現今，由於消費市場越來越大，科技日新月異，電子設備及功能日趨完善，我們越來越關注電子封裝的可靠度。電子封裝主要是保護IC零件的複雜結構，在半導體行業中有相當的重要性。我們的研究主旨是在評估電子封裝的可靠度，而加速熱循環測試（Accelerated Thermal Cycle Test, ATCT）是確保封裝可靠度的重要測試之一。 ATCT是測試電子封裝可靠度的一種好方法，但該實驗需要大量時間和成本，所需的時間可能長達數個月以上。為了有效減少測試時間，近年來業界經常使用有限元素分析（Finite Element Analysis, FEA）來代替實驗。
儘管FEA能夠節省大量的時間成本，但使用FEA仍然需要一些時間建立模型來獲得模擬結果，並且當研發人員未受過充足訓練時則會導致不同的研發人員所獲得的模擬結果不一致，進而造成人為誤差。而隨著近年來電腦設備的發展，計算性能變得非常強大，以及人工智慧蓬勃發展，因此本研究應用了機器學習（Machine Learning, ML）方法。透過去使用大量經過驗證的有限單元模型(Finite Element Model, FEM)之數據，來建立一組數據庫應用於機器學習中，那麼我們就可以立即通過機器學習方法來預估電子封裝結構的可靠度，它不僅省去建立模型和驗證的時間，同時也避免產生模擬上的人為誤差。
本研究使用隨機森林（Random Forest, RF）、極度隨機樹（Extremely Randomized Trees, ET）、自適應增強(Adaptive Boosting, AdaBoost)、梯度增強 (Gradient Boosting)總共四種集成學習演算法來評估晶圓級晶片尺寸封裝(Wafer Level Chip Scale Packaging, WLCSP)之可靠度。透過與實驗結果進行比對以驗證我們的模擬結果，在獲得驗證的模型後，利用相同的建模流程，藉由不同幾何尺寸的參數去生成具有不同數據量的資料數據集，探討不同數據量的分佈對於這四種演算法的影響，並且去找出預測性能最佳的演算法。
關鍵詞：加速熱循環測試、有限元素分析、晶圓級晶片尺寸封裝、
機器學習、隨機森林、極度隨機樹、自適應增強、梯度增強

Nowadays, as the consumer market is getting bigger and bigger, the technology is changing with each passing day, and the electronic equipment and functions are improving day by day. We are paying more and more attention to the reliability of electronic packaging. Electronic packaging is mainly to protect the complex structure of IC components, which is of considerable importance in the semiconductor industry. The main purpose of our research is to evaluate the reliability of electronic packaging, and Accelerated Thermal Cycle Testing (ATCT) is one of the important tests to ensure the reliability of the packaging. ATCT is a good method to test the reliability of electronic packaging, but the experiment requires a lot of time and cost. The time required to execute experiment may be as long as several months. In order to effectively reduce the test time, in recent years the industry has often used Finite Element Analysis (FEA) instead of experiments.
Although FEA can save a lot of time and cost, the use of FEA still requires some time to build a model to obtain simulation results, and when the researchers are not sufficiently trained, the simulation results obtained by different researchers will be inconsistent, resulting in personal error. With the development of computer equipment in recent years, computing performance has become very powerful, and with the booming development of artificial intelligence, so this research applies the machine learning (ML) method. By using a large number of verified Finite Element Model (FEM) to build a database for machine learning, then we can immediately use ML methods to evaluate the reliability of electronic packaging. It not only saves time to build models and verifications, but also avoids personal error in simulation.
This research uses Random Forest (RF), Extremely Randomized Trees (ET), Adaptive Boosting (AdaBoost), Gradient Boosting these four algorithms o evaluate the reliability of Wafer Level Chip Scale Packaging (WLCSP). We verify our simulation results by comparing with the experimental results. After obtaining the verified model, using the same modeling process to generate database with
different data volumes by using different geometrical parameters. To explore the influence of the distribution of different data volumes on these algorithms, and to find the algorithm with the best prediction performance.
Keywords：Accelerated Thermal Cycle Testing , Finite Element Analysis, Wafer Level Chip Size Packaging, Machine Learning, Random Forest, Extremely Randomized Trees, Adaptive Boosting, Gradient Boosting

[1] C. M. Liu, C. C. Lee, and K. N. Chiang, "Enhancing the reliability of wafer level packaging by using solder joints layout design," IEEE Transactions on Components and Packaging Technologies, vol. 29, no. 4, pp. 877-885, 2006.
