臺灣博碩士論文加值系統

Electromigration-induced degradation in solder joints can be classified into two types, pancake-type void formation and metallization consumption, which are driven by two different diffusion mechanisms. The void formation is caused by the Sn electromigration and the combined effect of tensile stress and vacancy supersaturation, while the metallization consumption is caused by the electromigration of metallization atoms (such as Cu or Ni) in the solder from cathode to anode. The rapid development of high-density interconnects raises the electron current density through the solder joints up to 104 A/cm2, resulting in more severe conditions for solder joints reliability.
The subjects of the dissertation include three parts. The first part of the study investigates the temperature effect on the electromigration-induced degradation mechanism. Both kinetic analysis and experimental observations demonstrate that temperature is one of the important factors affecting the electromigration behavior. At high temperature, because the magnitudes of Sn and Cu electromigration fluxes are within the same order of magnitude, both void formation and metallization consumption operate simultaneously. At low temperature, however, the Cu electromigration dominates over Sn, so the metallization layer is excessively consumed before the void starts to form and propagate. It implicates that the accelerated electromigration tests at high temperature may not provide a complete picture of electromigration-induced failure mechanism in solder joints. Finally, the kinetic analysis is extended to other fast diffusers considering both temperature and orientation effects.
From the first part of the study, it shows that electromigration-induced metallization dissolution or consumption, instead of void formation, can be the dominant degradation under certain conditions. However, current understanding of the electromigration-induced dissolution is not capable of elucidating the microscopic mechanisms and the origin of serrated cathode consumption observed by several research groups recently. In the second part of the study, a purposely designed experiment using Cu/Sn/Cu line-type solder interconnects is implemented in order to reveal the complete microstructural evolution of the consumption process at the cathode. The result shows that a pronounced and unstable grain boundary grooving between Cu6Sn5 grains occurs before the serrated cathode starts to develop. The morphological of the intermetallic compound changes from a layered structure to an unstable scalloped structure. The grooving is driven by the preferential dissolution at the Cu6Sn5 grain boundaries, a process similar to the formation of scallop-type Cu6Sn5 between molten solder and Cu. Because the diffusion and reaction are more significant at the valley of the grooves, the local consumption rate of Cu metallization increases. This non-uniform consumption of Cu eventually leads to a serrated cathode interface. The result indicates that the development of the serrated cathode interface may be very sensitive to the initial microstructure, such as the position and distribution of the Cu6Sn5 grain boundaries.
Despite the successful discovery of the microscopic mechanism of current-induced dissolution, its accompanied phenomenon, such as the backfill of Sn atoms, is not completely understood. The only thing that is ascertained is that it may be driven by the electromigration-induced stress field. The stress field has been known to be intimately related to defect kinetics, such as dislocation climb and the microscopic mechanism of diffusion creep. Therefore, in the third part of the study, a microscopic phase field dislocation climb model is proposed in order to uncover the coupling effects of the defect stress field and vacancy diffusion. The capability of the proposed model is further validated by several examples and demonstrations, including the classical Kirkendall effect and interdiffusion. The most promising feature of the model is that the constraint of zero vacancy chemical potential is released, so it is capable of being applied in the simulations with non-equilibrium vacancy concentration. Fast numerical methods to solve the problems of inhomogeneous elasticity and electric conduction are also proposed and validated in this part of the study. It is anticipated that in the future, the proposed model can be applied to the electromigration in solder interconnects, as long as the vacancy thermodynamic databases of the solder systems are developed.

