- Email: [email protected]
Systematic theoretical investigations of adsorption behavior on the GaAs(0 0 1)-c(4 × 4) surfaces
Applied Surface Science 237 (2004) 194–199 www.elsevier.com/locate/apsusc
Systematic theoretical investigations of adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces Tomonori Itoa,*, Kazumi Tsutsumidaa, Kohji Nakamuraa, Yoshihiro Kangawab, Kenji Shiraishic,d, Akihito Taguchie, Hiroyuki Kageshimae a Department of Physics Engineering, Mie University, 1515 Kamihama, Tsu 514-8507, Japan Department of Applied Chemistry, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan c Department of Physics, University of Tsukuba, Tennodai, Tsukuba 305-8271, Japan d Research Consortium for Synthetic Nano-Function Materials Project (SYNAF), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan e NTT Basic Research Laboratories, NTT Corporation, Atsugi 243-0198, Japan
b
Available online 30 July 2004
Abstract Adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces is systematically investigated by using our ab initio-based approach and the Monte Carlo methods. The change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of surface dimers as functions of temperature and As pressure. The calculated results imply that the c(4 4) surface with As dimers is stable at low temperatures less than ~400 K, whereas the surface with Ga–As dimers is stabilized at high temperatures in the range of ~400–700 K. The disordered dimer arrangements consisting of Ga and As substituted by each other in the c(4 4) unit cell hardly appear even at high temperatures such as ~800 K. We also investigate the behavior of Ga and As adatoms on these c(4 4) surfaces. The calculated results reveal that Ga atoms can adsorb and migrate on the surfaces while desorption of As adatoms proceeds without sufficient migration. Therefore, Ga adatoms play an important role for the epitaxial growth of GaAs on the GaAs(0 0 1)-c(4 4) surface. # 2004 Elsevier B.V. All rights reserved. PACS: 68.35.Bs; 68.43.Bc; 81.05.Ea Keywords: GaAs surfaces; Reconstruction; Adsorption behavior; Adatom migration; Ab initio calculations
1. Introduction
* Corresponding author. Tel.: +81 59 231 9724; fax: +81 59 231 9724. E-mail address: [email protected] (T. Ito).
Surface reconstructions on the GaAs(0 0 1) surface have been the object of significant scientific and technological interest, stemming not only from the rich variety of behavior exhibited by this surface but
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.06.125
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
also from the widespread use of epitaxially grown GaAs. Among them, the As-rich c(4 4) surface is technologically important since its surface reconstruction usually emerges in metal organic vapor phase epitaxy (MOVPE) and molecular beam epitaxy (MBE) environments. The atomic structure of the c(4 4) surface and adsorption behavior have therefore been intensively investigated from both experimental and theoretical viewpoints [1–9]. Recently, however, Ohtake et al. [10] proposed the new structure model of the c(4 4) surface with three Ga–As dimers per c(4 4) unit cell. This inspires us to study the adsorption behavior on the GaAs(0 0 1)-c(4 4) surface along with its stability from theoretical viewpoint. In this study, adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces is systematically investigated by using our ab initio-based approach with the Monte Carlo methods [11–13]. The change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of any kinds of surface dimers such as Ga–Ga, As–As, and Ga– As as functions of temperature and As pressure. In particular, the stability of the c(4 4) surface consisting of Ga–As dimers is investigated in detail by considering disordered dimer arrangements such as those consisting of two Ga–As dimers and one As–Ga dimer (where surface Ga and As atoms are replaced by each other) in the c(4 4) unit. Furthermore, we also study the behavior of Ga and As adatoms such as adsorption or desorption and migration on these c(4 4) surfaces. According to these investigations, it is emphasized that Ga adatoms play an important role for the epitaxial growth of GaAs on the c(4 4) surface.
