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Single Crystal Plasticity Finite Element Analysis of Cu6Sn5 Intermetallic

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Abstract

Due to the miniaturization of the solder joints in micro/nanoelectronic devices, the volume ratio of intermetallic (IMCs) materials has substantially increased. This increased ratio could affect the reliability of solder joints depending on the regime and the rate of the loading. Cu6Sn5 is the primary IMC layer in the solder joint, and the primary crack initiation is observed in Cu6Sn5 site in the literature. As the size of the joints becomes closer to the grain size, joints may only contain a few numbers of grains of Cu6Sn5. This manifests itself in statistical grain size effects, as well as anisotropy. Modeling these joints using bulk properties of Cu6Sn5 does not capture the actual behavior of these joints especially when plastic deformation is involved. Plastic deformation, starting at yield point, happens to be associated with the activation of slip systems. Deformation of a slip system of single crystal largely rests on the slip parameters such as critical resolved shear stress (CRSS), initial hardening modulus, and saturation stress (Stage I stress when large plastic flow occurs). However, no efforts have been made to capture the slip parameters of Cu6Sn5 experimentally or analytically because of the difficulties of using conventional mechanical tests to measure the slip parameters of HCP single crystals. Due to wide range of CRSS values, it becomes difficult to isolate a specific slip system in testing without activating the other slip systems. The crystal plasticity finite-element (CPFE) method takes into account the effect of anisotropy and slip system behavior in modeling materials. This work uses a combined strategy based upon experiments, modeling, and a comparative analysis to obtain slip system parameters that could predict the slip process of Cu6Sn5. Nanoindentation tests were performed on Cu6Sn5 single crystal to extract the load–displacement curves, and a CPFE nanoindentation model analysis along with custom user material was utilized to obtain set of crystal plasticity material parameters which can represent the plastic behavior of Cu6Sn5 IMC. These parameters were then used to predict shear yield strength and shear modulus of Cu6Sn5, and the findings were compared with the previously published values in the literature.

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References

  1. F. Ochoa, J.J. Williams, and N. Chawla: J. Electron. Mater., 2003, vol. 32, pp. 1414–20.

  2. H. Zou, Q. Zhu, and Z. Zhang: J. Alloys Compd., 2008, vol. 461, pp. 410–17.

  3. I. Panchenko, J. Grafe, M. Mueller, and K.-J. Wolter: IEEE 15th Electron. Packag. Technol. Conf. (EPTC 2013), 2013, vol. 318, pp. 318–23.

  4. M.N. Islam, A. Sharif, and Y.C. Chan: J. Electron. Mater., 2005, vol. 34, pp. 143–49.

  5. J.-M. Song, B.-R. Huang, C.-Y. Liu, Y.-S. Lai, Y.-T. Chiu, and T.-W. Huang: Mater. Sci. Eng. A, 2012, vol. 534, pp. 53–59.

  6. T. Laurila, V. Vuorinen, and J.K. Kivilahti: Mater. Sci. Eng. R Rep., 2005, vol. 49, pp. 1–60.

  7. S.F. Choudhury and L. Ladani: in ASME 2013 Int. Tech. Conf. Exhib. Packag. Integr. Electron. Photonic Microsystems (ASME), 2013.

  8. L. Jiang, H. Jiang, and N. Chawla: J. Electron. Mater., 2012, vol. 41, pp. 2083–88.

  9. J.W. Christian and S. Mahajan: Prog. Mater Sci., 1995, vol. 39, pp. 1–157.

  10. M.H. Yoo: Metall. Trans. A, 1981, vol. 12A, pp. 409–18.

  11. G. Timár and J.Q. da Fonseca: Metall. Mater. Trans. A, 2014, vol. 45A, pp. 5883–90.

  12. H. Wang, P.D. Wu, J. Wang, and C.N. Tomé: Int. J. Plast., 2013, vol. 49, pp. 36–52.

  13. B. Eidel: Acta Mater., 2011, vol. 59, pp. 1761–71.

  14. Y.S. Choi, M.A. Groeber, P.A. Shade, T.J. Turner, J.C. Schuren, D.M. Dimiduk, M.D. Uchic, and A.D. Rollett: Metall. Mater. Trans. A, 2014, vol. 45A, pp. 6352–59.