Acknowledgements i
摘要 iii
Abstract v
Contents viii
List of Figures x
List of Tables xx
Chapter 1 Introduction 1
Chapter 2 Literature Review 5
2-1 Electromigration 5
2-2 Electromigration in Metallic Interconnects 8
2-3 Electromigration in Solder Joints 12
2-4 Phase Field Method 23
Chapter 3 Temperature Effect on the Electromigration Behavior of Solder Joints 28
3-1 Motivation 28
3-2 Kinetic Analysis 29
3-3 Experimental 35
3-4 Results and Discussion 37
3-5 Generalization 42
3-6 Summary 52
Chapter 4 Mechanism of Serrated Cathode Dissolution in Cu/Sn/Cu Interconnects 54
4-1 Motivation 54
4-2 Experimental 56
4-3 Results 59
4-4 Discussion 68
4-5 Uncertainties and Limitations 76
4-6 Summary 77
Chapter 5 Development of a Microscopic Phase Field Model for Electromigration with Non-ideal Defect Sources/Sinks 79
5-1 Motivation 79
5-2 Introduction to Microelasticity 81
5-3 Inhomogeneous Electric Conduction 88
5-4 Phase Field Dislocation Climb Model 93
5-5 Limitations and Numerical Difficulties 117
5-6 Summary 118
Chapter 6 Conclusions 120
6-1 Conclusions 120
6-2 Directions for Future Research 122
References 126
Curriculum Vitae 136

[1]K. N. Tu, Journal of Applied Physics 94, 5451 (2003).
[2]H. B. Huntington, Thin Solid Films 25, 265 (1975).
[3]P. S. Ho, T. Kwok, Reports on Progress in Physics 52, 301 (1989).
[4]A. H. Verbruggen, IBM Journal of Research and Development 32, 93 (1988).
[5]C. Bosvieux, J. Friedel, Journal of Physics and Chemistry of Solids 23, 123 (1962).
[6]R. S. Sorbello, Physical Review B 31, 798 (1985).
[7]R. S. Sorbello, in Solid State Physics, H. Ehrenreich, F. Spaepen, Eds. (Academic Press, 1998), vol. 51, pp. 159-231.
[8]R. Landauer, J. W. F. Woo, Physical Review B 10, 1266 (1974).
[9]I. A. Blech, Journal of Applied Physics 47, 1203 (1976).
[10]I. A. Blech, C. Herring, Applied Physics Letters 29, 131 (1976).
[11]R. J. Gleixner, W. D. Nix, Journal of Applied Physics 86, 1932 (1999).
[12]M. A. Korhonen, P. Borgesen, K. N. Tu, and C. Y. Li, Journal of Applied Physics 73, 3790 (1993).
[13]M. E. Sarychev, Y. V. Zhitnikov, L. Borucki, C. L. Liu, and T. M. Makhviladze, Thin Solid Films 365, 211 (2000).
[14]M. E. Sarychev, Y. V. Zhitnikov, L. Borucki, C. L. Liu, and T. M. Makhviladze, Journal of Applied Physics 86, 3068 (1999).
[15]O. Kraft, E. Arzt, Acta Materialia 46, 3733 (1998).
[16]Rosenber.R, M. Ohring, Journal of Applied Physics 42, 5671 (1971).
[17]W. D. Nix, E. Arzt, Metallurgical Transactions a-Physical Metallurgy and Materials Science 23, 2007 (1992).
[18]R. J. Gleixner, B. M. Clemens, and W. D. Nix, Journal of Materials Research 12, 2081 (1997).
[19]M. R. Gungor, D. Maroudas, International Journal of Fracture 109, 47 (2001).
[20]D. R. Fridline, A. F. Bower, Journal of Applied Physics 85, 3168 (1999).
[21]D. Fridline, A. Bower, Journal of Applied Physics 91, 2380 (2002).
[22]A. F. Bower, S. Shankar, Modelling and Simulation in Materials Science and Engineering 15, 923 (2007).
[23]C. Y. Liu, J. T. Chen, Y. C. Chuang, L. Ke, and S. J. Wang, Applied Physics Letters 90, 112114 (2007).
[24]S. W. Chen, C. M. Chen, Jom-Journal of the Minerals Metals &; Materials Society 55, 62 (2003).
[25]C. M. Chen, S. W. Chen, Acta Materialia 50, 2461 (2002).
[26]C. M. Chen, S. W. Chen, Journal of Electronic Materials 28, 902 (1999).
[27]W. C. Liu, S. W. Chen, and C. M. Chen, Journal of Electronic Materials 27, L5 (1998).
[28]C. M. Chen, S. W. Chen, Journal of Electronic Materials 29, 1222 (2000).
