First-Principles Research On Physical Properties Of Sn-Based Intermetallics And Bond-Order Potential Of Sn

Micro-mechanical behavior and thermal property of solder joints should be accurately characterized to resolve the problem about electronics reliability. Recently, solder joints become increasingly small to meet the need of electronics miniaturization, and the volume fraction of intermetallics in solder joints increase. As a result, the solder joint cannot be simplified to an isotropy and homogenous solder alloy. In addition, conventional experimental researches utilize bulk materials as test samples; these researches emphasize the description of macro-phenomena using the top-down mode. However, this type of research has not been enough to obtain insightful view on the properties of micro-scale joints. In this paper, we determined the basic physical properties of the several intermetallics that exist in solder joints on an atomic level using the first-principles method, and established the interatomic potentials that can capture the metallic-covalent bonding characteristics ofβ-Sn crystal exactly; the results enriched the fundamental data and basic theory to investigate the reliability of solder joints. This paper includes the following contents.According to the characteristic of research object, we selected suitable calculation parameters; investigated in detail the relationship between the convergence of calculations and two key parameters, viz. energy cutoffs and k-point divisions; demonstrated the calculation results reliable. Initial geometrical configurations of the intermetallics were proposed by virtue of their real crystal structures, and these configurations were optimized to achieve the equilibrium structures with the predetermined sets of calculation parameters. The calculations showed good agreement with the experimental results, which proves their accuracy further.We set the strain of the optimized equilibrium cells to a finite value by applying a given homogeneous deformation to optimize the internal atomic coordinates and calculate the resulting stress; each of the second-order elastic constants of the single crystals was determined by means of a least-squares linear fit of stress against strain. Polyscrystalline elastic moduli were estimated from the compliance tensor components using the Voit, Reuss, and Voit-Reuss-Hill method, and the Hashin-Shtrikman scheme; the toughness (or brittleness) of the intermetallics was evaluated using the Pugh criterion. At the same time, the Debye temperatures and thermal conductivities were predicted from the calculated elastic constants.Anisotropic mechanical behaviors of these intermetallics were investigated by analyzing the directional dependence of bulk modulus and Young's modulus. The results indicated that virtually all intermetallics possess strong elastic anisotropy, and the anisotropy is not exactly attributable to the crystal symmetry, meaning that the elastic anisotropy of the compounds may be partially responsible for the discrepancy in the reported experimental results.Hydrostatic pressure test was simulated with first-principles method to determine IMC's equation of state, and to investigate the bonding characteristics, electronic structure, and their responses to applied pressures. The results showed that the IMCs are composed of the special interatomic combinations that encompasse both covalent and metallic characteristics, and the elastic anisotropy is caused by the directional character of the covalent bond.An analytical bond-order potential of Sn was proposed on the basis of Tersoff-Brenner model, and that was used to predict the crystal structures, binding energies, bond distances and strengths, and bulk modulus ofβ-Sn and bct-Sn. the potential was also used to calculate phonon DOS and heat capacity ofα-Sn andβ-Sn, and to investigate theα?βphase transition of Sn. All results indicated that the proposed interatomic potential can describe the bonding states of different phases of Sn accurately, and have a good transferability.