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GaAs(110) heteroepitaxy
Surface Science 433–435 (1999) 900–903 www.elsevier.nl/locate/susc
First-principles calculation for misfit dislocations in InAs/GaAs(110) heteroepitaxy Norihisa Oyama a, *, Eiji Ohta a, Kyozaburo Takeda b,c, Kenji Shiraishi c,d, Hiroshi Yamaguchi d a Department of Material Science, Faculty of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522 Japan b Department of Materials Science and Engineering, School of Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo, 169-8555 Japan c Advanced Research Institute for Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo, 169-0072, Japan d NTT Basic Research Laboratories, Morinosato-Wakamiya, Atsugi-si, Kanagawa, 243-0198 Japan
Abstract The misfit dislocation core structures in InAs/GaAs(110) heterostructures were calculated for InAs thicknesses of 2 and 4 ML using first-principles calculations. Dislocation cores with asymmetric five-fold coordinated In atoms were formed at the InAs/GaAs interface. This core structure is maintained even if the thickness of InAs epilayer increases. We also calculated for the GaAs/InAs(110) heterostructure and the core has a different structure at the very initial stage of heteroepitaxy. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Density functional calculations; Gallium arsenide; Indium arsenide; Semiconductor–semiconductor heterostructures
1. Introduction Highly strained InAs/GaAs heterostructures are the most promising systems for novel optoelectronic devices, such as high-speed low-noise laser diodes or high electron mobility transistors (HEMTs). It is well known, however, that many threading dislocations and misfit dislocations are generated which degrade the optical properties. These devices need high crystalline quality heterostructures and therefore, many experiments have been performed to improve the growth technology. In the past, the vast majority of works on InAs/GaAs heteroepitaxy have been performed on * Corresponding author. Fax: +81 45 563 0322. E-mail address: [email protected] (N. Oyama)
the GaAs(001) substrate. The problem of the InAs growth on the (001)-oriented GaAs substrate is that a transition of the growth mode from twodimensional (2D) to three-dimensional (3D) usually occurs (Stranski–Krastanov mode) under a conventional As-stable condition of an In/As flux ratio of about 10 and the critical thickness is only 1.5 ML. A lot of effort has been devoted to preventing the 3D nucleation, and 2D growth was realized by either using Te as surfactant, or by making growth under an In-stable condition [1,2]. InAs growth on a non-(001) oriented substrate is another way to overwhelm 3D nucleation [3]. Zhang et al. showed that the 2D growth mode was maintained during heteroepitaxy on the GaAs(110) substrate, and 90° perfect dislocations were generated in the [001] direction and confined
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N. Oyama et al. / Surface Science 433–435 (1999) 900–903
at the heterointerface [4]. Recent STM and RHEED observations have provided more detailed information on InAs/GaAs(110) heteroepitaxy. First, edge dislocations were generated when the InAs thickness was 2 or 3 ML, and the array of dark bands, which were assigned to the periodic generation of 90° dislocations, was completed by 5 ML [5,6 ]. The surface was depressed just above the core and the magnitude of vertical displacement depends on the InAs thickness. Second, the RHEED pattern shows that the strain relaxation of this system has strong anisotropy. A strain relaxation of about 86% occurred at 5 ML in the [11: 0] direction, whereas only a very small change was observed in the orthogonal [001] direction, which is parallel to the 90° perfect misfit dislocations. These experimental results indicate that the confinement of misfit dislocations at the heterointerface should make it possible to obtain a smooth growth surface. Therefore, it is of great importance to clarify the microscopic mechanism of this confinement of dislocations, although the growth mode is very sensitive to growth conditions such as growth temperature, growth rate, In/As flux ratio etc. However, there are few studies based on atomic-scale structures of misfit dislocations both theoretically and experimentally. In this paper, we studied for the first time the atomic and electronic structures of misfit dislocations of InAs/ GaAs(110) and GaAs/InAs(110) heterointerface with InAs epilayer thicknesses of 2 and 4 ML by first principles calculations.
