavior of Ga and As adatoms on the GaAs(001) surface with kinks and steps in a larger unit cell.
Acknowledgements We would like to thank Dr Shintaro Miyazawa and Dr Nobuyuki Imoto for their continuous encouragement and fruitful discussions throughout the research.
References [1] D.J. Chadi, J. Vac. Sci. Technol. A 5 (1987) 834. [2] M.D. Pashley, K.W. Haberern, W. Friday, J.M. Woodall, P.D. Kirchner, Phys. Rev. Lett. 50 (1988) 2176. [3] T. Hashizume, Q.K. Xie, J. Zhou, A. Ichimiya, T. Sakurai, Phys. Rev. Lett. 73 (1994) 2208. [4] T. Ohno, Phys. Rev. Lett. 70 (1993) 631. [5] J.E. Northrup, S. Froyen, Phys. Rev. Lett. 71 (1993)2276. [6] J.E. Northrup, S. Froyen, Phys. Rev. B 50 (1994) 2015. [7] K. Shiraishi, T. Ito, J. Cryst. Growth 150 (1995) 159. [8] K. Shiraishi, Thin Solid Films 272 (1996) 345. [9] T. Ito, K. Shiraishi, T. Ohno, Appl. Surf. Sci. 82/83 (1994) 208. [10] T. Ito, J. Appl. Phys. 77 (1995) 4845. [11] H.H. Farrell, J.P. Harbison, L.D. Peterson, J. Vac. Sci. Technol. B 5 (1987) 1482. [12] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 35 (1996) L949. [13] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 35 (1996) LI016. [14] H. Yamaguchi, Y. Horikoshi, Jpn. J. Appl. Phys. 30 ( 1991 ) 802. [15] M. Kasu, N. Kobayashi, H. Yamaguchi, Appl. Phys. Lett. 63 (1993) 678. [16] T. Ito, K. Shiraishi, Surf. Sci. 357/358 (1996) 486. [17] K. Shiraishi, T. Ito, Surf. Sci. 357/358 (1996) 451.
Surface Science 386 (1997) 241-244
Theoretical investigations of initial growth process on GaAs (001 ) surfaces T o m o n o r i Ito a.,, K e n j i Shiraishi b a N T T System Electronics Laboratories, 3-1, Morinosato Wakamiya, Atsugi-shi 243-01, Japan b N T T Basic Research Laboratories, 3-1, Morinosato Wakamiya, A tsugi-shi 243-01, Japan Received 5 November 1996; accepted for publication 26 February 1997
Abstract
This paper briefly reviews our latest achievements in theoretically approaching the initial growth process including adatom migration and changes in the atomistic structure on the GaAs(001)-(2 x4) surface. The calculations are performed using the ab initio pseudopotential method, empirical interatomic potential and Monte Carlo (MC) simulation. On the (2 x 4)ill surface, we found that Ga adatom migration strongly depends on the Ga adatom coverage during molecular-beam-epitaxy growth. This can be interpreted by the electron counting model. Based on these findings, migration potentials near the steps on the (2 x 4)fl2 surface can be successfully calculated using a simple energy formula. Using this energy formula, the newly developed electron-counting MC simulation results imply that the GaAs(001) surface changes its atomic arrangement from an initial (2 x4)f12 to (2 x4)fll via (2 x 4)ct. Further Ga and As adsorptions fill up the lattice sites in the missing dimer region continuing layer-by-layer growth. © 1997 Elsevier Science B.V. Keywords: Adatom kinetics; Computer simulations; Epitaxy; Gallium arsenide; Growth; Surface structure
I. Introduction
GaAs(001 ) surfaces are very interesting not only in terms of surface physics but also in terms of the semiconductor technology of thin-film growth. The GaAs(001) surface exhibits a sequence of reconstructions dependent on the surface stoichiometry, ranging from the As-rich c ( 4 x 4 ) structure to the Ga-rich c(8 x 2) reconstruction. Among these, the As-rich (2 x 4) surface is the most technologically important because molecular-beam-epitaxy (MBE) growth under As-rich conditions usually begins and ends with this surface. The atomic * Corresponding author. Tel: (+ 81 ) 462 40.2884; fax: (+ 81 ) 462 40.4351; e-mail: [email protected] 0039-6028/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0039-6028 (97)00320-8
structure of the (2 x 4) surface has therefore been intensively investigated from both experimental and theoretical viewpoints [1-6]. However, there have been very few theoretical studies on the initial MBE growth process that incorporate surface reconstructions. This paper briefly reviews our latest achievements in theoretically approaching the initial growth process including adatom migration and changes in the atomistic structure on the GaAs(001)-(2 x 4) surface. Ga adatom migration on the (2x4)fll surface is investigated using stochastic Monte Carlo (MC) simulation based on migration potentials obtained by ab initio calculations. Furthermore, migration potentials near steps on the (2 x 4)fl2 surface are evaluated
~ Ito, K. Shiraishi / Surface Science 386 (1997) 241-244
242
by a simple energy formula using empirical interatomic potential and an energy term extracted from the ab initio pseudopotential calculations. Based on successful applications of the simple energy formula, a newly developed electron-counting MC (ECMC) simulation procedure is performed to investigate changes in the atomistic structure of the (2 x 4) surface during MBE growth.
