Linear analysis of electromigration-induced void instability in Al-based interconnects

Abstract

Void shape changes induced by electromigration pose reliability problems in Al-based interconnects. Recent observations have shown that a rounded void sometimes collapses to a transverse slit in an interconnect with bamboo-like grain structure. This article provides a linear stability analysis for a circular void that is only partially conductive in an otherwise infinite conductive medium. The relation between the inner conductivity (i.e., the conductivity of the medium in the void) and the critical remote electric field intensity, Ecr, for the linear stability of the void is established. It is proven that when the inner conductivity becomes zero, Ecr goes to infinity, and we can look upon the inner conductivity of a vacuum void as zero. That is why the vacuum circular void is linearly stable. It is also shown that when the inner conductivity is very small, the stability of a void is sensitive to it. From the computational results, we know that if the inner conductivity is 0.1% of that outside the void, the Ecr is only twenty times of that for the dislocation loop case.