Current-induced forces: a simple derivation

TL;DR

This paper provides a straightforward derivation of the various forces acting on atoms in nanoscale conductors under current, emphasizing physical understanding and implications for nanowire stability.

Contribution

It introduces a simple derivation of five principal forces under current, highlighting two unique forces and their role in nanowire structural changes, accessible to physics undergraduates.

Findings

Electron wind and Lorentz-like forces are significant at nanowire surfaces.

Current-induced forces can lead to structural transformations and failure.

Limitations of Ehrenfest dynamics are discussed in the context of force noise.

Abstract

We revisit the problem of forces on atoms under current in nanoscale conductors. We derive and discuss the five principal kinds of force under steady-state conditions from a simple standpoint that - with the help of background literature - should be accessible to physics undergraduates. The discussion aims at combining methodology with an emphasis on the underlying physics through examples. We discuss and compare two forces present only under current - the non-conservative electron wind force and a Lorentz-like velocity-dependent force. It is shown that in metallic nanowires both display significant features at the wire surface, making it a candidate for the nucleation of current-driven structural transformations and failure. Finally we discuss the problem of force noise and the limitations of Ehrenfest dynamics.