現今電子封裝產業利用許多技術提高電子元件中積體電路的密度，為了製程與成本等考量，高分子材料被大量應用，但其機械性質與其他封裝材料不同，在主要受到熱負載的電子元件中，會有許多因熱膨脹係數不匹配而導致缺陷產生甚至產品失效的可能性，其中高分子材料與銅薄膜的界面就是容易產生裂縫或材料脫層的其中一個區域，因此本論文的目標是以破壞力學為基礎，分析高分子材料聚醯亞胺與銅之界面的破壞行為。
本研究分析了三種模型，分別為雙懸臂樑、四點彎矩以及重佈線模型，首先透過前兩者相對較簡單的模型，建立適當的分析流程與方法，透過有限元素軟體內建的黏彈性材料與黏塑性材料模型設定聚醯亞胺與銅的材料參數，並使用其中的接觸設定，模擬裂紋在成長前的狀態，接著透過節點釋放法使分析中各能量達到收斂，在確認能量守恆以及分析結果的正確性後，將這套流程與方法運用在較為複雜的重佈線模型中，分析真實的電子封裝結構在受到熱負載下的反應與界面裂紋破壞情形。
研究結果發現在不同破壞模式負載下，能量分配與損耗機制有很大的差異，在模式一負載即雙懸臂樑中，溫度低時整體結構較能儲存能量，而在混合模式負載即四點彎矩中，則容易產生黏塑消耗，因此整體能量損耗較雙懸臂樑來的大。在重佈線模型中，損失的能量會由結構原有的彈性位能提供，並主要透過黏塑消耗的方式損耗。

State-of-the-art packaging technologies often incorporate multilayers of polymers and metal conductors to increase the interconnect density in the electronic component. One of the key reliability concerns is the interface debonding driven by the thermomechanical stress under fabrication or under in-use conditions. In fan-in or fan-out redistribution interconnect, the interface of thin-film copper conductor and polyimide (PI) dielectric is where cracking or debonding prone to occur. This thesis investigated the debonding driving force of the Cu-PI interface and the effects of inelastic deformations of the thin films on the energy dissipation. Three cases of Cu-PI interface fracture have been analyzed by using finite element simulations: under Mode-I double cantilever beam (DCB) test, under mixed-mode four-point bending test, and under thermal excursion condition. The results indicate that the energy dissipation under Mode-I and mixed-moded loading conditions are through different mechanisms. In Mode-I dominant condition, the energy dissipation is mainly through interface separation, and the inelastic energy dissipations of the neighboring materials are relatively insignificant. On the other hand, in the mixed-moded condition, the viscoplastic energy dissipation of the Cu is significantly higher than the separation energy dissipation. The numerical procedure developed in this thesis can be adopted to evaluate the risk of debonding of multilayered interconnect structures.

[1] Z. Xiong and A. A. O. Tay,“Modeling of viscoelastic effects on interfacial delamination in IC packages,”in Proceedings of the Electronic Component and Technology Conference, Las Vegas, pp. 1326-1331, 2000.
[2] X. Han, F. Ellyin and Z. Xia,“Interface crack between two different viscoelastic media,”International Journal of Solids and Structures, vol. 38, pp. 7981-7997, 2001.
[3] T. L. Kuo and C. Hwu,“Interface corners in linear anisotropic viscoelastic materials,”International Journal of Solids and Structures, vol. 50, pp. 710-724, 2013.
[4] A. A. Griffith,“The phenomena of rupture and flow in solids,”Philosophical Transactions Royal Society of London, vol. 221, pp. 163-198, 1921.
[5] E. Orowan,“Energy criteria of fracture,”Welding Journal Research Supplement, vol. 34, pp. 157-160, 1955.
[6] G. R. Irwin,“Fracture,”Handbuch der Physik, (edited by S. Flugge), Springer-Verlag, Berlin, 1958, pp. 551-590.
[7] J. R. Rice,“An examination of the fracture mechanics energy balance from the point of view of continuum mechanics,”in Proceedings of the First International Conference on Fracture, Sendai, pp. 309-337, 1966.
[8] K. J. Miller and A. P. Kfouri,“Crack separation energy rates in elastic-plastic fracture mechanics,”Proceedings of the Institute of Mechanical Engineering, vol. 190, pp. 571-584, 1976.
