Theory of the driving force for electromigration

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Abstract
Using a linear-response formalism coupled with an infinite resummation, expressions are derived for the driving force of electromigration for a system of independent electrons moving among an array of selfconsistently screened ion potentials. We assume that the net scattering is weak, but do not expand in powers of the individual-ion scattering strengths nor do we take an average over the configuration of neighbors about the electromigrating ion. Our final formulas, which are tractable for evaluation, may be understood in terms of solutions of the Boltzmann equation. We discuss this interpretation and show how it resolves the question of the existence and quantitative significance of the Landauer resistivity dipoles. We also comment on the still-unresolved question of the "direct" force.