Skip to main content Accessibility help
×
Home

Structural and elastic properties of Cu6Sn5 and Cu3Snfrom first-principles calculations

  • Jiunn Chen (a1), Yi-Shao Lai, Ping-Feng Yang (a1), Chung-Yuan Ren (a2) and Di-Jing Huang (a3)...

Abstract

We investigated the elastic properties of two tin-copper crystalline phases, the η′-Cu6Sn5 and ε-Cu3Sn, which are often encountered in microelectronic packaging applications. The full elastic stiffness of both phases is determined based on strain-energy relations using first-principles calculations. The computed results show the elastic anisotropy of both phases that cannot be resolved from experiments. Our results, suggesting both phases have the greatest stiffness along the c direction, particularly showed the unique in-plane elastic anisotropy associated with the lattice modulation of the Cu3Sn superstructure. The polycrystalline moduli obtained using the Voigt-Reuss scheme are 125.98 GPa for Cu6Sn5 and 134.16 GPa for Cu3Sn. Our data analysis indicates that the smaller elastic moduli of Cu6Sn5 are attributed to the direct Sn–Sn bond in Cu6Sn5. We reassert the elastic modulus and hardness of both phases using the nanoindentation experiment for our calculation benchmark. Interestingly, the computed polycrystalline elastic modulus of Cu6Sn5 seems to be overestimated, whereas that of Cu3Sn falls nicely in the range of reported data. Based on the observations, the elastic modulus of Cu6Sn5 obtained from nanoindentation tests admit the microstructure effect that is absent for Cu3Sn is concluded. Our analysis of electronic structure shows that the intrinsic hardness and elastic modulus of both phases are dominated by electronic structure and atomic lattice structure, respectively.

