The Electromigration Force in Metallic Bulk

TL;DR

This paper analyzes the electromigration force in metals using quantum mechanical concepts, ab initio calculations, and linear-response theory, clarifying the physics and providing calculated wind valences for various metals.

Contribution

It demonstrates that ab initio local density treatments accurately represent electromigration forces without needing additional screening considerations.

Findings

Ab initio calculations of wind valence in FCC and BCC metals.

Linear-response approach effectively distinguishes direct and wind forces.

Local screening concepts are of limited practical value.

Abstract

The voltage induced driving force on a migrating atom in a metallic system is discussed in the perspective of the Hellmann-Feynman force concept, local screening concepts and the linear-response approach. Since the force operator is well defined in quantum mechanics it appears to be only confusing to refer to the Hellmann-Feynman theorem in the context of electromigration. Local screening concepts are shown to be mainly of historical value. The physics involved is completely represented in ab initio local density treatments of dilute alloys and the implementation does not require additional precautions about screening, being typical for jellium treatments. The linear-response approach is shown to be a reliable guide in deciding about the two contributions to the driving force, the direct force and the wind force. Results are given for the wind valence for electromigration in a number of FCC and BCC metals, calculated using an {\it ab initio} KKR-Green's function description of a dilute alloy.