[2] L. F. Coffin Jr, "A study of the effects of cyclic thermal stresses on a ductile metal," Transactions of the American Society of Mechanical Engineers, New York, vol. 76, pp. 931-950, 1954.
[3] S. S. Manson, "Behavior of materials under conditions of thermal stress," National Advisory Committee for Aeronautics, vol. 2933, pp. 317-350, 1953.
[4] R. Darveaux, K. Banerji, A. Mawer, G. Dody, and J. Lau, Reliability of plastic ball grid array assembly. New York: McGraw-Hill, 1995.
[5] R. Darveaux, "Effect of simulation methodology on solder joint crack growth correlation," in 2000 Proceedings. 50th Electronic components and technology conference (Cat. No. 00CH37070), Las Vegas, Nevada, USA, pp. 1048-1058, May 21-24, 2000.
[6] 吳凱強,“先進封裝錫球接點於不同溫度循環負載速率下之可靠度評估,” 博士論文, 國立清華大學動力機械工程學系, 2016.
[7] K. N. Chiang, W. H. Chen, and H. C. Cheng, "Large-Scaled 3-D area array electronic packaging analysis," CMSE Computer Modeling and Simulation in Engineering, vol. 4, No.1, pp. 4-11, 1999.
[8] 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.
[9] R. J. Solomonoff, "An inductive inference machine," in IRE Convention Record, Section on Information Theory, vol. 2, pp. 56-62, 1957.
[10] W. S. McCulloch and W. Pitts, "A logical calculus of the ideas immanent in nervous activity," The bulletin of mathematical biophysics, vol. 5, no. 4, pp. 115-133, 1943.
[11] 周佩勲, "以人工神經網路回歸模型評估晶圓級封裝之可靠度," 碩士論文, 國立清華大學動力機械工程學系, 2019.
[12] S. Hochreiter and J. Schmidhuber, "Long short-term memory," Neural computation, vol. 9, no. 8, pp. 1735-1780, 1997.
[13] 李育承, "以循環神經網路迴歸模型評估晶圓級封裝之可靠度," 碩士論文, 國立清華大學動力機械工程學系, 2019.
[14] 曾驛捷, "不同數據於循環神經網路模型對晶圓級封裝可靠度預估影響研究," 碩士論文, 國立清華大學動力機械工程學系, 2020.
[15] N. S. Altman, "An introduction to kernel and nearest-neighbor nonparametric regression," The American Statistician, vol. 46, no. 3, pp. 175-185, 1992.
[16] M. Sarkar and T. Y. Leong, "Application of K-nearest neighbors algorithm on breast cancer diagnosis problem," Proc AMIA Symp. pp.759-763, 2000.
[17] C. Cortes and V. Vapnik, "Support-vector networks," Machine learning, vol. 20, no. 3, pp. 273-297, 1995.
[18] 沈奕廷, "以支援向量迴歸模型評估晶圓級封裝之可靠度," 碩士論文, 國立清華大學動力機械工程學系, 2019.
[19] 賴柏瑞, "多核心及新型支援向量迴歸模型於晶圓級封裝可靠度預測之研究," 碩士論文, 國立清華大學動力機械工程學系, 2020.
[20] J. R. Quinlan, "Induction of decision trees," Machine learning, vol. 1, no. 1, pp. 81-106, 1986.
[21] L. Breiman, "Bagging predictors," Machine learning, vol. 24, no. 2, pp. 123-140, 1996.
[22] L. Breiman, "Random forests," Machine learning, vol. 45, no. 1, pp. 5-32, 2001.
[23] T. K. Ho, "Random decision forests," in Proceedings of 3rd international conference on document analysis and recognition, Montreal, Quebec, Canada, pp. 278-282, August 14-16, 1995.
[24] 蕭翔云, "以隨機森林回歸模型評估晶圓級封裝之可靠度," 碩士論文, 國立清華大學動力機械工程學系, 2019.
[25] P. Geurts, D. Ernst, and L. Wehenkel, "Extremely randomized trees," Machine learning, vol. 63, no. 1, pp. 3-42, 2006.
