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Structural properties and formation energies of monovacancy (V1), divacancy (V2) and hexavacancy (V6) in silicon have been comparatively studied with density functional theory (DFT), Stillinger-Weber (SW), EDIP and Tersoff methods. The validity and shortcomings of the three classical potentials are discussed in detail. It is found that the DFT method may provide accurate description of atomic structures and energies of vacancies. As to the empirical potentials, they cannot be used to investigate quantum mechanical effects such as Jahn-Teller distortion ocurring in the DFT relaxations. Moreover, EDIP and T3 give an outward relaxation in all cases, which is contrary to the DFT and SW directions. Therefore, they are unsuitable to the structural property calculations. Based on the results calculated mainly for structure properties and formation energies, it can be concluded that SW should be the best potential to describe V1, V2 and V6.
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Keywords:
- vacancy /
- first-principle /
- empirical potential
[1] ［1］Myronov M, Shiraki Y 2007 Jpn. J. Appl. Phys. Part 1. 46 721
[2] ［2］Dannefaer S, Mascher P, Kerr D 1986 Phys. Rev. Lett. 56 2195
[3] ［3］Wright A F 2006 Phys. Rev. B 74 165116
[4] ［4］EI-Mellouhi F, Mousseau N, Ordejon P 2004 Phys. Rev. B 70 205202
[5] ［5］Probert M I J, Payne M C 2003 Phys. Rev. B 67 075204
[6] ［6］Puska M J, Poykko S, Pesola M, Nieminen R M 1998 Phys. Rev. B 58 1318
[7] ［7］Lento J, Nieminen R M 2003 J. Phys.: Condens. Matter 15 4387
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[9] ［9］Justo J F, Bazant M Z, Kaxiras E, Bulatov V V, Yip S 1998 Phys. Rev. B 58 2539
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[12] ］Nagai Y, Inoue K, Tang Z, Yonenaga I, Chiba T, Saito M, Hasegawa M 2003 Physica B 340-342 518
[13] ］Iwata J I, Shiraishi K, Oshiyama A 2008 Phys. Rev. B 77 115208
[14] ］Wixom R R, Wright A F 2006 Phys. Rev. B 74 205208
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[16] ］Ogut S, Chelikowsky J R 1999 Phys. Rev. Lett. 83 3852
[17] ］Saito M, Oshiyama A 1994 Phys. Rev. Lett. 73 866
[18] ］Chadi D J, Chang K J 1988 Phys. Rev. B 38 1523
[19] ］Makhov D V, Lewis L J 2004 Phys. Rev. Lett. 92 255504
[20] ］Akiyama T, Oshiyama A 2001 J. Phys. Soc. Jpn. 70 1627
[21] ］Hastings J L, Estreicher S K, Fedders P A 1997 Phys. Rev. B 56 10215
[22] ］Staab T E M, Sieck A, Haugk M, Puska M J, Frauenheim Th, Leipner H S 2002 Phys. Rev. B 65 115210
[23] ］Qiao Y H, Wang S Q 2005 Acta Phys. Sin. 54 4827 (in Chinese) ［乔永红、 王绍青 2005 54 4827］
[24] ］Duesbery M S, Joos B, Michel D 1991 Phys. Rev. B 43 5143
[25] ］Poon T W, Yip S, Ho P S, Abraham F F 1990 Phys. Rev. Lett. 65 2161
[26] ］Porter L J, Yip S, Yamaguchi M, Kaburaki H, Tang M 1997 J. Appl. Phys. 81 96
[27] ］Godet J, Pizzagalli L, Brochard S, Beauchamp P 2003 J. Phys.: Condens. Matter 15 6943
[28] ］Stillinger F H, Weber T A 1985 Phys. Rev. B 31 5262
[29] ］Bazant M Z, Kaxiras E, Justo J F 1997 Phys. Rev. B 56 8542
[30] ］Tersoff J 1989 Phys. Rev. B 39 5566
[31] ］Sanchez-Portal D, Ordejon P, Artacho E, Soler J M 1997 Int. J. Quantum Chem. 65 453
[32] ］Soler J M, Artacho E, Gale J D, Garcia A, Junquera J, Ordejon P, Sanchez-Portal D 2002 J. Phys.: Condens. Matter 14 2745
[33] ］Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[34] ］Troullier N, Martins J L 1991 Phys. Rev. B 43 1993
