A finite-element analysis of in-grain microcracks caused by surface diffusion induced by electromigration

Abstract

Based on the classical theory of surface diffusion and evaporation-condensation, a finite-element method is developed for simulating the shape instability of in-grain microcracks in metallic materials caused by surface diffusion induced by electromigration. The validity of the method is confirmed by the agreement of the numerically simulated migration behavior, of a small, circular void with that predicted theoretically. The results indicate that the microcrack shape is governed by the electric field, χ, and the initial aspect ratio of the microcrack, β, and there exist critical values for these parameters. When χ < χc or β < βc, the microcrack will evolve into a stable shape as it migrates along the conductor, while when χ≥χc or β≥βc, the microcrack will split into two smaller microcracks. The splitting time of the microcrack decreases with an increase in the electric field or the aspect ratio, indicating that the increase of the electric field or the aspect ratio accelerates microcrack splitting. In addition, the critical electric field χc decreases as the aspect ratio increases, and the critical aspect ratio βc decreases as the electric field increases. In other words, the increase of the electric field or the aspect ratio is beneficial to microcrack splitting.