  15. M.G. Lee, H. Lim, B.L. Adams, J.P. Hirth, and R.H. Wagoner: Int. J. Plast., 2010, vol. 26, pp. 925–38.

  16. D. Esqué-de los Ojos, J. Očenášek, and J. Alcalá: Comput. Mater. Sci., 2014, vol. 86, pp. 186–92.

  17. O. Casals and S. Forest: Comput. Mater. Sci., 2009, vol. 45, pp. 774–82.

  18. P. Darbandi, T.R. Bieler, F. Pourboghrat, and T. Lee: J. Electron. Mater., 2012, vol. 42, pp. 201–14.

  19. R.J. Asaro and A. Needleman: Acta Metall., 1985, vol. 33, pp. 923–53.

  20. E. W. Schmid and W. Boas: 1950.

  21. R. Hill and J. R. Rice, J. Mech. Phys. Solids 20, pp. 401–13 (1972).

    Article  Google Scholar 

  22. J. R. Rice, J. Mech. Phys. Solids 19, pp. 433–55 (1971).

    Article  Google Scholar 

  23. Y. Huang: A User-material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program, Mech Report 178, Harvard University, Cambridge, MA, 1991. http://scholar.google.com/scholar?hl=en&q=huang+umat&btnG=&as_sdt=1%2C7&as_sdtp=

  24. E. H. Lee, J. Appl. Mech. 36, pp. 1–6 (1969).

    Article  Google Scholar 

  25. J. Pan and J. R. Rice, Int. J. Solids Struct. 19, 973–87 (1983).

    Article  Google Scholar 

  26. D. Peirce, R. J. Asaro, and A. Needleman, Acta Metall. 30, 1087–1119 (1982).

    Article  Google Scholar 

  27. U.F. Kocks: Metall. Trans., 1970, vol. 1, p. 1121–43.

    Google Scholar 

  28. A. Zamiri, T. R. Bieler, and F. Pourboghrat, J. Electron. Mater. 38: 231–40 (2008).

    Article  Google Scholar 

  29. P. Kratochvíl, P. Lukáč, and B. Sprušil, Czechoslov. J. Phys. 23, 621–26 (1973).

    Article  Google Scholar 

  30. H. E. Friedrich and B. L. Mordike, Magnesium Technology: Metallurgy, Design Data, Applications (Springer, 2006), p. 699.

    Google Scholar 

  31. Y. Yang, L. Wang, C. Zambaldi, P. Eisenlohr, R. Barabash, W. Liu, M.R. Stoudt, M.A. Crimp, and T.R. Bieler: JOM, 2011, vol. 63, pp. 66–73.

