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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.
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Keywords:
- silicon nano-film /
- Young' /
- s modulus
[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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[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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