[35] ］Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[36] ］Press W H, Teukolsky S A, Vetterling W T, Flannery B P 1992 Numerical Recipes in Fortran (2nd ed) (Cambridge: Cambridge University)
[37] ］Kittel C 1986 Introduction to Solid State Physics (New York: Wiley)
[38] ］Gunnarsson O, Jepsen O andAndersen O K 1983 Phys. Rev. B 27 7144
[39] ］Scheffler M, Vigneron J P, Bachelet G B 1985 Phys. Rev. B 31 6541
[40] ］Wang C Z, Chan C T, Ho K M 1991 Phys. Rev. Lett. 66 189
[41] ］Song E G, Kim E, Lee Y H, Hwang Y G 1993 Phys. Rev. B 48 1486
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[1] ［1］Myronov M, Shiraki Y 2007 Jpn. J. Appl. Phys. Part 1. 46 721
[2] ［2］Dannefaer S, Mascher P, Kerr D 1986 Phys. Rev. Lett. 56 2195
[3] ［3］Wright A F 2006 Phys. Rev. B 74 165116
[4] ［4］EI-Mellouhi F, Mousseau N, Ordejon P 2004 Phys. Rev. B 70 205202
[5] ［5］Probert M I J, Payne M C 2003 Phys. Rev. B 67 075204
[6] ［6］Puska M J, Poykko S, Pesola M, Nieminen R M 1998 Phys. Rev. B 58 1318
[7] ［7］Lento J, Nieminen R M 2003 J. Phys.: Condens. Matter 15 4387
[8] ［8］Schultz P A 2006 Phys. Rev. Lett. 96 246401
[9] ［9］Justo J F, Bazant M Z, Kaxiras E, Bulatov V V, Yip S 1998 Phys. Rev. B 58 2539
[10] ］Balamane H, Halicioglu T, Tiller W A 1992 Phys. Rev. B 46 2250
[11] ］Watkins G D, Corbett J W 1965 Phys. Rev. 138 A543
[12] ］Nagai Y, Inoue K, Tang Z, Yonenaga I, Chiba T, Saito M, Hasegawa M 2003 Physica B 340-342 518
[13] ］Iwata J I, Shiraishi K, Oshiyama A 2008 Phys. Rev. B 77 115208
[14] ］Wixom R R, Wright A F 2006 Phys. Rev. B 74 205208
[15] ］Ogut S, Chelikowsky J R 2001 Phys. Rev. B 64 245206
[16] ］Ogut S, Chelikowsky J R 1999 Phys. Rev. Lett. 83 3852
[17] ］Saito M, Oshiyama A 1994 Phys. Rev. Lett. 73 866
[18] ］Chadi D J, Chang K J 1988 Phys. Rev. B 38 1523
[19] ］Makhov D V, Lewis L J 2004 Phys. Rev. Lett. 92 255504
[20] ］Akiyama T, Oshiyama A 2001 J. Phys. Soc. Jpn. 70 1627
[21] ］Hastings J L, Estreicher S K, Fedders P A 1997 Phys. Rev. B 56 10215
[22] ］Staab T E M, Sieck A, Haugk M, Puska M J, Frauenheim Th, Leipner H S 2002 Phys. Rev. B 65 115210
[23] ］Qiao Y H, Wang S Q 2005 Acta Phys. Sin. 54 4827 (in Chinese) ［乔永红、 王绍青 2005 54 4827］
[24] ］Duesbery M S, Joos B, Michel D 1991 Phys. Rev. B 43 5143
[25] ］Poon T W, Yip S, Ho P S, Abraham F F 1990 Phys. Rev. Lett. 65 2161
[26] ］Porter L J, Yip S, Yamaguchi M, Kaburaki H, Tang M 1997 J. Appl. Phys. 81 96
[27] ］Godet J, Pizzagalli L, Brochard S, Beauchamp P 2003 J. Phys.: Condens. Matter 15 6943
[28] ］Stillinger F H, Weber T A 1985 Phys. Rev. B 31 5262
[29] ］Bazant M Z, Kaxiras E, Justo J F 1997 Phys. Rev. B 56 8542
[30] ］Tersoff J 1989 Phys. Rev. B 39 5566
[31] ］Sanchez-Portal D, Ordejon P, Artacho E, Soler J M 1997 Int. J. Quantum Chem. 65 453
[32] ］Soler J M, Artacho E, Gale J D, Garcia A, Junquera J, Ordejon P, Sanchez-Portal D 2002 J. Phys.: Condens. Matter 14 2745
[33] ］Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[34] ］Troullier N, Martins J L 1991 Phys. Rev. B 43 1993
[35] ］Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[36] ］Press W H, Teukolsky S A, Vetterling W T, Flannery B P 1992 Numerical Recipes in Fortran (2nd ed) (Cambridge: Cambridge University)
[37] ］Kittel C 1986 Introduction to Solid State Physics (New York: Wiley)
[38] ］Gunnarsson O, Jepsen O andAndersen O K 1983 Phys. Rev. B 27 7144
[39] ］Scheffler M, Vigneron J P, Bachelet G B 1985 Phys. Rev. B 31 6541
[40] ］Wang C Z, Chan C T, Ho K M 1991 Phys. Rev. Lett. 66 189
[41] ］Song E G, Kim E, Lee Y H, Hwang Y G 1993 Phys. Rev. B 48 1486
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