Electromigration theory unified

TL;DR

This paper unifies electromigration theory by showing the equivalence of Bosvieux and Friedel's formula with the linear-response approach, revealing partial screening effects that challenge previous assumptions of complete screening.

Contribution

It demonstrates the unification of electromigration theories and quantifies the partial screening effect, correcting earlier claims of full screening.

Findings

Screening is about 15%, not complete.

The theory aligns with the linear-response approach.

A crucial trap term was identified and accounted for.

Abstract

The starting formula of Bosvieux and Friedel for the force on an ion in a metal due to an applied voltage is shown to lead to the same description as the linear-response approach used in the field since its introduction by Kumar and Sorbello. By this electromigration theory has become a unified theory. It follows after accounting for a treacherous trap term, which at first sight seems to be zero. Up to now Bosvieux and Friedel claimed to predict a completely screened direct force, which means that only a wind force would be operative. In addition the amount of screening has been calculated up to second order in the potential of the migrating impurity, using a finite temperature version of the screening term derived by Sham. For a proton in a metal modeled as a jellium the screening appears to be about 15%, which is neither negligible nor reconcilable with the old full-screening point of view.