A physically based lifetime model for stress-induced voiding in interconnects

Abstract

We use a simple closed-form lifetime model for stress-induced voiding (SIV) or stress migration for Al- or Cu-based interconnects. Stress-induced voiding is treated as a process of void nucleation/growth and stress relaxation through atomic diffusion driven by a stress gradient. We developed a physically based method of modeling atomic diffusion and void growth, which explicitly accounts for the dependence of void growth on several factors including stress, temperature, diffusivity, and effective modulus. Based on basic physics associated with void growth, we define zones as SIV plate, SIV long line, and SIV short line, respectively, i.e., the three sequential stages for the process of void growth, depending on a nondimensional time-dependent parameter ψ and the aspect ratio of the interconnect. Simple form solutions to the governing equations that describe void growth are then sought for each scenario separately. Time to failure (TTF) is calculated as a function of stressing temperature, mechanical stress, interlayer dielectrics property, and line dimension based on an explicit formulation. The model provides insight into the separate impact of each input factor upon the SIV rate. We find that TTF is invariant with line width in the early zone (SIV plate), while void generation rate is linear with time. TTF is a strong function of line width for both the later zones. The void generation rate varies as the square root of time in the SIV long-line realm, but is constant with time in the SIV short-line zone.