Theory of electromigration in noble and transition metals

Abstract

We have used the scattering theory and the muffin-tin approximation to evaluate the electron wind force acting on an atom in an electric field. Within the relaxation-time approximation, the force depends in an intricate manner on the nature of the Fermi surface, the electronic wave functions, the Fermi velocities, and the host- and the solute-metal phase shifts. The formalism is general and applicable to both simple and transition metals. The effective valences for several solutes in noble-metal hosts have been evaluated. It is shown that in general the effective valence cannot be related to the residual resistivity of a solute, even for host metals which have nearly spherical Fermi surfaces but non-negligible phase shifts at the Fermi energy. However, for a jellium matrix, the electron wind force is directly proportional to the residual resistivity; this is a result which has been obtained here, within the framework of the Boltzmann equation, from a nonlinear calculation of the impurity potential.