[29]C. M. Chen, S. W. Chen, Journal of Materials Research 18, 1293 (2003).
[30]S. W. Chen, C. M. Chen, and W. C. Liu, Journal of Electronic Materials 27, 1193 (1998).
[31]S. W. Chen, C. H. Wang, Journal of Materials Research 22, 695 (2007).
[32]E. C. C. Yeh, W. J. Choi, K. N. Tu, P. Elenius, and H. Balkan, Applied Physics Letters 80, 580 (2002).
[33]Y. H. Lin, Y. C. Hu, C. M. Tsai, C. R. Kao, and K. N. Tu, Acta Materialia 53, 2029 (2005).
[34]Y. H. Lin, C. M. Tsai, Y. C. Hu, Y. L. Lin, and C. R. Kao, Journal of Electronic Materials 34, 27 (2005).
[35]Y. L. Lin, C. W. Chang, C. M. Tsai, C. W. Lee, and C. R. Kao, Journal of Electronic Materials 35, 1010 (2006).
[36]Y. C. Hu, Y. H. Lin, C. R. Kao, and K. N. Tu, Journal of Materials Research 18, 2544 (2003).
[37]C. Y. Liu, L. Ke, Y. C. Chuang, and S. J. Wang, Journal of Applied Physics 100, 083702 (2006).
[38]L. Y. Zhang, S. Q. Ou, J. Huang, K. N. Tu, S. Gee, and L. Nguyen, Applied Physics Letters 88, 012106 (2006).
[39]C. Chen, H. M. Tong, and K. N. Tu, Annual Review of Materials Research 40, 531 (2010).
[40]H. Gan, K. N. Tu, Journal of Applied Physics 97, 063514 (2005).
[41]C. M. Tsai, Y. L. Lin, J. Y. Tsai, Y. S. Lai, and C. R. Kao, Journal of Electronic Materials 35, 1005 (2006).
[42]J. R. Huang, C. M. Tsai, Y. W. Lin, and C. R. Kao, Journal of Materials Research 23, 250 (2008).
[43]M. Lu, D.-Y. Shih, P. Lauro, C. Goldsmith, and D. W. Henderson, Applied Physics Letters 92, 211909 (2008).
[44]K. Lee, K. S. Kim, Y. Tsukada, K. Suganuma, K. Yamanaka, S. Kuritani, and M. Ueshima, Journal of Materials Research 26, 467 (2011).
[45]K. Lee, K. S. Kim, Y. Tsukada, K. Suganuma, K. Yamanaka, S. Kuritani, and M. Ueshima, Microelectronics Reliability 51, 2290 (2011).
[46]B. F. Dyson, T. R. Anthony, and D. Turnbull, Journal of Applied Physics 38, 3408 (1967).
[47]D. C. Yeh, H. B. Huntington, Physical Review Letters 53, 1469 (1984).
[48]K. Lee, K-S Kim, and K. Suganuma, Journal of Materials Research 26, 2624 (2011).
[49]L. Q. Chen, Annual Review of Materials Research 32, 113 (2002).
[50]K. Thornton, J. Agren, and P. W. Voorhees, Acta Materialia 51, 5675 (2003).
[51]H. Emmerich, Advances in Physics 57, 1 (2008).
[52]Y. Wang, J. Li, Acta Materialia 58, 1212 (2010).
[53]W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Annual Review of Materials Research 32, 163 (2002).
[54]N. Provatas, K. Elder, Phase-field methods in materials science and engineering. (Wiley-VCH, Weinheim, 2010)
[55]J. W. Cahn, J. E. Hilliard, Journal of Chemical Physics 28, 258 (1958).
[56]S. M. Allen, J. W. Cahn, Acta Metallurgica 27, 1085 (1979).
[57]N. Moelans, B. Blanpain, and P. Wollants, Calphad-Computer Coupling of Phase Diagrams and Thermochemistry 32, 268 (2008).
[58]K. Wu, Y. A. Chang, and Y. Wang, Scripta Materialia 50, 1145 (2004).
