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The strain tensor arising from uniaxial stress along an arbitrary direction on the (001) surface of Si is calculated. With these uniaxial strain tensor, the band structure of silicon material under arbitrary uniaxial stress on the (001) surface is calculated using K ·P perturbation theory coupled with linear deformation potential theory. The relation between energy band structure and stress parameters (type, direction, magnitude) was obtained. Finally, the uniaxial stress induced band structure change, such as that of the conduction band (CB) and the valence band (VB) edge levels, CB and VB splitting energy and the bandgap is demonstrated. Results of these band structure can be used as a guide for the design and the selection of the optimum strain and crystal orientation configuration of uniaxial strained silicon devices.
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Keywords:
- uniaxial strained silicon /
- K ·P method /
- energy band structure
[1] Song J J, Zhang H M, Dai X Y, Hu H Y, Xuan R X 2010 Acta Phys. Sin. 59 580(in Chinese)[宋建军、张鹤鸣、戴显英、胡辉勇、宣荣喜2010 59 580]
[2] Sun G Y, Sun Y K, Nishida T, Thompson S E 2007 Appl. Phys.Lett. 102 084501
[3] Fischetti M V, Ren Z, Solomon P M, Yang M, Rim K 2003 J. Appl. Phys. 94 1079
[4] Phama A T, Jungemann C, Meinerzhagen B 2008 Solid-State Electronics 52 1437
[5] Ungersboeck E, Dhar S, Karlowatz G, Sverdlov V, Kosina H, Selberherr S 2007 IEEE Trans. on Electron Dev. 54 2183
[6] Song J J, Zhang H M, Hu H Y, Dai X Y, Xuan R X 2007 Chin. Phys. 16 3827
[7] Song J J, Zhang H M, Dai X Y, Hu H Y, Xuan R X 2009 Acta Phys. Sin. 58 7947(in Chinese) [宋建军、张鹤鸣、戴显英、胡辉勇、宣荣喜2009 58 7947]
[8] Cheng B W, Yao F, Xue C L, Zhang J G, Li C B, Mao R W, ZuoY H, Luo L P, Wang Q M 2005 Acta Phys. Sin. 54 4350 (in Chinese)[成步文、姚 飞、薛春来、张建国、李传波、毛容伟、左玉华、罗丽萍、王启明2005 54 4350]
[9] Song J J, Zhang H M, Dai X Y, Hu H Y, Xuan R X 2008 Acta Phys. Sin. 57 7228 (in Chinese) [宋建军、张鹤鸣、戴显英、胡辉勇、宣荣喜2008 57 7228]
[10] Xie X D, Lu D 1998 Energy Band Theory of Solids (Shangai: Fuda University Press) p58 (in Chinese) [谢希德、陆 栋 1998 固体能带理论(上海:复旦大学出版社)第58页]
[11] Madelung O 2003 Semiconductors: Data Handbook, Data in Science and Technology (3rd ed) (German: Springer Press) p16
[12] Kasper E 2002 Properties of Strained and Relaxed Silicon Germanium (Beijing: National Defense Industry Press) p114
[13] Smirnov S, Kosina H 2004 Solid-State Electronics 48 1325
[14] Manku T, Nathan A 1993 J. Appl. Phys. 73 1205
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[1] Song J J, Zhang H M, Dai X Y, Hu H Y, Xuan R X 2010 Acta Phys. Sin. 59 580(in Chinese)[宋建军、张鹤鸣、戴显英、胡辉勇、宣荣喜2010 59 580]
[2] Sun G Y, Sun Y K, Nishida T, Thompson S E 2007 Appl. Phys.Lett. 102 084501
[3] Fischetti M V, Ren Z, Solomon P M, Yang M, Rim K 2003 J. Appl. Phys. 94 1079
[4] Phama A T, Jungemann C, Meinerzhagen B 2008 Solid-State Electronics 52 1437
[5] Ungersboeck E, Dhar S, Karlowatz G, Sverdlov V, Kosina H, Selberherr S 2007 IEEE Trans. on Electron Dev. 54 2183
[6] Song J J, Zhang H M, Hu H Y, Dai X Y, Xuan R X 2007 Chin. Phys. 16 3827
[7] Song J J, Zhang H M, Dai X Y, Hu H Y, Xuan R X 2009 Acta Phys. Sin. 58 7947(in Chinese) [宋建军、张鹤鸣、戴显英、胡辉勇、宣荣喜2009 58 7947]
[8] Cheng B W, Yao F, Xue C L, Zhang J G, Li C B, Mao R W, ZuoY H, Luo L P, Wang Q M 2005 Acta Phys. Sin. 54 4350 (in Chinese)[成步文、姚 飞、薛春来、张建国、李传波、毛容伟、左玉华、罗丽萍、王启明2005 54 4350]
[9] Song J J, Zhang H M, Dai X Y, Hu H Y, Xuan R X 2008 Acta Phys. Sin. 57 7228 (in Chinese) [宋建军、张鹤鸣、戴显英、胡辉勇、宣荣喜2008 57 7228]
[10] Xie X D, Lu D 1998 Energy Band Theory of Solids (Shangai: Fuda University Press) p58 (in Chinese) [谢希德、陆 栋 1998 固体能带理论(上海:复旦大学出版社)第58页]
[11] Madelung O 2003 Semiconductors: Data Handbook, Data in Science and Technology (3rd ed) (German: Springer Press) p16
[12] Kasper E 2002 Properties of Strained and Relaxed Silicon Germanium (Beijing: National Defense Industry Press) p114
[13] Smirnov S, Kosina H 2004 Solid-State Electronics 48 1325
[14] Manku T, Nathan A 1993 J. Appl. Phys. 73 1205
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