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掺杂单晶硅纳米薄膜杨氏模量的多尺度理论模型

吕焕玲 王静

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掺杂单晶硅纳米薄膜杨氏模量的多尺度理论模型

吕焕玲, 王静

The multi-scale theoretical models of Young's modulus of doped monocrystalline silicon nano-film

Lv Huan-Ling, Wang Jing
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  • 硅纳米材料物理性能的研究对其在半导体技术中的应用是十分重要的. 而掺杂有利于改善硅纳米材料的物理特性, 提高应用价值, 所以本文基于半连续体模型运用Keating形变势, 通过模型计算, 研究了不同位置及不同掺杂浓度的单晶硅纳米薄膜[100]方向的杨氏模量, 分析了掺杂浓度及掺杂位置不同时硅膜杨氏模量与膜厚关系, 结果表明, 与纯硅膜杨氏模量相比, 不同位置的掺杂对硅膜杨氏模量的影响并不明显, 不同浓度的掺杂对硅膜杨氏模量的影响较小. 而随着硅膜厚度的不断增加, 掺杂硅膜杨氏模量与纯硅膜杨氏模量的变化趋势一致, 特别是较小尺寸时的硅膜杨氏模量变化较大. 说明影响硅膜杨氏模量的主要因素是硅膜厚度. 该计算结果对研究硅纳米材料的其他力学特性有一定的参考价值, 也为进一步研究掺杂对纳米硅材料力学性能的影响提供一种全新思路.
    The study of physical properties of silicon nano-materials is very important for its application in semiconductor technology. Doping is beneficial to improving the physical properties of silicon nano-materials, it can improve the application value as well. Young's modulus of the crystal in the direction of [100] of the doped silicon nano-film is studied by an analytical model, which is based on the semi-continuum approach. In the model, the strain energy is obtained from the Keating strain energy model. The relationship between the Young's modulus and film thickness are also discussed. Results show that the Young's modulus decreases with the increase of the thickness of the silicon film, especially with the small size; the variation tendency of the Young's modulus of doped silicon films is similar to the pure silicon film. And the Young's modulus decreases as the doping concentration decreases for different doping position. Neither the doping concentration nor the doping position, it is the thickness that shows the most important effect on the Young's modulus of the doped silicon nano-film. Findings in this paper may serve as a reference for similar study, and can offer a totally new idea of the doped monocrystalline silicon materials as well.
      通信作者: 王静, wjxju@163.cm
    • 基金项目: 国家自然科学基金(批准号:11064014)资助的课题.
      Corresponding author: Wang Jing, wjxju@163.cm
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11064014).
    [1]

    Li D S, Yang D R, Que D L 2000 Mater. Sci. Eng. 18 100104 (in Chinese) [李东升, 杨德仁, 阙端麟 2000 材料科学与工程 18 100104]

    [2]

    Jiang R H, Xiao S Z 2002 Semiconductor Technology 27 36 (in Chinese) [蒋荣华, 肖顺珍 2002 半导体技术 27 36]

    [3]

    Felthamand P, Banerjee R 1992 J. Mater. Sci. 27 1626

    [4]

    Fetterman G P, Greg S 2000 Lubricants World 10 1517

    [5]

    Lawn B R, Hockey B, Wiederhorn S 1980 J. Mater. Sci. 15 1207

    [6]

    Hauch J A, Holland D, Marder M P, Swinney H L 1999 Phys. Rev. Lett. 82 3823

    [7]

    Broughton J Q, Meli C A, Vashishta P, Kalia R 1997 Phys. Rev. B 56 1618

    [8]

    Li X X, Takahito O, Lin R M 2003 Microelectron Eng. 65 0112

    [9]

    Hu S M, Patrick W J 1975 J. Appl. Phys. 46 l8691874

    [10]

    Hu S M 1977 Appl. Phys. Lett. 31 53

    [11]

    Zeng Z D, Ma X Y, Chen J H, Zeng Y H, Yang D R, Liu Y G 2010 J. Appl. Phys. 107 15

    [12]

    Jing Y H, Aluru N R 2011 Comp Mater Sci. 50 3063

    [13]

    Jing Y H, Guo L H, Sun Y, Shen J, Aluru N R 2013 Surf Sci. 611 80

    [14]

    Pi X D 2012 J. Nanomater 2012 903912

    [15]

    Ma Y S, Chen X B, Pi X D, Yang D R 2012 J. Nanopart Res. 14 0208

    [16]

    Sun C T, Zhang H T 2003 J. Appl. Phys. 93 1212

    [17]

    Keating P N 1966 Phys. Rev. 145 637

    [18]

    Kang J C, Han Q J, Yin B L 2001 Computer Engineering and Application 18 141 (in Chinese) [康建初, 韩秋菊, 尹宝林 2001 计算机工程与应用 18 141]

    [19]

