臺灣博碩士論文加值系統

對於電子封裝結構的設計，需要考慮的設計參數眾多，如封裝元件內部各結構的幾何尺寸、材料性質、錫球的尺寸、數量與分布方式等，並需考慮業界當前製程技術。傳統的設計方式耗費的成本與時間將影響產品的上市時間與競爭力，半導體科技製程日新月異，為了縮短開發設計所需的時間成本，藉由有限單元法模擬的方式取代實驗，為產品帶來快速準確的評估優勢，搭配少量驗證用的實驗，節省開發時間與實驗所需的大量成本。然而不同的研究人員針對相同的結構設計不論是使用實驗設計(DOE)或模擬(Simulation)的方式，得到的結果皆有差異，因此本論文應用機器學習其中的人工神經網路演算法，從數據中統計導出最佳回歸模型，對特定的封裝結構設計範圍統合出適合的壽命預估公式，便能整合不同人員操作後結果的誤差。
本研究目標為探討並預測WLCSP封裝結構之可靠度，使用有限單元分析軟體ANSYS○R模擬封裝結構在熱循環負載測試下的受力狀態，利用體積權重的概念選定應力集中處之適用網格大小的尺寸劃分，將等效塑性應變入Coffin-Manson應變壽命預估模型，預估錫球的疲勞壽命數，比對數組模擬預測相對於實驗之誤差，固定模擬所使用的模型建構方式、錫球關鍵部位網格大小與理論方法相互搭配確認能夠有效驗證實驗結果來預估錫球壽命，並依據此模擬方式代替實驗大量建立不同設計參數的可靠度資料庫，提供人工神經網路之機器學習方法進行資料訓練，以程式語言Python應用機器學習scikit-learn封包，探討多層人工神經網路之隱藏層中神經元數最佳組合，並從數據中統計導出最佳回歸模型導出矩陣公式，此公式將可適用於合理的尺寸範圍內有效推估出封裝結構可靠度。

In regard to design of electronic packaging structure, we need to consider many types of parameter, Such as geometric dimensions of the internal structure of the packaged components, material properties and solder ball size, number and distribution, etc. Moreover, we need to premeditate current process technology in industry. In traditional design methods, cost and time spent will affect the time to market and its competitiveness. Semiconductor technology change progressively. In order to shorten the development time, replacing the experiments with the finite element method simulations. The product can be quickly and accurately evaluated with a small number of verification experiments. Simulations can speed up the development time and experimental cost. Although FEM is an appropriate way to assess reliability of packaging, different people do either experiment or simulation would have different results. Therefore, machine learning provides automatic analysis from data to obtain a regression model. FEM is capable to express the trend of experimental results. We can derive a formula from the regression model and get reliability instantly.
In environment of finite element analysis software ANSYS○R , we simulate the loading state of the package structure under the Thermal cycling test (TCT). Applying concept of volume weights to decide optimal mesh size at max distance neural point of solder. Coffin-Manson strain based life prediction model is applied to predict lifetime of SAC305 solder balls, and the lifetime results would be verified with experimental results. Confirming those the optimal mesh size of the key part of solder used in simulation, construction method of model and theoretical method can effectively verify experimental results. In the other words, we can establish a large number of data set for representing experiment according to simulation results. The data set would be trained and provided to machine learning method: linear regression and artificial network. The best regression learning models are derived from both of the method. In reasonable geometry structure of package, the models would be applied to assess reliability of the package.

摘要 I
Abstract III
目錄 V
圖目錄 VIII
表目錄 XII
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究目標 10
第二章 基礎理論 11
2.1 錫球外型預測 11
2.2 有限單元法基礎理論 14
2.2.1 線彈性有限單元理論 14
2.2.2 材料非線性理論 19
2.2.3 數值方法及收斂準則 21
2.3 硬化法則 22
2.3.1 等向硬化法則 23
2.3.2 動態硬化法則 24
2.4 Chaboche 模型 25
2.5 封裝結構可靠度之預測方法 27
2.5.1 Coffin-Manson應變法 27
2.5.2 Darveaux 能量密度法 28
2.6 機器學習 29
2.6.1 督導式學習 32
2.6.2 非督導式學習 33
2.6.3 強化式學習 34
2.7 回歸分析模型 35
2.7.1 線性回歸 35
2.7.2 人工神經網路(Artificial Neural Network) 37
2.7.3 支援向量機 (Support Vector Machine) 46
2.7.4 K-鄰近演算法 (K-nearest Neighbors Algorism) 48
2.7.5 決策樹 (Decision Tree) 49
2.8 資料特徵縮放 52
2.8.1 正規化 52
2.8.2 標準化 53
2.9 正規化(regularization) 53
2.10 模型收斂學習與效能評估 54
2.10.1梯度下降法 54
2.10.2誤差反向傳播法 56
2.10.3模型效能交叉驗證 58
第三章 有限單元模型之建立 60
3.1 有限單元模型基本假設 62
3.2 材料參數之設定 66
3.3 邊界條件設定 67
3.4 溫度負載設定 68
第四章 資料庫建立與機器學習預測結果討論 70
4.1 有限單元模擬驗證 70
4.2 資料庫建立 74
4.3 機器學習訓練結果 78
第五章 結論與未來工作 98
參考文獻 100
附錄：程式碼 105

[1] L. F. Coffin, "A study of the effects of cyclic thermal stresses on a ductile metal”, Tarnsactions-American Society of Mechanical Engineers Journal of Electronic Packaging, vol. 76, pp. 931-950, 1954.
