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研究生: 賴致廷
Lai, Chih-Ting
論文名稱: 粗糙度對單晶矽破壞強度影響研究
Investigation on the Roughness Effect of the Fracture Strength of SCS
指導教授: 江國寧
Chiang, Kuo-Ning
口試委員: 鄭仙志
蔡宏營
劉德騏
學位類別: 碩士
Master
系所名稱: 工學院 - 動力機械工程學系
Department of Power Mechanical Engineering
論文出版年: 2012
畢業學年度: 100
語文別: 中文
論文頁數: 61
中文關鍵詞: 單晶矽破壞強度粗糙度三點彎折實驗有限元素法
外文關鍵詞: single crystalline silicon, fracture strength, roughness, three point bending test, finite element method
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  • 單晶矽為半導體晶片常用之基板材料,但在封裝過程若設計不當則有可能因材料間熱膨脹係數不匹配而造成晶片破壞。許多學者藉由各種測試方式期望能得到矽晶片的破壞強度以改善製程良率,並發現當單晶矽試片尺寸縮小時其強度上升。然而,當製造較小尺寸試片時由於製造方式改變會造成粗糙度的改變,並影響破壞強度。因此,本研究的目的在於建立一套方法以獲得帶有粗糙度影響之破壞強度。
    由於實驗結果顯示側面粗糙度的影響較表面粗糙度的影響大,因此本研究聚焦於側面粗糙度對破壞強度的影響。首先,利用光學顯微鏡配合影像處理技術重建試片的側面粗糙度曲線,並獲得最大粗糙度高度R_max以及平均波峰間距S_m等粗糙度參數。接著,進行三點彎折實驗以獲得試片破壞時所需位移,並擬合韋伯分布曲線獲得最大近似估計量。最後,把粗糙度參數以及破壞時所需位移代入有等效凹槽的有限元素模型並進行求解,可得到試片破壞時凹槽頂端之第一主應力,即帶有側面粗糙度影響的單晶矽破壞強度。
    結果顯示帶有側面粗糙度影響的單晶矽破壞強度約為2.7 GPa,此數值與文獻相比在合理範圍內。儘管如此,本方法在表面存在研磨痕跡且痕跡與側面接近垂直時會造成高估的結果,若利用在表面拋光後的試片可望有較合理的結果。


    摘要 I Abstract II 致謝 IV 目錄 V 表目錄 VII 圖目錄 VIII 第一章 緒論 1 1.1 研究動機 1 1.2 文獻回顧 3 1.3 研究目標 7 第二章 基礎理論 10 2.1 有限元素法之接觸理論 10 2.1.1 拉格朗日乘子法 11 2.1.2 罰函數法 12 2.1.3 加強型拉格朗日乘子法 13 2.2 破壞準則 14 2.2.1 最大主應力破壞準則 14 2.2.2 最大剪應力破壞準則 15 2.2.3 最大畸變能破壞準則 16 2.3 統計方法 18 2.3.1 常態分布 18 2.3.2 最大極限值分布 22 2.3.3 韋伯分布 26 2.3.4 最大近似法 29 第三章 實驗方法 32 3.1 三點彎折實驗 32 3.1.1 實驗設備 32 3.1.2 試片製備 34 3.1.3 實驗流程 36 3.2 粗糙度量測實驗 37 3.2.1 粗糙度參數定義 37 3.2.2 實驗流程 38 3.2.3 重複性測試 39 第四章 實驗結果與討論 41 4.1 側面粗糙度量測結果 41 4.2 三點彎折實驗結果 45 4.3 結果討論 48 第五章 有限元素模擬結果與討論 49 5.1 有限元素模型 49 5.2 模擬結果 52 5.2.1 網格密度影響 52 5.2.2 側面粗糙度影響 54 5.3 模擬結果討論 55 第六章 結論與未來展望 57 參考文獻 59

