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

Published online by Cambridge University Press:  31 January 2011

Jiunn Chen ,
Yi-Shao Lai ,
Ping-Feng Yang ,
Chung-Yuan Ren  and
Di-Jing Huang
Jiunn Chen*
Affiliation:
Central Labs, Advanced Semiconductor Engineering, Inc., Kaohsiung 81170, Taiwan
Ping-Feng Yang
Affiliation:
Central Labs, Advanced Semiconductor Engineering, Inc., Kaohsiung 81170, Taiwan
Chung-Yuan Ren
Affiliation:
Department of Physics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Di-Jing Huang
Affiliation:
National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
*
a) Address all correspondence to this author. e-mail: [email protected]
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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.

Keywords

CompoundElastic propertiesNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 7 , July 2009 , pp. 2361 - 2372
Copyright
Copyright © Materials Research Society 2009

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References

1Tu, K.N. and Zeng, K.: Tin-lead (SnPb) solder reaction in flip chip technology. Mater. Sci. Eng., R 34, 1 (2001).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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.Google Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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.Google Scholar
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).CrossRefGoogle Scholar
8Holm, B., Ahuja, R., and Johansson, B.: Ab initio calculations of the mechanical properties of Ti3SiC2. Appl. Phys. Lett. 79, 1450 (2001).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
10Ghosh, G.: Elastic properties, hardness, and indentation fracture toughness of intermetallics relevant to electronic packaging. J. Mater. Res. 19, 1439 (2004).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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.Google Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
19Chen, J. and Lai, Y-S.: Towards elastic anisotropy and straininduced void formation in Cu-Sn crystalline phases. Microelectron. Reliab. 49, 264 (2009).CrossRefGoogle Scholar
20Larsson, A.K., Stenberg, L., and Lidin, S.: The superstructure of domain-twinned Cu6Sn5. Acta Crystallogr., Sect. B 50, 636 (1994).CrossRefGoogle Scholar
21Hyde, B. and Andersson, S.: Inorganic Crystal Structures (Wiley, New York, 1989).Google Scholar
22Watanabe, Y., Fujinaga, Y., and Iwasaki, H.: Lattice modulation in the long-period superstructure of Cu3Sn. Acta Crystallogr., Sect. B 39, 306 (1983).CrossRefGoogle Scholar
23Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. A 140, 1133 (1964).CrossRefGoogle Scholar
24Kresse, G. and Hafner, J.: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).CrossRefGoogle ScholarPubMed
25Kresse, G. and Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).CrossRefGoogle Scholar
26Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).CrossRefGoogle ScholarPubMed
27Perdew, J.P., Burke, K., and Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).CrossRefGoogle ScholarPubMed
28Ceperley, D.M. and Alder, B.J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566 (1980).CrossRefGoogle Scholar
29Nye, J.F.: Physical Properties of Crystal (Oxford Science Publications, Oxford, 1985).Google Scholar
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).CrossRefGoogle ScholarPubMed
31Fast, L., Wills, J.M., Johansson, B., and Eriksson, O.: Elastic constants of hexagonal transition metals. Theory Phys. Rev. B 51, 17431 (1995).CrossRefGoogle ScholarPubMed
32Reuss, Z.A.A.: Calculating the limit of Mishkristallen flowing due to the Plastizitatsbeding for monocrystals. Math. Mech. 9, 49 (1929).Google Scholar
33Voigt, W.: Textbook of Crystal Physics (Teubner, Leipzig, 1910).Google Scholar
34Hill, R.: The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. London 65, 350 (1952).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
37Li, X. and Bhushan, B.: A review of nanoindentation continuous stiffness measurement technique and its applications. Mater. Charact. 48, 11 (2002).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle ScholarPubMed
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
45Gilman, J.: Physical chemistry of intrinsic hardness. Mater. Sci. Eng., A 209, 74 (1996).CrossRefGoogle Scholar
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).CrossRefGoogle ScholarPubMed
47Ghosh, G.: First-principle calculation of phase stability and cohesive properties of Ni-Sn intermetallic. Metall Mater. Trans. A 40, 4 (2009).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
49Deng, X., Chawla, N., Chawla, K.K., and Koopman, M.: Deformation behavior of (Cu,Ag)-Sn intermetallics by nanoindentation. Acta Mater. 52, 4291 (2004).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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.Google Scholar
53Cabaret, R., Guillet, L., and LeRoux, R.: The elastic properties of metallic alloys. J. Inst. Met. 75, 391 (1949).Google Scholar
54Ostrovskaya, L.M., Rodin, V.N., and Kuznetsov, A.I.: Soviet J. Non-Ferrous Metall. 26, 90 (1985).Google Scholar
55Burkhardt, W. and Schubert, K.: Z. Metallkd. 50, 442 (1959).Google Scholar