[2] S. S. Manson, “Behavior of materials under conditions of thermal stress”, National Advisory Committee for Aeronautics-Techncal Note 2933, pp. 317-350, 1953.
[3] R. Darveaux, K. Banerji, A Mawer, and G. Dody, “Reliability of plastic ball grid array assembly”, Ball Grid Array Technology, Edited by J. Lau, McGraw-Hill, Inc. (New York, 1995).
[4] R. Darveaux, “Effect of simulation methodology on solder joint crack growth correlation”, Proc. 50th IEEE Electron. Comp. Technol. Conf. (ECTC'00), 2000.
[5] K. C. Wu, C. H. Lee, and K. N. Chiang, "Characterization of thermal cycling ramp rate and dwell time effects on AF (Acceleration Factor) Estimation," Electronic Components Technology Conference (ECTC ), Las Vegas, NV, USA, May 31- June 3, 2016
[6] . C. Wu, S. Y. Lin, T. Y. Hung and K. N. Chiang, “Reliability Assessment of Packaging Solder Joints Under Different Thermal Cycle Loading Rates”, IEEE Transactions on Device and Materials Reliability, vol. 15, no. 3, pp. 437-442, Sept. 2015.
[7] R. Darveaux, “Effect of simulation methodology on solder joint crack growth correlation and fatigue life prediction”, J. Electron. Packag., vol. 124, no. 3, pp. 147-154, Jul. 2002.
[8] K. N. Chiang, H. C. Cheng, and W. H. Chen, “Large-Scaled 3-D area array electronic packaging analysis”, Journal of Computer Modeling and Simulation in Engineering, Vol. 4, No.1, pp. 4-11, 1999.
[9] C. Y. Tsou, T. N Chang, K. C. Wu, P. L. Wu and K.N. Chiang, “Reliability Assessment using Modified energy based model for WLCSP Solder Joints”, ICEP2017, Yamagata, Japan, April 19-22, 2017.
[10] W. H. Chen, H. C. Cheng and H. A. Shen, “An effective methodology for thermal characterization of electronic packaging”, IEEE Transactions on Components and Packaging Technologies, vol. 26, no. 1, pp. 222-232, March 2003.
[11] E. F. Alsina, M. Chica, K. Trawiński, A. Regattieri, “On the use of machine learning methods to predict component reliability from data-driven industrial case studies”, The International Journal of Advanced Manufacturing Technology, Vol. 94, Issue 5–8, pp. 2419–2433, 2018.
[12] S. Aich, K. Younga, K. L. Hui, A. A. Al-Absi and M. Sain, “A nonlinear decision tree based classification approach to predict the Parkinson's disease using different feature sets of voice data”, 2018 20th International Conference on Advanced Communication Technology (ICACT), pp. 638-642, Chuncheon-si Gangwon-do, Korea, 11-14 Feb., 2018.
[13] I. Takigawa, K. Shimizu, K. Tsuda, S. Takakusagi, “Machine Learning Predictions of Factors Affecting the Activity of Heterogeneous Metal Catalysts”, In: Tanaka I. (eds) Nanoinformatics. Springer, Singapore, 2018
[14] D. Wu, C. Jennings , J. Terpenny, R. X. Gao, S. Kumara, “A Comparative Study on Machine Learning Algorithms for Smart Manufacturing: Tool Wear Prediction Using Random Forests”, Journal of Manufacturing Science and Engineering, Vol.139, Issue 7, 2017.