2. Computational details We used the norm-conserving pseudopotential method based on local density functional theory (LDF ) [7,8]. For Ga and As, we used separable pseudopotentials [9], and the local cut-off radii for separable potentials were carefully determined in order to avoid ghost states [10]. However, we used non-separable ones for the In atoms. The exchange-correlation potentials had the Ceparley– Alders functional form parameterized by Perdew and Zunger. The wavefunction was expanded into a plane wave basis set corresponding to the kinetic energy cut-off of 7.29 Ry.
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We used the repeat slab model to study the InAs/GaAs(110) heteroepitaxy. At the interface on InAs unit for every 15 GaAs units were forcibly removed in the direction of [11: 0] direction in order to describe misfit dislocations. This periodic removal of InAs units is based on the experimentally observed period of misfit dislocations of ˚ . This separation of misfit dislocation cor~60 A responds to the complete strain relief in the [11: 0] direction due to the lattice mismatch of ~7.2%. We investigated 2 and 4 ML thicknesses of InAs epilayers and GaAs substrates were approximated by the 4 ML slab. Ga and As atoms in the deepest layer of the GaAs substrate were terminated by the hypothetical hydrogen atoms to describe the semi-infinite substrate. Termination with hypothetical hydrogen atoms is a very powerful method and its details have been described elsewhere [11].
3. Results and discussion Fig. 1a shows the calculated InAs/GaAs(110) heterointerface with an InAs thickness of 2 ML. The 90° perfect misfit dislocations were formed in the direction of [001]. In this structure, the most noticeable point is the formation of five-fold coordinated In atoms that have covalent bonds with the nearest five As atoms along the dislocation line. Each Ga atoms below this In atom forms bonds with the nearest three As atoms and has one empty dangling bond. These results were obtained by charge density investigations. The Ga atom in the core is pushed ˚ compared with the downward more than 0.5 A adjacent atoms. The epilayer surface was depressed as seen in the STM observation just above the dislocation line due to the strain field caused by the misfit dislocations. The vertical displacement ˚. of the As atoms that we calculated is 0.702 A Lattice strain is localized primarily in the small area just around the dislocation core, and the InAs and GaAs layers near the core are remarkable tensed (~117%) and compressed (~95%) respectively. As seen in Fig. 1a, this structure does not possess mirror symmetry. In this dislocation core, cation atoms, In and Ga atoms, face each other when we look from the [001] direction.
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N. Oyama et al. / Surface Science 433–435 (1999) 900–903
Fig. 1. Obtained dislocation core structure of the InAs/GaAs(110) heterointerface. The thickness of the InAs layer is (a) 2 ML and (b) 4 ML. White, gray, and black circles indicate In, Ga, and As atoms respectively. The numbers in the ˚ ). figure represent bond lengths (A
Fig. 1b shows the InAs/GaAs(110) heterostructure obtained with an InAs thickness of 4 ML. The overall profile of this structure is very similar to that of 2 ML, including the atomic structure of the asymmetric dislocation core and bond lengths just around the dislocation line. This means that the core structure does not change even when the thickness of the epilayer increases. ˚ for The vertical surface displacement is 0.702 A ˚ for 4 ML, respectively. STM 2 ML and 0.522 A observation shows that the vertical surface displacement decreases as the thickness of the InAs increases. The magnitude of the vertical displacement and its epilayer thickness dependence are qualitatively in good agreement with the experiments. Next, we consider the Ga/As/InAs(110) heteroepitaxy. For quantum well structures such as GaAs/InAs/GaAs, it is important to investigate GaAs/InAs heteroepitaxy as well as InAs/GaAs heteroepitaxy. We calculated the atomic and electronic structures of the misfit dislocation in
