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α-, β-和γ-Si3N4 高压下的电子结构和相变: 第一性原理研究

余本海 陈东

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α-, β-和γ-Si3N4 高压下的电子结构和相变: 第一性原理研究

余本海, 陈东

First-principles study on the electronic structure and phase transition of α-, β- and γ-Si3N4

Yu Ben-Hai, Chen Dong
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  • 本文采用第一性原理框架下的赝势平面波方法结合振动类德拜模型研究了α,β和γ-Si3N4在高温下的点阵常数,弹性常数和弹性模量.研究发现三种同质异相体的体模量都很高.β-Si3N4在低温下表现出脆性,在高温下则表现出延展性.γ-Si3N4在低温和高温下都是脆性的共价化合物.β → γ 相变的相界斜率为正值,说明在较高温度时合成γ-Si3N4所需的压强也较高.α → γ 相变的相界可以表示成 P=16.29- 1.835-10-2 T+9.33945-10-5T2-2.16759-10-7T3+2.91795-10-10T4.本文还分析了Si3N4同质异相体在高压下的态密度和能带.在α-Si3N4中主要是Si-s, p和N-s,p的轨道杂化对晶体的稳定性起作用.α和β-Si3N4都具有ΓV-ΓC类型的间接带隙(分别是4.9~eV和4.4~eV)而γ-Si3N4具有直接带隙(3.9~eV). 研究还发现α-Si3N4和β-Si3N4的价带顶分别沿着Γ-M和Γ-A方向.本文的计算结果和已有的实验数据是一致的.
    The high-temperature lattice constants and elastic moduli of the silicon nitrides are calculated using the plane-wave pseudo-potential method combined with the vibrational Debye-like model. β-Si3N4 is ductile at low temperature and brittle at high temperature. γ-Si3N4 is found to be brittle and covalent in nature. We find a positive slope of the β→γ phase boundary, hence, at higher temperatures it requires higher pressures to synthesize γ -Si3N4. The α → γ phase boundary may be expressed as P=16.29-1.835-10-2 T+9.33945-10-5T2-2.16759-10-7 T3+2.91795-10-10T4. We also obtain the electronic structures and energy bands of Si3N4 with and without pressure. The interaction between Si-s, p and N-s, p plays a dominant role in the stability of α-Si3N4. The α- and β-Si3N4 have the ΓV-ΓC indirect band gaps (4.9~eV and 4.4~eV) while γ-Si3N4 has a direct band gap(3.9~eV). The tops of the valence bands for α- and β-Si3N4 are along the Γ-M and Γ-A direction, respectively. Our results are consistent with the experimental data and the theoretical results.
    • 基金项目: 国家自然科学基金(批准号: 11005088, 11105115)、河南省基础与前沿技术研究计划项目(批准号: 112300410021)和河南教育厅项目(批准号: 12A140010) 资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11005088, 11105115), the Program of Basic and Advanced Technology of Henan Province, China (Grant No. 112300410021), and the Key Project of Henan Educational Committee (Grant No. 12A140010).
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    Kuwabara A, Matsunaga K, Tanaka I 2008 Phys. Rev. B 78 064104

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    Kiefer B, Shieh S R, Duffy T S, Sekine T 2005 Phys. Rev. B 72 014102

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    Zerr A, Miehe G, Serghiou G, Schwarz M, Kroke E, Riedel R, Fueb H, Kroll P, Boehler R 1999 Nature 400 340

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    Schwarz M, Miehe G, Zerr A, Kroke E, Poe B T, Fuess H, Riedel R 2000 Adv. Mater. 12 883

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    Soignard E, Somayazulu M, Dong J J, Sankey O F, McMillan P F 2001 J. Phys.: Condens. Matter 13 557

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    Togo A, Kroll P 2008 NIC Symposium 39 95

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    Mo S D, Ouyang L Z, Ching W Y, Tanaka I, Koyama Y, Riedel R 1999 Phys. Rev. Lett. 83 5046

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    Jiang J Z, Lindelv H, Gerward L, Stahl K, Recio J M, Mori-Sanchez P, Carlson S, Mezouar M, Dooryhee E, Fitch A, Frost D J 2002 Phys. Rev. B 65 161202R

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    Meléndez-Martinez J J, Dominguez-Rodriguez A 2004 Prog. Mater. Sci. 49 19

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    Bermudez V M 2005 Surf. Sci. 579 11