[59]K. S. Wu, S. L. Chen, F. Zhang, and Y. A. Chang, Journal of Phase Equilibria and Diffusion 30, 571 (2009).
[60]J. Z. Zhu, Z. K. Liu, V. V, and L. Q. Chen, Scripta Materialia 46, 401 (2002).
[61]H.-S. Kim, H.-J. Lee, Y.-S. Yu, and Y.-S. Won, Acta Materialia 57, 1254 (2009).
[62]H.-S. Kim, Y. S. Won, and Y. H. Kwak, Scripta Materialia 62, 29 (2010).
[63]K. K. Hong, J. Y. Huh, Journal of Electronic Materials 35, 56 (2006).
[64]J. Y. Huh, K. K. Hong, Y. B. Kim, and K. T. Kim, Journal of Electronic Materials 33, 1161 (2004).
[65]M. S. Park, R. Arroyave, Journal of Electronic Materials 38, 2525 (2009).
[66]I. Steinbach, F. Pezzolla, Physica D 134, 385 (1999).
[67]S. G. Kim, W. T. Kim, and T. Suzuki, Physical Review E 60, 7186 (1999).
[68]M. S. Park, R. Arroyave, Journal of Electronic Materials 39, 2574 (2010).
[69]M. S. Park, R. Arroyave, Computational Materials Science 50, 1692 (2011).
[70]M. S. Park, R. Arroyave, Acta Materialia 60, 923 (2012).
[71]M. S. Park, S. L. Gibbons, and R. Arroyave, Acta Materialia 60, 6278 (2012).
[72]W. Villanueva, W. J. Boettinger, G. B. McFadden, and J. A. Warren, Acta Materialia 60, 3799 (2012).
[73]M. S. Park, R. Arroyave, Acta Materialia 58, 4900 (2010).
[74]J. F. Li, P. A. Agyakwa, and C. M. Johnson, Acta Materialia 59, 1198 (2011).
[75]M. Mahadevan, R. M. Bradley, Physical Review B 59, 11037 (1999).
[76]M. Mahadevan, R. M. Bradley, Physica D 126, 201 (1999).
[77]D. Kim, W. Lu, Journal of the Mechanics and Physics of Solids 54, 2554 (2006).
[78]D. N. Bhate, A. F. Bower, and A. Kumar, Journal of the Mechanics and Physics of Solids 50, 2057 (2002).
[79]D. N. Bhate, A. Kumar, and A. F. Bower, Journal of Applied Physics 87, 1712 (2000).
[80]F. H. Huang, H. B. Huntington, Physical Review B 9, 1479 (1974).
[81]N. Saunders, A. Miodownik, Journal of Phase Equilibria 11, 278 (1990).
[82]K. N. Tu, Solder joint technology : materials, properties, and reliability. Springer series in materials science (Springer, New York, 2007)
[83]H. T. Orchard, A. L. Greer, Applied Physics Letters 86, 231906 (2005).
[84]P. Gordon, Principles of phase diagrams in materials systems. (McGraw-Hill, New York, 1968)
[85]J. H. Shim, C. S. Oh, B. J. Lee, and D. N. Lee, Zeitschrift fur Metallkunde 87, 205 (1996).
[86]K. W. Moon, W. J. Boettinger, U. R. Kattner, F. S. Biancaniello, and C. A. Handwerker, Journal of Electronic Materials 29, 1122 (2000).
[87]Y. W. Lin, J. H. Ke, H. Y. Chuang, Y. S. Lai, and C. R. Kao, Journal of Applied Physics 107, 073516 (2010).
[88]C. E. Ho, S. C. Yang, and C. R. Kao, Journal of Materials Science-Materials in Electronics 18, 155 (2007).
[89]P. Nash, A. Nash, Journal of Phase Equilibria 6, 350 (1985).
[90]S. W. Chen, C. N. Chiu, and K. C. Hsieh, Journal of Electronic Materials 36, 197 (2007).
[91]I. Karakaya, W. Thompson, Journal of Phase Equilibria 8, 340 (1987).
[92]Y. Xie, Z. Qiao, Journal of Phase Equilibria 17, 208 (1996).