2.
Adatom
migration
on the surface
During MBE growth, adatom migration on a reconstructed semiconductor surface is crucial in controlling atomic arrangements. In this section, the migration of Ga adatoms on the (2 x 4)ill surface (see Fig. 3c) is theoretically investigated using the stochastic MC approach based on the migration potentials obtained by our ab initio total energy calculations [7,8]. Calculated migration potentials indicate that a stable adsorption site strongly depends on Ga adatom coverage and changes from an As dimer region to a missing dimer region as the number of Ga adatoms increases. Based on this, MC simulation of 20 x 20 square sublattices was performed at 600°C and a growth rate of 2 ML s -1 [7-10].
Fig. 1 shows the ratio n/N of the number of Ga adatoms n in the dimer region (closed squares) and missing dimer region (open squares) to the total number of surface lattice sites N as a function of surface coverage 0. This figure implies that Ga adatoms favorably exist in the dimer region at the initial stage of growth, that is, 0 < 0.1. The number of Ga adatoms in the missing dimer region is found to linearly increase with increasing coverage and to approach that in the dimer region in the 0.1<0<0.3 range. At higher adatom coverage 0>0.3, again, the number of Ga adatoms on As dimers linearly increases, whereas the number of Ga adatoms in the missing dimer region stays nearly constant. This is because anisotropic migration is suppressed at higher adatom coverage resulting from the migration potential with lower activation barriers. Similar qualitative trends were also found in Alo.sGao.sAs [9,10]. This migration behavior reflects the coverage dependence of the migration potentials. This suggests that atomic arrangements resulting from adatom migration can be obtained by considering stable lattice sites in migration potentials, because effective activation barriers are sufficiently low at typical growth temperatures such as 600°C.
3. 0.5
....
0.4
I ....
•
, ....
I ....
, ....
dimer region
0.3
0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
O Fig. 1. Calculated results on the (2 x 4)fll surface for the ratio
n/N representing the number of Ga adatoms n to the total number of lattice sites N as a function of coverage in the dimer region (ll) and missing dimer region ([]) on the (2x4)fll surface.
Adatom
migration
potentials
near steps
Farrell et al. [11] proposed a simple criterion for predicting the static surface reconstructions of GaAs(001 ) and growth mechanisms, where all As dangling bonds are kept filled and all Ga dangling bonds are empty. This leads to an electron counting model which can specify the stability of a compound-semiconductor surface based on a simple analysis of the dangling-bond energy levels. According to our ab initio calculations, stable Ga adsorption on the (2 x 4)fll surface can be characterized by considering the strain energy and the electron counting model [7]. Based on this, we proposed a simple energy formula for the system E=Ebond+AEbond [12]. Here Ebond is described in terms of interatomic energies based on the empirical interatomic potential and AEbond is given by the number of electrons AZ remaining in the dangling bonds on the surface.
Z Ito, K. Shiraishi / Surface Science 386 (1997) 241-244
243
It is well-known that adatoms impinging on the surfaces migrate on the growing surface and are finally captured at growth sites such as steps and kinks. However, there have been very few theoretical studies, incorporating surface reconstructions, on stable growth sites of GaAs(001 ) surfaces. To check the versatility of the energy formula, this section discusses stable growth sites on a (2 x 4)/32 surface with steps or kinks. The calculated migration potentials of a Ga adatom near the A- and B-type steps on the (2 x 4)fl2 surface are shown in Fig. 2 [12]. A difference between the A- and B-type steps explicitly appears in the migration potential near the step edges. The A-type edge does not affect the migration potential significantly, whereas
the migration potential energy has the lowest value at the lattice sites on the lower terrace near the B-type step edge as denoted by A in Fig. 2b. This is due to the fact that the Ga adatom located at the A site in the missing dimer row is weakly stretched by an As-dimer and As atom at the regular fcc sublattice and can be dimerized with another Ga atom to reduce the number of electrons in the G a dangling bonds. This suggests that the B-type steps, unlike A-type steps, provide active sites for GaAs growth on the (2 x4)/32 surface. Opposite qualitative trends were found in the calculations on the c(4 × 4) surface [13]. These findings are consistent with previously reported experimental results [ 14,15].
