First-principles calculations of elastic properties of Cu3Sn superstructure

Abstract

We report the elastic properties of Cu3Sn superstructure based on first-principles calculations. Polycrystalline Young’s modulus and Poisson’s ratio are deduced from the calculated elastic stiffness. The calculations of electronic structures with the principal strains along different directions unravel the electronic nature of anisotropic elasticity of Cu3Sn. Weak Sn–Cu bonding in Cu3Sn suggests that Sn atoms are the dominant diffusion species, revealing the mechanism of vacancy formation within the Cu3Sn superstructure.

Crystal size and direction dependence of the elastic properties of Cu3Sn through molecular dynamics simulation and nanoindentation testing

“…The converged values of the elastic moduli of the Cu 3 Sn monocrystals are about E 1 = 129.9 GPa, E 2 = 131.6 GPa and E 3 = 99.0 GPa along the three orthorhombic axes, and the corresponding shear moduli are G 12 = 66.2 GPa, G 13 = 40.5 GPa and G 23 = 58.5 GPa, in which the subscripts 1, 2 and 3 denote the orthorhombic axes a, b and c. It is evident that the Cu 3 Sn monocrystal exhibits a strong elastic anisotropy, where the strongest tensile strength exists in the b orthorhombic axis and the weakest one in the c orthorhombic axis, and the strongest shear strength in the a-b plane and the weakest one in the a-c plane. The comparison between the present calculation results and the published data [16], obtained from first-principles calculations, is shown in Table 4. There is only about 1-10% difference between them.…”

“…On the other hand, recent great progress in computational methods has allowed the predictions of the mechanical properties of nanocrystals through firstprinciples calculations based on density functional theory (DFT) [15]. For example, Chen et al [16] performed density functional theory (DFT) calculations within the generalized-gradient approximation (GGA) [17] using the Vienna Ab-initio Simulation Package (VASP) [18] to assess the elastic properties of Cu 3 Sn monocrystal. Pang et al [19] carried out first-principles calculations based on the plane wave pseudo-potential method of DFT, combining with GGA, as implemented in the DACAPO™ package [20] to investigate the elastic properties of single crystal Cu 3 Sn.…”

“…To the authors' best knowledge, this would be the first study examining the topic using MD simulation. The calculated elastic properties of the monocrystals are compared with the literature data obtained from first-principles calculations [16]. Furthermore, first-principles calculations based on DFT are also performed to investigate the electronic structure of the single crystal.…”

Electromigration Reliability and Morphologies of Cu Pillar Flip-Chip Solder Joints with Cu Substrate Pad Metallization

“…8b that Cu 3 Sn phases closely attached to the Cu pillar, (Cu,Ni) 6 Sn 5 , and Ni at the location where Ni was 18 proposed that (Cu,Ni) 6 Sn 5 may share a monoclinic lattice structure similar to that of Cu 6 Sn 5 , which is considered to be structurally unstable compared to the face-centered cubic (FCC) close-packed lattice structure of Cu 3 Sn. 19 It is well known that g-Cu 6 Sn 5 undergoes a transformation into e-Cu 3 Sn by the requirement of thermodynamic equilibrium in conventional Sn-Pb solder systems. Although to the best of our knowledge, theoretical calculations on the thermodynamics of ternary Sn-Ag-Cu solder systems are currently unavailable, similar formation kinetics may also account for the observed Cu 3 Sn in Fig.…”

Nanotribological Characteristics of Cu6Sn5, Cu3Sn, and Ni3Sn4 Intermetallic Compounds

“…The nanoindentation technique, [9][10][11][12][13][14][15][16][17] on the other hand, has been shown to be capable of capturing feasible YoungÕs moduli and hardnesses of these IMCs. [18][19][20] Our intention in our work here was to investigate further the nanotribological behaviors of Cu 6 Sn 5 , Cu 3 Sn, and Ni 3 Sn 4 binary IMCs, following the nanoscratch technique. Understanding the tribological behavior is beneficial to the prevention of losses resulting from wear and friction on the surface of the material.…”