臺灣博碩士論文加值系統

本研究主要針對PBGA元件，以實驗、有限元素分析與理論的相互配合，探討PBGA元件於共振環境下之振動壽命。實驗部分，以正弦波用待測電路板之第一自然振動頻率進行振動測試直到元件失效，取得PBGA元件之振動壽命實驗數據。同時，本研究亦透過理論計算方式，對PBGA元件之振動壽命進行估算。然而進行壽命估算，必先掌握PBGA元件內錫球之振動應力及應變。因此採用有限元素分析，對PBGA元件在實際振動測試條件下同步進行振動模擬分析，計算其內部錫球之應力、應變值。在進行振動分析時，電路板之楊氏係數及阻尼係數，影響分析結果至鉅。有鑑於此，針對這些關鍵性係數，利用板及薄膜理論以有限元素法寫成質量、剛性及阻尼矩陣，建構成平板之數學系統方程式，進而求得數值上之頻率響函數，然後與模態實驗取得電路板之頻率響函數作比對，並運用基因演算法鑑別出電路板之楊氏係數與阻尼值(?悀????nDamping)做為振動分析之用。

經由振動分析所得振動負載下之錫球應變，為彈性應變及塑性應變之總合。而當外加負載增加時，錫球所承受之塑性效應亦提高，而其塑性效應影會響壽命預估之準確性。因此，利用總應變壽命理論將塑性應變值納入疲勞壽命計算內，用以修正塑性應變造成之效應，並得到較佳之壽命預估值。此外，研究亦以應變能理論計算電子元件之振動壽命值，並與實驗比對。然而其結果顯示，配合文獻中之材料疲勞常數，應用上述總應變壽命理論及應變能理論，計算所得之壽命值與實驗值略有差異。因此，本研究更進一步，以實驗壽命值及分析所得之應力、應變、應變能數據進行曲線嵌合，找出更符合實驗壽命值之材料疲勞常數。最後更以基因演算法，配合ANSYS對錫球尺寸做最佳化設計，提供一個在設計階段即可預先掌握元件可靠度之有效方法。

In this study, the reliability of the PBGA components under vibration loading when at resonance is investigated by integrating practices of vibration fatigue life test, finite element analysis and theoretical estimation. In the fatigue life test, the printed circuit board(PCB) is excited at its first natural frequency with a series of sinusoidal vibrations of various displacement amplitudes until component failure is observed. Meanwhile, the theoretical calculations for the fatigue life are also conducted. However, the prerequisites such as the strain and stress data for the calculation are obtained firstly with the finite element analysis(FEA). But the material properties, especially the damping and the Young’s modulus of the printed circuit board, dominate the simulated results. Therefore, these mass, damping and stiffness matrices are deduced with the plate and membrane theories are determined with a self written FEA program. And the resulting theoretical frequency response function can thus be calculated. Besides, the results are compared with the real frequency response function from the modal test of the printed circuit board. Further, the Yong’s modulus and damping of the PCB are obtained by coping with the genetic algorithm in the comparison process. These material properties are then finally used in the further analysis.

The stress and strain data as obtained with the FEA are typically resulted from both the elastic and plastic deformation of the PCB. With the increase of excitation, the plastic effect will be enhanced and then causes the inaccuracy of the estimated life which is based on the life theory. Therefore, the life theory of total strain which includes the plastic strain effects is utilized to evaluate the fatigue life of the PBGA components. It is found that the fatigue life as calculated with the total strain life theory has better consistency with that from the experimental life data. In addition, the life estimation with stain energy density method is also conducted for the study. However, the estimated life from both methods has some extent of inconsistency with the experimental life. It is suspected that the material fatigue constants as referred from the literatures might be the reason. For better improve the accuracy, both the life tested and the stress and strain calculated are processed with the curve fitting method to find out a set of material fatigue constants for the current case. The life calculated by this way turns out to have better match with the experimental data. Finally, the optimum design of the solder balls is undertaken with the genetic algorithm and ANSYS analysis. It is believed that method developed can offer a systematic approach to predict and manipulate the life of PBGA components at the design stage.