2. Computational methods Adsorption–desorption behavior can be described by comparing the free energy of ideal gas per one particle (chemical potential) m with the adsorption energy Ead. The chemical potential m of the ideal gas such as Ga or As atom is given by the following equation [11–13]. "
# kB T 2pmkB T 3=2 g m ¼ kB T ln p h2
(1)
195
where kB is the Boltzmann’s constant, T the gas temperature, g the degree of degeneracy of electron energy level, p the beam equivalent pressure (BEP) of the particle, m the mass of one particle, and h the Planck’s constant. The chemical potential of As2 in the vapor phase mAs2 is given by: mAs2 ¼ kB T ln½g ztrans zrot zvibr ;
(2)
where ztrans, zrot and zvibr are the partition functions for the translational motion, the rotational motion and the vibrational motion, respectively. The adsorption energy Ead is obtained by ab initio calculations. In the present work, we used the firstprinciples pseudopotential method based on the local-density functional formalism [14]. We adopt Kleinman–Bylander’s separable pseudopotentials and the cut-off value of local potential was carefully chosen so as to prevent ghost bands [15]. The conventional repeated slab geometry is employed to simulate the surface. The unit super cell consists of six atomic layers of GaAs, an atomic layer of fictitious H atoms and a vacuum region equivalent to about 15 atomic layers in thickness. The validity of the thickness in this repeated slab model was carefully checked. Using these chemical potential and adsorption energies, the change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of surface dimers as functions of temperature and As pressure. Based on these results, phase diagram of the c(4 4) surface is obtained. Furthermore, we study the stability of disordered dimer arrangements for the c(4 4) surface with three Ga–As dimers in detail, where surface Ga and As atoms are randomly replaced by each other in the c(4 4) unit cell, using Metropolis Monte Carlo (MMC) simulations. In the MMC simulation we employ the energy of various disordered dimer arrangements in the c(4 4) surface unit cell obtained by the ab initio calculations to equilibrate the surface. Therefore, the long-range interaction between dimers is not taken into account in the simulation. The dimer arrangements are recorded for a lattice size of 100 100 c(4 4) surface unit cell. Periodic boundary conditions are imposed on the xy plane. Adsorption behavior of Ga and As atoms on the c(4 4) surfaces are also investigated using m, Ead and migration potential obtained by the ab initio
196
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
calculations. Kinetic Monte Carlo (KMC) simulation is applied to estimate surface lifetime t and diffusion length L of one adatom impinging on the surfaces. In the calculation procedure, we incorporate competition between the diffusion probability in the conventional Arrhenius form and the desorption probability. The diffusion coefficient D is estimated by D = L2/(2t). We employ the c(4 4) surface unit cell with periodic boundary conditions on the xy plane. 3. Results and discussion Fig. 1 shows the calculated phase diagram of the GaAs(0 0 1)-c(4 4) surfaces with different dimer constituents as functions of temperature and As pressure. This figure implies that the c(4 4) surface with As dimers is stable at low temperatures less than ~400 K. On the other hand, the surface with Ga–As dimers is stabilized at high temperatures in the range
Fig. 1. Calculated phase diagram of the GaAs(0 0 1)-c(4 4) surfaces as functions of temperature and As BEP. The c(4 4) surface with Ga–As dimers is stable in region A, whereas the surface with As dimers is stable in region B. Shaded bar denotes temperature range of the c(4 4) surface with Ga–As dimers observed by experiments [10].
of ~400–700 K. This reflects that the desorption energy of As dimer (1.78 eV) is smaller than that of Ga–As dimer (4.31 eV). Previously reported STM observations imply that the c(4 4) surface with Ga–As dimers is stable in the temperature range of 473 K–723 K [10], which can be favorably compared with our calculated results as shown in Fig. 1. Although the experimental results were obtained under As4 fluxes different from As2 in our calculations, it is well known that both As2 and As4 molecules impinging on the surface desorb from the surface via some processes beyond 450 K [16,17]. This implies that type of As molecules does not affect the surface reconstruction in the temperature range of the c(4 4) surface with Ga–As dimers obtained by our calculations. Consequently, our calculated results are consistent with the experimental results. Furthermore, if the c(4 4) periodicity is kept, we found that two Ga– As dimers and one Ga–Ga dimer in the c(4 4) unit appears within the temperature range of ~700–710 K because of large desorption energy of Ga dimer (6.40 eV). This is in contrast to situation at boundary between the c(4 4) surfaces with As–As dimers and Ga–As dimers, where three As dimers simultaneously replaced by Ga–As dimers. This is also due to the fact that desorption energy of Ga–As dimer is much larger than that of As dimer. Our MMC calculations for the c(4 4) surface with Ga–As dimers suggest that the disordered dimer arrangements, consisting of two Ga–As dimers and one As–Ga (Ga and As are substituted by each other) dimer in the c(4 4) unit cell, hardly appear even at high temperatures such as ~700 K. Here, the ratio of disordered dimer arrangements is less than 10%. This is because the energy of disordered dimer arrangements is higher than ordered dimer arrangements by 0.1–0.3 eV per c(4 4) surface unit cell. These results are consistent with experimental results obtained by Ohtake et al., [18] where STM observations and ab initio calculations reveal that the disordered dimer arrangements with higher energy appears only up to ~10%. Therefore, the c(4 4) surface without disordered dimer arrangements is suitable for investigating the adsorption behavior at conventional growth temperatures. Fig. 2 shows the calculated migration potentials for Ga and As adatoms on the c(4 4) surface with Ga–As dimers. The calculated results imply that Ga
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
197
Fig. 2. Calculated migration potentials for Ga (closed diamond) and As (open diamond) adatoms on the GaAs(0 0 1)-c(4 4) surface with Ga–As dimers.
