Phase-field modelling of electromigration-induced intergranular slit propagation in metal interconnects

We use a phase-field method to elucidate grain-boundary grooving as a mechanism of genesis and subsequent propagation of intergranular slit in metal interconnects under concurrent surface and grain boundary diffusion. Surface diffusion is assumed to be the rate limiting transport mechanism. Accelerated grain-boundary grooving induced by electromigration is shown to ensue a narrow channel-like slit which advances at a steady state along the grain-boundary preserving its shape near the tip region. The slit characteristics namely the width and velocity dependence on electric field derived are shown to be in excellent agreement with the sharp interface calculations which treat the tip region of the slit independently. Furthermore, the simulations reveal that for the same magnitude of electric field, a slit conceived from a smaller grain exhibits a slower kinetics and delay damage dissemination. The apparent discrepancy from the sharp interface description is resolved on the basis of curvature gradient and electromigration-induced surface flux which heal the root during groove to slit transition and is predominant in smaller grains. Finally, drawing analogy from the nucleation and growth models of electromigration voids, failure due to intergranular slit is divided into serial process of initial grooving followed by slit propagation stage. The lifetime analysis suggests the grooving stage to be the rate determining step in the failure process, yielding an exponent of 1.33 in Black's law.