Fig. 2. Obtained dislocation core structure of the GaAs/InAs(110) heterointerface. The thickness of the GaAs layer is (a) 2 ML and (b) 3 ML. White, gray, and black circles indicate In, Ga, and As atoms, respectively. The numbers in ˚ ). the figure represent bond lengths (A
order to investigate GaAs/InAs(110) heteroepitaxy from the viewpoint of dislocation confinement, although it is well known that 2D growth hardly occurs for GaAs epilayers whose surface free energy is not smaller than that of the InAs substrates. Fig. 2a shows the calculated structure of GaAs/InAs(110) heteroepitaxy with a GaAs thickness of 2 ML. The thickness of our InAs substrate ˚. is 4 ML and the width of the unit cell is ~12 A The core structure is very different from that of InAs/GaAs(110) interface, and As atoms face each other when we look from the [001] direction and the atoms on the surface layer are pushed upwards. There are no five-fold coordinated In atoms in the dislocation core and anion atoms are located in the dislocation line. The Ga atoms on the top GaAs surface layer just above the dislocation core have bonds with the As atoms on the top InAs layer, and the As atoms on the second top GaAs surface layer have perfectly filled dangling bonds. This core structure does possess mirror symmetry
N. Oyama et al. / Surface Science 433–435 (1999) 900–903
in contrast to the InAs/GaAs(110) systems. Moreover, a total energy investigation shows that this structure is energetically more stable than that of the coherent structure. It should be noted that this structure is not maintained during heteroepitaxy. The core structure of the GaAs/InAs(110) heterostructure obtained for a GaAs thickness of 3 ML is shown in Fig. 2b. As seen in Fig. 2b, the core structure is similar to that at the InAs/GaAs(110) heterointerfaces, and five-fold coordinated In atoms appear in the core. Therefore, the dislocation core structure given in Fig. 2a is a transient structure which appears only at the very initial stage of GaAs/InAs heteroepitaxy, and changes as the InAs epilayer thickness increases. Consequently, a change in the core structure during GaAs grown on InAs substrate makes it difficult to obtain smooth growth surfaces as well as the higher surface free energy of GaAs epilayers.
4. Conclusion We calculated the atomic and electronic structures of misfit dislocations at InAs/GaAs(110) heterointerfaces by first principles calculations. The calculation results show that the core confined at the heterointerface has five-fold coordinated In atoms. Moreover, this core structure is maintained even if the thickness of the InAs epilayer changes. On the other hand, different core structures with perfectly filled As dangling bonds appears at the
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very initial stage of GaAs/InAs heteroepitaxy, and change as the epilayer thickness increases.
Acknowledgements This work was partly supported by the JSPS Research for Future Programs in the Area of Atomic Scale Surface and Interface Dynamics, the High-tech Research Center Project, and the Ministry of Education, Science, Sports and Culture of Japan.
References [1] N. Grandjean, J. Massie, V.H. Etgens, Phys. Rev. Lett. 69 (1992) 796. [2] A. Trapert, E. Trourie, K.H. Ploog, J. Cryst. Growth 146 (1995) 368. [3] H. Yamaguchi, J.G. Belk, X.M. Zhang, J.L. Sudijono, M.R. Fahy, T.S. Jones, D.W. Pashley, B.A. Joyce, Phys. Rev. B 55 (1997) 1337. [4] X. Zhang, D.W. Pashley, L. Hart, J.H. Neave, P.N. Fawcett, B.A. Joyce, J. Cryst. Growth 131 (1993) 300. [5] J.G. Belk, J.L. Sudijono, X.M. Zhang, J.H. Neave, T.S. Jones, B.A. Joyce, Phys. Rev. Lett. 78 (1997) 475. [6 ] B.A. Joyce, J.L. Sudijono, J.G. Belk, H. Yamaguchi, X.M. Zhang, H.T. Dobbs, A. Zangwill, D.D. Vvedensky, T.S. Jones, Jpn. J. App. Phys. 36 (1997) 4111. [7] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [8] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [9] L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. [10] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 26 (1982) 4199. [11] K. Shiraishi, J. Phys. Soc. Jpn. 59 (1990) 3455.