    Huang Q A 1996 Silicon Micromachining Technology (Beijing: Science Press) p259 (in Chinese) [黄庆安 1996 硅微机械加工技术 (北京: 科学出版社) 第259页]

    [20]

    Burlakov V M, Briggs G A D, Sutton A P 2001 Appl. Phys. Lett. 86 3052

    [21]

    Alfthan S V, Kuronen A, Kaski K 2003 Phys. Rev. B 68 073203

    [22]

    Huang Z L 1998 Elastic Mechanics Introductory Tutorial (Volume 2) (Beijing: Higher Education Press) pp8-10 (in Chinese) [徐芝纶 1998 弹性力学简明教程(北京: 高等教育出版社)第 8–10 页]

    [23]

    Wang J 2008 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese) [王静 2008 博士学位论文(南京: 东南大学)]

    [24]

    Rucker H, Methfessel M 1995 Phys. Rev. B 52 11059

    [25]

    Wang J 2012 The Sixth Asia-Pacific Conference on Transducers and Micro/Nano Technologies, Nanjing, China, July 8-11, 2012 ac12000109

    [26]

    Li X X, Takahito O, Wang Y L, Masayoshi E 2003 Appl. Phys. Lett. 83 3180

  • [1]

    Li D S, Yang D R, Que D L 2000 Mater. Sci. Eng. 18 100104 (in Chinese) [李东升, 杨德仁, 阙端麟 2000 材料科学与工程 18 100104]

    [2]

    Jiang R H, Xiao S Z 2002 Semiconductor Technology 27 36 (in Chinese) [蒋荣华, 肖顺珍 2002 半导体技术 27 36]

    [3]

    Felthamand P, Banerjee R 1992 J. Mater. Sci. 27 1626

    [4]

    Fetterman G P, Greg S 2000 Lubricants World 10 1517

    [5]

    Lawn B R, Hockey B, Wiederhorn S 1980 J. Mater. Sci. 15 1207

    [6]

    Hauch J A, Holland D, Marder M P, Swinney H L 1999 Phys. Rev. Lett. 82 3823

    [7]

    Broughton J Q, Meli C A, Vashishta P, Kalia R 1997 Phys. Rev. B 56 1618

    [8]

    Li X X, Takahito O, Lin R M 2003 Microelectron Eng. 65 0112

    [9]

    Hu S M, Patrick W J 1975 J. Appl. Phys. 46 l8691874

    [10]

    Hu S M 1977 Appl. Phys. Lett. 31 53

    [11]

    Zeng Z D, Ma X Y, Chen J H, Zeng Y H, Yang D R, Liu Y G 2010 J. Appl. Phys. 107 15

    [12]

    Jing Y H, Aluru N R 2011 Comp Mater Sci. 50 3063

    [13]

    Jing Y H, Guo L H, Sun Y, Shen J, Aluru N R 2013 Surf Sci. 611 80

    [14]

    Pi X D 2012 J. Nanomater 2012 903912

    [15]

    Ma Y S, Chen X B, Pi X D, Yang D R 2012 J. Nanopart Res. 14 0208

    [16]

    Sun C T, Zhang H T 2003 J. Appl. Phys. 93 1212

    [17]

    Keating P N 1966 Phys. Rev. 145 637

    [18]

    Kang J C, Han Q J, Yin B L 2001 Computer Engineering and Application 18 141 (in Chinese) [康建初, 韩秋菊, 尹宝林 2001 计算机工程与应用 18 141]

    [19]

    Huang Q A 1996 Silicon Micromachining Technology (Beijing: Science Press) p259 (in Chinese) [黄庆安 1996 硅微机械加工技术 (北京: 科学出版社) 第259页]

    [20]

    Burlakov V M, Briggs G A D, Sutton A P 2001 Appl. Phys. Lett. 86 3052

    [21]

    Alfthan S V, Kuronen A, Kaski K 2003 Phys. Rev. B 68 073203

    [22]

    Huang Z L 1998 Elastic Mechanics Introductory Tutorial (Volume 2) (Beijing: Higher Education Press) pp8-10 (in Chinese) [徐芝纶 1998 弹性力学简明教程(北京: 高等教育出版社)第 8–10 页]

    [23]

    Wang J 2008 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese) [王静 2008 博士学位论文(南京: 东南大学)]

    [24]

    Rucker H, Methfessel M 1995 Phys. Rev. B 52 11059

    [25]

    Wang J 2012 The Sixth Asia-Pacific Conference on Transducers and Micro/Nano Technologies, Nanjing, China, July 8-11, 2012 ac12000109

    [26]

    Li X X, Takahito O, Wang Y L, Masayoshi E 2003 Appl. Phys. Lett. 83 3180

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出版历程
  • 收稿日期:  2015-06-02
  • 修回日期:  2015-07-27
  • 刊出日期:  2015-12-05

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