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Performance enhancement of strained Si material originates from the stress on it, which can be measured by Raman spectroscopy. A study of the theoretical model of strain-induced Raman spectrum frequency shift in strained Si material is of profound theoretical and practical significance. The Raman frequency shift of strained Si is significantly correlated with the stress intensity, the stress type and the crystal plane. However, the corresponding reports republished are lacking in integrality and systematization in the process of modeling. In this paper, according to the theory of Raman spectroscopy, based on Secular equation and Raman selection rules, quantitative relationships between strain tensor and Raman frequency shift for uniaxial and biaxial strained Si grown on (001), (101), and (111) SiGe substrates are achieved. On this basis, theoretical models of mechanical stress and Raman spectrum for uniaxial and biaxial strained Si materials grown on (001), (101), and (111) SiGe substrates are obtained using Hooke's law, respectively. The procedure for setling up these models is elaborate and systematic and the results obtained are comprehensive and quantificational, which can provide an important reference for the stress analysis in strained Si material.
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Keywords:
- strained Si /
- Raman spectroscopy /
- stress
[1] Song J J, Zhang H M, Hu H Y, Dai X Y, Xuan R X 2010 Acta Phys. Sin. 59 2064 (in Chinese) [宋建军, 张鹤鸣, 胡辉勇, 戴显英, 宣荣喜 2010 物理学报 59 2064]
[2] Song J J, Zhang H M, Hu H Y, Dai X Y, Xuan R X 2010 Science in China 53 454
[3] Zhang J H, Gu F, Liu Q Q, Gu B, Li M 2010 Acta Phys. Sin. 59 4226 (in Chinese) [张加宏, 顾芳, 刘清惓, 顾斌, 李敏 2010 物理学报 59 4226]
[4] Gao H, Ikeda K, Hata S, Nakashima H, Wang D, Nakashima H 2011 Acta Materialia 59 2882
[5] Song J J, Zhang H M, Hu H Y, Fu Q 2009 Science in China 52 546
[6] Haugerud B M, Nayeem M B, Krithivasan R, Lu Y, Zhu C D, Cressler J D, Belford R E, Joseph A J 2005 Solid-State Electronics 49 986
[7] Olsen S H, Dobrosz P, Agaiby M B, Tsang Y L, Alatise O, Bull S J, O’Neill A G, Moselund K E, Ionescu A M, Majhi P, Buca D, Mantl S, Coulson H 2008 Materials Science in Semiconductor Processing 11(5-6) 271
[8] Mermoux M, Crisci A, Baillet F, Destefanis V, Rouchon D, Papon A M, Hartmann J M 2010 J. Appl. Phys. 107 013512
[9] Qian J 2003 MS Thesis (Beijing: The Chinese Academy of Sciences) (in Chinese) [钱劲 2003 硕士论文(北京: 中国科学院研究生院)]
[10] Narayanan S, Kalidindi S R, Schadler L S 1997 J. Appl. Phys. 82 2595
[11] Qiu Y, Lei Z K, Kang Y L, Hu M, Xu H, Niu H P 2004 Journal of Mechanical Strength 26 389
[12] Anastassakis E, Pinczuk A, Burstein E 1970 Solid State Communications 8 133
[13] Anastassakis E, Cantarere A, Cardona M 1990 Phys. Rev. B 41 7529
[14] Brantley W A 1973 J. Appl. Phys. 44 534
[15] Loudon R 1964 Adv. Phys. 13 423
[16] Song J J, Mao Y F, Shan H S, Yang C D, Li Y M, Zhang H M, Hu H Y 2010 IEEE International Asia Conference on Optical Instrument and Measurement Shenzhen 120—122
[17] Wolf I D 1996 Semicond. Sci. Technol. 11 139
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[1] Song J J, Zhang H M, Hu H Y, Dai X Y, Xuan R X 2010 Acta Phys. Sin. 59 2064 (in Chinese) [宋建军, 张鹤鸣, 胡辉勇, 戴显英, 宣荣喜 2010 物理学报 59 2064]
[2] Song J J, Zhang H M, Hu H Y, Dai X Y, Xuan R X 2010 Science in China 53 454
[3] Zhang J H, Gu F, Liu Q Q, Gu B, Li M 2010 Acta Phys. Sin. 59 4226 (in Chinese) [张加宏, 顾芳, 刘清惓, 顾斌, 李敏 2010 物理学报 59 4226]
[4] Gao H, Ikeda K, Hata S, Nakashima H, Wang D, Nakashima H 2011 Acta Materialia 59 2882
[5] Song J J, Zhang H M, Hu H Y, Fu Q 2009 Science in China 52 546
[6] Haugerud B M, Nayeem M B, Krithivasan R, Lu Y, Zhu C D, Cressler J D, Belford R E, Joseph A J 2005 Solid-State Electronics 49 986
[7] Olsen S H, Dobrosz P, Agaiby M B, Tsang Y L, Alatise O, Bull S J, O’Neill A G, Moselund K E, Ionescu A M, Majhi P, Buca D, Mantl S, Coulson H 2008 Materials Science in Semiconductor Processing 11(5-6) 271
[8] Mermoux M, Crisci A, Baillet F, Destefanis V, Rouchon D, Papon A M, Hartmann J M 2010 J. Appl. Phys. 107 013512
[9] Qian J 2003 MS Thesis (Beijing: The Chinese Academy of Sciences) (in Chinese) [钱劲 2003 硕士论文(北京: 中国科学院研究生院)]
[10] Narayanan S, Kalidindi S R, Schadler L S 1997 J. Appl. Phys. 82 2595
[11] Qiu Y, Lei Z K, Kang Y L, Hu M, Xu H, Niu H P 2004 Journal of Mechanical Strength 26 389
[12] Anastassakis E, Pinczuk A, Burstein E 1970 Solid State Communications 8 133
[13] Anastassakis E, Cantarere A, Cardona M 1990 Phys. Rev. B 41 7529
[14] Brantley W A 1973 J. Appl. Phys. 44 534
[15] Loudon R 1964 Adv. Phys. 13 423
[16] Song J J, Mao Y F, Shan H S, Yang C D, Li Y M, Zhang H M, Hu H Y 2010 IEEE International Asia Conference on Optical Instrument and Measurement Shenzhen 120—122
[17] Wolf I D 1996 Semicond. Sci. Technol. 11 139
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