adatoms favor the lattice site E and As adatoms favorably reside in the lattice site L. In general, adatoms on the compound semiconductor surfaces favor the lattice sites to lower strain energy and suppress the number of electrons remaining in the surface dangling bonds [19]. The lattice sites E and L do not suppress the number of electrons in the dangling bonds but lower the strain energies because of the formation of interatomic bonds with As atoms at the regular fcc sublattice sites in the second layer. Furthermore, these favorable lattice sites for adatoms can be simply interpreted by the coordination number. Ga adatom located at the E site is stabilized by forming Ga–As bonds with ideal coordination number 4 for GaAs, whereas As adatoms at the L site with As– As bonds have the coordination number 2 which is close to ideal coordination number 3 for As. Moreover, it is found that migration potential for Ga adatoms is fairly smaller than those for As adatoms particularly along the lattice sites H–J. Migration probabilities estimated by the Arrhenius form suggest that As adatoms hardly migrate and stay the lattice sites between K and M even at high temperatures. Similar tendency was also found in the calculated migration potentials on the c(4 4) surface with As dimers. Fig. 3 shows the adsorption–desorption transition curve for Ga adatom (Fig. 3(a)) and As adatom
Fig. 3. Calculated adsorption–desorption transition curve for: (a) Ga adatom and (b) As adatom as functions of temperature and BEPs.
(Fig. 3(b)) on the c(4 4) surface consisting of Ga–As dimers as functions of temperature and BEPs. Similar results were obtained for the c(4 4) surface consisting of As dimers. The calculated results reveal that Ga adatoms can adsorb even at high temperatures, while desorption of As adatoms occurs even at low temperatures on the c(4 4) surfaces. This is because the desorption energy of Ga adatom (~3 eV) is much larger than that of As adatom (~0.4 eV). The difference in desorption energy between Ga and As adatoms is due to the fact that Ga adatom located at the most favorable lattice site E forms strong interatomic bonds with As atoms in contrast with the formation of weak As–As bonds for As adatom at the L sites. Thus, these results reveal that Ga atoms can adsorb and migrate on the surfaces while desorption of As adatoms proceeds without sufficient migration. Therefore, Ga adatoms play an important role for the epitaxial growth of GaAs on the c(4 4) surfaces.
198
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
results were obtained under As4 fluxes different from As2 in our calculations, As molecules are mainly consumed to grow GaAs during growth and thus do not change surface reconstruction itself. Considering the fact that Ga adatom migration specifying lifetime of Ga strongly depends on surface reconstruction, difference in type of As molecule does not affect the qualitative difference between Ga adatom migration on these two GaAs(0 0 1)-c(4 4) surfaces. Furthermore, previously reported KMC simulations imply that the reentrant behavior of intensity of RHEED can be interpreted by step density oscillation due to enhancement of Ga adatom migration on GaAs(0 0 1) surface assuming excess As surface at low temperatures [21]. According to these results, our ab initio-based results support the migration enhancement in the KMC simulations at low temperatures and thus are qualitatively consistent with experimental results. Fig. 4. Calculated diffusion coefficients of Ga adatom on the GaAs(0 0 1)-c(4 4) surfaces as a function of reciprocal temperature. A and B denote stable temperature range of the GaAs(0 0 1)c(4 4) surface with Ga–As dimers and As dimers, respectively.
