Local-field method for resistivity and electromigration in metallic microstructures: Application to thin films

A local-field method is described for determining the microscopic potential, the electrical resistivity, and the electromigration driving force on an impurity in a metallic microstructure. The method is an extension of Landauers picture of residual-resistivity dipoles to microstructures, with greater emphasis placed upon the details of the quantum-mechanical scattering process. Using a microscopic, surface-impurity model for surface roughness, we apply the method to a metallic thin film. When the film thickness is smaller than the mean free path, the surface resistivity is found to have oscillatory behavior as a function of film thickness. The form of the oscillations depends upon multiple scattering between the surface impurity and the film surfaces. In thicker films, the Fuchs-Sondheimer result is recovered. The local potential set up by impurity scattering is dipolar in the near- and far-field regions. However, unlike the case of residual-resistivity dipoles in bulk, the effective dipole strength is generally different in the two regions. It is found that the residual-resistivity dipole field decays less rapidly with distance in a thin film than in bulk, thus resulting in a larger voltage drop across an impurity in a thin film. This field enhancement is expected in low-dimensional systems.