The total current-induced force on atoms in a wire which contained a vacancy was calculated by using the self-consistent 1-electron density matrix in the presence of an electric current; with no separation into electron-wind and direct forces. By integrating the total current-induced force, the change in vacancy migration energy due to the current was calculated. The change in migration energy with current was used to deduce an effective electromigration driving force.

Electromigration of Vacancies in Copper. J.Hoekstra, A.P.Sutton, T.N.Todorov, A.P.Horsfield: Physical Review B, 2000, 62[13], 8568-72