The calculated diffusion coefficient of Ga adatom on the c(4 4) surfaces is shown in Fig. 4 as a function of reciprocal temperature. In the calculation, the arithmetical mean over the 10,000 trials is computed for Ga diffusion at each temperature. We use the extrapolated value of diffusion coefficient from the calculated results at high temperatures ~1000 (K). This is because the desorption probability is too small to simulate long diffusion at the conventional growth temperatures at the present time. Fig. 4 suggests that the diffusion coefficient on the c(4 4) surface with Ga–As dimers decreases with temperature such as D ~ 106 (cm2/s) at 750 K to D ~ 1010 (cm2/s) at 400 K. However, the surface structural change to the c(4 4) surface with As dimers makes diffusion coefficient increase up to D ~ 106 (cm2/s) at 400 K again. Shen et al. [20] found reflection high-energy electron diffraction (RHEED) oscillation during GaAs growth at temperatures as low as 150 8C under high As flux condition. They reported that the RHEED oscillation shows a reentrant behavior; clear oscillation at high temperatures, very weak oscillation at the intermediate temperature range, and again clear oscillation at low temperatures [20]. Although the experimental
4. Conclusion In this paper, adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces is systematically investigated by using our ab initio-based approach and Metropolis and kinetic Monte Carlo methods. The change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of surface dimers as functions of temperature and As pressure. The calculated results imply that the c(4 4) surface with As dimers is stable at low temperatures less than ~400 K, whereas the surface with Ga–As dimers is stabilized at high temperatures in the range of ~400–700 K. Based on this finding, we investigated the behavior of Ga and As adatoms on these c(4 4) surfaces. The calculated results reveal that Ga atoms can adsorb and migrate on the surfaces while desorption of As adatoms proceeds without sufficient migration. Therefore, Ga adatoms play an important role for the epitaxial growth of GaAs on the c(4 4) surfaces. The diffusion coefficient estimated by the results obtained in this study suggests that the surface structural change between c(4 4) surfaces consisting of As dimers and Ga–As dimers strongly affects the adatom diffusion across the surface. The results give one possible explanation for understanding the reentrant behavior in the RHEED oscillation during GaAs
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
growth at low temperatures. Although these results should be checked from various viewpoints, this approach using chemical potential with ab initio and the Monte Carlo methods is feasible for investigating realistic growth processes as functions of temperature and BEPs.
Acknowledgements This work was partly supported by NEDO under International Joint Research Program and Nanotechnology Materials Program.
References [1] D.K. Biegelsen, R.D. Bringans, J.E. Northrup, L.E. Swartz, Phys. Rev. B 41 (1990) 5701. [2] T. Ohno, Phys. Rev. Lett. 70 (1993) 631. [3] J.E. Northrup, S. Froyen, Phys. Rev. Lett. 71 (1993) 2276. [4] A.P. Patne, P.H. Fuoss, D.W. Kisker, G.B. Stephenson, S. Brennan, Phys. Rev. B 49 (1994) 14427. [5] A.R. Avery, D.M. Holmes, J.L. Sudijono, T.S. Jones, B.A. Joyce, Surf. Sci. 323 (1995) 91.
199
[6] N. Moll, A. Kley, E. Pehlke, M. Scheffler, Phys. Rev. B 54 (1996) 8844. [7] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 37 (1998) L262. [8] J.G. LePage, M. Alouani, D.L. Dorsey, J.W. Wilkins, P.E. Blochi, Phys. Rev. B 58 (1998) 1499. [9] A. Nagashima, M. Tazima, A. Nishimura, Y. Takagi, J. Yoshino, Surf. Sci. 493 (2001) 227. [10] A. Ohtake, J. Nakamura, S. Tsukamoto, N. Koguchi, A. Natori, Phys. Rev. Lett. 89 (2002) 206102. [11] Y. Kangawa, T. Ito, A. Taguchi, K. Shiraishi, T. Ohachi, Surf. Sci. 493 (2001) 178. [12] Y. Kangawa, T. Ito, A. Taguchi, K. Shiraishi, T. Irisawa, T. Ohachi, Appl. Surf. Sci. 190 (2002) 517. [13] Y. Kangawa, T. Ito, Y.S. Hiraoka, A. Taguchi, K. Shiraishi, T. Ohachi, Surf. Sci. 507–510 (2002) 285. [14] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) 1133. [15] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 44 (1991) 8503. [16] C.T. Foxon, B.A. Joyce, Surf. Sci. 50 (1975) 434. [17] C.T. Foxon, B.A. Joyce, Surf. Sci. 64 (1977) 293. [18] A. Ohtake, J. Nakamura, S. Tsukamoto, N. Koguichi, A. Natori, Meeting Abstracts of the Physical Society of Japan, Volume 58, Issue 1 (58th Annual Meeting, 2003), Pt. 4, 852 pp. [19] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 37 (1998) 4234. [20] A. Shen, Y. Horikoshi, H. Ohno, S.P. Guo, Appl. Phys. Lett. 71 (1997) 1540. [21] H. Yasuda, H. Ohno, Appl. Phys. Lett. 74 (1999) 3275.