[9] J. R. Rice,“A path independent integral and the approximation analysis of strain concentration by notches and cracks,”Journal of Applied Mechanics, vol. 1, pp. 379-386, 1968.
[10] C. F. Shih,“Cracks on bimaterial interfaces:elasticity and plasticity aspects,” Materials Science and Engineering, vol. 143, pp. 77-90, 1991.
[11] V. Tvergaard and J. W. Hutchinson,“The influence of plasticity on mixed mode interface toughness,”Journal of the Mechanics and Physics of Solids, vol. 41, pp. 1119-1135, 1993.
[12] A. O. Ayhan and H. F. Nied,“Finite element analysis of interface cracking in semiconductor packages,”IEEE Transactions on Components and Packaging Technology, vol. 22, pp. 503-511, 1999.
[13] Y. Gu, T. Nakamura, W. T. Chen and B. Cotterell,“Interfacial delamination near solder bumps and UMB in flip-chip packages,”Journal of Electronic Packaging, vol. 123, pp. 295-301, 2001.
[14] V. Tvergaard,“Resistance curves for mixed mode interface crack growth between dissimilar elastic–plastic solids,”Journal of the Mechanics and Physics of Solid, vol. 49, pp. 2689-2703, 2001.
[15] H. T. Wang, G. Z. Wang, F. Z. Xuan and S. T. Tu,“Numerical investigation of ductile crack growth behavior in a dissimilar metal welded joint,”Nuclear Engineering and Design, vol. 241, pp. 3234-3243, 2011.
[16] L. Anand,“Constitutive equations for hot-working of metals,”International Journal of Plasticity, vol. 1, pp. 213-231, 1985.
[17] G. Z. Wang, Z. N. Cheng, K. Becker and J. Wilde,“Applying Anand model to represent the viscoplastic deformation behavior of solder alloys,”Journal of Electronic Packaging, vol. 123, pp. 247-253, 2001.
[18] 吳芯霈, 細銅線黏塑性模型及其於電子封裝可靠度分析之應用, 國立成功大學機械工程所碩士學位論文, 2020.
[19] S. Ostlund,“On numerical modeling and fracture criteria of dynamic elastic-viscoplastic crack growth,”International Journal of Fracture, vol. 44, pp. 283-299, 1990.
[20] S. Rangaraj and K. Kokini,“Interface thermal fracture in functionally graded zirconia-mullite–bond coat alloy thermal barrier coatings,”Acta Materialia Incorporated, vol. 51, pp. 251-267, 2002.
[21] M. J. Heffes and H. F. Nied,“Analysis of interfacial cracking in flip chip packages with viscoplastic solder deformation,”Journal of Electronic Packaging, vol. 126, pp. 135-141, 2004.
[22] W. H. Bang, M. W. Moon, C. U. Kim, S. H. Kang, J. P. Jung and K. H. Oh,“Study of fracture mechanics in testing interfacial fracture of solder joints,”Journal of Electronic Materials, vol. 37, pp. 417-428, 2008.
[23] C. T. Sun and C. Y. Wang,“A new look at energy release rate in fracture mechanics,”International Journal of Fracture, vol. 113, pp. 295-307, 2002.
[24] N. V. De Carvalho, R. Krueger, G. E. Mabson and L. R. Deobald,“Combining progressive nodal release with the virtual crack closure technique to model fatigue delamination growth without re-meshing,”in Proceedings of the AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Florida, pp. 1468-1483, 2018.
[25] J. X. Zhang and H. Murakawa,“A potential node release technique for estimating ductile crack growth in metallic materials,”2000. Available: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.820.6771&rep=rep1&type=pdf. [accessed : 15/7/2022].
[26] 許佳桂, 高分子薄膜與銅界面脫層之成長分析, 國立成功大學機械工程所碩士學位論文, 2016.
[27] 楊家明, 濕度相依聚醯亞胺黏彈模型及其於扇出型封裝吸濕模擬之應用, 國立成功大學機械工程所碩士學位論文, 2021.
[28] CORROSIONPEDIA,“Glass transition temperature (Tg),”15/3/2021. https://www.corrosionpedia.com/definition/593/glass-transition-temperature-tg. [accessed : 15/7/2022].
[29] 吳竣丞, 覆晶封裝底填膠黏彈特性及破壞力學分析, 國立成功大學機械工程所碩士學位論文, 2021.