- Email: [email protected]
First-principles study of strain effects on Mn in Si
ARTICLE IN PRESS
Physica B 376–377 (2006) 672–676 www.elsevier.com/locate/physb
First-principles study of strain effects on Mn in Si S. Yabuuchia,, E. Ohtaa, H. Kageshimab, A. Taguchib a
Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1, Hiyoshi, Kohoku-Ku, Yokohama 223-8522, Japan b NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan
Abstract The effects of strain on Mn impurities in Si were investigated by using first-principles calculations. It is shown that substitutional Mn is stabilized and that the magnetic moment is maintained when a tensile strain is given. This suggests that the tensile strain is effective for improving the crystallinity of epitaxial films. Under high Mn concentration conditions, the substitutional Mn complex can cause a structural change and decrease the lattice constant of the crystal. Thus, the formation of shrinked epitaxial films can cause a structural change related to the substitutional Mn complexes, which might make it impossible to obtain the ferromagnetic property. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Pp; 71.55.Cn; 71.15.Mb Keywords: First-principles calculation; Magnetic semiconductor; Si; Strain
1. Introduction Recently many researchers have investigated merging spin degrees of freedom into conventional semiconductor electronics. Special attention has been given to diluted magnetic semiconductors (DMSs), which have been shown to be successful for integrating ferromagnetism through doping of a semiconductor crystal with an additional transition metal impurity such as Mn [1]. A Mndoped III–V semiconductor, such as Ga1xMnxAs or In1xMnxAs is an attractive material which has carrierinduced ferromagnetism and magnetic properties that can be controlled by using field effects or light illumination [2–5]. Since the group-IV semiconductors such as Si are the keystones of semiconductor electronics, ferromagnetic semiconductors based on Si are very important in device and process technology. Several experimental and theoretical studies have been carried out for Si and Ge-based DMSs. Park et al. investigated fabricating Ge1xMnx by using molecular beam epitaxy and confirmed a magnetically ordered phase from ferromagnetic interaction up to Corresponding author. Tel.: +81 422 22 2964; fax: +81 45 566 1587.
E-mail address: [email protected] (S. Yabuuchi). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.169
116 K, along with a p-type character and hole-mediated exchange [6]. Recently it was reported that Mn ion implantation can realize ferromagnetic behavior above room temperature [7]. Several theoretical studies for Siand Ge-based DMSs have also been conducted. Dalpian et al. reported the stability of Mn impurities in Si and on the surface; they showed that the formation energy of Mn in Si is high and most stable site is the interstitial tetrahedral site in bulk Si [8]. Miura et al. also reported that Mn cluster is more stable than isolated Mn in Si [9]. Actually the solubility of Mn in Si is very low and interstitial impurity can diffuse more easily than substitutional one and undesired magnetic clusters such as Mn clusters and silicide are easily formed [10–12]. Thus, it is difficult to fabricate high-quality crystalline DMSs by Mn doping in Si. In an attempt to overcome these difficulties, we considered the effect of the strain. Since Mn has a different atomic radius from Si, the strain could modify the stability of the doped Mn. If we use epitaxial growth, the strain can be easily introduced. We investigated such strain effects on Mn impurities in Si by using the first-principles calculations. It is shown that the substitutional Mn is stabilized and that the magnetic moment is maintained when a tensile strain is given. This suggests that the tensile strain is
ARTICLE IN PRESS S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