Systematic theoretical investigations of adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces Tomonori Itoa,*, Kazumi Tsutsumidaa, Kohji Nakamuraa, Yoshihiro Kangawab, Kenji Shiraishic,d, Akihito Taguchie, Hiroyuki Kageshimae a Department of Physics Engineering, Mie University, 1515 Kamihama, Tsu 514-8507, Japan Department of Applied Chemistry, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan c Department of Physics, University of Tsukuba, Tennodai, Tsukuba 305-8271, Japan d Research Consortium for Synthetic Nano-Function Materials Project (SYNAF), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan e NTT Basic Research Laboratories, NTT Corporation, Atsugi 243-0198, Japan
b
Available online 30 July 2004
Abstract Adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces is systematically investigated by using our ab initio-based approach and the Monte Carlo methods. The change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of surface dimers as functions of temperature and As pressure. The calculated results imply that the c(4 4) surface with As dimers is stable at low temperatures less than ~400 K, whereas the surface with Ga–As dimers is stabilized at high temperatures in the range of ~400–700 K. The disordered dimer arrangements consisting of Ga and As substituted by each other in the c(4 4) unit cell hardly appear even at high temperatures such as ~800 K. We also investigate the behavior of Ga and As adatoms on these c(4 4) surfaces. The calculated results reveal that Ga atoms can adsorb and migrate on the surfaces while desorption of As adatoms proceeds without sufficient migration. Therefore, Ga adatoms play an important role for the epitaxial growth of GaAs on the GaAs(0 0 1)-c(4 4) surface. # 2004 Elsevier B.V. All rights reserved. PACS: 68.35.Bs; 68.43.Bc; 81.05.Ea Keywords: GaAs surfaces; Reconstruction; Adsorption behavior; Adatom migration; Ab initio calculations
1. Introduction
* Corresponding author. Tel.: +81 59 231 9724; fax: +81 59 231 9724. E-mail address: [email protected] (T. Ito).
Surface reconstructions on the GaAs(0 0 1) surface have been the object of significant scientific and technological interest, stemming not only from the rich variety of behavior exhibited by this surface but
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.06.125
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
also from the widespread use of epitaxially grown GaAs. Among them, the As-rich c(4 4) surface is technologically important since its surface reconstruction usually emerges in metal organic vapor phase epitaxy (MOVPE) and molecular beam epitaxy (MBE) environments. The atomic structure of the c(4 4) surface and adsorption behavior have therefore been intensively investigated from both experimental and theoretical viewpoints [1–9]. Recently, however, Ohtake et al. [10] proposed the new structure model of the c(4 4) surface with three Ga–As dimers per c(4 4) unit cell. This inspires us to study the adsorption behavior on the GaAs(0 0 1)-c(4 4) surface along with its stability from theoretical viewpoint. In this study, adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces is systematically investigated by using our ab initio-based approach with the Monte Carlo methods [11–13]. The change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of any kinds of surface dimers such as Ga–Ga, As–As, and Ga– As as functions of temperature and As pressure. In particular, the stability of the c(4 4) surface consisting of Ga–As dimers is investigated in detail by considering disordered dimer arrangements such as those consisting of two Ga–As dimers and one As–Ga dimer (where surface Ga and As atoms are replaced by each other) in the c(4 4) unit. Furthermore, we also study the behavior of Ga and As adatoms such as adsorption or desorption and migration on these c(4 4) surfaces. According to these investigations, it is emphasized that Ga adatoms play an important role for the epitaxial growth of GaAs on the c(4 4) surface.
