A study of stress-driven diffusive growth of voids in encapsulated interconnect lines

Abstract

Stress-driven diffusive growth of voids in encapsulated interconnect lines is studied. By calculating the rate of growth of a single void in a passivated line subjected to an initial hydrostatic tension stress and by assuming that failure occurs when the void reaches a critical size, a model for failure of encapsulated interconnect lines by stress voiding can be developed. The model for the prediction of void growth and failure is based on two limiting kinds of void growth. In one limit, which applies at short times, radial displacements occur by diffusional flow processes around the growing void and relax the local hydrostatic tension stress. In the long time limit, vacancies flow to the void from distant parts of the line by diffusion along grain boundaries, thereby relaxing the stress in a growing section of the line. A model based on a combination of these behaviors leads to a failure law for aluminum lines of the form tfσ2/d = 1019.2 exp(Q/RT) where tf is the failure time in seconds, σ is the initial hydrostatic tension stress in the line in Pa, d is the grain size in meters, and the activation energy, Q = 80.9 kJ/mol, is close to that for grain boundary diffusion in aluminum. The model predictions appear to be in good agreement with the few experiments on stress voiding that have been conducted.