Electromigration of vacancies in copper

Abstract

The total current-induced force on atoms in a Cu wire containing a vacancy are calculated using the self-consistent one-electron density matrix in the presence of an electric current, without separation into electron-wind and direct forces. By integrating the total current-induced force, the change in vacancy migration energy due to the current is calculated. We use the change in migration energy with current to infer an effective electromigration driving force ${\mathbf{F}}_{e}.$ Finally, we calculate the proportionality constant ${\ensuremath{\rho}}^{*}$ between ${\mathbf{F}}_{e}$ and the current density in the wire.