effective for improving the crystallinity of the epitaxial films. 2. Method We performed first-principles calculations based on density-functional theory within generalized gradient approximation (GGA) and local spin density approximation (LSD). We used the Vanderbilt ultrasoft pseudopotential [13,14] for Mn, the Troullier-Martins pseudopotential [15] for Si, and a plane-wave basis set up to 25 Ry. All calculations have been done with TAPP [16,17]. We calculated bulk Si and cubic MnSi in order to check the accuracy of the pseudopotentials we used. For bulk Si, the calculated lattice constant is 5.46 A˚, which reproduced an experimental value of 5.43 A˚ within 0.6% error. For bulk cubic MnSi, the calculated lattice constant is 4.58 A˚, which agrees well with the experimental value of 4.558 A˚ [18]. For Mn impurity in Si, we used a 16-atom unit cell and put one or two Mn atoms in it on various positions. We used kpoint sampling of 4 4 2 in the Brillouin zone and optimized the atomic configurations to evaluate their magnetic moments. We regarded the atomic position fully relaxed when all atomic force components were smaller than 0.05 eV/A˚. From the results we estimated the total energy, formation energy, and magnetic moment of Mn impurity in Si and their dependence on the strain effects. The formation energy Ef is calculated by the following equations: E f ¼ E Total nSi mSi nMn mMn ,
(1)
mSi ¼ E Total ðSiðdÞÞ,
(2)
mMn ¼ E Total ðMnSiÞ E Total ðSiðdÞÞ,
(3)
673
where E Total is the total energy of the unit cell which is a function of the lattice constant d, mSi is the Si chemical potential, mMn is the Mn chemical potential in bulk MnSi, nSi is the number of Si atoms in the unit cell, and nMn is the number of Mn atoms in the unit cell. E Total (MnSi) and E Total (Si(d)) represent the total energy of bulk cubic MnSi and that of bulk Si with the lattice constant d. Since we want to discuss how to avoid the segregation of MnSi from the Mn-doped Si, we define mMn as Eq. (3). In our calculation, the formation energy Ef of a substitutional Mn impurity in Si is 2.96 eV, when the lattice constant is the experimental value of 5.43 A˚ [19]. The interstitial tetrahedral impurity has a formation energy of 2.50 eV, and the interstitial hexagonal impurity has a formation energy of 3.20 eV. Thus, the interstitial tetrahedral site is the most stable site for the isolated Mn impurity in Si. In the substitutional site the magnetic moment is 3.00mB, whereas in the interstitial tetrahedral site it is 3.19mB, and in the interstitial hexagonal site it is 3.09mB. The calculated result is in good agreement with the previous report [8]. The nearest-neighbor Mn–Si distance is about 2.39, 2.44 and 2.37 A˚, for the substitutional site, interstitial tetrahedral site, and interstitial hexagonal site, respectively. These distances are longer than that of bulk Si. 3. Results and discussions We investigated the effects of three-dimensional isotropic strain on the isolated Mn in Si. The stability of the total energy with isolated substitutional and interstitial tetrahedral Mn in Si shows that the lattice constants of the crystals are slightly larger than that of bulk Si. Fig. 1(a) shows the formation energy of the isolated Mn in Si as a function of lattice constant. When the lattice constant 4
4.0
3
3.5
Magnetic Moment [B]
Formation energy [eV]
sub inter
3.0
2
1 sub inter
2.5
0 90 (a)
95 100 105 Lattice Constant [%]
110
90 (b)
95 100 105 Lattice Constant [%]
110
Fig. 1. (a) Formation energy and (b) magnetic moment of the isolated substitutional and the interstitial tetrahedral site Mn in Si as a function of the lattice constant. The lattice constant of 100% corresponds to the calculated value of 5.46 A˚. Circles and squares are the isolated substitutional and the interstitial tetrahedral Mn in Si, respectively.
ARTICLE IN PRESS S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
674
6
8
5
inter-inter
6
Formation Energy [eV]
Total Energy Change [eV]
sub-sub
4
4
3
2
2
sub-sub inter-inter
1
0
0 90 (a)
95 100 105 Lattice Constant [%]
110
90 (b)
95 100 105 Lattice Constant [%]
110
Fig. 2. (a) Total energy and (b) formation energy of the substitutional and interstitial tetrahedral Mn complexes in Si as a function of the lattice constant. All atomic configurations were optimized. The lattice constant of 100% corresponds to the calculated value of 5.46 A˚. Circles and squares are the substitutional and the interstitial tetrahedral Mn complexes in Si, respectively.