    Article  Google Scholar 

  32. P. A. Sabnis, S. Forest, N. K. Arakere, and V. A. Yastrebov, Int. J. Plast. 51, 200–217 (2013).

    Article  Google Scholar 

  33. L. Li, L. Shen, G. Proust, C. K. S. Moy, and G. Ranzi, Mater. Sci. Eng. A 579, 41–49 (2013).

    Article  Google Scholar 

  34. S. F. Choudhury and L. Ladani, J. Electron. Mater. 43, 996–1004 (2014).

    Article  Google Scholar 

  35. C. Zambaldi, Y. Yang, T. R. Bieler, and D. Raabe, J. Mater. Res. 27, 356–67 (2011).

    Article  Google Scholar 

  36. J. Gong and A. J. Wilkinson, Acta Mater. 57, pp. 5693–5705 (2009).

    Article  Google Scholar 

  37. M. H. Yoo, S. R. Agnew, J. R. Morris, and K. M. Ho, Mater. Sci. Eng. A 321, pp. 87–92 (2001).

    Article  Google Scholar 

  38. K. Ito and V. Vitek, Philos. Mag. A 81, 1387–1407 (2001).

    Article  Google Scholar 

  39. X.-L. Nan, H.-Y. Wang, L. Zhang, J.-B. Li, and Q.-C. Jiang: Scripta Mater. 67, 443–46 (2012).

    Article  Google Scholar 

  40. A. Chapuis and J. H. Driver, Acta Mater. 59, 1986–94 (2011).

    Article  Google Scholar 

  41. Y. B. Chun and C. H. J. Davies, Mater. Sci. Eng. A 528, 3489–95 (2011).

    Article  Google Scholar 

  42. Y. N. Wang and J. C. Huang, Acta Mater. 55, 897–905 (2007).

    Article  Google Scholar 

  43. A. Gangulee, G. C. Das, and M. B. Bever, Metall. Trans. 4, 2063–66 (1973).

    Article  Google Scholar 

  44. M. Dao, N. Chollacoop, K. J. Van Vliet, T. a. Venkatesh, and S. Suresh, Acta Mater. 49, 3899–3918 (2001).

    Article  Google Scholar 

  45. A. K. Bhattacharya and W. D. Nix, Int. J. Solids Struct. 24, 881–91 (1988).

    Article  Google Scholar 

  46. N. T. S. Lee, V. B. C. Tan, and K. M. Lim, Appl. Phys. Lett. 88, 031913 (2006).

    Article  Google Scholar 

  47. U. Borg and J. W. Kysar, Int. J. Solids Struct. 44, 6382–97 (2007).

    Article  Google Scholar 

  48. F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler, and D. Raabe, Acta Mater. 58, 1152–1211. (2010).

    Article  Google Scholar 

  49. J.-M. Song, Y.-L. Shen, C.-W. Su, Y.-S. Lai, and Y.-T. Chiu, Mater. Trans. 50, 1231–34 (2009).

    Article  Google Scholar 

  50. M. Liu, C. Lu, and K. A. Tieu: in TMS 2014 Ann. Meet. Suppl. Proc., 2014, vol. 317, pp. 317–37

  51. O. Casals, J. Ocenasek, and J. Alcala, Acta Mater. 55, 55–68 (2007).

    Article  Google Scholar 

  52. G. M. Pharr and A. Bolshakov, J. Mater. Res. 17, 2660–71 (2011).

    Article  Google Scholar 

  53. K. L. Johnson and K. L. Johnson, Contact Mechanics (Cambridge University Press, 1987), pp. 1–452.

    Google Scholar 

  54. Y. Liu, S. Varghese, J. Ma, M. Yoshino, H. Lu, and R. Komanduri, Int. J. Plast. 24, 1990–2015 (2008).

    Article  Google Scholar 

  55. W. G. Mao, Y. G. Shen, and C. Lu, J. Eur. Ceram. Soc. 31, 1865–71 (2011).

    Article  Google Scholar 

  56. G. Ghosh and M. Asta, J. Mater. Res. 20, 3102–17 (2005).

    Article  Google Scholar 

  57. Q. K. Zhang, J. Tan, and Z. F. Zhang, J. Appl. Phys. 110, 014502 (2011).

    Article  Google Scholar 

Download references

Acknowledgments

This paper is based upon work supported by the National Science Foundation under CMMI Grant No. 1242141, 1415165, 1416682, and 0927319. The authors greatly appreciate the support from NSF. The authors would like to acknowledge the central Analytical Facility which is supported by The University of Alabama, for providing the SEM and EBSD facility. The UA MINT center is acknowledged for the use of nanoindentation equipment.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Connecticut, Storrs, CT, 06269-3139, USA

    Soud Farhan Choudhury (Graduate Student) & Leila Ladani (Associate Professor)

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  1. Soud Farhan Choudhury
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  2. Leila Ladani
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Correspondence to Soud Farhan Choudhury.

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Manuscript submitted July 22, 2014.

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Choudhury, S.F., Ladani, L. Single Crystal Plasticity Finite Element Analysis of Cu6Sn5 Intermetallic. Metall Mater Trans A 46, 1108–1118 (2015). https://doi.org/10.1007/s11661-014-2696-0

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