First-principles calculation for misfit dislocations in InAs/GaAs(110) heteroepitaxy Norihisa Oyama a, *, Eiji Ohta a, Kyozaburo Takeda b,c, Kenji Shiraishi c,d, Hiroshi Yamaguchi d a Department of Material Science, Faculty of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522 Japan b Department of Materials Science and Engineering, School of Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo, 169-8555 Japan c Advanced Research Institute for Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo, 169-0072, Japan d NTT Basic Research Laboratories, Morinosato-Wakamiya, Atsugi-si, Kanagawa, 243-0198 Japan
Abstract The misfit dislocation core structures in InAs/GaAs(110) heterostructures were calculated for InAs thicknesses of 2 and 4 ML using first-principles calculations. Dislocation cores with asymmetric five-fold coordinated In atoms were formed at the InAs/GaAs interface. This core structure is maintained even if the thickness of InAs epilayer increases. We also calculated for the GaAs/InAs(110) heterostructure and the core has a different structure at the very initial stage of heteroepitaxy. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Density functional calculations; Gallium arsenide; Indium arsenide; Semiconductor–semiconductor heterostructures
1. Introduction Highly strained InAs/GaAs heterostructures are the most promising systems for novel optoelectronic devices, such as high-speed low-noise laser diodes or high electron mobility transistors (HEMTs). It is well known, however, that many threading dislocations and misfit dislocations are generated which degrade the optical properties. These devices need high crystalline quality heterostructures and therefore, many experiments have been performed to improve the growth technology. In the past, the vast majority of works on InAs/GaAs heteroepitaxy have been performed on * Corresponding author. Fax: +81 45 563 0322. E-mail address: [email protected] (N. Oyama)
the GaAs(001) substrate. The problem of the InAs growth on the (001)-oriented GaAs substrate is that a transition of the growth mode from twodimensional (2D) to three-dimensional (3D) usually occurs (Stranski–Krastanov mode) under a conventional As-stable condition of an In/As flux ratio of about 10 and the critical thickness is only 1.5 ML. A lot of effort has been devoted to preventing the 3D nucleation, and 2D growth was realized by either using Te as surfactant, or by making growth under an In-stable condition [1,2]. InAs growth on a non-(001) oriented substrate is another way to overwhelm 3D nucleation [3]. Zhang et al. showed that the 2D growth mode was maintained during heteroepitaxy on the GaAs(110) substrate, and 90° perfect dislocations were generated in the [001] direction and confined
0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 99 ) 0 05 2 4 -5
N. Oyama et al. / Surface Science 433–435 (1999) 900–903
at the heterointerface [4]. Recent STM and RHEED observations have provided more detailed information on InAs/GaAs(110) heteroepitaxy. First, edge dislocations were generated when the InAs thickness was 2 or 3 ML, and the array of dark bands, which were assigned to the periodic generation of 90° dislocations, was completed by 5 ML [5,6 ]. The surface was depressed just above the core and the magnitude of vertical displacement depends on the InAs thickness. Second, the RHEED pattern shows that the strain relaxation of this system has strong anisotropy. A strain relaxation of about 86% occurred at 5 ML in the [11: 0] direction, whereas only a very small change was observed in the orthogonal [001] direction, which is parallel to the 90° perfect misfit dislocations. These experimental results indicate that the confinement of misfit dislocations at the heterointerface should make it possible to obtain a smooth growth surface. Therefore, it is of great importance to clarify the microscopic mechanism of this confinement of dislocations, although the growth mode is very sensitive to growth conditions such as growth temperature, growth rate, In/As flux ratio etc. However, there are few studies based on atomic-scale structures of misfit dislocations both theoretically and experimentally. In this paper, we studied for the first time the atomic and electronic structures of misfit dislocations of InAs/ GaAs(110) and GaAs/InAs(110) heterointerface with InAs epilayer thicknesses of 2 and 4 ML by first principles calculations.