目 錄

中文摘要..…………………………………………………………………..I
英文摘要………………………………………………………..….………II
誌謝……………………………………………………..…..…...….………IV
目錄………………………………………………….…….......…………...V
表目錄 ……………………………………………………...……...…….VIII
圖目錄.....…………………………………………………………...…….IX
符號說明……...………………………………………………...….…….XII
第一章 緒論…..….………………………………………………….…….1
1.1前言……………………………………………………………...……1
1.2文獻回顧…………………………………………………………...…2
1.3研究動機…………………………………………...…………………4
1.4本文架構………………………………………………………..…….4
第二章電路板材料性質之鑑別…………………………..……………….6
2.1電路板有限元素理論之推導…………………...…………………....7
2.1.1平板之應力應變關係式…………………...…………………...7
2.1.2平板及薄膜理論之推導說明…………………...…………..….8
2.1.3 薄膜理論推導………………….................…………...……….8
2.1.4 平板理論推導………………….................……………….….12
2.2理論推導之驗証…………………..…….................…………..……15
2.3 楊氏係數及阻尼值之鑑別..…….................………...………..……18
2.3.1 頻率響應函數理論推導……...………………………………18
2.3.2基因演算法用於鑑別材料常數之驗証……...…………….…21
2.3.3 模態實驗與材料常數鑑別結果………………...…..…..……24
第三章有限元素分析……………………..………………………….......28
3.1 PBGA有限元素模型建立…………………………...……………..28
3.2材料常數設定……………………………………………………….31
3.3有限元素模型驗証……………………………………….................34
3.4分析模組簡介……………………………………...………………..36
3.5有限元素分析結果………………………………...………………..38
第四章振動疲勞實驗與壽命理論計算……………………….………....40
4.1振動疲勞壽命實驗………….............................................................40
4.2總應變(Total Strain )疲勞壽命計算………………...........................45
4.2.1 總應變疲勞壽命理論介紹…………………...........................45
4.2.2 總應變能壽命計算結果討論...................................................47
4.2.3 材料疲勞常數之曲線嵌合.......................................................49
4.3 應變能(Strain-Energy Based Approach)疲勞壽命理論....................52
4.3.1應變能疲勞壽命理論介紹........................................................52
4.3.2 應變能壽命計算結果討論.......................................................53
第五章 鍚球尺寸參數最佳化設計…...………………………………....56
5.1基因演算法流程…………….………………………………………57
5.2參數化有限元素模型之建立……..……………….……….……….58
5.3最佳化設計之定義及最佳化結果………………….……..….…….61
第六章結論與未來展望……………….…….……………...…………....63
6.1研究結果與討論…………………….…...……………………….....63
6.2未來展望…………………....................………………………….…66
參考文獻…………………………………………………………...…......67









表目錄

表2.1板之自然振動頻率解析解……………………..…….……….…..16
表2.2理論解及解析解比較………………..………………..…..…...….16
表2.3基因演算法設定參數…..……..…...…………………….….…….23
表2.4基因演算法及模態實驗之頻率值與響應值比較……….……….27
表3.1有限元素分析所使用之材料常數……………….………....……..34
表3.2模態分析及模態實驗所得之自然頻率比較…….…….……...…..35
表3.3不同激振強度下應力及應變值數據….……….…………...……..38
表4.1 IPC-9701定義之元件破壞準則….……………….………..……..42
表4.2 PBGA 元件於不同振動負載下之壽命值….…………….......…..44
表4.3各激振條件之錫球應力應變及壽命值….………………...……..48
表4.4不同激振條件下之累積應變能密度值與壽命值….……...……..55
表5.1基因演算法設定參數….…………………………………...……..62
表5.2演算所得之最佳上下焊墊尺寸及其壽命值….…………………..62
表6.1演算所得之最佳上下焊墊尺寸及其壽命值……………………..64





