Phase field simulation of the instability and splitting processes of elliptical inclusions in interconnects due to anisotropic interface diffusion under electric and stress fields

Abstract

Electromigration and stress migration induced failure of thin-film metal interconnects is one of the most challenging material reliability issues for microelectronic circuits toward ultra-large-scale integrated circuits. Based on the theory of anisotropic interface diffusion, a modified Cahn–Hilliard phase field model is established to elucidate the instability and splitting processes of elliptical inclusions under the multi-physics field. The reliability of the model is verified by comparing numerical and theoretical solutions for the evolution of circular inclusions under electric and stress fields, respectively. The numerical results elaborate on the role of the conductivity ratio, the elastic modulus ratio, the aspect ratio, the electric field, the stress field, the linewidth, and the anisotropic interface diffusion mobility on morphological evolution using an adaptive mesh finite element method. The numerical results show that the larger the electric and stress fields, the greater the aspect ratio larger than 1 or smaller than 1, and the more easily the elliptical inclusions split into several small inclusions or get destabilized. The smaller the linewidth, the easier it is for the inclusions to migrate toward the edge of the line, severely reducing the conductivity of the line. Under anisotropic interface diffusion, lower misorientations favor a steady-state, whereas higher values render the inclusion unstable, splitting, or bifurcating into more small ones. Moreover, the splitting time of the elliptical inclusion decreases with an increase in the electric field, the stress field, and the misorientations, then increases, and subsequently decreases with an increase in the aspect ratio.