A New Ion Diffusion Model Applied to Lead-free Solder*

The spread of Lead-free solder based on Sn-Cu alloy has been long prevented by the joint cracking on Cu board, which is known to be caused by Kirkendall effect. This work evaluated the diffusion coefficient of Cu ion in ε-Cu₃Sn from ab initio approach, which has been realized, for the first time, by introducing our own modeling. So far the applications of ab initio calculation for ion vacancy diffusion have been restricted to just simplest crystals like FCC, BCC, and HCP. ε-Cu₃Sn has, however, rather complex structure and also long-range periodicity. To overcome the difficulties coming from them, we reached a new understanding for the long-range structure and then established an insightful approximation to reduce the complexity of the structure based on the diffusion barriers for the possible ion jumps, calculated by climbing-NEB (nudged elastic band) method. Finally, our model succeeded to give better estimation of the Cu diffusion coefficient than MD, when referring to the experimental values.