2. Computational details We used the norm-conserving pseudopotential method based on local density functional theory (LDF ) [7,8]. For Ga and As, we used separable pseudopotentials [9], and the local cut-off radii for separable potentials were carefully determined in order to avoid ghost states [10]. However, we used non-separable ones for the In atoms. The exchange-correlation potentials had the Ceparley– Alders functional form parameterized by Perdew and Zunger. The wavefunction was expanded into a plane wave basis set corresponding to the kinetic energy cut-off of 7.29 Ry.
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We used the repeat slab model to study the InAs/GaAs(110) heteroepitaxy. At the interface on InAs unit for every 15 GaAs units were forcibly removed in the direction of [11: 0] direction in order to describe misfit dislocations. This periodic removal of InAs units is based on the experimentally observed period of misfit dislocations of ˚ . This separation of misfit dislocation cor~60 A responds to the complete strain relief in the [11: 0] direction due to the lattice mismatch of ~7.2%. We investigated 2 and 4 ML thicknesses of InAs epilayers and GaAs substrates were approximated by the 4 ML slab. Ga and As atoms in the deepest layer of the GaAs substrate were terminated by the hypothetical hydrogen atoms to describe the semi-infinite substrate. Termination with hypothetical hydrogen atoms is a very powerful method and its details have been described elsewhere [11].
3. Results and discussion Fig. 1a shows the calculated InAs/GaAs(110) heterointerface with an InAs thickness of 2 ML. The 90° perfect misfit dislocations were formed in the direction of [001]. In this structure, the most noticeable point is the formation of five-fold coordinated In atoms that have covalent bonds with the nearest five As atoms along the dislocation line. Each Ga atoms below this In atom forms bonds with the nearest three As atoms and has one empty dangling bond. These results were obtained by charge density investigations. The Ga atom in the core is pushed ˚ compared with the downward more than 0.5 A adjacent atoms. The epilayer surface was depressed as seen in the STM observation just above the dislocation line due to the strain field caused by the misfit dislocations. The vertical displacement ˚. of the As atoms that we calculated is 0.702 A Lattice strain is localized primarily in the small area just around the dislocation core, and the InAs and GaAs layers near the core are remarkable tensed (~117%) and compressed (~95%) respectively. As seen in Fig. 1a, this structure does not possess mirror symmetry. In this dislocation core, cation atoms, In and Ga atoms, face each other when we look from the [001] direction.
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N. Oyama et al. / Surface Science 433–435 (1999) 900–903
Fig. 1. Obtained dislocation core structure of the InAs/GaAs(110) heterointerface. The thickness of the InAs layer is (a) 2 ML and (b) 4 ML. White, gray, and black circles indicate In, Ga, and As atoms respectively. The numbers in the ˚ ). figure represent bond lengths (A
Fig. 1b shows the InAs/GaAs(110) heterostructure obtained with an InAs thickness of 4 ML. The overall profile of this structure is very similar to that of 2 ML, including the atomic structure of the asymmetric dislocation core and bond lengths just around the dislocation line. This means that the core structure does not change even when the thickness of the epilayer increases. ˚ for The vertical surface displacement is 0.702 A ˚ for 4 ML, respectively. STM 2 ML and 0.522 A observation shows that the vertical surface displacement decreases as the thickness of the InAs increases. The magnitude of the vertical displacement and its epilayer thickness dependence are qualitatively in good agreement with the experiments. Next, we consider the Ga/As/InAs(110) heteroepitaxy. For quantum well structures such as GaAs/InAs/GaAs, it is important to investigate GaAs/InAs heteroepitaxy as well as InAs/GaAs heteroepitaxy. We calculated the atomic and electronic structures of the misfit dislocation in