increases, the formation energy of substitutional Mn decreases about 0.16 eV at most, and that of interstitial tetrahedral Mn in Si also decreases. Fig. 1(b) shows the magnetic moment of the isolated substitutional and interstitial tetrahedral Mn in Si as a function of the lattice constant. When the lattice constant increases, the magnetic moment of the substitutional site stays at 3.0mB, whereas that of the interstitial tetrahedral site slightly increases. When the lattice constant decreases, the magnetic moments of substitutional and interstitial tetrahedral Mn drastically decrease. In the case of tensile strain, the formation energies of the Mn impurity in Si decrease and the magnetic moments do not change [20]. The larger lattice constant for Mn-doped Si is consistent with the fact that the bond length of Si–Mn is longer than that of Si–Si, found in results for the experimental lattice constant. Next, we put two Mn atoms on neighboring substitutional or interstitial tetrahedral sites and investigated the effects of three-dimensional isotropic strain on Mn complexes in Si to simulate the high Mn-concentration conditions. Fig. 2(a) shows the total energy change as a function of the lattice constant. The most stable lattice constant of the substitutional Mn complex in Si is about 97%. Total energy change shows that the lattice constant of Si containing the substitutional Mn complex decreases from that of bulk Si, while the lattice constant of Si containing the interstitial tetrahedral Mn complex slightly increases as does that of Si containing the isolated Mn. Fig. 2(b) shows the formation energy as a function of the lattice constant. When the lattice constant increases, the formation energy of the interstitial tetrahedral Mn complex decreases as well as isolated Mn in Si. When the lattice constant decreases, the formation energy of the substitu-
tional Mn complex in Si drastically decreases. The substitutional Mn complex might be impossible to show the ferromagnetic property because its magnetic moment is antiferromagentism. Since we previously found a longer bond length of Mn–Si than that of Si–Si, these results seem contradictory. To clarify the reason why the substitutional Mn complex is so stable with the decreased lattice constants, we investigated the atomic configurations at 94.6%, 101.9%, and 106.7%. Fig. 3 shows the optimized atomic structures for each lattice constant. As shown in the figure, the atomic positions are much disturbed, except for the case which is 101.9% of the calculated lattice constant of bulk Si (Fig. 3(a)). When the lattice constant is 106.7% (Fig. 3(b)), the Mn–Mn bond is broken and each Mn seems to position itself at the interstitial tetrahedral site. On the other hand, when the lattice constant is 94.6% (Fig. 3(c)), the coordination number of Mn is seven, which is larger than the coordination number of four for the substitutional site. Since the large coordination number is generally observed in the Mn silicide, it seems that the structure change is related to the formation of silicide. For cubic MnSi, there are four Si and four Mn atoms, in the cubic unit cell with the lattice constant of 4.558 A˚, while Si crystal has eight Si atoms in the cubic unit cell with the lattice constant of 5.43 A˚. Thus, it is considered that the formation of silicide-like structure causes the shrinking of the crystal. All these results suggest that the higher coordination and shrinking preferability are shown in the high Mn-concentration Si. According to these results, the following can be concluded. Since the Mn–Si distance is larger than the Si–Si distance, the Mn-doped Si crystal prefers to expand.
ARTICLE IN PRESS S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
(a)
675
(b)
[101]
: Mn
: Si [010]
(c) Fig. 3. Optimized atomic configurations of the substitutional Mn complexes in Si at lattice constants of (a) 101.9%, (b) 106.7%, and (c) 94.6% of the calculated stable lattice constant.
Actually, when the lattice constant increases, the formation energy of isolated Mn decreases and the isolated Mn is stabilized. Therefore, we consider that a tensile strain is efficient for the formation and stabilization of isolated Mn. Additionally, if substitutional Mn complexes are formed, they might show undesirable antiferromagnetism as the magnetic moment. The total energies show that the lattice constant decreases when the substitutional complexes are formed. Thus, if shrinked areas are formed in Mn-doped Si, those areas could be related to the higher Mnconcentration condition and such shrinked films are considered to be inappropriate for DMS.
5. Conclusion In this study, we have shown that tensile strain stabilizes substitutional Mn and retains the magnetic moment. This suggests that the tensile strain can be efficiently used to improve the crystallinity of epitaxial films.
