A diffuse interface or phase-field model was developed for the simulation of electromigration and stress-induced void evolution in interconnect lines. The approach was based upon the introduction of an order parameter field which characterized the damaged state of the interconnect. The order parameter took on distinct uniform values within the material and the void, and varied rapidly from one to the other over narrow interfacial layers which were associated with the void surface. The evolution of this order parameter was shown to be governed by a Cahn-Hilliard type equation. An asymptotic analysis of the equation demonstrated that the zero contour of the order parameter traced the motion of a void which evolved via diffusion under the combined effects of stress and electron wind. An implicit finite-element scheme was used to solve the modified Cahn-Hilliard equation. The diffuse-interface model was used to simulate a range of problems which involved void evolution in interconnect lines. The results were shown to be in excellent agreement with those obtained previously by using equivalent sharp-interface models.

Diffuse Interface Model for Electromigration and Stress Voiding. D.N.Bhate, A.Kumar, A.F.Bower: Journal of Applied Physics, 2000, 87[4], 1712-21