伴隨著人類對電子產品日益增長的需求，電子封裝逐漸向著微型化、高密度的方向發展。本篇論文所探討的晶圓級尺寸封裝(Wafer Level Chip Scale Package, WLPCSP)，其最顯著的特點就在於能夠有效減小封裝的體積。WLSCP自2000年以來經過長遠而迅速的發展,便成為了目前市場上主流的電子封裝形式之一。有別於早期傳統封裝技術，其基本的工藝思路是直接在晶圓上進行封裝製程，最後切割晶圓直接得到封裝成品。
電子封裝的可靠性評估便是本篇論文的研究目的。對於WLCSP，晶片通過錫球和基板進行連接，在實際工作期間需要經受一定週期的高低溫溫度循環，器件中不同材料間的熱膨脹係數(CTE)的失配導致錫球產生了一定的熱應力和熱應變，造成了應變能的積累，最終導致了封裝的失效。所以說，錫球的熱-機械可靠性對封裝可靠度評估的影響尤為顯著。傳統封裝可靠性評估的重要手段之一便是熱循環負載測試(Thermal cyclic test, TCT)，但由於每一次的熱循環負載測試會花費數月之久，從而大大增加時間成本，降低產品研發速率，不利於產品的市場化競爭。為了降低時間成本，一般會於封裝研發過程中採用有限單元模擬的方法來代替TCT。
雖然有限單元法(FEM)相較於傳統TCT大大地降低了時間成本，但是另一方面FEM並沒有傳統實驗方法統一規定的流程，不同研究人員由於其自身能力以及建模思路和側重不同，造成相當程度上的模擬誤差。為解決這一問題，並進一步減少FEM中建模與驗證的時間成本，本論文研究利用核嶺回歸（KRR）機器學習演算法，對晶圓級尺寸封裝進行可靠度評估。同時進一步用聚類（Cluster）算法解決在大規模數據集下，KRR機器學習演算法的CPU時間成本問題

With the increasing demand for electronic products, electronic packaging is gradually developing in the direction of miniaturization and high density. The most significant advantage of Wafer Level Chip Scale Package (WLCSP) is that it can effectively reduce the volume of the package. The basic process idea is to directly perform the packaging process on the wafer, and finally cut the wafer to directly obtain the packaged product.
The reliability evaluation of electronic packaging is the research purpose of this paper. For WLCSP, the wafer is connected to the substrate through solder balls and needs to undergo a certain period of high and low temperature cycles during actual work. The mismatch of the coefficient of thermal expansion (CTE) between different materials leads to the failure of the package. Therefore, the thermal-mechanical reliability of the solder ball has a particularly significant impact on the reliability evaluation of the package. One of the important methods of traditional package reliability evaluation is the thermal cycle load test (TCT). However, each thermal cycle load test will take several months, which greatly increases the time cost, reduces the product development rate, and it is not conducive to product market competition. In order to reduce the time cost, the finite element method (FEM) is generally used to replace TCT in the process of packaging development.
Although FEM greatly reduces the time cost compared with TCT, FEM does not have a unified procedure for the traditional experimental method. Different researchers due to their own abilities and different modeling ideas and emphasis, cause the considerable degree of simulation error. In order to solve this problem and further reduce the time cost of modeling and verification in FEM, this paper studies the use of Kernel Ridge Regression (KRR) machine learning algorithm to evaluate the reliability of wafer-level packaging. At the same time, the cluster algorithm is further used to solve the CPU time cost problem of the KRR machine learning algorithm under large-scale data sets.

[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] 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," 碩士論文, 國立清華大學動力機械工程學系, 2016.
[5] 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," in 2017 International Conference on Electronics Packaging (ICEP), 2017:IEEE, pp. 7-15.
[6] K. N. Chiang, H. C. Cheng, and W. H. Chen, "Large-Scaled 3-D area array electronic packaging analysis," Computer Modeling and Simulation in Engineering, 1999, vol. 4, No.1, pp. 4-11, 1999.
[7] R. J. Solomonoff, "An inductive inference machine," in IRE Convention Record, Section on Information Theory, 1957, vol. 2, pp. 56-62.
[8] Arthur E. Hoerl and Robert W. Kennard, "Ridge Regression: Biased Estimation for Nonorthogonal Problems," Technometrics, vol. 12, no. 1, pp. 55-67, 1970.
[9] T. D. Dwivedi, V. K. Srivastava and RL Hall, "Finite Sample Properities of Ridge Estimators ," Technometrics, vol. 12, no. 2, pp. 205-212, 1980.
[10] F. Akdeniz, G. Yüksel, and A. T. Wan, "The moments of the operational almost unbiased ridge regression estimator," Applied Mathematics and Computation, vol. 153, no. 3, pp. 673-684, 2004.
[11] K. Ohtani, "The General Expression for the Moments of Lawless and Wang'S Ordinary Ridge Regression Estimator," Communications in Statistics-Theory and Methods, pp. 2755-2774, 2019.
[12] F. Lawlessj and P. Wang, " A Silulation Study of Ridge and other Regression Estimators," Communications in Statistics, pp. 307-323, 2010.
[13] Y. M. Al-Hassan, "Performance of a new ridge regression estimator," Journal of the Association of Arab Universities for Basic and Applied Sciences, vol. 9, no. 1, pp. 23-26, 2010.