圖目錄

圖1.1電子元件在振動環境下之失效模式……………….………….…..2
圖1.2研究流程圖………………………………….……………....….…..5
圖2.1薄膜元素座標系統圖……………………….……………....….…..9
圖2.2平板元素座標系統圖……………….………………………..........12
圖2.3理論解及解析解自然頻率比較圖…………………....…………..17
圖2.4板之前四模態振型...…….………………………………...….…..17
圖2.5不同阻尼值下之頻率響應函數……………………….....…...…..20
圖2.6 不同楊氏係數下之頻率響應函數……….…….……...…….…...20
圖2.7基因演算法流程……………………...……………………..…….21
圖2.8適應值之計算…………………..………………………...………..22
圖2.9頻率響函數比較圖…………………………………………....…..23
圖2.10頻譜分析儀…………………..……………..…………….…...…25
圖2.11模態測試實驗架設示意圖………………………………...….…25
圖2.12模態測試外力施加點與量測點示意圖……..…………………..26
圖2.13電路板模態測試所得之頻率響應函數………..………………..26
圖2.14模態實驗與經基因演算法計算所得之頻率響應函數………….27
圖3.1測試用電路板實體及其尺寸……………………………….…….28
圖3.2 PBGA元件尺寸……………….…………………………….…….29
圖3.3 FCBGA各部分結構示意圖…………………………….……..….30
圖3.4有限元素分析模型示意圖……………..…………………..……..30
圖3.5 FCBGA 內部鍚球網格規劃…………………………...…..….….31
圖3.6 Ramberg-Osgood 應力應變曲線………………………………….33
圖3.7電路板於模態測試時夾持狀況示意圖…….…………..………...34
圖3.8電路板之頻率響應函數……………….……………….………....35
圖3.9有限元素析模型邊界條件設定…………..……………………....35
圖3.10簡諧分析設定示意圖………………………………………...….36
圖3.11暫態分析下時間與位移關係圖………………..……….……….37
圖3.12角落錫球之應力分佈情況………………..….…………....…….38
圖3.13錫球於各方向上之塑性應力及應變示意圖………………...…..39
圖4.1元件內Daisy Chain 電路原理示意圖..…………………..…..…..41
圖4.2測試用電路板與其上單一元件之近觀圖…………………..….....43
圖4.3快速動態訊號擷取系統架設示意圖…………….………....……..43
圖4.4振動疲勞實驗示意圖…………………….……..…………………44
圖4.5總應變對應疲勞壽命關係圖……………………………….…….47
圖4.6各激振條件下鍚球所受應力應變及壽命示意圖……………..…49
圖4.7曲線嵌合所得之疲勞壽命值與文獻計算值之比較…….……….51
圖4.8塑性應變對應力遲滯曲線圖…………………....…………….…..53
圖4.9各激振條件下時間及累積應變能密度圖………….…...………...54
圖4.10應變能對應於疲勞壽命圖…………………..…...…….………...55
圖5.1壽命與應力在設計上之關係示意圖……………..………………56
圖5.2鍚球尺寸參數最佳化設計流程圖………………………….…….58
圖5.3鍚球幾何關係示意圖……………………….………………….….59
圖5.4不同焊墊尺寸下之鍚球幾何外型.………….………………….…60
圖6.1總應變及應變能疲勞壽命理論估算之壽命值與實驗值比對.…..64

1.T. E. Wong, F. W. Palmieri and H. S. Fenger, “Under-Filied BGA Solder Joints Vibration Fatigue Damage”, IEEE Society Conference on Thermal Phenomena, 2002.
2.T. E. Wong, B. A. Reed, H. M. Cohen and D. W. Chu, “Development of BGA Solder Joints Vibration Fatigue Life Prediction Model”, IEEE Electronic Components and Technology Conference, 1999.
3.T. E. Wong, F. W. Palmieri, B. A. Reed, H. S. Fenger, H. M. Cohen and K. T. Teshiba, “Durability/Reliability of BGA Solder Joints under Vibration Environment”, IEEE Electronic Components and Technology Conference, 2000.
4.S.S.Manson, “Fatigue: A Complex Subject-Some Simple Approximations”, Experimental Mechanics, Vol. 5, No. 7, pp.193-226, July 1965.
5.Donald B. Barker, Abhijit Dasgupta and Michael G. Pecht, “PWB Solder Joint Life Calculations Under Thermal and Vibrational Loading”, IEEE Proceedings Annual Reliability and Maintainability Symposium, pp. 451-459, 1991.
6.Q. J. Yang, H. L. J. Pang, Z. P. Wang, G. H. Lim, F. F. Yap, and R. M. Lin, “Vibration Reliability Characterization of PBGA Assembly”, Microelectronics Reliability, Vol. 16, May 1999
7.Q. J. Yang, G. H. Lim, H. L. J. Pang and Z. P. Wang, “Vibration Reliability Test of PBGA Assembly”, IEEE Electronics Packaging Technology Conference, 1998.
8.Q. J. Yang, Z. P. Wang, G. H. Lim, John H. L. Pang, F. F. Yap and R. M. Lin, “Reliability of PBGA Assemblies Under Out-of-Plane Vibration Excitations”, Transactions on Components and Packaging Technologies, Vol. 25, No. 2, June 2002.
9.Dave S. Steinberg, “Vibration Analysis for Electronic Equipment”, Second Edition, John Wiley & Sons, New York, 1988.