Acknowledgments We would like to thank Dr. Yoshiteru Takagi and Dr. Kazuyuki Uchida for their valuable discussions. A part of this work is done by using the Supercomputer Center, Institute for Solid State Physics, University of Tokyo. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
H. Ohno, Science 281 (1998) 951. H. Ohno, et al., Nature 408 (2000) 944. A. Oiwa, et al., Appl. Phys. Lett. 78 (2001) 518. A. Oiwa, et al., Appl. Phys. Lett. 88 (2002) 137202. A.M. Nazmul, et al., Jpn. J. Appl. Phys. 43 (2004) L233. Y.D. Park, et al., Science 295 (2002) 651. M. Bolduc, et al., Phys. Rev. B 71 (2005) 033302. G.M. Dalpian, et al., Phys. Rev. B 68 (2003) 113310. Y. Miura, et al., J. Phys.: Condens. Matter 16 (2004) S5735. H.H. Woodbury, G.W. Ludwing, Phys. Rev. 117 (1960) 102. Y. Kamon, et al., Physica B 308-310 (2001) 391. Q. Zhang, et al., Surf. Sci. 507–510 (2002) 453.
ARTICLE IN PRESS 676 [13] [14] [15] [16] [17]
S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
D. Vanderbilt, Phys. Rev. B 41 (1990) 892. K. Laasonen, et al., Phys. Rev. B 47 (1993) 10142. N. Troullier, J.L. Martins, Phys. Rev. Lett. 43 (1991) 1993. J. Yamauchi, et al., Phys. Rev. B 54 (1996) 5586. M. Tsukada, et al., Computer program package TAPP, University of Tokyo, Tokyo, Japan, 1983–2005. [18] O. Nakanishi, et al., J. Magn. Magn. Mater. 15–18 (1980) 879.
[19] Landolt-Bornstein: in: O. Madelung (Ed.), Numerical Data and Functional Relationships in Science and Technology, New Series, Group III, vol. 17A, Springer, Berlin, 1982. [20] Our preliminary 64-atom unit cell calculations show that the formation energy of the isolated substitutional Mn decreases by about 0.14 eV at most where it decreases by 0.16 eV with the 16-atom unit cell calculations. They also show that the magnetic moment of the site also stays at 3.0mB.
Physica B 376–377 (2006) 672–676 www.elsevier.com/locate/physb
First-principles study of strain effects on Mn in Si S. Yabuuchia,, E. Ohtaa, H. Kageshimab, A. Taguchib a
Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1, Hiyoshi, Kohoku-Ku, Yokohama 223-8522, Japan b NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan
Abstract The effects of strain on Mn impurities in Si were investigated by using first-principles calculations. It is shown that substitutional Mn is stabilized and that the magnetic moment is maintained when a tensile strain is given. This suggests that the tensile strain is effective for improving the crystallinity of epitaxial films. Under high Mn concentration conditions, the substitutional Mn complex can cause a structural change and decrease the lattice constant of the crystal. Thus, the formation of shrinked epitaxial films can cause a structural change related to the substitutional Mn complexes, which might make it impossible to obtain the ferromagnetic property. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Pp; 71.55.Cn; 71.15.Mb Keywords: First-principles calculation; Magnetic semiconductor; Si; Strain
1. Introduction Recently many researchers have investigated merging spin degrees of freedom into conventional semiconductor electronics. Special attention has been given to diluted magnetic semiconductors (DMSs), which have been shown to be successful for integrating ferromagnetism through doping of a semiconductor crystal with an additional transition metal impurity such as Mn [1]. A Mndoped III–V semiconductor, such as Ga1xMnxAs or In1xMnxAs is an attractive material which has carrierinduced ferromagnetism and magnetic properties that can be controlled by using field effects or light illumination [2–5]. Since the group-IV semiconductors such as Si are the keystones of semiconductor electronics, ferromagnetic semiconductors based on Si are very important in device and process technology. Several experimental and theoretical studies have been carried out for Si and Ge-based DMSs. Park et al. investigated fabricating Ge1xMnx by using molecular beam epitaxy and confirmed a magnetically ordered phase from ferromagnetic interaction up to Corresponding author. Tel.: +81 422 22 2964; fax: +81 45 566 1587.
