Mechanical and electronic properties of Ag₃Sn intermetallic compound in lead free solders using ab initio atomistic calculation

First principle calculations based on density functional theory (DFT) are used to calculate the structural, elastic and electronic properties of tin-silver intermetallic compound (Ag₃Sn), found mainly in lead free solder joints. In present work, for the exchange-correlation energy, generalized gradient approximation (GGA) functional is used. The calculated lattice constants are found to be within 2% error of the experimental values. All single crystal elastic constants are computed from which values of shear modulus, bulk modulus, Young's modulus and Poisson's ratio for polycrystalline Ag ₃Sn are calculated using Voigt and Hill approximations. To explain the scatter in the experimentally determined values of elastic constants, directional dependence of bulk modulus and Young's modulus are estimated. The values of Young's modulus calculated along different planes are found to be in same range as experimentally determined values. Various anisotropic indices like universal anisotropic index, Zener anisotropic index, shear anisotropic index and others are calculated to study elastic anisotropy. Further anisotropy in Poisson's ratio is studied by calculating their values along six lower-index planes. The value of Debye temperature calculated using elastic data of present work is found be to higher than the values obtained using resistivity measurement, which can be attributed to temperature dependence. Electronic properties are studied via the band structure and total and partial density of states. The density of state (DOS) of Ag₃Sn has a characteristic main peak which is mainly dominated by Ag-d states. At the Fermi level, the total DOS value is found to be 1.97 states/eV with major contribution coming from Sn p states and minor contribution from Sn s and Ag s, p and d states.