[15] M. Pecht, R. Jaai, “A prognostics and health management roadmap for information and electronics-rich systems”, Microelectronics Reliability, Vol.50, Issue 3, pp. 317-323, 2010.
[16] T. N. Chang, C. Y. Tsou, B. H. Wang, K. N. Chiang,” Novel wafer level packaging for large die size device”, ICEP2017, Yamagata, Japan, April 19-22, 2017.
[17] N. S. Altman, “An introduction to kernel and nearest-neighbor nonparametric regression”, The American Statistician, Vol. 46, Issue 3, 1992.
[18] J. R. Quinlan, “Induction of Decision Trees”, Machine Learning, Vol.1, Issue 1, pp. 81–106, 1986.
[19] B. Li and P. D. Franzon, “Machine learning in physical design”, 2016 IEEE 25th Conference on Electrical Performance Of Electronic Packaging And Systems (EPEPS), San Diego, CA, pp. 147-150, 2016.
[20] C. Cortes, V. Vapnik, “Support-Vector Networks”, Machine Learning, Vol. 20, Issue 3, pp. 273–297, 1995.
[21] V.Vapnik, “The Nature of Statistical Learning Theory,” Springer-Verlag, New York, 1995.
[22] R. M. Balabin, E. I. Lomakina, “upport vector machine regression (SVR/LS-SVM)-an alternative to neural networks (ANN) for analytical chemistry?”, The Analyst , Vol. 136, Issue 8, pp. 1703–1712, 2011.
[23] R. Khelif, B. Chebel-Morello, S. Malinowski, E. Laajili, F. Fnaiech and N. Zerhouni, “Direct Remaining Useful Life Estimation Based on Support Vector Regression”, IEEE Transactions on Industrial Electronics, vol. 64, no. 3, pp. 2276-2285, March 2017.
[24] B. E. Boser, I. M. Guyon, V. N. Vapnik, “A training algorithm for optimal margin classifiers”, COLT '92 Proceedings of the fifth annual workshop on Computational learning theory, pp. 144-152, Pittsburgh, Pennsylvania, USA — July 27 - 29, 1992.
[25] T. K. Ho, “Random Decision Forest”, Proceedings of 3rd International Conference on Document Analysis and Recognition, Montreal, Que., pp. 278-282 vol.1, Washington, DC, USA, 1995.
[26] L. S. Goldmann, “Geometry optimization of controlled collapse interconnections”, IBM Journal of Research and Development, Vol. 13, pp. 251-265, May 1969.
[27] S. M. Heinrich, M. Schaefer, S. A. Schroeder, and P. S. Lee, “Peidiction of solder joint geomertry on array-type interconnections”, American Society of Mechanical Engineers Journal of Electronic Packaging, Vol. 118, pp. 114-121, 1996.
[28] K. A. Brakke, “Surface Evolver Manual”, version 2.01 Minneapolis, MN: The Geometry Center, 1996.
[29] L. Li and B. H. Yeung, “Wafer Level and Flip Chip Design Through Solder Prediction Models and Validation”, IEEE Transactions on Components and Packaging Technologies, Vol. 24, No. 4, pp. 650-654, 2001.
[30] B. H. Yeung, T. T. Lee, “Evaluation and optimization of package processing and design through solder joint profile prediction”, IEEE Transactions on Advanced Packaging, Vol. 26, No. 1, pp. 68–74, 2003.
[31] K. J. Bathe, Finite Element Procedures in Engineering Analysis: Prentice Hall, 1982.
[32] S. Timoshenko, Theory of Elasticity: Mcgraw-Hill College, 1970.
[33] C. L. Dym, and I. H. Shames, Solid Mechanics: A Variational Approach, Augmented Edition: Springer, 2013.
[34] W. N. Findley, J. S. Lai, and K. Onaran, “Creep and relaxation of nonlinear viscoelastic materials”, with an introduction to linear viscoelasticity: Amsterdam ; New York : North-Holland Pub. Co. : sole distributors for the U.S.A. and Canada, Elsevier/North Holland, 1976.
[35] R. D. Cook, D. S. Malkus, M. E. Plesha, R. J. Witt, “Concepts and Applications of Finite Element Analysis”, Wiley; 4th edition, 2001.
[36] J. Chakrabarty, “Theory of Plasticity”, Butterworth-Heinemann, 3th edition, 2006.
[37] N. E. Dowling, “Mechanical Behavior of Materials: Engineering Methods for Deformation”, Fracture, and Fatigue, Upper Saddle River, New Jersey: Prentice-Hall, Inc, 1999.