E-mail address: [email protected] (S. Yabuuchi). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.169
116 K, along with a p-type character and hole-mediated exchange [6]. Recently it was reported that Mn ion implantation can realize ferromagnetic behavior above room temperature [7]. Several theoretical studies for Siand Ge-based DMSs have also been conducted. Dalpian et al. reported the stability of Mn impurities in Si and on the surface; they showed that the formation energy of Mn in Si is high and most stable site is the interstitial tetrahedral site in bulk Si [8]. Miura et al. also reported that Mn cluster is more stable than isolated Mn in Si [9]. Actually the solubility of Mn in Si is very low and interstitial impurity can diffuse more easily than substitutional one and undesired magnetic clusters such as Mn clusters and silicide are easily formed [10–12]. Thus, it is difficult to fabricate high-quality crystalline DMSs by Mn doping in Si. In an attempt to overcome these difficulties, we considered the effect of the strain. Since Mn has a different atomic radius from Si, the strain could modify the stability of the doped Mn. If we use epitaxial growth, the strain can be easily introduced. We investigated such strain effects on Mn impurities in Si by using the first-principles calculations. It is shown that the substitutional Mn is stabilized and that the magnetic moment is maintained when a tensile strain is given. This suggests that the tensile strain is
ARTICLE IN PRESS S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
effective for improving the crystallinity of the epitaxial films. 2. Method We performed first-principles calculations based on density-functional theory within generalized gradient approximation (GGA) and local spin density approximation (LSD). We used the Vanderbilt ultrasoft pseudopotential [13,14] for Mn, the Troullier-Martins pseudopotential [15] for Si, and a plane-wave basis set up to 25 Ry. All calculations have been done with TAPP [16,17]. We calculated bulk Si and cubic MnSi in order to check the accuracy of the pseudopotentials we used. For bulk Si, the calculated lattice constant is 5.46 A˚, which reproduced an experimental value of 5.43 A˚ within 0.6% error. For bulk cubic MnSi, the calculated lattice constant is 4.58 A˚, which agrees well with the experimental value of 4.558 A˚ [18]. For Mn impurity in Si, we used a 16-atom unit cell and put one or two Mn atoms in it on various positions. We used kpoint sampling of 4 4 2 in the Brillouin zone and optimized the atomic configurations to evaluate their magnetic moments. We regarded the atomic position fully relaxed when all atomic force components were smaller than 0.05 eV/A˚. From the results we estimated the total energy, formation energy, and magnetic moment of Mn impurity in Si and their dependence on the strain effects. The formation energy Ef is calculated by the following equations: E f ¼ E Total nSi mSi nMn mMn ,
(1)
mSi ¼ E Total ðSiðdÞÞ,
(2)
mMn ¼ E Total ðMnSiÞ E Total ðSiðdÞÞ,
(3)
673
where E Total is the total energy of the unit cell which is a function of the lattice constant d, mSi is the Si chemical potential, mMn is the Mn chemical potential in bulk MnSi, nSi is the number of Si atoms in the unit cell, and nMn is the number of Mn atoms in the unit cell. E Total (MnSi) and E Total (Si(d)) represent the total energy of bulk cubic MnSi and that of bulk Si with the lattice constant d. Since we want to discuss how to avoid the segregation of MnSi from the Mn-doped Si, we define mMn as Eq. (3). In our calculation, the formation energy Ef of a substitutional Mn impurity in Si is 2.96 eV, when the lattice constant is the experimental value of 5.43 A˚ [19]. The interstitial tetrahedral impurity has a formation energy of 2.50 eV, and the interstitial hexagonal impurity has a formation energy of 3.20 eV. Thus, the interstitial tetrahedral site is the most stable site for the isolated Mn impurity in Si. In the substitutional site the magnetic moment is 3.00mB, whereas in the interstitial tetrahedral site it is 3.19mB, and in the interstitial hexagonal site it is 3.09mB. The calculated result is in good agreement with the previous report [8]. The nearest-neighbor Mn–Si distance is about 2.39, 2.44 and 2.37 A˚, for the substitutional site, interstitial tetrahedral site, and interstitial hexagonal site, respectively. These distances are longer than that of bulk Si. 3. Results and discussions We investigated the effects of three-dimensional isotropic strain on the isolated Mn in Si. The stability of the total energy with isolated substitutional and interstitial tetrahedral Mn in Si shows that the lattice constants of the crystals are slightly larger than that of bulk Si. Fig. 1(a) shows the formation energy of the isolated Mn in Si as a function of lattice constant. When the lattice constant 4
4.0
3
3.5
Magnetic Moment [B]
Formation energy [eV]
sub inter
3.0
2
1 sub inter
2.5
0 90 (a)
95 100 105 Lattice Constant [%]
110
90 (b)
95 100 105 Lattice Constant [%]
110
Fig. 1. (a) Formation energy and (b) magnetic moment of the isolated substitutional and the interstitial tetrahedral site Mn in Si as a function of the lattice constant. The lattice constant of 100% corresponds to the calculated value of 5.46 A˚. Circles and squares are the isolated substitutional and the interstitial tetrahedral Mn in Si, respectively.