[93]F. Vnuk, M. H. Ainsley, and R. W. Smith, Journal of Materials Science 16, 1171 (1981).
[94]K. Moon, W. Boettinger, U. Kattner, F. Biancaniello, and C. Handwerker, Journal of Electronic Materials 29, 1122 (2000).
[95]B. F. Dyson, Journal of Applied Physics 37, 2375 (1966).
[96]H. Okamoto, T. Massalski, Journal of Phase Equilibria 5, 492 (1984).
[97]L. H. Xu, J. K. Han, J. J. Liang, K. N. Tu, and Y. S. Lai, Applied Physics Letters 92, 262104 (2008).
[98]J. W. Nah, J. O. Suh, K. N. Tu, S. W. Yoon, V. S. Rao, V. Kripesh, and F. Hua, Journal of Applied Physics 100, 123513 (2006).
[99]S. W. Liang, T. L. Shao, C. Chen, E. C. C. Yeh, and K. N. Tu, Journal of Materials Research 21, 137 (2006).
[100]G. C. Xu, F. Guo, X. T. Wang, Z. D. Xia, Y. P. Lei, Y. W. Shi, and X. Y. Li, Journal of Alloys and Compounds 509, 878 (2011).
[101]J. H. Ke, T. L. Yang, Y. S. Lai, and C. R. Kao, Acta Materialia 59, 2462 (2011).
[102]W. J. Deng, K. L. Lin, Y. T. Chiu, and Y. S. Lai, in Electronic Components and Technology Conference (ECTC), 2011.
[103]L. Ma, G. Xu, J. Sun, F. Guo, and X. Wang, Journal of Materials Science 46, 4896 (2011).
[104]C. H. Wang, C. Y. Kuo, H. H. Chen, and S. W. Chen, Intermetallics 19, 75 (2011).
[105]T. C. Chiu, K. L. Lin, Intermetallics 23, 208 (2012).
[106]T. Laurila, V. Vuorinen, and J. K. Kivilahti, Materials Science &; Engineering R-Reports 49, 1 (2005).
[107]T. C. Huang, T. L. Yang, J. H. Ke, C. C. Li, and C. R. Kao, Journal of Alloys and Compounds 555, 237 (2013).
[108]K. J. Zeng, R. Stierman, T. C. Chiu, D. Edwards, K. Ano, and K. N. Tu, Journal of Applied Physics 97, 024508 (2005).
[109]Y. W. Wang, Y. W. Lin, and C. R. Kao, Microelectronics Reliability 49, 248 (2009).
[110]Y. W. Wang, Y. W. Lin, C. T. Tu, and C. R. Kao, Journal of Alloys and Compounds 478, 121 (2009).
[111]J. Yu, J. Y. Kim, Acta Materialia 56, 5514 (2008).
[112]M. Onishi, H. Fujibuchi, Transactions of the Japan Institute of Metals 16, 539 (1975).
[113]A. Hayashi, C. R. Kao, and Y. A. Chang, Scripta Materialia 37, 393 (1997).
[114]J. O. Suh, K. N. Tu, G. V. Lutsenko, and A. M. Gusak, Acta Materialia 56, 1075 (2008).
[115]R. A. Gagliano, M. E. Fine, Journal of Electronic Materials 32, 1441 (2003).
[116]D. Ma, W. D. Wang, and S. K. Lahiri, Journal of Applied Physics 91, 3312 (2002).
[117]V. I. Dybkov, Reaction diffusion and solid state chemical kinetics. (IPMS Publications, Kyiv, 2002)
[118]M. F. Abdulhamid, C. Basaran, Journal of Electronic Packaging 131, 011002 (2009).
[119]H. Y. Chen, C. Chen, and K. N. Tu, Applied Physics Letters 93, 122103 (2008).
[120]H. Y. Chen, C. Chen, Journal of Materials Research 26, 983 (2011).
[121]U. Gosele, K. N. Tu, Journal of Applied Physics 53, 3252 (1982).
[122]H. C. Yu, A. Van der Ven, and K. Thornton, Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science 43A, 3481 (2012).
