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Metallurgical and Materials Transactions A

, Volume 46, Issue 3, pp 1108–1118 | Cite as

Single Crystal Plasticity Finite Element Analysis of Cu6Sn5 Intermetallic

  • Soud Farhan Choudhury
  • Leila Ladani
Article

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.

Keywords

Solder Joint Slip System Crystal Plasticity Critical Resolve Shear Stress Slip Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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.

References

  1. 1.
    F. Ochoa, J.J. Williams, and N. Chawla: J. Electron. Mater., 2003, vol. 32, pp. 1414–20.Google Scholar
  2. 2.
    H. Zou, Q. Zhu, and Z. Zhang: J. Alloys Compd., 2008, vol. 461, pp. 410–17.Google Scholar
  3. 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.Google Scholar
  4. 4.
    M.N. Islam, A. Sharif, and Y.C. Chan: J. Electron. Mater., 2005, vol. 34, pp. 143–49.Google Scholar
  5. 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.Google Scholar
  6. 6.
    T. Laurila, V. Vuorinen, and J.K. Kivilahti: Mater. Sci. Eng. R Rep., 2005, vol. 49, pp. 1–60.Google Scholar
  7. 7.
    S.F. Choudhury and L. Ladani: in ASME 2013 Int. Tech. Conf. Exhib. Packag. Integr. Electron. Photonic Microsystems (ASME), 2013.Google Scholar
  8. 8.
    L. Jiang, H. Jiang, and N. Chawla: J. Electron. Mater., 2012, vol. 41, pp. 2083–88.Google Scholar
  9. 9.
    J.W. Christian and S. Mahajan: Prog. Mater Sci., 1995, vol. 39, pp. 1–157.Google Scholar
  10. 10.
    M.H. Yoo: Metall. Trans. A, 1981, vol. 12A, pp. 409–18.Google Scholar
  11. 11.
    G. Timár and J.Q. da Fonseca: Metall. Mater. Trans. A, 2014, vol. 45A, pp. 5883–90.Google Scholar
  12. 12.
    H. Wang, P.D. Wu, J. Wang, and C.N. Tomé: Int. J. Plast., 2013, vol. 49, pp. 36–52.Google Scholar
  13. 13.
    B. Eidel: Acta Mater., 2011, vol. 59, pp. 1761–71.Google Scholar
  14. 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.Google Scholar
  15. 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.Google Scholar
  16. 16.
    D. Esqué-de los Ojos, J. Očenášek, and J. Alcalá: Comput. Mater. Sci., 2014, vol. 86, pp. 186–92.Google Scholar
  17. 17.
    O. Casals and S. Forest: Comput. Mater. Sci., 2009, vol. 45, pp. 774–82.Google Scholar
  18. 18.
    P. Darbandi, T.R. Bieler, F. Pourboghrat, and T. Lee: J. Electron. Mater., 2012, vol. 42, pp. 201–14.Google Scholar
  19. 19.
    R.J. Asaro and A. Needleman: Acta Metall., 1985, vol. 33, pp. 923–53.Google Scholar
  20. 20.
    E. W. Schmid and W. Boas: 1950.Google Scholar
  21. 21.
    R. Hill and J. R. Rice, J. Mech. Phys. Solids 20, pp. 401–13 (1972).CrossRefGoogle Scholar
  22. 22.
    J. R. Rice, J. Mech. Phys. Solids 19, pp. 433–55 (1971).CrossRefGoogle Scholar
  23. 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. 24.
    E. H. Lee, J. Appl. Mech. 36, pp. 1–6 (1969).CrossRefGoogle Scholar
  25. 25.
    J. Pan and J. R. Rice, Int. J. Solids Struct. 19, 973–87 (1983).CrossRefGoogle Scholar
  26. 26.
    D. Peirce, R. J. Asaro, and A. Needleman, Acta Metall. 30, 1087–1119 (1982).CrossRefGoogle Scholar
  27. 27.
    U.F. Kocks: Metall. Trans., 1970, vol. 1, p. 1121–43.Google Scholar
  28. 28.
    A. Zamiri, T. R. Bieler, and F. Pourboghrat, J. Electron. Mater. 38: 231–40 (2008).CrossRefGoogle Scholar
  29. 29.
    P. Kratochvíl, P. Lukáč, and B. Sprušil, Czechoslov. J. Phys. 23, 621–26 (1973).CrossRefGoogle Scholar