10.John H. Lau, K. Gratalo, E. Schneider, T. Marcotte and T. Baker, “Solder Joint Reliability of Large Plastic Ball Grid Array Assemblies Under Bending, Twisting, and Vibration Conditions”, Circuit World, Vol. 22, No. 1, pp. 27-32, 1995.
11.H. S. Blank, “Accelerated Vibration Fatigue Life Testing of Leads and Soldered Joints”, Microelectronics and Reliability, Vol. 15, pp. 213-219, 1979.
12.Ron S. Li, “A Methodology for Fatigue Prediction of Electronic Components Under Random Vibration Load”, Journal of Electronic Packaging, Vol. 123, pp. 394-400, December, 2001.
13.G. Bartlett, and W. Yacovitch, “Ruggedizing the BGA for High Vibration”, Mercury Computer Systems, Inc., Chelmsford, Mass., Electronic Packaging & Production, pp. 84-91, October 1997
14.X.Q. Shi, H.L.J. Pang, W. Zhou, and Z.P. Wang, “A Modified Energy-Based Low Cycle Fatigue Model for Eutectic Solder Alloy”, Scripta Materialia, Vol. 41, No. 3, pp.289-296,1999.
15.C. Andersson, Z. Lai, H. Jiang and Y. Yu, “Comparison of Isothermal Mechanical Fatigue Properties of Lead-Free Solder Joints and Bulk Solders’, Materials Science and Engineering, Vol. 394, pp.20-27, 2005.
16.John H.L. Pang, B.S. Xiong, T.H. Low, “Low Cycle Fatigue Models for Lead-Free Solders”, Thin Solid Films, Vol. 462, pp.408-412, 2004.
17.Peter A. Engel, “ Structural Analysis of Printed Circuit Board Systems”, Springer-Verlag, New York, 1993.
18.Ansel C. Ugural, “Stresses in Plates and Shells”, Second Edition, McGraw-Hill, Singapore, 1999.
19.J. S. Przemieniecki, “Theory of Matrix Structure Analysis”, McGraw-Hill, New York, 1968.
20.Michael E. Plesha, David S. Malkus, ”Concepts and Applications of Finite Element Analysis”, Third Edition, Wiley, New York, 1989.
21.D.J. Gorman, “Free Vibration Analysis of Rectangular Plates”, Elsevier North Holland, 1982.
22.D.J. Gorman, ”Vibration Analysis of Plates by the Superposition Method”, Word Scientific, 1999.
23.Daniel J. Inman, “Engineering Vibration”, Simon & Schuster, Singapore, 1996.
24.周鵬程，“遺傳演算法原理與應用”，全華出版，2001。
25.許瑞峰, “微小材料機械特測試系統之設計製作與其在電子封裝與高分子材料上之應用”, 國立成功大學,機械工程研究所碩士論文,中華民國九十二年七月。
26.Norman E. Dowling, “Mechanical Behavior of Material: Engineering Methods of Deformation, Fracture, and Fatigue”, Second Editions, Prentice Hall, New Jersey, 1999.
27.IPC-9701, Performance Test Methods and Qualification Requirements for Surface Mount Solder Attachments, Jan. 2002.
28.L. F. Coffin, “A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal,” Trans. ASME, Vol. 76, pp. 931-950, 1954.
29.S. S. Manson, “Behavior of Materials under Conditions of Thermal Stress,” Heat Transfer Symposium, pp.9-75, 1953.
30.O. H. Basquin, “The Exponential Low of Endurance Tests,” Am. Soc. Test. Mater. Proc., Vol. 10, pp. 625-630, 1910.
31.J.D. Morrow, “Cyclic Plastic Strain Energy and Fatigue of Metals”, ASTM STP 378, pp.45-87, 1964.
32.Solomon H. D. and Tolksdorf E. D., “Energy Approach to the Fatigue of 60/40 Solder: Part I – Influence of Temperature and Cycle Frequency”, ASME Trans., J. ElectronicPackg., Vol.117, pp.130-135,1995.
33.Solomon H. D. and Tolksdorf E. D., “Energy Approach to the Fatigue of 60140 Solder: Part I1 – Influence of Hold Time and Asymmetric Loading”, ASME Trans., J. Electronic Packg., Vol.118, pp.67-71, 1996.