本文係針對晶圓級晶片尺寸封裝(WLCSP)之熱疲勞可靠度分析，以熱循環實驗計算此封裝體熱疲勞可靠度並使用有限元素法進行數值模擬以得到熱疲勞壽命預測模型，最後透過田口法進行模擬及因子變異分析以進行最佳化設計。
首先以產業界常用焊錫材料SAC405 (Sn95.5Au4Cu0.5)為封裝體錫球接點進行熱循環實驗探討熱疲勞可靠度，並將實驗完成之試片進行破壞檢測。檢測結果顯示錫球產生裂縫導致元件損壞。第二部分為焊錫材料特性量測，本文根據阿南德黏塑性模型(Anand Model)描述焊錫材料性質，並進行在不同負載下之拉伸實驗及潛變實驗，並由實驗結果曲線擬合阿南德模型。數值模擬將以ANSYS軟體進行分析。首先建立總體模型及子模型。總體模型用於模擬在各溫度點下封裝體及電路板之翹區且比對由先進視覺地形反射分析實驗量測翹曲值以驗證模型精準度。子模型將以封裝體角落易損壞位置進行模擬分析，並計算錫球在熱循環負載下產生之塑性功。最後以實驗及模擬結果進行熱疲勞壽命預測。田口法將用於最佳化分析，本文針對此WLCSP封裝體挑選出八個影響封裝體熱疲勞壽命之控制因子並依照L18(21x37)直交表配置因子進行模擬。模擬結果進行變異分析(Analysis of variance, ANOVA)顯示對於WLCSP封裝體進行底部填膠、更換低銀焊錫SACX0307及降低晶片厚度可有效改善熱疲勞可靠度。透過最佳化組合，本文針對以SAC405為錫球材料之WLCSP封裝體進行最佳化設計，並以模擬方法進行分析及壽命預測。
經由本文之研究及最佳化設計，WLCSP封裝體經由模擬預測之熱疲勞壽命相較於原始設計封裝體提升約180%，且達到第一失效週期大於500週期之目標。因此希望藉由本文研究，提供於學術及產業界未來探討WLCSP熱疲勞可靠度之方法及方向。

The objective of this study is to investigate the thermal fatigue reliability of the 196L WLCSP by adopting finite element method and series of tests. The Morrow’s life prediction model was developed and Taguchi method was used to optimal design.
First of all, thermal cyclic tests (TCT) were done to estimate the reliability of the packages that soldering in PB-free SAC405(95.5Sn4Ag0.5Cu). The failure analysis showed that crack propagation in the solder ball was the main reason for the package failure. Therefore, before the simulation, the material properties of the solder were measured. A series of tensile tests and creep tests of SAC405 and SACx0307(99Sn0.3Ag0.7Cu) were conducted, The Anand’s viscoplastic model was fitted based on the test data. The equivalent model and sub-model were built and verified by measuring waparges from Digital Image Correlation (DIC) test and FE simulation. Submodeling method was implemented to study the viscoplastic behavior of the SAC405 solder ball. Plastic work of solder ball was calculated from simulation. By correlating the PLWK and 1st failed TCT cycle, the Morrow’s fatigue prediction model was adopted. The Taguchi method along with the technique of analysis of variance (ANOVA) were applied to optimal design process. Eight control factors are considered according to the ANOVA results, three important factors such as underfilling, solder materials and die thickness were obtained.
In the last part, optimal factors were used to simulate the package soldering in SAC405 and predict the thermal fatigue life. The results of fatigue life of optimal design were almost 180% of the original design. The findings provide the academic world and manufacturers some suggestions for reliability analysis and improvement of WLCSP.