    [1] 江國寧, 微電子系統封裝基礎理論與應用技術, 滄海書局, 2006.
    [2] S. F. Popelar, “An Investigation into the Fracture of Silicon Die Used in Flip Chip Applications,” Proceedings 4th International Symposium on Advanced Packaging Materials Processes, Property and Interfaces, pp. 41-48, Braselton, USA, March 15-18, 1998.
    [3] F. X. Che, T. C. Chai, S. P. S. Lim, R. Rajoo, and X. Zhang, “Design and Reliability Analysis of Pyramidal Shape 3-Layer Stacked TSV Die Package,” 2011 IEEE 61st Electronic Components and Technology Conference, pp. 1428-1435, Lake Buena Vista, USA, May 31-June 3, 2011.
    [4] W. Weibull, A Statistical Theory of the Strength of Materials, Generalstabens litografiska anstalts, Stockholm, 1939.
    [5] G. L. Pearson, W. T. Read Jr., and W. L. Feldmann, “Deformation and Fracture of Small Silicon Crystals,” Acta Metallurgica, Vol. 5, pp. 181-191, 1957.
    [6] T. Namazu, Y. Isono, and T. Tanaka, “Evaluation of Size Effect on Mechanical Properties of Single Crystal Silicon by Nanoscale Bending Test Using AFM,” Journal of Microelectromechanical Systems, Vol. 9, pp. 450-459, 2000.
    [7] I. Paul, B. Majeed, K. M. Razeeb, and J. Barton, “Statistical Fracture Modelling of Silicon with Varying Thickness,” Acta Materialia, Vol. 54, pp. 3991-4000, 2006.
    [8] S. Chen, T. Y. Kuo, H. T. Hu, J. R. Lin, and S. P. Yu, “The Evaluation of Wafer Thinning and Singulating Processes to Enhance Chip Strength,” 2005 proceedings 55th Electronic Components and Technology Conference, Vol. 2, pp. 1526-1530, Lake Buena Vista, USA, May 31-June 4, 2005.
    [9] A. A. Wereszczak, A. S. Barnes, and K. Breder, “Probabilistic Strength of {111} n-type Silicon,” Journal of Materials Science: Materials in Electronics, Vol. 11, pp. 291-303, 2000.
    [10] A. A. Griffith, “The Phenomena of Rupture and Flow in Solids,” Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 221, pp. 163-198, 1921.
    [11] S. M. Hu, “Critical Stress in Silicon Brittle Fracture, and Effect of Ion Implantation and Other Surface Treatments,” Journal of Applied Physics, Vol. 53, pp. 3576-3580, 1982.
    [12] S. Andrews and H. Sehitoglu, “A Computer Model for Fatigue Crack Growth from Rough Surfaces,” International Journal of Fatigue, Vol. 22, pp. 619-630, 2000.
    [13] R. E. Peterson, Stress Concentration Factors, John Wiley and Sons, New York, 1974.
    [14] B. Bhushan and G. B. Agrawal, “Stress Analysis of Nanostructures Using a Finite Element Method,” Nanotechnology, Vol. 13, pp. 515-523, 2002.
    [15] H. H. Chang, T. Y. Hung, and K. N. Chiang, "Residual Stress Effect of Electromigration Behavior on Aluminum Strip," Proceedings Materials for Advanced Metallization Conference, Grenoble, France, March 11-14, 2012
    [16] Z. H. Zhong, Finite Element Procedures for Contact-Impact Problems, Oxford, New York, 1993.
    [17] M. H. Aliabadi and C. A. Brebbia, Computational Methods in Contact Mechanics, Computational Mechanics Publications, UK, 1993.
    [18] S. Timoshenko, Strength of Materials, D. Van Nostrand Company, New Jersey, 1956.
    [19] J. A. Collins, Failure of Materials in Mechanical Design, John Wiley and Sons, New York, 1993.
    [20] R. C. Juvinall, Stress, Strain, and Strength, McGraw-Hill, New York, 1967.
    [21] G. P. Cherepanov, Mechanics of Brittle Fracture, McGraw-Hill, New York, 1979.
    [22] E. Castillo, A. S. Hadi, N. Balakrishnan and J. M. Sarabia, Extreme Value and Related Models with Applications in Engineering and Science, John Wiley and Sons, New Jersey, 2005.
    [23] T. A. Severini, Elements of Distribution Theory, Cambridge University Press, New York, 2005.
    [24] W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data, John Wiley and Sons, New York, 1998.
    [25] N. Otsu, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Transactions on System, Man, and Cybernetics, Vol. SMC-9, No. 1, pp. 62-66, 1979.
    [26] J. J. Wortman and R. A. Evans, “Young’s Modulus, Shear Modulus, and Poisson’s Ratio in Silicon and Germanium,” Journal of Applied Physics, Vol. 36, pp. 153-156, 1965.
    [27] B. Bhushan and G. B. Agrawal, “Finite Element Analysis of Nanostructures with Roughness and Scratches,” Ultramicroscopy, Vol. 97, pp. 495-507, 2003.
    [28] A. Kelly, Strong Solids, Oxford University Press, London, 1973.

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