  30. 30.
    H. E. Friedrich and B. L. Mordike, Magnesium Technology: Metallurgy, Design Data, Applications (Springer, 2006), p. 699.Google Scholar
  31. 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.CrossRefGoogle Scholar
  32. 32.
    P. A. Sabnis, S. Forest, N. K. Arakere, and V. A. Yastrebov, Int. J. Plast. 51, 200–217 (2013).CrossRefGoogle Scholar
  33. 33.
    L. Li, L. Shen, G. Proust, C. K. S. Moy, and G. Ranzi, Mater. Sci. Eng. A 579, 41–49 (2013).CrossRefGoogle Scholar
  34. 34.
    S. F. Choudhury and L. Ladani, J. Electron. Mater. 43, 996–1004 (2014).CrossRefGoogle Scholar
  35. 35.
    C. Zambaldi, Y. Yang, T. R. Bieler, and D. Raabe, J. Mater. Res. 27, 356–67 (2011).CrossRefGoogle Scholar
  36. 36.
    J. Gong and A. J. Wilkinson, Acta Mater. 57, pp. 5693–5705 (2009).CrossRefGoogle Scholar
  37. 37.
    M. H. Yoo, S. R. Agnew, J. R. Morris, and K. M. Ho, Mater. Sci. Eng. A 321, pp. 87–92 (2001).CrossRefGoogle Scholar
  38. 38.
    K. Ito and V. Vitek, Philos. Mag. A 81, 1387–1407 (2001).CrossRefGoogle Scholar
  39. 39.
    X.-L. Nan, H.-Y. Wang, L. Zhang, J.-B. Li, and Q.-C. Jiang: Scripta Mater. 67, 443–46 (2012).CrossRefGoogle Scholar
  40. 40.
    A. Chapuis and J. H. Driver, Acta Mater. 59, 1986–94 (2011).CrossRefGoogle Scholar
  41. 41.
    Y. B. Chun and C. H. J. Davies, Mater. Sci. Eng. A 528, 3489–95 (2011).CrossRefGoogle Scholar
  42. 42.
    Y. N. Wang and J. C. Huang, Acta Mater. 55, 897–905 (2007).CrossRefGoogle Scholar
  43. 43.
    A. Gangulee, G. C. Das, and M. B. Bever, Metall. Trans. 4, 2063–66 (1973).CrossRefGoogle Scholar
  44. 44.
    M. Dao, N. Chollacoop, K. J. Van Vliet, T. a. Venkatesh, and S. Suresh, Acta Mater. 49, 3899–3918 (2001).CrossRefGoogle Scholar
  45. 45.
    A. K. Bhattacharya and W. D. Nix, Int. J. Solids Struct. 24, 881–91 (1988).CrossRefGoogle Scholar
  46. 46.
    N. T. S. Lee, V. B. C. Tan, and K. M. Lim, Appl. Phys. Lett. 88, 031913 (2006).CrossRefGoogle Scholar
  47. 47.
    U. Borg and J. W. Kysar, Int. J. Solids Struct. 44, 6382–97 (2007).CrossRefGoogle Scholar
  48. 48.
    F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler, and D. Raabe, Acta Mater. 58, 1152–1211. (2010).CrossRefGoogle Scholar
  49. 49.
    J.-M. Song, Y.-L. Shen, C.-W. Su, Y.-S. Lai, and Y.-T. Chiu, Mater. Trans. 50, 1231–34 (2009).CrossRefGoogle Scholar
  50. 50.
    M. Liu, C. Lu, and K. A. Tieu: in TMS 2014 Ann. Meet. Suppl. Proc., 2014, vol. 317, pp. 317–37Google Scholar
  51. 51.
    O. Casals, J. Ocenasek, and J. Alcala, Acta Mater. 55, 55–68 (2007).CrossRefGoogle Scholar
  52. 52.
    G. M. Pharr and A. Bolshakov, J. Mater. Res. 17, 2660–71 (2011).CrossRefGoogle Scholar
  53. 53.
    K. L. Johnson and K. L. Johnson, Contact Mechanics (Cambridge University Press, 1987), pp. 1–452.Google Scholar
  54. 54.
    Y. Liu, S. Varghese, J. Ma, M. Yoshino, H. Lu, and R. Komanduri, Int. J. Plast. 24, 1990–2015 (2008).CrossRefGoogle Scholar
  55. 55.
    W. G. Mao, Y. G. Shen, and C. Lu, J. Eur. Ceram. Soc. 31, 1865–71 (2011).CrossRefGoogle Scholar
  56. 56.
    G. Ghosh and M. Asta, J. Mater. Res. 20, 3102–17 (2005).CrossRefGoogle Scholar
  57. 57.
    Q. K. Zhang, J. Tan, and Z. F. Zhang, J. Appl. Phys. 110, 014502 (2011).CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of ConnecticutStorrsUSA

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