Structural and elastic properties of Cu 6 Sn 5 and Cu 3 Sn from first-principles calculations
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Yi-Shao Li and Ping-Feng Yang Central Labs, Advanced Semiconductor Engineering, Inc., Kaohsiung 81170, Taiwan
Chung-Yuan Ren Department of Physics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Di-Jing Huang National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan (Received 1 December 2008; accepted 6 April 2009)
We investigated the elastic properties of two tin-copper crystalline phases, the Z0 -Cu6Sn5 and e-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 take the microstructure effect that is absent for Cu3Sn. 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.
I. INTRODUCTION
Tin–copper (Sn–Cu) alloys have been used since ancient times. At present, they are attracting considerable interest because the growth of Sn–Cu intermetallic compounds (IMCs) plays an important role in the kinetics of the soldering reaction. In the temperature range of soldering, the interfacial reaction between the molten Snbased solders with Cu-pad finish results in the formation of Sn–Cu crystalline phases: the Z0 -Cu6Sn5 and e-Cu3Sn. The former (hereafter abbreviated as Cu6Sn5) appears as scallop-like grains, and the latter (Cu3Sn) has a layertype microstructure between the Cu6Sn5 and the Cu finish. A robust metallurgical bond is desirable to achieve in the formation of these IMC layers. Their kinetic formation is essential for the integrity of solder joints not only in conventional Sn-Pb but also in Pb-free solder a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0273 J. Mater. Res., Vol. 24, No. 7, Jul 2009
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systems; therefore, these two compounds have been extensively studied over the past decades.1,2 Because the fraction of IMC layer to the total thickness of solder is increasing with the d
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