Diffusion is an important mechanism for failure inducing phenomena in many applications. The common Pb-free solder alloys used in the current generation of electronics packages are complex multiphase multicomponent materials. As the scale of the solder joint decreases, it becomes increasingly important to account for the effect of surface phenomena such as grain boundary evolution, surface diffusion and interfacial reactions in the mechanics of the solder joints. The dynamics of these diffusion driven interfacial phenomena are affected by the state of stress and the electric current in the solid. The primary challenges to modeling the dynamics of evolution are the tracking of the interface while satisfying the boundary conditions for the bulk problem.
In previous work, the authors utilized the phase field method in conjunction with a commercial finite element code to study the effect of stress and electrical fields on the diffusion driven evolution of voids in solder interconnects. The utilization of commercial tools for the simulation of the stress, electrical and thermal fields allowed for the use of pre-existing meshes and allowed the study of electromigration failure in assemblies of solder joints. However, the use of commercial tools can be expensive and the options for parallel simulation are limited, restricting the size and complexity of the simulations.
In this work, the authors describe DiffCode, a parallel adaptive finite element code for three-Dimensional simulation of electromigration and stress migration driven failure due to void evolution and growth in solder as well as line interconnects using the phase field method. Several illustrative two-dimensional and three-dimensional electromigration driven void evolution simulations are demonstrated using the code.
Free Energy Density for Gauge Background Fields at Finite Temperature
