Elastic properties of (Cu,Ni)₆SN₅ ternary crystal structure using first-principle approach

The Cu₆Sn₅ intermetallic compound (IMC) is an important interfacial reactive product in electronic packaging. The properties of Cu₆Sn₅ have been demonstrated to be crucial to the interface reliability at the solder interconnections. Due to the element inter-diffusion between the packaging side and PCB (printed circuit board) side during soldering process, a ternary Cu₆Sn₅-based Cu-Ni-Sn intermetallic compound is often generated. This ternary phase exhibits a similar crystal structure as Cu₆Sn₅ phase, in which the Ni atoms are regarded as the solubility by replacing the Cu atoms. Therefore, this CuNi-Sn ternary phase is labeled as (Cu_6-x, Ni_x)Sn ₅. It has been found that the Cu₆Sn₅ unit cell consists of 44 atoms, in which 24 atoms are Cu and 20 atoms are Sn. The 24 Cu atoms occupy 4a, 4e, 8f1 and 8f2 sites, while 20 Sn atoms occupy 4e, 8f1 and 8f2 sites. The reported experimental results are quite sparse and thus a fundamental calculation is required. In this paper, the elastic stiffness of (Cu_6-x, Ni_x)Sn₅ crystal structure is calculated based on the first-principle approach within density functional theory. The results indicate that Cu₆Sn₅ phase show a nearly isotropic elasticity. However for the phase Cu5NilSn5 (x = 1) where Ni atom at 4a space site, the elasticity shows slightly anisotropic. With the Ni solubility increase (x=2), the anisotropic elasticity of Cu4Ni2Sn5 phase becomes profound. The density of states (DOS) and partial density of states (PDOS) from individual element contributions, as well as the hybridization between the element states are simulated herein to reveal the mechanism of the anisotropic elasticity of (Cu_6-x, Ni_x)Sn₅ phase due to the occupancy of Ni atoms.