Phase field simulation of the void destabilization and splitting processes in interconnects under electromigration induced surface diffusion

Abstract

Interconnect lines of integrated circuits inevitably exist micro-damage, such as voids, inclusions or cracks. Under the effect of different intrinsic physical mechanisms as well as external driving forces, the micro-damage will have different morphological evolution and even destabilize and split, which can affect the various properties of the interconnects. Based on the theory of diffusion interface of microstructure evolution in solid materials, a phase field model is established to simulate the morphological evolution of micro-damage in the interconnect line under electromigration-induced surface diffusion. Unlike the previously published work, the bulk free energy density and the degenerate mobility used in the model are both constructed by quartic double-well potential function. The applicability of the model for the morphological evolution of intracrystalline voids is proved by asymptotic analysis. The governing equation of the phase field method is solved by finite element method. And, the validity of the method is confirmed by the agreement of the numerical solutions with the theoretical solutions of a small circular void. The effects of the relative electric field intensity Χ, the linewidth h ∽ and the initial aspect ratio β on void evolution are discussed in detail. The results indicate that the intracrystalline voids drift in the direction of the electric field, and there is a destabilization critical value Χ cr . When Χ ≧Χ cr , there exist two splitting forms after destabilization for circular void, type I and type II, respectively. The value of Χ cr decreases as h ∽ decreases or β increases. The smaller h ∽ or the larger β is more prone to cause void destabilization. The effect of h ∽ or β on Χ cr is more significant as h ∽ or β is relatively small. In particular, when h ∽ or β is sufficiently large, there exists upper or lower limit for Χ cr , respectively.