Three dimensional finite element analysis of the evolution of voids and thin films by strain and electromigration induced surface diffusion

摘要

We describe a three-dimensional finite element method for predicting the behavior of a solid which changes its shape as a result of strain and electromigration induced surface diffusion. The numerical procedure is described in detail. To demonstrate the accuracy and capabilities of the method, it is used to solve two problems of interest to the microelectronics industry. First, the method is used to predict the motion and evolution of voids in an idealized interconnect line due to electromigration and strain induced surface diffusion. The results are compared and contrasted with existing two-dimensional finite element simulations. In particular, we determine the conditions where three-dimensional simulations are necessary to accurately predict the behavior of the void. Secondly, the method is used to conduct fully three-dimensional simulations of strain induced roughening on the surface of a thin epitaxial film. The results are compared with the first order perturbation theory. It is shown that the first order theory provides a good approximation only for very small roughness amplitudes. In addition, it is shown that the nature of the roughness that develops on the surface is strongly sensitive to the three-dimensional shape of the initial imperfection on the surface, and is also influenced by the thickness of the epitaxial film.