The influence of a field-dependent total effective charge number on the interfacial migration rate and the phase growth behavior during intermediate phase growth with electromigration present

Intermediate phase growth with electromigration present is important to the performance of solder joints in integrated circuits. Rather than treating the total effective charge number Z_t of electromigration as constant, in this paper Z_t is treated as a field-dependent function whose contributions arising from both the crystal impurities and imperfections within the bulk and the compositional and phase-field variations across the interface. A diffuse interface model is used to investigate the interfacial migration and phase growth behavior in a binary diffusion couple with a diffusion-controlled mechanism for interfacial reactions. Simulation results show that, compared with the interfacial contribution to Z_t, the difference in the bulk contributions to Z_t across an interface, which separates two phases at equilibriums, is dominant to the migration rate of this interface; while during the growth of an intermediate phase, the value of Z_t within the bulk of the intermediate phase is dominant to the growth rate of this phase, because a larger Z_t leads to a larger effective driving force for electromigration and thus a faster migration rate of atoms across the intermediate phase. In both cases when the interfacial reactions are diffusion controlled, the influence from the interfacial contribution to Z_t was shown to be almost negligible, because a large increase of Z_t within the interfaces will not affect the overall migration rate of atoms significantly.