近年來，基於市場需求之因素，電子產品的功能性愈來愈強，且其形體逐漸趨於輕、薄、短、小以便於攜帶。而為了達成以上之趨勢，除了在IC設計之技術開發外，電子封裝之可靠度也備受重視，電子封裝之技術也必須與時俱進，從傳統的引腳通孔技術(Pin Through Hole, PTH)，發展到表面黏著技術(Surface Mount Technology, SMT)，進一步到面積陣列的形式(Area Array Type)。而封裝的形式也從雙列直插封裝(Dual In-line Package, DIP)等傳統封裝，進展到覆晶(Flip Chip, FC)、晶片級封裝(Chip Scale Package, CSP)、晶圓級封裝(Wafer Level Package, WLP)，甚至到3D堆疊的形式。而本研究聚焦在晶圓級封裝的可靠度預估。
獲得封裝體可靠度的實驗有多種，而本研究探討的是熱循環負載測試(Thermal Cycling Test, TCT)。任何產品要生產前必定要經過此測試，以確保其可靠度。然而，於參數設計階段，用實驗進行參數設計，是不符合市場需求的，因其花費時間過長，一次實驗需花費數個月的時間。因此，業界常引進有限單元分析之模擬方法，進行參數設計的部分，因其花費時間比實驗短，只需要數天的時間，當然，在此之前，模擬方法必須經過實驗的驗證。然而，對於有限單元分析方法，不同的研究人員，因其背景的不同，或因其模擬方法不同，可能得到不同的結果。因此，為了統一不同研究者所造成之差異，本研究引進機器學習方法。機器學習是達成人工智慧的方法之一，其中有多種演算法，而本研究聚焦於支援向量迴歸(Support Vector Regression, SVR)演算法。且機器學習模型建立之後，可測試多次，而測試時間遠遠低於一秒，這對封裝體參數設計也具有相當的優勢。
而本研究之步驟如下所述。首先，模擬須被實驗驗證，確認模擬方法可信，模擬等同於實驗。接下來，使用模擬建立WLCSP可靠度資料庫，以供機器學習訓練及測試。而本研究聚焦之演算法為支援向量迴歸。並且會探討不同訓練資料庫大小之表現，亦會說明固定訓練資料庫之特徵邊界之重要性，以及測試資料數量之影響。

In recent years, to meet the market demand, electronic products must become more functional. And they must be lighter, thinner, shorter, and smaller due to portability. For the purpose of the above trends, besides the development of IC design technology, the reliability of electronic packaging is also valued. And the technology of electronic packaging should also keep pace with the times. From the traditional pin through hole technology (PTH), developed to Surface Mount Technology (SMT), and further to the Area Array Type. The form of packaging has also evolved from traditional packaging such as Dual In-line Package (DIP) to Flip Chip (FC), Chip Scale Package (CSP), and Wafer Level Package (WLP), even to the technology of 3D stacked. This research focuses on the reliability prediction of Wafer Level Package.
There are many kinds of experiments to obtain the reliability of the package, and this research discusses on the thermal cycling test (TCT). Any product must pass this test before it is produced to ensure its reliability. However, in the parameter design stage, the use of experiments for parameter design can’t meet the market demand. Because it takes too long, an experiment takes several months. Therefore, the industry often introduces the simulation method of finite element analysis. The parameter design takes less time than the experiment and only takes a few days. Of course, the simulation method must be verified by the experiment before this. However, for finite element analysis methods, different researchers may obtain different results due to their different backgrounds or their simulation methods. Therefore, in order to unify the differences caused by different researchers, this research introduces machine learning methods. Machine learning is one of the methods to achieve artificial intelligence. There are many algorithms in machine learning. This research focuses on the Support Vector Regression (SVR) algorithm. And after the machine learning model is established, it can be tested multiple times, and the test time is much less than one second, which also an advantage for the package parameter design.
The steps of this study are as follows. First of all, the simulation must be verified by experiments to confirm that the simulation method is credible, and the simulation is equivalent to the experiment. Next, use simulation to build a WLCSP reliability database for machine learning training and testing. The algorithm that this research focuses on is support vector regression. It will also explore the performance of different training data sizes, and also explain the importance of fixing the feature boundary of training dataset, and the influence of the number of testing data.

[1] L. S. Goldmann, "Geometric optimization of controlled collapse interconnections," IBM Journal of Research and Development, vol. 13, no. 3, pp. 251-265, 1969.
[2] 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, no. 3, pp. 114-121, 1996.
[3] K. A. Brakke, "The surface evolver," Experimental Mathematics, vol. 1, no. 2, pp. 141-165, 1992.
[4] 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, vol. 76, no. 6, pp. 931-950, 1954.
[5] S. S. Manson, Behavior of materials under conditions of thermal stress. National Advisory Committee for Aeronautics, 1953.
[6] R. Darveaux, K. Banerji, A. Mawer, G. Dody, and J. Lau, Reliability of plastic ball grid array assembly. New York: McGraw-Hill, 1995.
[7] R. Darveaux, "Effect of simulation methodology on solder joint crack growth correlation and fatigue life prediction," Journal of Electronic Packaging, vol. 124, no. 3, pp. 147-154, 2002.
[8] K. Wu, "Reliability assessment of advanced packaging solder joints under different thermal cycling ramp rates," NTHU, PH. D dissertation, 2016.
[9] 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.
[10] 李至軒, "潛變行為對晶圓級封裝之可靠度影響分析," 碩士論文, 動力機械工程學系, 國立清華大學, 2015.
[11] K. N. Chiang and W. L. Chen, "Electronic packaging reflow shape prediction for the solder mask defined ball grid array," Journal of Electronic Packaging, vol. 120, no. 2, pp. 175-178, 1998.