2. Computational methods Adsorption–desorption behavior can be described by comparing the free energy of ideal gas per one particle (chemical potential) m with the adsorption energy Ead. The chemical potential m of the ideal gas such as Ga or As atom is given by the following equation [11–13]. "
# kB T 2pmkB T 3=2 g m ¼ kB T ln p h2
(1)
195
where kB is the Boltzmann’s constant, T the gas temperature, g the degree of degeneracy of electron energy level, p the beam equivalent pressure (BEP) of the particle, m the mass of one particle, and h the Planck’s constant. The chemical potential of As2 in the vapor phase mAs2 is given by: mAs2 ¼ kB T ln½g ztrans zrot zvibr ;
(2)
where ztrans, zrot and zvibr are the partition functions for the translational motion, the rotational motion and the vibrational motion, respectively. The adsorption energy Ead is obtained by ab initio calculations. In the present work, we used the firstprinciples pseudopotential method based on the local-density functional formalism [14]. We adopt Kleinman–Bylander’s separable pseudopotentials and the cut-off value of local potential was carefully chosen so as to prevent ghost bands [15]. The conventional repeated slab geometry is employed to simulate the surface. The unit super cell consists of six atomic layers of GaAs, an atomic layer of fictitious H atoms and a vacuum region equivalent to about 15 atomic layers in thickness. The validity of the thickness in this repeated slab model was carefully checked. Using these chemical potential and adsorption energies, the change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of surface dimers as functions of temperature and As pressure. Based on these results, phase diagram of the c(4 4) surface is obtained. Furthermore, we study the stability of disordered dimer arrangements for the c(4 4) surface with three Ga–As dimers in detail, where surface Ga and As atoms are randomly replaced by each other in the c(4 4) unit cell, using Metropolis Monte Carlo (MMC) simulations. In the MMC simulation we employ the energy of various disordered dimer arrangements in the c(4 4) surface unit cell obtained by the ab initio calculations to equilibrate the surface. Therefore, the long-range interaction between dimers is not taken into account in the simulation. The dimer arrangements are recorded for a lattice size of 100 100 c(4 4) surface unit cell. Periodic boundary conditions are imposed on the xy plane. Adsorption behavior of Ga and As atoms on the c(4 4) surfaces are also investigated using m, Ead and migration potential obtained by the ab initio
196
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
calculations. Kinetic Monte Carlo (KMC) simulation is applied to estimate surface lifetime t and diffusion length L of one adatom impinging on the surfaces. In the calculation procedure, we incorporate competition between the diffusion probability in the conventional Arrhenius form and the desorption probability. The diffusion coefficient D is estimated by D = L2/(2t). We employ the c(4 4) surface unit cell with periodic boundary conditions on the xy plane. 3. Results and discussion Fig. 1 shows the calculated phase diagram of the GaAs(0 0 1)-c(4 4) surfaces with different dimer constituents as functions of temperature and As pressure. This figure implies that the c(4 4) surface with As dimers is stable at low temperatures less than ~400 K. On the other hand, the surface with Ga–As dimers is stabilized at high temperatures in the range
Fig. 1. Calculated phase diagram of the GaAs(0 0 1)-c(4 4) surfaces as functions of temperature and As BEP. The c(4 4) surface with Ga–As dimers is stable in region A, whereas the surface with As dimers is stable in region B. Shaded bar denotes temperature range of the c(4 4) surface with Ga–As dimers observed by experiments [10].
of ~400–700 K. This reflects that the desorption energy of As dimer (1.78 eV) is smaller than that of Ga–As dimer (4.31 eV). Previously reported STM observations imply that the c(4 4) surface with Ga–As dimers is stable in the temperature range of 473 K–723 K [10], which can be favorably compared with our calculated results as shown in Fig. 1. Although the experimental results were obtained under As4 fluxes different from As2 in our calculations, it is well known that both As2 and As4 molecules impinging on the surface desorb from the surface via some processes beyond 450 K [16,17]. This implies that type of As molecules does not affect the surface reconstruction in the temperature range of the c(4 4) surface with Ga–As dimers obtained by our calculations. Consequently, our calculated results are consistent with the experimental results. Furthermore, if the c(4 4) periodicity is kept, we found that two Ga– As dimers and one Ga–Ga dimer in the c(4 4) unit appears within the temperature range of ~700–710 K because of large desorption energy of Ga dimer (6.40 eV). This is in contrast to situation at boundary between the c(4 4) surfaces with As–As dimers and Ga–As dimers, where three As dimers simultaneously replaced by Ga–As dimers. This is also due to the fact that desorption energy of Ga–As dimer is much larger than that of As dimer. Our MMC calculations for the c(4 4) surface with Ga–As dimers suggest that the disordered dimer arrangements, consisting of two Ga–As dimers and one As–Ga (Ga and As are substituted by each other) dimer in the c(4 4) unit cell, hardly appear even at high temperatures such as ~700 K. Here, the ratio of disordered dimer arrangements is less than 10%. This is because the energy of disordered dimer arrangements is higher than ordered dimer arrangements by 0.1–0.3 eV per c(4 4) surface unit cell. These results are consistent with experimental results obtained by Ohtake et al., [18] where STM observations and ab initio calculations reveal that the disordered dimer arrangements with higher energy appears only up to ~10%. Therefore, the c(4 4) surface without disordered dimer arrangements is suitable for investigating the adsorption behavior at conventional growth temperatures. Fig. 2 shows the calculated migration potentials for Ga and As adatoms on the c(4 4) surface with Ga–As dimers. The calculated results imply that Ga
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
197
Fig. 2. Calculated migration potentials for Ga (closed diamond) and As (open diamond) adatoms on the GaAs(0 0 1)-c(4 4) surface with Ga–As dimers.