[123]D. W. Stevens, G. W. Powell, Metallurgical Transactions a-Physical Metallurgy and Materials Science 8, 1531 (1977).
[124]I. Daruka, I. A. Szabo, D. L. Beke, C. S. Cserhati, A. Kodentsov, and F. J. J. vanLoo, Acta Materialia 44, 4981 (1996).
[125]D. L. Beke, I. A. Szabo, Z. Erdelyi, and G. Opposits, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 387, 4 (2004).
[126]A. G. Khachatur&;#65056;i&;#65057;an, Theory of structural transformations in solids. (Wiley, New York, 1983)
[127]J. D. Eshelby, Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 241, 376 (1957).
[128]S. Y. Hu, L. Q. Chen, Acta Materialia 49, 1879 (2001).
[129]Y. U. Wang, Y. M. Jin, and A. G. Khachaturyan, Journal of Applied Physics 92, 1351 (2002).
[130]Y. Shen, Y. Li, Z. H. Li, H. B. Wan, and P. L. Nie, Scripta Materialia 60, 901 (2009).
[131]S. Nemat-Nasser, M. Hori, Micromechanics : overall properties of heterogeneous materials. (Elsevier, Amsterdam ; New York, ed. 2nd rev., 1999)
[132]J. Qu, M. Cherkaoui, Fundamentals of micromechanics of solids. (Wiley, Hoboken, N.J., 2006)
[133]H. Z. Chen, Y. C. Shu, Journal of Applied Physics 113, 123506 (2013).
[134]Y. W. Zhang, A. F. Bower, L. Xia, and C. F. Shih, Journal of the Mechanics and Physics of Solids 47, 173 (1999).
[135]Y. U. Wang, Y. M. Jin, A. M. Cuitino, and A. G. Khachaturyan, Acta Materialia 49, 1847 (2001).
[136]D. Rodney, Y. Le Bouar, and A. Finel, Acta Materialia 51, 17 (2003).
[137]C. Shen, Y. Wang, Acta Materialia 51, 2595 (2003).
[138]F. R. N. Nabarro, Philosophical Magazine 42, 1224 (1951).
[139]T. Mura, Micromechanics of defects in solids. (Distributors the U.S. and Canada, Kluwer Boston, Higham, Mass., 1982)
[140]A. P. Sutton, R. W. Balluffi, Interfaces in crystalline materials. (Oxford University Press, Oxford, 1995)
[141]J. P. Hirth, J. Lothe, Theory of dislocations. (Wiley, New York, ed. 2nd, 1982)
[142]R. Peierls, Proceedings of the Physical Society 52, 34 (1940).
[143]F. R. N. Nabarro, Proceedings of the Physical Society 59, 256 (1947).
[144]M. Peach, J. S. Koehler, Physical Review 80, 436 (1950).
[145]J. Weertman, Philosophical Magazine 11, 1217 (1965).
[146]J. Lothe, J. P. Hirth, Journal of Applied Physics 38, 845 (1967).
[147]R. W. Balluffi, S. M. Allen, W. C. Carter, and R. A. Kemper, Kinetics of Materials. (J. Wiley &; Sons, Hoboken, N.J., 2005)
[148]R. W. Balluffi, physica status solidi (b) 31, 443 (1969).
[149]M. J. Turunen, V. K. Lindroos, Philosophical Magazine 27, 81 (1973).
[150]F. R. N. Nabarro, Philosophical Magazine 16, 231 (1967).
[151]J. R. Manning, Physical Review B 4, 1111 (1971).
[152]L. S. Darken, Transactions of the American Institute of Mining and Metallurgical Engineers 175, 184 (1948).
[153]W. Shockley, Imperfections in nearly perfect crystals : symposium held at pocono manor. (Wiley, New York, 1952)
[154]N. Moelans, Acta Materialia 59, 1077 (2011).
[155]S. Y. Hu, J. Murray, H. Weiland, Z. K. Liu, and L. Q. Chen, Calphad - Computer Coupling of Phase Diagrams and Thermochemistry 31, 303 (2007).