Copyright

Corresponding author

a) Address all correspondence to this author. e-mail: asesrrc@gmail.com

References

Hide All
1Tu, K.N. and Zeng, K.: Tin-lead (SnPb) solder reaction in flip chip technology. Mater. Sci. Eng., R 34, 1 (2001).
2Laurila, T., Vuoriene, V., and Kivilahti, J.K.: Interfacial reactions between lead-free solders and common base material. Mater. Sci. Eng., R 49, 1 (2005).
3Nakamura, M.: Intermetallic Compounds, vol. 2 (reprint volumes), edited by Westbrook, J.H. and Fleischer, R.L. (John Wiley and Sons, London, UK, 1995), p. 2.
4Ravindran, P., Fast, L., Korzhavyi, P.A., and Johansson, B.: Densityfunctional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2. J. Appl. Phys. 84, 4891 (1998).
5Panda, K.B. and Chandran, K.S.R.: Determination of elastic constant of titanium diboride (TiB2) from first principles using FLAPW implementation of the density-functional theory. Comput. Mater. Sci. 35, 134 (2006).
6Mehl, M.J., Klein, B.M., and Papaconstantantopoulos, D.A.: Intermetallic Compounds: Principles and Practice, vol. 1, edited by Massalski, T.B. (John Wiley and Sons, London, UK, 1965), p. 295.
7Ikehata, H., Nagasako, N., Furuta, T., Fukumoto, A., Miwa, K., and Saito, T.: First-principles calculations for development of low elastic modulus Ti alloys. Phys. Rev. B 70, 174113 (2004).
8Holm, B., Ahuja, R., and Johansson, B.: Ab initio calculations of the mechanical properties of Ti3SiC2. Appl. Phys. Lett. 79, 1450 (2001).
9Sun, Z., Ahuja, R., Li, S., and Schneider, J.M.: Structure and bulk modulus of M2AlC (M=Ti, V, and Cr). Appl. Phys. Lett. 83, 899 (2003).
10Ghosh, G.: Elastic properties, hardness, and indentation fracture toughness of intermetallics relevant to electronic packaging. J. Mater. Res. 19, 1439 (2004).
11Ghosh, G. and Asta, M.: Phase stability, phase transformations, and elastic properties of Cu6Sn5: Ab initio calculations and experimental results. J. Mater. Res. 20, 3102 (2005).
12Lee, N.T.S., Tan, V.B.C., and Lim, K.M.: First-principle calculations of structural and mechanical properties of Cu6Sn5. Appl. Phys. Lett. 88, 031913 (2006).
13An, R., Wang, C., Tian, Y., and Wu, H.: Determination of the elastic properties of Cu3Sn through first-principles calculations. J. Electron. Mater. 37, 477 (2008).
14Pang, X.Y., Wang, S.Q., Zhang, L., Liu, Z.Q., and Shang, J.K.: First principles calculation of elastic and lattice constants of orthorhombic Cu3Sn crystal. J. Alloys Compd. 466, 517 (2008).
15Chen, J., Lai, Y-S, and Yang, P-F.: First-principles calculations of elastic properties of Cu-Sn crystalline phases, in Proceedings of IMPACT 2007 (2nd Int. Microsystems, Packaging, Assembly, and Circuits Technology Conf., Taipei, Taiwan, 2007), p. 193.
16Chen, J., Lai, Y-S., Ren, C-Y., and Huang, D-J.: First-principles calculations of elastic properties of Cu3Sn superstructure. Appl. Phys. Lett. 92, 081901 (2008).
17Yu, C., Liu, J., Lu, H., Li, P., and Chen, J.: First-principles investigations of the structural and electronic properties of Cu6-xNixSn5 intermetallic compounds. Intermetallics 15, 1471 (2007).
18Yu, H., Vuorinen, V., and Kivilahti, J.: Effect of Ni on the formation of Cu6Sn5 and Cu3Sn intermetallics. IEEE Trans. Electron. Packag. Manuf. 30, 293 (2007).
19Chen, J. and Lai, Y-S.: Towards elastic anisotropy and straininduced void formation in Cu-Sn crystalline phases. Microelectron. Reliab. 49, 264 (2009).
20Larsson, A.K., Stenberg, L., and Lidin, S.: The superstructure of domain-twinned Cu6Sn5. Acta Crystallogr., Sect. B 50, 636 (1994).
21Hyde, B. and Andersson, S.: Inorganic Crystal Structures (Wiley, New York, 1989).
22Watanabe, Y., Fujinaga, Y., and Iwasaki, H.: Lattice modulation in the long-period superstructure of Cu3Sn. Acta Crystallogr., Sect. B 39, 306 (1983).
23Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. A 140, 1133 (1964).
24Kresse, G. and Hafner, J.: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).
25Kresse, G. and Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).
26Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
27Perdew, J.P., Burke, K., and Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
28Ceperley, D.M. and Alder, B.J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566 (1980).
