Electromigration theory unified

Faculty of Sciences/Natuurkunde en Sterrenkunde, Vrije Universiteit De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

Received: 23 August 2005
Accepted: 4 October 2005

Abstract

The starting formula of Bosvieux and Friedel (J. Phys. Chem. Solids, 23 (1962) 123) 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 (Thin Solid Films, 25 (1975) 25). By this electromigration theory has become a unified theory. This 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 (Phys. Rev. B, 12 (1975) 3142). 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.