ARTICLE IN PRESS S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
674
6
8
5
inter-inter
6
Formation Energy [eV]
Total Energy Change [eV]
sub-sub
4
4
3
2
2
sub-sub inter-inter
1
0
0 90 (a)
95 100 105 Lattice Constant [%]
110
90 (b)
95 100 105 Lattice Constant [%]
110
Fig. 2. (a) Total energy and (b) formation energy of the substitutional and interstitial tetrahedral Mn complexes in Si as a function of the lattice constant. All atomic configurations were optimized. The lattice constant of 100% corresponds to the calculated value of 5.46 A˚. Circles and squares are the substitutional and the interstitial tetrahedral Mn complexes in Si, respectively.
increases, the formation energy of substitutional Mn decreases about 0.16 eV at most, and that of interstitial tetrahedral Mn in Si also decreases. Fig. 1(b) shows the magnetic moment of the isolated substitutional and interstitial tetrahedral Mn in Si as a function of the lattice constant. When the lattice constant increases, the magnetic moment of the substitutional site stays at 3.0mB, whereas that of the interstitial tetrahedral site slightly increases. When the lattice constant decreases, the magnetic moments of substitutional and interstitial tetrahedral Mn drastically decrease. In the case of tensile strain, the formation energies of the Mn impurity in Si decrease and the magnetic moments do not change [20]. The larger lattice constant for Mn-doped Si is consistent with the fact that the bond length of Si–Mn is longer than that of Si–Si, found in results for the experimental lattice constant. Next, we put two Mn atoms on neighboring substitutional or interstitial tetrahedral sites and investigated the effects of three-dimensional isotropic strain on Mn complexes in Si to simulate the high Mn-concentration conditions. Fig. 2(a) shows the total energy change as a function of the lattice constant. The most stable lattice constant of the substitutional Mn complex in Si is about 97%. Total energy change shows that the lattice constant of Si containing the substitutional Mn complex decreases from that of bulk Si, while the lattice constant of Si containing the interstitial tetrahedral Mn complex slightly increases as does that of Si containing the isolated Mn. Fig. 2(b) shows the formation energy as a function of the lattice constant. When the lattice constant increases, the formation energy of the interstitial tetrahedral Mn complex decreases as well as isolated Mn in Si. When the lattice constant decreases, the formation energy of the substitu-
tional Mn complex in Si drastically decreases. The substitutional Mn complex might be impossible to show the ferromagnetic property because its magnetic moment is antiferromagentism. Since we previously found a longer bond length of Mn–Si than that of Si–Si, these results seem contradictory. To clarify the reason why the substitutional Mn complex is so stable with the decreased lattice constants, we investigated the atomic configurations at 94.6%, 101.9%, and 106.7%. Fig. 3 shows the optimized atomic structures for each lattice constant. As shown in the figure, the atomic positions are much disturbed, except for the case which is 101.9% of the calculated lattice constant of bulk Si (Fig. 3(a)). When the lattice constant is 106.7% (Fig. 3(b)), the Mn–Mn bond is broken and each Mn seems to position itself at the interstitial tetrahedral site. On the other hand, when the lattice constant is 94.6% (Fig. 3(c)), the coordination number of Mn is seven, which is larger than the coordination number of four for the substitutional site. Since the large coordination number is generally observed in the Mn silicide, it seems that the structure change is related to the formation of silicide. For cubic MnSi, there are four Si and four Mn atoms, in the cubic unit cell with the lattice constant of 4.558 A˚, while Si crystal has eight Si atoms in the cubic unit cell with the lattice constant of 5.43 A˚. Thus, it is considered that the formation of silicide-like structure causes the shrinking of the crystal. All these results suggest that the higher coordination and shrinking preferability are shown in the high Mn-concentration Si. According to these results, the following can be concluded. Since the Mn–Si distance is larger than the Si–Si distance, the Mn-doped Si crystal prefers to expand.