Fig. 2. Obtained dislocation core structure of the GaAs/InAs(110) heterointerface. The thickness of the GaAs layer is (a) 2 ML and (b) 3 ML. White, gray, and black circles indicate In, Ga, and As atoms, respectively. The numbers in ˚ ). the figure represent bond lengths (A
order to investigate GaAs/InAs(110) heteroepitaxy from the viewpoint of dislocation confinement, although it is well known that 2D growth hardly occurs for GaAs epilayers whose surface free energy is not smaller than that of the InAs substrates. Fig. 2a shows the calculated structure of GaAs/InAs(110) heteroepitaxy with a GaAs thickness of 2 ML. The thickness of our InAs substrate ˚. is 4 ML and the width of the unit cell is ~12 A The core structure is very different from that of InAs/GaAs(110) interface, and As atoms face each other when we look from the [001] direction and the atoms on the surface layer are pushed upwards. There are no five-fold coordinated In atoms in the dislocation core and anion atoms are located in the dislocation line. The Ga atoms on the top GaAs surface layer just above the dislocation core have bonds with the As atoms on the top InAs layer, and the As atoms on the second top GaAs surface layer have perfectly filled dangling bonds. This core structure does possess mirror symmetry
N. Oyama et al. / Surface Science 433–435 (1999) 900–903
in contrast to the InAs/GaAs(110) systems. Moreover, a total energy investigation shows that this structure is energetically more stable than that of the coherent structure. It should be noted that this structure is not maintained during heteroepitaxy. The core structure of the GaAs/InAs(110) heterostructure obtained for a GaAs thickness of 3 ML is shown in Fig. 2b. As seen in Fig. 2b, the core structure is similar to that at the InAs/GaAs(110) heterointerfaces, and five-fold coordinated In atoms appear in the core. Therefore, the dislocation core structure given in Fig. 2a is a transient structure which appears only at the very initial stage of GaAs/InAs heteroepitaxy, and changes as the InAs epilayer thickness increases. Consequently, a change in the core structure during GaAs grown on InAs substrate makes it difficult to obtain smooth growth surfaces as well as the higher surface free energy of GaAs epilayers.
4. Conclusion We calculated the atomic and electronic structures of misfit dislocations at InAs/GaAs(110) heterointerfaces by first principles calculations. The calculation results show that the core confined at the heterointerface has five-fold coordinated In atoms. Moreover, this core structure is maintained even if the thickness of the InAs epilayer changes. On the other hand, different core structures with perfectly filled As dangling bonds appears at the
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very initial stage of GaAs/InAs heteroepitaxy, and change as the epilayer thickness increases.
Acknowledgements This work was partly supported by the JSPS Research for Future Programs in the Area of Atomic Scale Surface and Interface Dynamics, the High-tech Research Center Project, and the Ministry of Education, Science, Sports and Culture of Japan.
References [1] N. Grandjean, J. Massie, V.H. Etgens, Phys. Rev. Lett. 69 (1992) 796. [2] A. Trapert, E. Trourie, K.H. Ploog, J. Cryst. Growth 146 (1995) 368. [3] H. Yamaguchi, J.G. Belk, X.M. Zhang, J.L. Sudijono, M.R. Fahy, T.S. Jones, D.W. Pashley, B.A. Joyce, Phys. Rev. B 55 (1997) 1337. [4] X. Zhang, D.W. Pashley, L. Hart, J.H. Neave, P.N. Fawcett, B.A. Joyce, J. Cryst. Growth 131 (1993) 300. [5] J.G. Belk, J.L. Sudijono, X.M. Zhang, J.H. Neave, T.S. Jones, B.A. Joyce, Phys. Rev. Lett. 78 (1997) 475. [6 ] B.A. Joyce, J.L. Sudijono, J.G. Belk, H. Yamaguchi, X.M. Zhang, H.T. Dobbs, A. Zangwill, D.D. Vvedensky, T.S. Jones, Jpn. J. App. Phys. 36 (1997) 4111. [7] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [8] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [9] L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. [10] X. Gonze, R. Stumpf, M. Scheffler, Phys. Rev. B 26 (1982) 4199. [11] K. Shiraishi, J. Phys. Soc. Jpn. 59 (1990) 3455.