Phonon-assisted diffusion and electromigration of light interstitials in metals.

Abstract

We present a microscopic description of phonon-assisted diffusion of light interstitial impurities in metals including migration in the presence of an electron current (electromigration). The approach is self-consistent without separation into two parts (atom diffusion and electron scattering) and is appropriate for the regime of incoherent nonadiabatic atom hopping between polaron-type states at adjacent interstices. A general expression is obtained in the linear-response approximation for both the diffusion and the electron conduction contributions to atomic current. The atom current is shown to be related to an effective driving force through a Nernst-Einstein expression, and this driving force is shown to be the sum of a direct force and a wind force from the electron flow. The wind force in the general case is not determined by the Fiks-Huntington ballistic-model expression but decreases rapidly with the quantity ${\mathit{k}}_{\mathit{F}}$d, where ${\mathit{k}}_{\mathit{F}}$ is the electron Fermi momentum and d is the hopping distance. This decrease is due to strong recoil effects associated with momentum transfer to the lattice. Our results do not require the validity of the Condon approximation of small-polaron theory.