Multi-phase-field modelling of electromigration-induced void migration in interconnect lines having bamboo structures

Abstract

Predicting the evolution of voids induced by electromigration (EM) in interconnect lines is an important aspect of improving the reliability of miniaturized integrated circuits. In this paper, we propose a new multi-phase-field (MPF) model to simulate void evolution in polycrystalline interconnect lines on a three-dimensional (3D) basis. This model was validated by comparing simulations of 3D void migration in a single crystal copper line with analytical solutions. We also performed a parametric study intended to elucidate the key factors associated with void evolution leading to line breakage. This study determined that critical void evolution in copper straight interconnect lines having a bamboo structure depends on the ratio of the diffusion coefficient of atoms at the grain boundaries to that at the void surfaces. Simulations in which multiple voids migrated by EM in a bamboo line mimicking a via site in an integrated circuit showed that such voids tend to accumulate and break the interconnect line above the via. By comparing simulation results to experimental data, this work also confirmed that the MPF model can predict the break point of an interconnect line as caused by EM.