ARTICLE IN PRESS S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
(a)
675
(b)
[101]
: Mn
: Si [010]
(c) Fig. 3. Optimized atomic configurations of the substitutional Mn complexes in Si at lattice constants of (a) 101.9%, (b) 106.7%, and (c) 94.6% of the calculated stable lattice constant.
Actually, when the lattice constant increases, the formation energy of isolated Mn decreases and the isolated Mn is stabilized. Therefore, we consider that a tensile strain is efficient for the formation and stabilization of isolated Mn. Additionally, if substitutional Mn complexes are formed, they might show undesirable antiferromagnetism as the magnetic moment. The total energies show that the lattice constant decreases when the substitutional complexes are formed. Thus, if shrinked areas are formed in Mn-doped Si, those areas could be related to the higher Mnconcentration condition and such shrinked films are considered to be inappropriate for DMS.
5. Conclusion In this study, we have shown that tensile strain stabilizes substitutional Mn and retains the magnetic moment. This suggests that the tensile strain can be efficiently used to improve the crystallinity of epitaxial films.
Acknowledgments We would like to thank Dr. Yoshiteru Takagi and Dr. Kazuyuki Uchida for their valuable discussions. A part of this work is done by using the Supercomputer Center, Institute for Solid State Physics, University of Tokyo. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
H. Ohno, Science 281 (1998) 951. H. Ohno, et al., Nature 408 (2000) 944. A. Oiwa, et al., Appl. Phys. Lett. 78 (2001) 518. A. Oiwa, et al., Appl. Phys. Lett. 88 (2002) 137202. A.M. Nazmul, et al., Jpn. J. Appl. Phys. 43 (2004) L233. Y.D. Park, et al., Science 295 (2002) 651. M. Bolduc, et al., Phys. Rev. B 71 (2005) 033302. G.M. Dalpian, et al., Phys. Rev. B 68 (2003) 113310. Y. Miura, et al., J. Phys.: Condens. Matter 16 (2004) S5735. H.H. Woodbury, G.W. Ludwing, Phys. Rev. 117 (1960) 102. Y. Kamon, et al., Physica B 308-310 (2001) 391. Q. Zhang, et al., Surf. Sci. 507–510 (2002) 453.
ARTICLE IN PRESS 676 [13] [14] [15] [16] [17]
S. Yabuuchi et al. / Physica B 376–377 (2006) 672–676
D. Vanderbilt, Phys. Rev. B 41 (1990) 892. K. Laasonen, et al., Phys. Rev. B 47 (1993) 10142. N. Troullier, J.L. Martins, Phys. Rev. Lett. 43 (1991) 1993. J. Yamauchi, et al., Phys. Rev. B 54 (1996) 5586. M. Tsukada, et al., Computer program package TAPP, University of Tokyo, Tokyo, Japan, 1983–2005. [18] O. Nakanishi, et al., J. Magn. Magn. Mater. 15–18 (1980) 879.
[19] Landolt-Bornstein: in: O. Madelung (Ed.), Numerical Data and Functional Relationships in Science and Technology, New Series, Group III, vol. 17A, Springer, Berlin, 1982. [20] Our preliminary 64-atom unit cell calculations show that the formation energy of the isolated substitutional Mn decreases by about 0.14 eV at most where it decreases by 0.16 eV with the 16-atom unit cell calculations. They also show that the magnetic moment of the site also stays at 3.0mB.