空位的第一性原理及经验势函数的对比研究

王超营; 王振清; 孟庆元

doi:10.7498/aps.59.3370

摘要

利用第一性原理及Stillinger-Weber（SW）,EDIP和Tersoff经验势函数对比研究了硅中单空位(V1)、双空位(V2)和六边形空位环(V6)的结构特性及形成能.讨论了经验势函数描述空位时的优点和缺点.结果发现，第一性原理方法可以精确描述空位的原子结构及能量特性，而短程有效的经验势函数无法描述空位所固有的量子效应，如Jahn-Teller变形等.另外，由于经验势函数自身的缺陷，EDIP和T3无法应用于空位结构特性的计算.虽然

关键词:

Abstract

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.

Keywords:

作者及机构信息

(1)哈尔滨工程大学航天与建筑工程学院工程力学系,哈尔滨 150001; (2)哈尔滨工业大学航天科学与力学系,哈尔滨 150001

基金项目: 国家自然科学基金（批准号：10772062）资助的课题.

Authors and contacts

(1)哈尔滨工程大学航天与建筑工程学院工程力学系,哈尔滨 150001; (2)哈尔滨工业大学航天科学与力学系,哈尔滨 150001

参考文献

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[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
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[17]	］Saito M, Oshiyama A 1994 Phys. Rev. Lett. 73 866
[18]	］Chadi D J, Chang K J 1988 Phys. Rev. B 38 1523
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[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

施引文献

[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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