[14] P. H. Chou, S. Y. Liang, K. N. Chiang, "Reliability Assessment of Wafer Level Package Using Artificial Neural Network Regression Model", Journal of Mechanics, Vol. 35, Issue 6, Pages 829-837, 2019.
[15] H. Y. Hsiao and K. N. Chiang, "AI-Assisted Reliability Life Prediction Model for Wafer-Level Packaging using the Random Forest Method", Journal of Mechanics, Volume 37, pages 28-36, 2021.
[16] S. K. Panigrahy, Y. C. Tseng, B. R. Lai, and K. N. Chiang, "An Overview of AI-Assisted Design-on-Simulation Technology for Reliability Life Prediction of Advanced Packaging", Materials, 14, 5342, 2021.
[17] Pang-Ning Tan, "数据挖掘导论," 人民郵局出版社, 2011.
[18] J. Macqueen, " Some Methods for Classification and Analysis of Multi Variate Observations," Berkeley Symposium on Mathematical Statistics and Probability, 1967, pp. 281-297.
[19] L.S. Goldmann, "Geometric optimization of controlled collapse interconnections," IBM Journal of Research and Development, vol. 13, no. 3, pp. 251-265, 1969.
[20] 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.
[21] K. A. Brakke, "Surface evolver manual," Mathematics Department, Susquehanna Univerisity, Selinsgrove, PA, vol. 17870, no. 2.24, p. 20, 1994.
[22] S. P. Timoshenko and J. Goodier, Theory of elasticity. Mcgraw-Hill College, 2011.
[23] N. E. Dowling, Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. Pearson, 2012
[24] R. Cook, D. Malkus, M. Plesha, and R. Witt, "Concepts and Applications of Finite Element Analysis, Wiley," 2002.
[25] 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.
[26] 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.
[27] R. Darveaux, "Effect of simulation methodology on solder joint crack growth correlation," in 2000 Proceedings. 50th Electronic components and technology conference (Cat. No. 00CH37070), 2000: IEEE, pp. 1048-1058.
[28] D. J. Tylavsky and G. R. Sohie, "Generalization of the matrix inversion lemma," Proceedings of the IEEE, vol. 74, no. 7, pp. 1050-1052, 1986.
[29] 胡善杰, "在雲計算的數據挖掘算法的並行運算," 電子科技大學, 2013.
[30] D. Arthur and S. Vassilvitskii, "K-means++: The advantages of careful seeding," Stanford, 2006.
[31] B. Rogers and C. Scanlan, "Improving WLCSP reliability through solder joint geometry optimization," in International Symposium on Microelectronics, 2013, vol. 2013, no. 1: International Microelectronics Assembly and Packaging Society, pp. 000546-000550.
[32] M. C. Hsieh and S. L. Tzeng, “Solder joint fatigue life prediction in large size and low cost wafer-level chip scale packages,” 2014 15th International Conference on Electronic Packaging Technology, Chengdu, China, August 12-15, 2014.
[33] M. C. Hsieh, “Modeling correlation for solder joint fatigue life estimation in wafer-level chip scale packages,” 2015 10th International Microsystems, Packaging, Assembly and Circuits Technology Conference (IMPACT), Taipei, Taiwan, Oct 21-23, 2015.
[34] M. Motalab, M. Mustafa, J. C. Suhling, J. Zhang, J. Evans, M. J. Bozack, & 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, San Francisco, USA, July 16-18, 2013.
[35] B. Klaus-Jürgen, "Finite element procedures in engineering analysis," Prentice-Hall, Inc, Englewood Cliffs, New Jersey, vol. 7632, p. 1982, 1982.
[36] W. N. Findley, J. Lai, and K. Onaran, "Creep and relaxation of nonlinear viscoelastic materials (with an Introduction to Linear Viscoelasticity). ," Amesterdam: North-Holland publishing Company, 1976.
[37] R. Cook, D. Malkus, M. Plesha, and R. Witt, "Concepts and Applications of Finite Element Analysis, Wiley," 2002.
[38] J. Chakrabarty, Theory of plasticity. Elsevier, 2012.
[39] N. E. Dowling, Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. Pearson, 2012..
[40] W. F. Chen and D. J. Han, Plasticity for structural engineers. J. Ross Publishing, 2007.
[41] R. Darveaux, K. Banerji, A. Mawer, G. Dody, and J. Lau, Reliability of plastic ball grid array assembly. New York: McGraw-Hill, 1995.
[42] Y. Bao and Z. Liu, "A fast grid search method in support vector regression forecasting time series," in International Conference on Intelligent Data Engineering and Automated Learning, 2006: Springer, pp. 504-511.
[43] Y.-Y. Ou, G.-H. Chen, and Y.-J. Oyang, "Expediting model selection for support vector machines based on an advanced data reduction algorithm," in Pacific Rim International Conference on Artificial Intelligence, 2006: Springer, pp. 1017-1021.
[44] Hsu, C., Chang, C. and Lin, C. " A Practical Guide to Support Vector Classication," 2008.
[45] J. Bergstra and Y. Bengio, "Random search for hyper-parameter optimization," Journal of machine learning research, vol. 13, no. 2, 2012.