Electromigration simulation with consideration of the atomic concentration gradient

An enhanced finite element modeling methodology based on commercial software ANSYS Multi-physics and FORTRAN code is developed for the simulation of electromigration. The electronic migration formulation taking into account the effects of the atomic concentration gradient (ACG) has been developed to show the difference in the electromigration (EM) failure mechanisms. An improved algorithm of total atomic flux and corresponding EM formulation are presented with the electro-migration, the thermo-migration, the stress-migration and the atomic concentration gradient migration. The interaction of the various driving forces during the EM process is investigated. Finite element simulations are performed for solder joints under high current density with and without consideration of atomic concentration gradient. Simulations show that atomic concentration gradient migration can’t be ignored. It is also found that the atomic concentration distribution majorly depends on the current density, atomic concentration gradient and the stress gradient of the structure.