謝誌 ii
摘要 iii
Abstract iv
目錄 V
圖次 ix
表次 Xiii
第一章 緒論 1
1-1 前言 1
1-2 封裝簡介 1
1-2-1 封裝目的、層級 1
1-2-2 覆晶封裝步驟 2
1-2-3 WLCSP晶圓級晶片尺寸構裝 3
1-3 研究動機 3
1-4 文獻回顧 4
1-5 組織與章節 6
第二章 理論基礎 8
2-1 有限元素分析理論 8
2-2 線性及非線性分析理論 9
2-2-1 線性分析理論 9
2-2-2 非線性分析理論 9
2-3 材料特性 10
2-3-1 潛變 11
2-3-2 黏塑性材料 12
2-4 韋伯分布 14
2-5 疲勞壽命預測模型 16
2-6 實驗設計及參數最佳化 16
2-6-1 田口品質工程法 16
2-6-2 變異分析 17
第三章 實驗與數值模擬 23
3-1 實驗規劃及數值模擬流程 23
3-2 實驗試片 23
3-2-1 無鉛銲錫試片 23
3-2-2 封裝體及電路板試片 23
3-3 先進視覺地形反射分析實驗(AVATAR) 24
3-3-1 實驗說明 24
3-3-2 先進視覺地形反射分析儀 24
3-3-3 先進視覺地形反射分析實驗過程 25
3-4 阿南德黏塑性實驗 25
3-4-1 阿南德實驗說明 25
3-4-2 實驗設備 26
3-4-3 實驗過程 26
3-5 熱循環實驗(Thermal Cyclic Test) 27
3-5-1 實驗說明 27
3-5-2 實驗設備 27
3-5-3 熱循環實驗規範 27
3-5-4 熱循環實驗過程 28
3-6 ANSYS數值模擬 28
3-6-1 材料性質設定 28
3-6-2 ANSYS數值模擬流程 28
3-7 最佳化分析及控制參數規劃 31
3-7-1 品質特性 31
3-7-2 控制因子及直交表選定 31
第四章 實驗及模擬結果 51
4-1 先進視覺地形反射分析實驗結果 51
4-2 熱循環實驗 51
4-3 無鉛銲錫黏塑性測量實驗 52
4-3-1 拉伸實驗結果 52
4-3-2 潛變實驗結果 52
4-3-3 阿南德黏塑性模型擬合 53
4-4 數值模擬結果 53
4-4-1 模型收斂性分析 54
4-4-2 總體模型翹區分析結果 54
4-4-3 子模型模擬結果 55
4-5 熱疲勞壽命預測 55
第五章 分析與討論 82
5-1 田口法控制因子分析 82
5-1-1 錫球塑性功密度增量 82
5-2 變異分析 83
5-2-1 錫球塑性功密度變異分析 84
5-3 最佳化分析 85
5-3-1 錫球材料SAC405最佳化設計 85
第六章 結論 92
參考文獻 94

[1] 許明哲，先進微電子3D-IC構裝，五南圖輸出版公司，2014
[2] 鍾文仁、陳佑任，IC封裝製程與CAE應用，全華科技圖書股份有限公司，2005
[3] G.Z. Wang, Z.N. Cheng, K. Becker, J. Wilde, “Applying Anand Model to Represent the Viscoplastic Deformation Behavior of Solder Alloys,”Journal of Eletronic Packing,2001.
[4] Robert Darveaux, Iwona Turlik, Lih-Tyng Hwang, Arnold Reisman, “Thermal Stress Analysis of a Multichip Package Design,” IEEE,1989.
[5] Chandra Williams, Kok Ee Tan, John H.L. Pang, “Thermal Cycling Fatigue Analysis of SAC387 Solder Joints,”IEEE,2010.
[6] Qiang Wang, Yuanxiang Zhang, Lihua Liang, “Anand Parameter Test for Pb-Free Material SnAgCu and Life Prediction for a CSP,”IEEE,2007.
[7] H. Xiao, D.J. Luo, Y.B. Zou, “Damage Behavoir and Life Prediction for Lead-Free Solder joints in a CSP Assembly under Thermal Cycling,” International Conference on Reliability, Maintainability and Safety,2014.