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    Belkada R, Kohyama M, Shibayanagi T, Naka M 2002 Phys. Rev. B 65 092104

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    Ching W Y, Ouyang L Z, Gale J D 2000 Phys. Rev. B 61 8696

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    Grün R 1979 Acta Cryst. B 35 800

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    Kohn W, Sham L J 1965 Phys. Rev. 140 A1133

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    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

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    Blanco M A, Francisco E, Luana V 2004Comput. Phys. Commun. 158 57

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    Hu C E, Zeng Z Y, Cheng Y, Chen X R, Cai L C 2008 Chin. Phys. B 17 3867

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    Marian C M, Gastreich M, Gale J D 2000 Phys. Rev. B 62 3117

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    Hirosaki N, Ogata S, Kocer C, Kitagawa H, Nakamura Y 2002 Phys. Rev. B 65 134110

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    Yashima M, Ando Y, Tabira Y 2007 J. Phys. Chem. B 111 3609

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    Sin'ko G V, Smirnow N A 2002 J. Phys.: Condens. Matter 14 6989

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    Jiang C, Lin Z, Zhao Y 2009 Phys. Rev. Lett. 103 185501

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    Wang H, Chen Y, Kaneta Y, Iwata S 2006 J. Phys.: Condens. Matter 18 10663

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    Wang A J, Shang S L, Du Y, Kong Y, Zhang L J, Chen L, Zhao D D, Liu Z K 2010 Comput. Mater. Sci. 48 705

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    Southworth D R, Barton R A, Verbridge S S, Llic B, Fefferman A D, Craighead H G, Parpia J M 2009 Phys. Rev. Lett. 102 225503

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    Shebanova O, Soignard E, Mcmillan P F 2006 High Pres. Res. 26 87

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    Kroll P, Milko M, Anorg Z 2003 Allg. Chem. 629 1737

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    Goumri-Said S, Kanoun M B 2008 Comput. Mater. Sci. 43 243

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    Kocer C, Hirosaki N, Ogata S 2003 Phys. Rev. B 67 035210

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    Dong J J, Deslippe J, Sankey O F, Soignard E, McMillan P F 2003 Phys. Rev. B 67 094104

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    Yu B H, Chen D, Li Y B, Jia Y L 2012 Acta Metal. Sin. (Engl. Lett.) 25 131

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    Jiang J Z, Kragh F, Frost D J, Stahl K, Lindelov H 2001 J. Phys.: Condens. Matter 13 L515

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    Zhang Y, Navrotsky A, Sekine T 2006 J. Mater. Res. 21 41

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  • [1]

    Mori-Sánchez P, Marqués M, Beltrán A, Jiang J Z, Gerward L, Recio J M 2003 Phys. Rev. B 68 064115

    [2]

    Xu B, Dong J, McMillan P, Shebanova O, Salamat A 2011 Phys. Rev. B 84 014113

    [3]

    Kuwabara A, Matsunaga K, Tanaka I 2008 Phys. Rev. B 78 064104

    [4]

    Zhang C, Sun J X, Tian R G, Zou S Y 2007 Acta Phys. Sin. 56 5969 (in Chinese) [张超, 孙久勋, 田荣刚, 邹世勇 2007 物理学报 56 5969]

    [5]

    Zerr A, Kempf M, Schwarz M, Kroke E, Göken M, Riedel R 2002 J. Am. Ceram. Soc. 85 86

    [6]

    Paszkowicz W, Minikayev R, Piszora P, Knapp M, Bähtz C, Recio J M, Marqués M, Mori-Sánchez P, Gerward L, Jiang J Z 2004 Phys. Rev. B 69 052103

    [7]

    Kiefer B, Shieh S R, Duffy T S, Sekine T 2005 Phys. Rev. B 72 014102

    [8]

    Ching W Y, Mo S D, Ouyang L Z, Rulis P 2002 J. Am. Ceram. Soc. 85 75

    [9]

    Xu Y N, Ching W Y 1995 Phys. Rev. B 51 17379

    [10]

    Zerr A, Miehe G, Serghiou G, Schwarz M, Kroke E, Riedel R, Fueb H, Kroll P, Boehler R 1999 Nature 400 340

    [11]

    Schwarz M, Miehe G, Zerr A, Kroke E, Poe B T, Fuess H, Riedel R 2000 Adv. Mater. 12 883