adatoms favor the lattice site E and As adatoms favorably reside in the lattice site L. In general, adatoms on the compound semiconductor surfaces favor the lattice sites to lower strain energy and suppress the number of electrons remaining in the surface dangling bonds [19]. The lattice sites E and L do not suppress the number of electrons in the dangling bonds but lower the strain energies because of the formation of interatomic bonds with As atoms at the regular fcc sublattice sites in the second layer. Furthermore, these favorable lattice sites for adatoms can be simply interpreted by the coordination number. Ga adatom located at the E site is stabilized by forming Ga–As bonds with ideal coordination number 4 for GaAs, whereas As adatoms at the L site with As– As bonds have the coordination number 2 which is close to ideal coordination number 3 for As. Moreover, it is found that migration potential for Ga adatoms is fairly smaller than those for As adatoms particularly along the lattice sites H–J. Migration probabilities estimated by the Arrhenius form suggest that As adatoms hardly migrate and stay the lattice sites between K and M even at high temperatures. Similar tendency was also found in the calculated migration potentials on the c(4 4) surface with As dimers. Fig. 3 shows the adsorption–desorption transition curve for Ga adatom (Fig. 3(a)) and As adatom
Fig. 3. Calculated adsorption–desorption transition curve for: (a) Ga adatom and (b) As adatom as functions of temperature and BEPs.
(Fig. 3(b)) on the c(4 4) surface consisting of Ga–As dimers as functions of temperature and BEPs. Similar results were obtained for the c(4 4) surface consisting of As dimers. The calculated results reveal that Ga adatoms can adsorb even at high temperatures, while desorption of As adatoms occurs even at low temperatures on the c(4 4) surfaces. This is because the desorption energy of Ga adatom (~3 eV) is much larger than that of As adatom (~0.4 eV). The difference in desorption energy between Ga and As adatoms is due to the fact that Ga adatom located at the most favorable lattice site E forms strong interatomic bonds with As atoms in contrast with the formation of weak As–As bonds for As adatom at the L sites. Thus, these results reveal that Ga atoms can adsorb and migrate on the surfaces while desorption of As adatoms proceeds without sufficient migration. Therefore, Ga adatoms play an important role for the epitaxial growth of GaAs on the c(4 4) surfaces.
198
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
results were obtained under As4 fluxes different from As2 in our calculations, As molecules are mainly consumed to grow GaAs during growth and thus do not change surface reconstruction itself. Considering the fact that Ga adatom migration specifying lifetime of Ga strongly depends on surface reconstruction, difference in type of As molecule does not affect the qualitative difference between Ga adatom migration on these two GaAs(0 0 1)-c(4 4) surfaces. Furthermore, previously reported KMC simulations imply that the reentrant behavior of intensity of RHEED can be interpreted by step density oscillation due to enhancement of Ga adatom migration on GaAs(0 0 1) surface assuming excess As surface at low temperatures [21]. According to these results, our ab initio-based results support the migration enhancement in the KMC simulations at low temperatures and thus are qualitatively consistent with experimental results. Fig. 4. Calculated diffusion coefficients of Ga adatom on the GaAs(0 0 1)-c(4 4) surfaces as a function of reciprocal temperature. A and B denote stable temperature range of the GaAs(0 0 1)c(4 4) surface with Ga–As dimers and As dimers, respectively.