[8] Tong Hong Wang, Yi-Shao Lai, Jenq-Dah Wu, “Submodeling Analysis for Plasticity-Involved Thermomechanical Problems,” The 27th Conference on Theoretical and Applied Mechanics,2003.
[9] F.X. Che, John H.L. Pang, “Thermal Fatigue Reliability Analysis for PBGA with Sn-3.8Ag-0.7Cu Solder Joints,” Electronics Packing Technology Conference,2004
[10] Yu Po Wang, Vito Lin, Eason Chen, Daniel Lee, “CSP package and Ball Design for Board Level Characteristic,”IEEE,2011
[11] Yi-Shao Lai, Tong Hong Wang, “Optimal design towards enhancement of board-level thermomechanical reliability of wafer-level chip-scale packages,”Elsevier,2006
[12] 李輝煌，ANSYS工程分析：基礎與觀念，高立圖書有限公司，2009年。
[13] John Hock Lye Pang , “Lead Free Solder Mechanics and Reliability,” Springer,2012.
[14] Dominique Francois, Andre Pineau, Andre Zaoui, “Mechanical Behaviour of Materials Volume II : Vicsoplasticity, Damage, Fracture, and Contact Mechanics,” Springer-Science+Business Media, B.V. .
[15] L. Anand, “Constitutive Equation for The Rate-Dependent Deformation of Metels at Elevated Temperature,” Transactions of The ASME, Vol.104,pp.12-17,1982.
[16] Ralph I. Stephens, Ali Fatemi, Robert R. Stephens, Henry O. Fuchs, “Metal Fatigue In Engineering,” Wiley, 2001.
[17] Chin-Diew Lai, “Generalized Weibull Distributions,” Springer .
[18] John H. Lau, “Solder Joint Reliability Theory and application,” Van Nostrand Reinhold, 1991.
[19] John H. L. Pang , B.S. Xiong and T.H. Low, “Creep and Fatigue Characterization of Lead Free 95.5Sn-3.8Ag-0.7Cu Solder,” ECTC, 2004.
[20] 李輝煌，田口方法：品質設計的原理與實務，高立圖書有限公司出版，2011年。
[21] 謝宇涵，銅柱凸塊再循環溫度負載下之可靠度研究，國立中山大學機械與機電工程研究所碩士論文，2014年。
[22] 郭昱綸，覆晶球柵陣列電子封裝體在溫度循環下的熱應力與熱應變分析，國立中山大學機械與機電工程研究所碩士論文，2003年。
[23] “Temperature Cycling,” JESD22-A104-D, JEDEC Solid State Technology Association, MARCH 2009.
[24] “ANSYS Modeling and Meshing Guide,” ANSYS Release 15.0. ANSYS,ING.
[25] Róbert Huňady, Martin Hagara, František Trebuňa, “The Measurement of Standing Wave Pattern by using High-speed Digital Image Correlation,” Science and Education Publishing, 2013.
[26] W. Qiang, L. Lihua, C. Xuefan, W. Xiaohong, Y. Liu, S. Irving, T. Luk, “Experimental determination and modification of Anand model constants for Pb-free material 95.5Sn4.0Ag0.5Cu,” in EUROSIME Conf. IEEE, 2007.
[27] T. Reinikainen, P. Marjamaki, and J. Kivilahti, “Deformation characteristics and microstructural evolution of SnAgCu solder joints,” in EUROSIME Conf. IEEE, 2005.
[28] D. Blass, M. Meilunas, and P. Borgesen, “On the Incorporation of Fine Pitch Lead Free CSPs in High Reliability SnPb Based Mivroelectronics Assemblies,” IEEE,2011.
[29] Shan Gao, Jupyo Hong, Jinsu Kim, Jingu Kim, Seogmoon Choi, Sung Yi, “Reliability evaluation and structure design optimization of Wafer Level Chip Scale Package(WLCSP),” IEEE, 2008.