[38] J. L. Chaboche, “Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity”, International Journal of Plasticity, Vol. 5, pp. 247-302, 1989.
[39] J. L. Chaboche, “On Some Modifications of Kinematic Hardening to Improve the Description of Ratchetting Effect”, International Journal of Plasticity, Vol. 7, pp. 661-678, 1991.
[40] B. S. Everitt, S. Landau, M. Leese, D. Stahl, “Miscellaneous Clustering Methods”, in Cluster Analysis, 5th Edition, John Wiley & Sons, Ltd, Chichester, UK, 2011.
[41] L. F. Coffin, “A study of the effects of cyclic thermal stress on a ductile metal”, Transactions ASME, Vol. 76, pp. 931-950, 1954.
[42] E. Alpaydim, “Introduction to Machine Learning”, MIT Press, 2014.
[43] S. Raschka, “Python Machine Learning”, Packt Publishing, 2015
[44] R. Hanke, “Theorizing masculinity with/in the media,” Communication Theory, pp.183-202, 1998.
[45] F. Rosenblatt, “The Perceptron, a Perceiving and Recognizing Automaton Project Para”, Cornell Aeronautical Laboratory, 1957
[46] C. Bishop, “Pattern Recognition and Machine Learning”, Springer, New York, USA, 2006.
[47] H. Robbins, S. Monro, “A Stochastic Approximation Method”, The Annals of Mathematical Statistics, Vol. 22, No. 3, pp. 400-407, 1951
[48] I. Goodfellow, Y. Bengio , A.Courville, Deep Learning, The MIT Press, 2016
[49] M. C. Hsieh and S. L. Tzeng, "Solder joint fatigue life prediction in large size and low cost wafer-level chip scale packages," IEEE Electronic Packaging Technology (ICEPT), pp. 496–501, 2015.
[50] M. C. Hsieh, “Modeling correlation for solder joint fatigue life estimation in wafer-level chip scale packages”, International Microsystems, Packagings, Assembly and Circuits Technology Conference (IMPACT), pp. 65–68, Taipei, Taiwan, 21-23 Oct. 2015.
[51] B. Rogers and C. Scanlan, “Improving WLCSP Reliability Through Solder Joint Geometry Optimization” International Symposium on Microelectronics, vol. 2013, no. 1, pp. 546-550, Orlando, Florida, USA, 2 Oct. 2013.
[52] J. Chang, L. Wang, J. Dirk, and X. Xie, “Finite Element Modeling Predicts the Effects of Voids on Thermal Shock Reliability and Thermal Resistance of Power Device”, Welding Journal , Vol. 85, pp. 63-70, 2006.
[53] Y. J. Xu, L. Q. Wang, F. S. Wu, W. S. Xia, H. Liu, “Effect of Interface Structure on Fatigue Life under Thermal Cycle with SAC305 Solder Joint”, IEEE Electronic Packaging Technology International Conference, pp. 959-964, Dalian, China, Aug 11-14, 2013.
[54] W. S. McCulloch, W. Pitts, “A logical calculus of the ideas immanent in nervous activity”, The bulletin of mathematical biophysics, Vol.5, Issue 4, pp 115–133, 1943.
[55] M.T. Hagan, M.B. Menhaj, "Training feedforward networks with the Marquardt algorithm", IEEE Trans. Neural Netw., vol. 5, no. 6, pp. 989-993, 1994.
[56] Hochreiter, Sepp, Schmidhuber, J¨urgen, “Long short-term memory.” Neural computation, Vol 9, Issue 8, pp.1735-1780, 1997.
[57] T. Mikolov, M. Karafiát, L. Burget, J. Černocký, S. Khudanpur, ”Recurrent Neural Network Based Language Model”.
[58] D. H. Hubel and T. N. Wiesil “Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex” J. Physiology, Vol. 160, Issue 1 pp. 106-154, Jan 1962
[59] Y. Lecun, L. Bottou, Y. Bengio, P. Haffner ” Gradient-based learning applied to document recognition” IEEE, Vol 86, Issue 11, Nov 1998
[60] A. Krizhevsky, I. Sutskever, G. K. Hinton “ImageNet classification with deep convolutional neural networks”, International Conference on Neural Information Processing Systems, pp. 1097-1105, Lake Tahoe, Nevada, December 03 - 06, 2012.
[61] 鄒承諺，以修正型能量密度法評估晶圓級封裝之可靠度，國立清華大學動力機械工程學系，碩士論文，2017.