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单轴、双轴应变Si拉曼谱应力模型

王程 王冠宇 张鹤鸣 宋建军 杨晨东 毛逸飞 李永茂 胡辉勇 宣荣喜

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单轴、双轴应变Si拉曼谱应力模型

王程, 王冠宇, 张鹤鸣, 宋建军, 杨晨东, 毛逸飞, 李永茂, 胡辉勇, 宣荣喜

Stress models relevant to Raman spectrum in uniaxial/biaxial strained Si

Wang Cheng, Wang Guan-Yu, Zhang He-Ming, Song Jian-Jun, Yang Chen-Dong, Mao Yi-Fei, Li Yong-Mao, Hu Hui-Yong, Xuan Rong-Xi
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  • 本文依据拉曼光谱原理, 基于Secular方程及拉曼选择定则分别获得了单轴、 双轴(001), (101), (111)应变Si材料应变张量与拉曼谱线移动的定量关系, 并在此基础上, 基于广义胡克定律最终建立了单轴、双轴(001), (101), (111)应变Si材料拉曼谱峰与应力的理论关系模型. 该模型建立过程详细、系统, 所得结果全面、量化, 可为应变Si材料应力的测试分析提供重要理论参考.
    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.
    • 基金项目: 国家部委资助项目(批准号: 51308040203, 6139801), 中央高校基本科研业务费(批准号: 72105499, 72104089)和陕西省自然科学基础研究计划项目(批准号: 2010JQ8008)资助的课题.
    • Funds: Project supported by the National Ministries and Commissions (Grant Nos. 51308040203, 6139801), the Fundamental Research Funds for the Central Universities (Grant Nos. 72105499, 72104089), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2010JQ8008).
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    Song J J, Zhang H M, Hu H Y, Fu Q 2009 Science in China 52 546

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    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

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    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

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    Mermoux M, Crisci A, Baillet F, Destefanis V, Rouchon D, Papon A M, Hartmann J M 2010 J. Appl. Phys. 107 013512

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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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出版历程
  • 收稿日期:  2011-05-13
  • 修回日期:  2011-06-15
  • 刊出日期:  2012-02-05

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