    [12]

    Soignard E, Somayazulu M, Dong J J, Sankey O F, McMillan P F 2001 J. Phys.: Condens. Matter 13 557

    [13]

    Togo A, Kroll P 2008 NIC Symposium 39 95

    [14]

    Kruger M B, Nguyen J H, Li Y M, Caldwell W A, Manghnani M H, Jeanloz R 1997 Phys. Rev. B 55 3456

    [15]

    Danilenko N V, Oleinik G S, Dobrovol'skii V D, Britun V F, Semenenko N P 1992 Powder Metal. Met. Ceram. 31 1035

    [16]

    Butler I S, Huang Y 1992 Appl. Spectrosc. 46 1303

    [17]

    Yu B H, Liu M L, Chen D 2011 Acta Phys. Sin. 60 087105 (in Chinese) [余本海, 刘墨林, 陈东 2011 物理学报 60 087105]

    [18]

    Ching W Y 1990 J. Am. Ceram. Soc. 73 641

    [19]

    Liu A Y, Cohen M L 1990 Phys. Rev. B 41 10727

    [20]

    Mo S D, Ouyang L Z, Ching W Y, Tanaka I, Koyama Y, Riedel R 1999 Phys. Rev. Lett. 83 5046

    [21]

    Jiang J Z, Lindelv H, Gerward L, Stahl K, Recio J M, Mori-Sanchez P, Carlson S, Mezouar M, Dooryhee E, Fitch A, Frost D J 2002 Phys. Rev. B 65 161202R

    [22]

    Togo A, Kroll P 2008 J. Comput. Chem. 29 2255

    [23]

    Ordonez S, Iturriza I, Castro F 1999 J. Mater. Sci. 34 147

    [24]

    Fang C M, de Wijs G A, Hintzen H T, de With G 2003 J. Appl. Phys. 93 5175

    [25]

    Meléndez-Martinez J J, Dominguez-Rodriguez A 2004 Prog. Mater. Sci. 49 19

    [26]

    Bermudez V M 2005 Surf. Sci. 579 11

    [27]

    Belkada R, Kohyama M, Shibayanagi T, Naka M 2002 Phys. Rev. B 65 092104

    [28]

    Ching W Y, Ouyang L Z, Gale J D 2000 Phys. Rev. B 61 8696

    [29]

    Weiss J 1981 Annu. Rev. Mater. Sci. 11 381

    [30]

    Grün R 1979 Acta Cryst. B 35 800

    [31]

    Kohn W, Sham L J 1965 Phys. Rev. 140 A1133

    [32]

    Pickeet W E 1989 Comput. Phys. Rep. 9 115

    [33]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [34]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [35]

    Blanco M A, Francisco E, Luana V 2004Comput. Phys. Commun. 158 57

    [36]

    Hu C E, Zeng Z Y, Cheng Y, Chen X R, Cai L C 2008 Chin. Phys. B 17 3867

    [37]

    Marian C M, Gastreich M, Gale J D 2000 Phys. Rev. B 62 3117

    [38]

    Hirosaki N, Ogata S, Kocer C, Kitagawa H, Nakamura Y 2002 Phys. Rev. B 65 134110

    [39]

    Yashima M, Ando Y, Tabira Y 2007 J. Phys. Chem. B 111 3609

    [40]

    Borgen O, Seip H M 1961 Acta Chem. Scand. 15 1789

    [41]

    Ching W Y, Xu Y N, Gale J D, Rühle M 1998 J. Am. Ceram. Soc. 81 3189

    [42]

    Priest H F, Burns F C, Priest G L, Skaar E C 1973 J. Am. Ceram. Soc. 56 395

    [43]

    Fast L, Wills J M, Johansson B, Eriksson O 1995 Phys. Rev. B 51 17431

    [44]

    Sin'ko G V, Smirnow N A 2002 J. Phys.: Condens. Matter 14 6989

    [45]

    Jiang C, Lin Z, Zhao Y 2009 Phys. Rev. Lett. 103 185501

    [46]

    Pugh S F 1954 Philos. Mag. 45 823

    [47]

    Han I S, Seo D W, Kim S Y, Hong K S, Guahk K H, Lee K S 2008 J. Eur. Ceram. Soc. 28 1057

    [48]

    Shein I R, Ivanovskii A I 2008 Scr. Mater. 59 1099

    [49]