[26] Y. Freund and R. E. Schapire, "A desicion-theoretic generalization of on-line learning and an application to boosting," Journal of computer and system sciences, vol. 55, no. 1, pp. 119-139, 1997.
[27] J. H. Friedman, "Greedy function approximation: a gradient boosting machine," Annals of statistics, pp. 1189-1232, 2001.
[28] L. S. Goldmann, "Geometric optimization of controlled collapse interconnections," IBM Journal of Research and Development, vol. 13, no. 3, pp. 251-265, May, 1969.
[29] S. M. Heinrich, M. Schaefer, S. A. Schroeder, and P. S. Lee, "Prediction of solder joint geometries in array-type interconnects," American Society of Mechanical Engineers Journal of Electronic Packaging, vol. 118, pp. 114-121, 1996.
[30] K. A. Brakke, "Surface evolver manual," Mathematics Department, Susquehanna Univerisity, Selinsgrove, PA, vol. 17870, no. 2.24, p. 20, 1994.
[31] S. P. Timoshenko and J. Goodier, " Theory of elasticity. Mcgraw-Hill Book Company, " lnc. New York, 1951.
[32] K. J. Bathe, Finite element procedures in engineering analysis. Prentice-Hall, 1982.
[33] 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, 1976.
[34] R. Cook, D. Malkus, M. Plesha, and R. Witt, "Concepts and Applications of Finite Element Analysis, Wiley," 2002.
[35] J. Chakrabarty, Theory of plasticity. Elsevier, 2012.
[36] N. E. Dowling, Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. Pearson, 2012.
[37] J. L. Chaboche, "Constitutive equations for cyclic plasticity and cyclic viscoplasticity," International journal of plasticity, vol. 5, no. 3, pp. 247-302, 1989.
[38] J. L. Chaboche, "On some modifications of kinematic hardening to improve the description of ratchetting effects," International journal of plasticity, vol. 7, no. 7, pp. 661-678, 1991.
[39] A. Mahmoudi, S. Pezeshki-Najafabadi, and H. Badnava, "Parameter determination of Chaboche kinematic hardening model using a multi objective Genetic Algorithm," Computational Materials Science, vol. 50, no. 3, pp. 1114-1122, 2011.
[40] W. F. Chen and D. J. Han, Plasticity for structural engineers. J. Ross Publishing, 2007.
[41] D.E. Rumelhart, G.E. Hinton, and R.J. Williams,“Learning Representations by Back-propagating errors,” nature, vol. 323, no, 6088, pp. 533-536, 1986.
[42] J. Duchi, E. Hazan, and Y. Singer, "Adaptive subgradient methods for online learning and stochastic optimization," Journal of machine learning research, vol. 12, no. 7, pp. 2,121-2,159, 2011.
[43] T. Tieleman and G. Hinton, "Lecture 6.5-rmsprop, coursera: Neural networks for machine learning," University of Toronto, Technical Report, 2012.
[44] D. P. Kingma and J. Ba, "Adam: A method for stochastic optimization," International Conference on Learning Representations, (ICLR 2014), Banff, Canada, April 14-16, 2014.
[45] B. Rogers and C. Scanlan, "Improving WLCSP reliability through solder joint geometry optimization," in International Symposium on Microelectronics, Orlando, USA, Vol.1, pp. 546-550, September 30 – October 3, 2013.
[46] M. C. Hsieh and S. L. Tzeng, "Solder joint fatigue life prediction in large size and low cost wafer-level chip scale packages," in 2014 15th International Conference on Electronic Packaging Technology, Chengdu, China, August 12-15, 2014.
[47] M. C. Hsieh, "Modeling correlation for solder joint fatigue life estimation in wafer-level chip scale packages," in 2015 10th International Microsystems, Packaging, Assembly and Circuits Technology Conference (IMPACT), Taipei, Taiwan, October 21-23, 2015.
[48] M. Motalab et al., "Thermal cycling reliability predictions for PBGA assemblies that include aging effects," ASME 2013 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems, San Francisco, USA , July 16-18, 2013.
[49] 蔡宗樺, "數據分布於隨機森林模型對晶圓級封裝之可靠度預估影響研究," 碩士論文, 國立清華大學動力機械工程學系, 2020.