29Nye, J.F.: Physical Properties of Crystal (Oxford Science Publications, Oxford, 1985).
30Söderlind, P., Eriksson, O., Wills, J.M., and Boring, A.M.: Theory of elastic constants of cubic transition metals and alloys. Phys. Rev. B 48, 5844 (1993).
31Fast, L., Wills, J.M., Johansson, B., and Eriksson, O.: Elastic constants of hexagonal transition metals. Theory Phys. Rev. B 51, 17431 (1995).
32Reuss, Z.A.A.: Calculating the limit of Mishkristallen flowing due to the Plastizitatsbeding for monocrystals. Math. Mech. 9, 49 (1929).
33Voigt, W.: Textbook of Crystal Physics (Teubner, Leipzig, 1910).
34Hill, R.: The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. London 65, 350 (1952).
35Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).
36Yang, P-F., Lai, Y-S., Jian, S-R., Chen, J., and Chen, R-S.: Nanoindentation identifications of mechanical properties of Cu6Sn5, Cu3Sn, and Ni3Sn4 intermetallic compounds derived by diffusion couples. Mater. Sci. Eng., A 485, 305 (2008).
37Li, X. and Bhushan, B.: A review of nanoindentation continuous stiffness measurement technique and its applications. Mater. Charact. 48, 11 (2002).
38Kim, H.K., Liou, H.K., and Tu, K.N.: Three-dimensional morphology of a very rough interface formed in the soldering reaction between eutectic SnPb and Cu. Appl. Phys. Lett. 66, 2337 (1995).
39Ma, D., Wang, W.D., and Lahiri, S.K.: Scallop formation and dissolution of Cu-Sn intermetallic compound using solder reflow. J. Appl. Phys. 91, 3312 (2002).
40Suh, J.O., Tu, K.N., and Tamura, N.: Dramatic morphological change of scallop-type Cu6Sn5 formed on (001) single crystal copper in reaction between molten SnPb solder and Cu. Appl. Phys. Lett. 91, 051907 (2007).
41Kim, H.K. and Tu, K.N.: Kinetic analysis of the soldering reaction between eutectic SnPb alloy and Cu accompanied by ripening. Phys. Rev. B 53, 16027 (1996).
42Suh, J.O., Tu, K.N., Lutsenko, G.V., and Gusak, A.M.: Size distribution and morphology of Cu6Sn5 scallops in wetting reaction between molten solder and copper. Acta Mater. 56, 1075 (2008).
43Clerc, D.G. and Ledbetter, H.M.: Mechanical hardness: A semiempirical theory based on screened electrostatics and elastic shear. J. Phys. Chem. Solids 59, 1071 (1998).
44Jhi, S-H., Ihm, J., Louie, S.G., and Cohen, M.L.: Electronic mechanism of hardness enhancement in transition-metal carbonitrides. Nature 399, 132 (1999).
45Gilman, J.: Physical chemistry of intrinsic hardness. Mater. Sci. Eng., A 209, 74 (1996).
46Gao, F., He, J., Wu, E., Liu, S., Yu, D., Li, D., Zhang, S., and Tian, Y.: Hardness of covalent crystals. Phys. Rev. Lett. 91, 015502 (2003).
47Ghosh, G.: First-principle calculation of phase stability and cohesive properties of Ni-Sn intermetallic. Metall Mater. Trans. A 40, 4 (2009).
48Deng, X., Koopman, M., Chawla, N., and Chawla, K.K.: Young's modulus of (Cu,Ag)-Sn intermetallics measured by nanoindentation. Mater. Sci. Eng., A 364, 240 (2004).
49Deng, X., Chawla, N., Chawla, K.K., and Koopman, M.: Deformation behavior of (Cu,Ag)-Sn intermetallics by nanoindentation. Acta Mater. 52, 4291 (2004).
50Jang, G-Y., Lee, J-W., and Duh, J-G.: The nanoindentation characteristics of Cu6Sn5, Cu3Sn, and Ni3Sn4 intermetallic compounds in the solder bump. J. Electron. Mater. 33, 1103 (2004).
51Chromik, R.R., Vinci, R.P., Allen, S.L., and Notis, M.R.: Nanoindentation measurements on Cu-Sn and Ag-Sn intermetallics formed in Pb-free solder joints. J. Mater. Res. 18, 2251 (2003).
52Field, R.J., Low, S.R. III and Lucey, J.G.K.: Metal Science of Joining, edited by Cieslak, M.J., Perepezko, J.H., Kang, S., and Glicksman, M.E. (TMS, Warrendale, PA, 1991), pp. 165–174.
53Cabaret, R., Guillet, L., and LeRoux, R.: The elastic properties of metallic alloys. J. Inst. Met. 75, 391 (1949).
54Ostrovskaya, L.M., Rodin, V.N., and Kuznetsov, A.I.: Soviet J. Non-Ferrous Metall. 26, 90 (1985).
55Burkhardt, W. and Schubert, K.: Z. Metallkd. 50, 442 (1959).

Keywords

Structural and elastic properties of Cu6Sn5 and Cu3Snfrom first-principles calculations

  • Jiunn Chen (a1), Yi-Shao Lai, Ping-Feng Yang (a1), Chung-Yuan Ren (a2) and Di-Jing Huang (a3)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed