本研究主要是針對FCBGA元件，進行四點彎曲測試，以瞭解其可承受之疲勞壽命。並經由實驗、有限元素分析與理論分析的相互配合，探討實驗測試過程中，元件失效與元件壽命之關連性。
實驗使用具有Daisy Chain之FCBGA元件，其將各錫球之電路串聯，並利用微材料試驗機(Micro Material Tester)，於不同環境溫度下，做電路板循環下壓之四點彎曲測試，用以觀察其Daisy Chain是否失效，並以有限元素分析之方法，來模擬真實受力情況下錫球接合處之應力大小，再與實驗所獲得的疲勞循環數相互配合對照。並以Weibull分佈之可靠度分析，配合疲勞壽命理論，估算錫球之疲勞壽命，並透過光學顯微鏡觀察錫球裂縫的產生。
研究結果發現，錫球之疲勞破壞位置在錫球與電路板接合界面上，與相關文獻中所述之破壞位置及實驗結果吻合。本研究對於電子系統元件之壽命分析，提供一個有效的可靠度驗證模式，利用此模式可檢驗並提高電子元件或系統的使用壽命，以達到提升可靠度的目的。

In this study, it is aimed to check the electronic component fatigue life with the four-point-bend test for FCBGA components. The resulting component life are determined by combining both the finite element analysis(FEA) technique and the theoretical calculation.

The experiment is conducted first by taking FCBGA components with the daisy chain circuits and mounted them on a PWB. The four-point bend test is performed on a micro material tester with different temperature settings. In the FEA, it uses the real displacements in the bending test as an input to the model. The resulting stresses of solder balls can be obtained. These stresses and the number of fatigue cycles as obtained in the bending test can then be plotted as the fatigue stress-cycle curve. Furthermore, the Weibull’s reliability analysis and fatigue theory are used to calculate the fatigue life.

The experimental results indicate that the failure cracks are located at the interface between solder balls and PWB. The procedures as described in the study provide an effective way in verifying the life of the electronic system. The method can be applied to the study of reducing the occurrence of unexpected component failure and also the improvement of their reliability in the electronic system design.

中文摘要…………………………………………………………………i
英文摘要…………………………………………………………………ii
誌謝………………………………………………………………iii
目錄………………………………………………………………iv
表目錄…………………………………………………………vii
圖目錄…………………………………………………………viii
符號說明…………………………………………………………………xiii
第一章 緒論…………………………………………………………1
1.1 研究背景與目的……………………………………………3
1.2 文獻回顧……………………………………………4
第二章 可靠度分析與疲勞壽命理論………………………………7
2.1 可靠度分析……………………………………………………8
2.2 疲勞壽命理論…………………………………………………13
2.2.1 塑性應變理論模式……………………………………17
2.2.2 潛變應變理論模式……………………………………20
2.2.3 能量理論模式…………………………………………22
2.2.4 累積損傷理論模式………………………………………23
2.2.5 加速測試經驗模式……………………………………25
第三章 錫球受力之力學分析………………………………………26
3.1 以彈簧模擬錫球受力變形…………………………………26
3.1.1 邊緣單排錫球……………………………………………26
3.1.2 僅四周邊緣具有錫球……………………………………28
3.1.3 一般BGA構裝之陣列排列方式………………………30
3.1.4單顆錫球之受力模式……………………………………31
3.2 在溫度效應下模擬錫球受力與變形………………………33
3.2.1 受力與彎矩………………………………………………35
3.2.2 應力……………………………………………………38
第四章 實驗方法與結果比較.………………………………………41
4.1 實驗設備與架設方式…………………………………………41
4.1.1 實驗設備.………………………………………………43
4.1.2 四點彎曲測試試片………………………………………46
4.1.3 實驗架設.………………………………………………47
4.2 實驗量測原理…………………………………………………51
4.3 實驗結果.………………………………………………………53
4.3.1 常溫下四點彎曲循環下壓測試…………………………53
4.3.2不同溫度之一次下壓與循環彎曲測試..………………55
4.4 錫球破壞情形………………………………………………60
第五章 有限元素分析…………………………………………………67
5.1 有限元素模型建構…………………………………………68
5.2 結構負載與邊界條件…………………………………………72
5.3 應力分析結果…………………………………………………72
5.4溫度對於分析應力之影響……………………………………75
5.5模型簡化對於應力差異之影響………………………………82
第六章 結果討論………………………………………………………87
6.1可靠度分析及錫球疲勞壽命之探討…………………………87
6.2 力學理論分析…………………………………………………90
第七章 結論與未來展望………………………………………………91
7.1結論……………………………………………………………91
7.2未來研究發展…………………………………………………92
參考文獻.………………………………………………………………93

1.John H. Lau, “Ball Grid Array Technology,” McGraw-Hill, Inc., New York, 1995.
2.J. Schijvey, “A Normal Distribution or a Weibull Distribution for Fatigue Lives,” Fatigue & Fracture of Engineering Materials & Structures, Vol. 16, pp. 851-859, 1993.
3.S. Tanaka, M. Ichikawa, and S. Akita, “A Probabilistic Investigation of Fatigue Life and Cumulative Cycle Ratio,” Engineering Fracture Mechanics, Vol. 20, pp. 501-503, 1984.
4.C. Kanchanomai, Y. Miyashita, and Y. Mutoh, “Low-Cycle Fatigue and Mechanisms of A Lead-Free Solder 96.5Sn/3.5Ag,” Journal of Electronic Materials, Vol. 31, pp. 142-151, 2002.
5.C. Kanchanomai, and Y. Miyashita, “Low-Cycle Fatigue Behavior and Mechanical of A Eutectic Sn-Pb Solder 63Sn/37Pb,” International Journal of Fatigue, Vol. 24, pp. 671-683, 2002.
6.C. Kanchanomai, S. Yamamoto, Y. Miyashita, Y. Mutoh, and A. J. McEvily “Low-Cycle Fatigue Test for Solders Using Non-Contact Digital Image Measurement System,” International Journal of Fatigue, Vol. 24, pp. 57-67, 2002.
7.H. Nayeb-Hashemi, and P. Yang, “Mixed Mode I/II Fracture and Fatigue Crack Growth along 63Sn/37Pb Solder/Brass Interface,” International Journal of Fatigue, Vol. 23, pp. S325-S335, 2001.
8.R. Ghaffarian, and N. P. Kim, “Ball Grid Array Reliability Assessment for Aerospace Application,” Microelectronics Reliability, Vol. 39, pp. 107-112, 1999.
9.P. L. Tu, Y. C. Chan, K. C. Hung, and J. K. L. Lai, “Comparative Study of Micro-BGA Reliability under Bending Stress,” IEEE Transactions on Advanced Packaging, Vol. 23, No. 4, pp. 750-756, 2000.
10.L. Leicht, and A. Skipor, “Mechanical Cycling Fatigue of PBGA Package Interconnects,” Microelectronics Reliability, Vol. 40, pp. 1129-1133, 2000.
11.Bryan Dodson, “Weibull Analysis, ” ASQC Quality Press, Wisconsin, 1994.
12.陳志仁，「BGA受循環彎曲作用下之疲勞破壞分析與可靠度評估」，國立台灣大學，機械工程學研究所碩士論文，中華民國九十二年五月。
13.王宣勝，「Sn-58Bi、Sn-51In、Sn-37Pb球格陣列構裝的動態疲勞分析及可靠度分析」，國立台灣大學，材料科學與工程學研究所博士論文，中華民國九十二年六月。
14.L. F. Coffin, “A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal,” Trans. ASME, Vol. 76, pp. 931-950, 1954.
15.S. S. Manson, “Behavior of Materials under Conditions of Thermal Stress,” Heat Transfer Symposium, pp.9-75, 1953.
16.O. H. Basquin, “The Exponential Low of Endurance Tests,” Am. Soc. Test. Mater. Proc., Vol. 10, pp. 625-630, 1910.
17.H. D. Solomon, “Fatigue of 60/40 Solder,” IEEE Transactions on Components, Hybrids and Manufacturing Technology, Vol. CHMT-9, pp. 91-104, 1986.
18.W. Engelmaier, “Fatigue Life of Leadless Chip Carrier Solder Joints During Power Cycling,” IEEE Transactions on Components, Hybrids and Manufacturing Technology, Vol. CHMT-6(3), pp.232-237, 1983.
19.S. Knecht, and L. R. Fox, “Constitutive Relation and Creep-Fatigue Life Model for Eutectic Tin-Lead Solder,” IEEE Transactions on Components, Hybrids and Manufacturing Technology, Vol. CHMT-13(2), pp.424-433, 1990.
20.Norman E. Dowling, “Mechanical Behavior of Materials,” Second Edition, Prentice-Hall, New Jersey, 1999.
21.J. Morrow, “Cyclic Plastic Strain Energy and Fatigue of Metals,” in Internal Friction Damping and Cyclic Plasticity, ASTM S TP378, Philadelphia, pp. 45-87, 1965.
22.H. U. Akay, Y. Tong, and N. Paydar, “Thermal Fatigue Analysis of a SMT Solder Joint Using a Nonlinear FEM Approach,” The International Journal of Microelectronics and Electronic Packaging, Vol. 16, No. 2, pp. 79-88, 1993.
23.J. Liang, N. Gollhardt, P. S. Lee, S. Heinrich, and S. Schroeder, “An Intergrated Fatigue Life Prediction Methodology for Optimum Design and Reliability Assessment of Solder Interconnections,” Advances in Electronic Packaging, Vol. 2, pp. 1583-1592, 1997.
24.P. C. Paris, and F. Erdogan, “A Rational Analytic Theory of Fatigue,” The Trend in Engineering 13, pp. 9-14, 1961.
25.R. Darveaux, K. Barnerji, A. Mawer, and G. Dody, “Reliability of Plastic Ball Grid Array Assembly,” Ball Grid Array Technology, J. Lau, ed., McGraw-Hill, Inc., New York, pp. 379-442, 1995.
26.J. H. Norris, and A. H. Landzberg, IBM Journal of Research and Development, pp. 266-271, 1969.
27.B. Vandevelde, E. Beyne, D. Vandepitte and M. Baelmans, “Analytical Thermo-Mechanical Model for Non-Underfilled Area Array Flip Chip Assemblies,” Journal of Electronic Packaging, Vol. 126, pp. 351-358, September 2004.
28.IPC-9701, Performance Test Methods and Qualification Requirements for Surface Mount Solder Attachments, Jan. 2002.
29.A. Skipor, and L. Leicht, “Mechanical Bending Fatigue Reliability and Its Application to Area Array Packaging,” Electronic Components and Technology Conference, Orlando, pp. 606-612, 29 May-1 June 2001.
30.John H. L. Pang, Kar Hwee Ang, Xunquig Q. Shi, and Z. P. Wang, “Mechanical Deflection System (MDS) Test and Methodology for PBGA Solder Joint Reliability,” IEEE Transactions on Advanced Packaging, Vol. 24, No.4, pp. 507-514, November 2001.
31.楊裕州，「電路板上PBGA元件之振動疲勞壽命試驗與可靠度分析」，私立元智大學，機械工程研究所碩士論文，中華民國九十二年七月。
32.J. D. Wu, S. H. Ho, P. J. Zheng, C. C. Liao, and S. C. Hung, “An Experimental Study of Failure and Fatigue Life of a Stacked CSP Subjected to Cyclic Bending,” Electronic Components and Technology Conference, Orlando, pp. 1081-1086, 29 May-1 June 2001.
33.Qizhou Yao, Jianmin Qu, Jiali Wu, and C.P. Wong, “Adhesion Enhancement of Underfill Materials by Silane Additives,” International Symposium on Advanced Packaging Materials, Braselton, pp. 27-30, March 1999.
34.Scott F. Popelar, “An Investigation Into the Fracture of Silicon Die Used in Flip Chip Applications,” International Symposium on Advanced Packaging Materials, Braselton, pp. 41-48, March 1998.
35.Akito Yoshida, and Isao Kudo, “Board Level Reliability for Laminate CSP,” Electronics Manufacturing Technology Symposium, Austin, pp. 315-322, October 1998.
36.Qizhou Yao, Jianmin Qu, Jiali Wu, and C.P. Wong, “Characterization of Underfill/Substrate Interfacial Toughness Enhancement by Silane Additives,” IEEE Transactions on Electronic Packaging Manufacturing, Vol. 22, No.4. pp. 264-267, October 1999.
37.Lei L. Mercado, and Vijay Sarihan, “Evaluation of Die Edge Cracking in Flip-Chip PBGA Packages,” Thermal and Thermomechanical Phenomena in Electronic Systems, Las Vegas, pp. 73-78, May 2000.
38.Phil Geng, Philip Chen, and Yun Ling, “Effect of Strain Rate on Solder Joint Failure under Mechanical Load,” Electronic Components and Technology Conference, San Diego, pp. 974-978, May 2002.
39.S. Shetty, V. Lehtinen, A. Dasgupta, V. Halkola, and T. Reinikainen, “Fatigue of Chip Scale Package Interconnects Due to Cyclic Bending,” Journal of Electronic Packaging, Vol. 123, No. 3, pp. 302-308, September 2001.
40.Ph. Clot, J,-F. Zeberli, J.-M. Chenuz, F. Ferrando, and D. Styblo, “Flip-Chip on Flex for 3D Packaging,” Electronics Manufacturing Technology Symposium, Austin, pp.36-41, Oct.1999.
41.J.-B. Han, “Flip-Chip BGA Design to Avert Die Cracking,” Journal of Electronic Packaging, Vol. 123, No. 1, pp. 58-63, March 2001.
42.C. M. Lawrence Wu, Robert K. Y. Li, and N. H. Yeung, “Impact Resistance of SM Joints Formed With ICA,” Journal of Electronic Packaging, Vol. 124, No. 4, pp. 374-378, December 2002.
43.A. A. O. Tay, and T. Y. Lin, “Influence of Temperature, Humidity and Defect Location on Delamination in Plastic IC Packages,” Inter Society Conference on Thermal Phenomena, Seattle, pp. 179-184, May 1998.
44.A. Soper, G. Pozza, M. Ignat, and G. Parat, “Mechanical Response of Solder Joints in Flip-Chip Type Structures,” Microelectronics and Reliability Vol. 37, No. 10-11, pp. 1783-1786, October 1997.
45.Larry Leicht, and Andrew Skipor, “Mechanical cycling fatigue of PBGA package interconnects,” Microelectronics and Reliability, Vol. 40, No. 7, pp. 1129-1133, July 2000.
46.K. Jonnalagadda, “Reliability of via-in-pad structures in mechanical cycling fatigue,” Microelectronics and Reliability, Vol. 42, No. 2, pp. 253-258, February 2002.
47.S.H.Shi, Q.Yao, and C.P.Wong, “Study on the Correlation of Flip-Chip Reliability with Mechanical Properties of No-Flow Underfill Materials,” IEEE International Symposium on Advanced Packaging Materials, Braselton, pp. 271-277, March 2000.