(a)
4. Structural change of the surface
[i~ol [1 10]
(b)
,
To apply the energy formula to MBE growth simulation, we developed a new electron counting MC ( E C M C ) method to investigate the structural change of the GaAs(001) surface during MBE growth [16]. In the calculation procedure, equilibrium atomic arrangements are obtained by lowering the energy E = Ebond+ AEbond according to the Metropolis MC algorithm. Here As adsorption occurs when Ga adatom coverage exceeds 0.25 based on our ab initio calculations of As 2 adsorption energy [17]. A typical adsorption sequence on the GaAs(001)-(2 x 4)fl2 surface obtained by ECMC simulation is shown in Fig. 3. The GaAs(001)
(a)O-o-o.o.o-~ (b)O.*-o-o-o-o~ (c)O-o-o.o-o-o-o-~ 0--o
[1
_
Fig. 2. Calculated migration potentials for a Ga atom on (a) the (2 x4)/32 surface with A-type steps and (b) the 132surface with B-typesteps. Large and small open circlesdenote As atoms on the upper and lower terraces, respectively.The valleyon the contour map corresponds to the missing dimer row. The preferential lattice site in the missing dimer row near a B-type step is labeled A in (b).
0-,,o
,-~[1 ~o]
Fig. 3. Calculated results for the structural change from the GaAs(001 )-(2 x 4)/?2 surface. Shaded and open circles denote Ga and As atoms, respectively.
244
T. [to, K. Shiraishi / Surface Science 386 (1997) 241-244
surface changes its structure from (2 ×4)32 in Fig. 3a to another electronically stable (2 × 4)~ as shown in Fig. 3b. On the (2 ×4)/~1 formed by subsequent As adsorption, shown in Fig. 3c, Ga adatoms occupy the lattice sites on the As-dimers at low Ga adatom coverage in Fig. 3d. As the coverage increases, Ga adatoms tend to reside in the lattice sites in the missing dimer region in Fig. 3e. This coverage dependence of the Ga adsorption site is consistent with the ab initiobased MC simulation presented in the previous section. Further As adsorptions fill up the lattice sites in the missing dimer region, shown in Fig. 3f, continuing layer-by-layer growth restoring the electron counting model. These results imply that the ECMC approach is a feasible method for investigating stable lattice sites for adatoms during MBE growth.
5. Summary Ab initio-based calculations have clarified various elemental processes of MBE growth on the GaAs(001)-(2×4) surfaces, such as the strong dependence of cation migration and anion adsorption on adatom coverage. The complicated initial growth processes on the GaAs(001)-(2 ×4) surfaces can be qualitatively interpreted by simple energy analysis including ECMC simulation based on the empirical interatomic potential and the electron counting model. Our successful applications suggest that ECMC is a feasible approach to simulate MBE growth of compound semiconduc-
tors. We are currently developing an ECMC technique to investigate the dynamic behavior of Ga and As adatoms on the GaAs(001) surface with kinks and steps in a larger unit cell.
Acknowledgements We would like to thank Dr Shintaro Miyazawa and Dr Nobuyuki Imoto for their continuous encouragement and fruitful discussions throughout the research.
References [1] D.J. Chadi, J. Vac. Sci. Technol. A 5 (1987) 834. [2] M.D. Pashley, K.W. Haberern, W. Friday, J.M. Woodall, P.D. Kirchner, Phys. Rev. Lett. 50 (1988) 2176. [3] T. Hashizume, Q.K. Xie, J. Zhou, A. Ichimiya, T. Sakurai, Phys. Rev. Lett. 73 (1994) 2208. [4] T. Ohno, Phys. Rev. Lett. 70 (1993) 631. [5] J.E. Northrup, S. Froyen, Phys. Rev. Lett. 71 (1993)2276. [6] J.E. Northrup, S. Froyen, Phys. Rev. B 50 (1994) 2015. [7] K. Shiraishi, T. Ito, J. Cryst. Growth 150 (1995) 159. [8] K. Shiraishi, Thin Solid Films 272 (1996) 345. [9] T. Ito, K. Shiraishi, T. Ohno, Appl. Surf. Sci. 82/83 (1994) 208. [10] T. Ito, J. Appl. Phys. 77 (1995) 4845. [11] H.H. Farrell, J.P. Harbison, L.D. Peterson, J. Vac. Sci. Technol. B 5 (1987) 1482. [12] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 35 (1996) L949. [13] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 35 (1996) LI016. [14] H. Yamaguchi, Y. Horikoshi, Jpn. J. Appl. Phys. 30 ( 1991 ) 802. [15] M. Kasu, N. Kobayashi, H. Yamaguchi, Appl. Phys. Lett. 63 (1993) 678. [16] T. Ito, K. Shiraishi, Surf. Sci. 357/358 (1996) 486. [17] K. Shiraishi, T. Ito, Surf. Sci. 357/358 (1996) 451.