[12] C. Tsou, T. Chang, K. Wu, P. Wu, and K. Chiang, "Reliability assessment using modified energy based model for WLCSP solder joints," 2017 International Conference on Electronics Packaging (ICEP 2017), Yamagata, Japan, April 19-22, 2017.
[13] 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.
[14] P. Chou, K. Chiang, and S. Y. Liang, "Reliability assessment of wafer level package using artificial neural network regression model," Journal of Mechanics, vol. 35, no. 6, pp. 829-837, 2019.
[15] J. R. Quinlan, "Induction of decision trees," Machine Learning, vol. 1, no. 1, pp. 81-106, 1986.
[16] T. K. Ho, "Random decision forests," 1995 International Conference on Document Analysis and Recognition (ICDAR 1995), Montreal, Quebec, Canada, August 14-16, 1995.
[17] 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, 動力機械工程學系, 國立清華大學, 2019.
[18] 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, 動力機械工程學系, 國立清華大學, 2020.
[19] C. Cortes and V. Vapnik, "Support-vector networks," Machine Learning, vol. 20, no. 3, pp. 273-297, 1995.
[20] V. Vapnik, S. E. Golowich, and A. J. Smola, "Support vector method for function approximation, regression estimation and signal processing," Advances in Neural Information Processing Systems 9 (NIPS 1996), Denver, Colorado, USA, December 2-5, 1996.
[21] A. J. Smola and B. Schölkopf, "A tutorial on support vector regression," Statistics and Computing, vol. 14, no. 3, pp. 199-222, 2004.
[22] V. Cherkassky and Y. Ma, "Practical selection of SVM parameters and noise estimation for SVM regression," Neural Networks, vol. 17, no. 1, pp. 113-126, 2004.
[23] S. Bergman, The kernel function and conformal mapping. American Mathematical Soc., 1970.
[24] M. Gönen and E. Alpaydın, "Multiple kernel learning algorithms," The Journal of Machine Learning Research, vol. 12, no. 64, pp. 2211-2268, 2011.
[25] B. M. Henrique, V. A. Sobreiro, and H. Kimura, "Stock price prediction using support vector regression on daily and up to the minute prices," The Journal of Finance and Data Science, vol. 4, no. 3, pp. 183-201, 2018.
[26] W. Yang, M. Deng, F. Xu, and H. Wang, "Prediction of hourly PM2.5 using a space-time support vector regression model," Atmospheric Environment, vol. 181, pp. 12-19, 2018.
[27] B. Suvarna, B. Lakshmi Nandipati, and M. Nirupama Bhat, "Support vector regression for predicting COVID-19 cases," European Journal of Molecular & Clinical Medicine, vol. 7, no. 3, pp. 4882-4893, 2020.
[28] 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, 動力機械工程學系, 國立清華大學, 2019.
[29] 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, 動力機械工程學系, 國立清華大學, 2020.
[30] K. J. Bathe, Finite element procedures in engineering analysis. Prentice-Hall, 1982.
[31] W. N. Findley and F. A. Davis, Creep and relaxation of nonlinear viscoelastic materials. Courier Corporation, 2013.
[32] R. D. Cook, Concepts and applications of finite element analysis. John wiley & sons, 2007.
[33] N. E. Dowling, Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. Pearson, 2012.
[34] J.-L. Chaboche, "Constitutive equations for cyclic plasticity and cyclic viscoplasticity," International Journal of Plasticity, vol. 5, no. 3, pp. 247-302, 1989.
[35] 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.
[36] K. N. Chiang and C. A. Yuan, "An overview of solder bump shape prediction algorithms with validations," IEEE Transactions on Advanced Packaging, vol. 24, no. 2, pp. 158-162, 2001.
[37] 鄒承諺, "以修正型能量密度法評估晶圓級封裝之可靠度," 碩士論文, 動力機械工程學系, 國立清華大學, 2017.
[38] K. 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, 2015.
[39] Y. Lee and K. Chiang, "Reliability Assessment of WLCSP using Energy Based Model with Inelastic Strain Energy Density," 2019 International Conference on Electronics Packaging (ICEP 2019), Niigata, Japan, April 17-20, 2019.
[40] F. Pedregosa et al., "Scikit-learn: Machine learning in Python," The Journal of Machine Learning Research, vol. 12, no. 85, pp. 2825-2830, 2011.
[41] B. Rogers and C. Scanlan, "Improving WLCSP reliability through solder joint geometry optimization," International Symposium on Microelectronics, vol. 41, no. 1, pp. 14-17, 2013.
[42] M. C. Hsieh and S. L. Tzeng, "Solder joint fatigue life prediction in large size and low cost wafer-level chip scale packages," 2014 International Conference on Electronic Packaging Technology (ICEPT 2014), Chengdu, China, August 12-15, 2014.
[43] M. C. Hsieh, "Modeling correlation for solder joint fatigue life estimation in wafer-level chip scale packages," 2015 International Microsystems, Packaging, Assembly and Circuits Technology Conference (IMPACT 2015), Taipei, Taiwan, October 21-23, 2015.
[44] M. Motalab, M. Mustafa, J. C. Suhling, J. Zhang, J. Evans, M. J. Bozack, and P. Lall, "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 (InterPACK 2013), San Francisco, USA, July 16-18, 2013.
[45] Y. J. Xu, L. Q. Wang, F.S. Wu, W. S. Xia, and H. Liu, "Effect of interface structure on fatigue life under thermal cycle with SAC305 solder joints," 2013 International Conference on Electronic Packaging Technology (ICEPT 2013), Dalian, China, August 11-14, 2013.