The calculated diffusion coefficient of Ga adatom on the c(4 4) surfaces is shown in Fig. 4 as a function of reciprocal temperature. In the calculation, the arithmetical mean over the 10,000 trials is computed for Ga diffusion at each temperature. We use the extrapolated value of diffusion coefficient from the calculated results at high temperatures ~1000 (K). This is because the desorption probability is too small to simulate long diffusion at the conventional growth temperatures at the present time. Fig. 4 suggests that the diffusion coefficient on the c(4 4) surface with Ga–As dimers decreases with temperature such as D ~ 106 (cm2/s) at 750 K to D ~ 1010 (cm2/s) at 400 K. However, the surface structural change to the c(4 4) surface with As dimers makes diffusion coefficient increase up to D ~ 106 (cm2/s) at 400 K again. Shen et al. [20] found reflection high-energy electron diffraction (RHEED) oscillation during GaAs growth at temperatures as low as 150 8C under high As flux condition. They reported that the RHEED oscillation shows a reentrant behavior; clear oscillation at high temperatures, very weak oscillation at the intermediate temperature range, and again clear oscillation at low temperatures [20]. Although the experimental
4. Conclusion In this paper, adsorption behavior on the GaAs(0 0 1)-c(4 4) surfaces is systematically investigated by using our ab initio-based approach and Metropolis and kinetic Monte Carlo methods. The change in stable structure of the c(4 4) surfaces is clarified by considering adsorption or desorption of surface dimers as functions of temperature and As pressure. The calculated results imply that the c(4 4) surface with As dimers is stable at low temperatures less than ~400 K, whereas the surface with Ga–As dimers is stabilized at high temperatures in the range of ~400–700 K. Based on this finding, we investigated the behavior of Ga and As adatoms on these c(4 4) surfaces. The calculated results reveal that Ga atoms can adsorb and migrate on the surfaces while desorption of As adatoms proceeds without sufficient migration. Therefore, Ga adatoms play an important role for the epitaxial growth of GaAs on the c(4 4) surfaces. The diffusion coefficient estimated by the results obtained in this study suggests that the surface structural change between c(4 4) surfaces consisting of As dimers and Ga–As dimers strongly affects the adatom diffusion across the surface. The results give one possible explanation for understanding the reentrant behavior in the RHEED oscillation during GaAs
T. Ito et al. / Applied Surface Science 237 (2004) 194–199
growth at low temperatures. Although these results should be checked from various viewpoints, this approach using chemical potential with ab initio and the Monte Carlo methods is feasible for investigating realistic growth processes as functions of temperature and BEPs.
Acknowledgements This work was partly supported by NEDO under International Joint Research Program and Nanotechnology Materials Program.
References [1] D.K. Biegelsen, R.D. Bringans, J.E. Northrup, L.E. Swartz, Phys. Rev. B 41 (1990) 5701. [2] T. Ohno, Phys. Rev. Lett. 70 (1993) 631. [3] J.E. Northrup, S. Froyen, Phys. Rev. Lett. 71 (1993) 2276. [4] A.P. Patne, P.H. Fuoss, D.W. Kisker, G.B. Stephenson, S. Brennan, Phys. Rev. B 49 (1994) 14427. [5] A.R. Avery, D.M. Holmes, J.L. Sudijono, T.S. Jones, B.A. Joyce, Surf. Sci. 323 (1995) 91.
199
[6] N. Moll, A. Kley, E. Pehlke, M. Scheffler, Phys. Rev. B 54 (1996) 8844. [7] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 37 (1998) L262. [8] J.G. LePage, M. Alouani, D.L. Dorsey, J.W. Wilkins, P.E. Blochi, Phys. Rev. B 58 (1998) 1499. [9] A. Nagashima, M. Tazima, A. Nishimura, Y. Takagi, J. Yoshino, Surf. Sci. 493 (2001) 227. [10] A. Ohtake, J. Nakamura, S. Tsukamoto, N. Koguchi, A. Natori, Phys. Rev. Lett. 89 (2002) 206102. [11] Y. Kangawa, T. Ito, A. Taguchi, K. Shiraishi, T. Ohachi, Surf. Sci. 493 (2001) 178. [12] Y. Kangawa, T. Ito, A. Taguchi, K. Shiraishi, T. Irisawa, T. Ohachi, Appl. Surf. Sci. 190 (2002) 517. [13] Y. Kangawa, T. Ito, Y.S. Hiraoka, A. Taguchi, K. Shiraishi, T. Ohachi, Surf. Sci. 507–510 (2002) 285. [14] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) 1133. [15] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 44 (1991) 8503. [16] C.T. Foxon, B.A. Joyce, Surf. Sci. 50 (1975) 434. [17] C.T. Foxon, B.A. Joyce, Surf. Sci. 64 (1977) 293. [18] A. Ohtake, J. Nakamura, S. Tsukamoto, N. Koguichi, A. Natori, Meeting Abstracts of the Physical Society of Japan, Volume 58, Issue 1 (58th Annual Meeting, 2003), Pt. 4, 852 pp. [19] T. Ito, K. Shiraishi, Jpn. J. Appl. Phys. 37 (1998) 4234. [20] A. Shen, Y. Horikoshi, H. Ohno, S.P. Guo, Appl. Phys. Lett. 71 (1997) 1540. [21] H. Yasuda, H. Ohno, Appl. Phys. Lett. 74 (1999) 3275.