Stress effects on grain boundary grooving in polycrystalline interconnects: Insights from phase-field simulations

Abstract

We develop a multi-phase-field framework to investigate stress-modulated grain boundary grooving in polycrystalline metal interconnects. Larché–Cahn stress-diffusion coupling is incorporated into the surface-diffusion-driven morphological evolution equations, enabling concurrent simulation of free-surface grooving and grain boundary migration. The stress-free limit reproduces the classical Mullins t1/4 kinetics, validating the model against the analytical benchmark. Applied tensile stress markedly accelerates groove deepening relative to the stress-free baseline, while compression retards it; the groove-root geometry amplifies the far-field hydrostatic stress by nearly a factor of two, progressively intensifying the stress-diffusion coupling as grooves sharpen. Elastic mismatch between neighboring grains introduces an additional mechanism whereby groove roots migrate laterally under applied loading, thereby coupling surface grooving to stress-driven grain boundary motion. Extending to three-dimensional polycrystalline interconnects, we identify triple junctions as preferential failure sites where geometric constraint concentrates both diffusive flux and hydrostatic stress. High grain boundary mobility promotes concurrent coarsening and localized slit formation, accelerating degradation, while low mobility produces slower, less severe damage. These findings establish groove-root stress amplification and junction-controlled localization as the dominant mechanisms linking mechanical loading to morphological degradation in metal interconnects.