Creep flow, diffusion, and electromigration in small scale interconnects

This paper proposes a three-dimensional electromigration model for void evolution in small scale interconnects. Concurrent kinetics of creep flow and surface diffusion as well as the effect of the surrounding material is considered to provide better understanding of the evolution process. The multiple kinetics and energetics are incorporated into a diffusive interface model. A semi-implicit Fourier spectral method and the preconditioned biconjugate-gradient method are proposed for the computations to achieve high efficiency and numerical stability. We systematically studied kinetic processes in diffusion dominated to creep dominated regime. Which process dominates, as revealed by the analysis, is determined by a combination of viscosity, mobility, interconnect thickness, and void radius. Previous studies on electromigration suggest that a circular void subjected to an electron wind force and surface diffusion is always stable against any small shape perturbation. Our simulations show that a shape that is stable in surface diffusion can become unstable in a creep dominated process, which leads to a quite different void morphology. A spherical void can evolve into a bowl shape and further break into smaller voids. It is also shown that the interconnect geometry has an important effect. r 2006 Elsevier Ltd. All rights reserved.