A finite-element analysis of intragranular microcracks in metal interconnects due to surface diffusion induced by stress migration

Abstract

Based on the classical theory of surface diffusion and evaporation–condensation, a finite-element program is developed for simulating the shape instability of intragranular microcracks in metal interconnects due to surface diffusion induced by stress migration. Unlike previously published works, this paper also explores the effects of the linewidth, the applied stress and the initial aspect ratio of the microcrack. The results indicate that there exists a critical value of the linewidth h⌢c for the intragranular microcrack under compressive and tensile stress. When h⌢>h⌢c, the microcrack will directly evolve into a cylinder. When h⌢⩽h⌢c, the microcrack will split into three parts. There also exist critical values of stress, σ⌢c, and aspect ratio, βc. When σ⌢<σ⌢c or β<βc, the microcrack will directly evolve into a cylinder. When σ⌢⩾σ⌢c or β⩾βc, the microcrack will split into three small microcracks. The splitting time of the microcrack increases as the linewidth increases, while it decreases with increasing stress or aspect ratio. In addition, the microcrack has a stronger dependence on the linewidth when the applied stress is lower.