A phase field model for electromigration-induced surface evolution

Abstract

In this study, a phase field model is presented to study the effects of electromigration on the surface evolution of single crystal Al metal interconnects. Two dimensional computer simulations are performed for the surface evolution of metal interconnects due to electromigration in various conditions, such as anisotropy in diffusivity, different initial void sizes, and different crystallographic directions compared to the direction of the ambient electric field. From the results of computer simulations, it may be seen that the types of anisotropy and the relative direction of the diffusivity are the decisive factors in motion and shape change. As the symmetry of anisotropy in diffusivity decreases, the void evolves into a more unstable shape. Moreover, the voids of the system with two-fold diffusion symmetry are most likely to evolve into slits when the crystallographic direction is toward a specific orientation compared to the direction of the ambient electric field.