    Haines J, Léger J M, Bocquillon G 2001 Ann. Rev. Mater. Res. 31 1

    [50]

    Wang H, Chen Y, Kaneta Y, Iwata S 2006 J. Phys.: Condens. Matter 18 10663

    [51]

    Wang A J, Shang S L, Du Y, Kong Y, Zhang L J, Chen L, Zhao D D, Liu Z K 2010 Comput. Mater. Sci. 48 705

    [52]

    Watari K 2001 J. Ceram. Soc. Jpn. 109 S7

    [53]

    Vogelgesang R, Grimsditch M, Wallace J S 2000 Appl. Phys. Lett. 76 982

    [54]

    Wendel J A, Goddard III W A 1992 J. Chem. Phys. 97 5048

    [55]

    Southworth D R, Barton R A, Verbridge S S, Llic B, Fefferman A D, Craighead H G, Parpia J M 2009 Phys. Rev. Lett. 102 225503

    [56]

    Shebanova O, Soignard E, Mcmillan P F 2006 High Pres. Res. 26 87

    [57]

    Dodd S P, Cankurtaran M, Saunders G A, James B 2001 J. Mater. Sci. 36 2557

    [58]

    Kroll P, Milko M, Anorg Z 2003 Allg. Chem. 629 1737

    [59]

    Goumri-Said S, Kanoun M B 2008 Comput. Mater. Sci. 43 243

    [60]

    Kocer C, Hirosaki N, Ogata S 2003 Phys. Rev. B 67 035210

    [61]

    Dong J J, Deslippe J, Sankey O F, Soignard E, McMillan P F 2003 Phys. Rev. B 67 094104

    [62]

    Sekine T, Tansho M, Kanzaki M 2001 Appl. Phys. Lett. 78 3050

    [63]

    Chen X R, Li X F, Cai L C, Zhu J 2006 Solid State Commun. 139 246

    [64]

    Yu B H, Chen D, Li Y B, Jia Y L 2012 Acta Metal. Sin. (Engl. Lett.) 25 131

    [65]

    Jiang J Z, Kragh F, Frost D J, Stahl K, Lindelov H 2001 J. Phys.: Condens. Matter 13 L515

    [66]

    Zhang Y, Navrotsky A, Sekine T 2006 J. Mater. Res. 21 41

    [67]

    Sekine T, He H, Kobayashi T, Zhang M, Xu F 2000 Appl. Phys. Lett. 76 3706

    [68]

    Ren S Y, Ching W Y 1981 Phys. Rev. B 23 5454

    [69]

    Jiang J Z, Stahl K, Berg R W, Frost D J, Zhou T J, Shi P X 2000 Europhys. Lett. 51 62

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出版历程
  • 收稿日期:  2011-12-26
  • 修回日期:  2012-04-01

α-, β-和γ-Si3N4 高压下的电子结构和相变: 第一性原理研究

  • 1. 信阳师范学院物理电子工程学院, 信阳 464000
    基金项目: 国家自然科学基金(批准号: 11005088, 11105115)、河南省基础与前沿技术研究计划项目(批准号: 112300410021)和河南教育厅项目(批准号: 12A140010) 资助的课题.

摘要: 本文采用第一性原理框架下的赝势平面波方法结合振动类德拜模型研究了α,β和γ-Si3N4在高温下的点阵常数,弹性常数和弹性模量.研究发现三种同质异相体的体模量都很高.β-Si3N4在低温下表现出脆性,在高温下则表现出延展性.γ-Si3N4在低温和高温下都是脆性的共价化合物.β → γ 相变的相界斜率为正值,说明在较高温度时合成γ-Si3N4所需的压强也较高.α → γ 相变的相界可以表示成 P=16.29- 1.835-10-2 T+9.33945-10-5T2-2.16759-10-7T3+2.91795-10-10T4.本文还分析了Si3N4同质异相体在高压下的态密度和能带.在α-Si3N4中主要是Si-s, p和N-s,p的轨道杂化对晶体的稳定性起作用.α和β-Si3N4都具有ΓV-ΓC类型的间接带隙(分别是4.9~eV和4.4~eV)而γ-Si3N4具有直接带隙(3.9~eV). 研究还发现α-Si3N4和β-Si3N4的价带顶分别沿着Γ-M和Γ-A方向.本文的计算结果和已有的实验数据是一致的.

English Abstract

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