Electromigration drift velocity in Cu interconnects modeled with the level set method

Abstract

Electromigration (EM) drift velocity (DV) experiments in polycrystalline pure Cu lines are simulated numerically with the level set method. The simulation is based on a grain boundary (GB) grooving model, incorporating an electric field. The model is distinguished by two key requirements imposed at the triple point where two surfaces and a GB meet: that of GB and surface flux coupling (flux continuity), and that of permanent equilibrium between surface and GB tensions. Surface diffusion exists only at the advancing cathode edge, and is driven both by local curvature gradients and by the local field. Using independent, literature diffusivity values, the simulation yields both the DV prefactor and the EM activation energy in an Arrhenius-type expression. An excellent match is obtained with experimental DV values in the T range of 573–723 K. Some implications regarding the material transport mechanism are discussed.