Relaxation between electrons and surface phonons in nanoscale metal films

TL;DR

This paper extends the Two Temperature model to include surface phonons in nanoscale metal films, deriving energy transfer rates that are significantly lower than bulk phonons, highlighting surface effects on electron-phonon relaxation.

Contribution

It introduces a geometric constraint for surface phonons into the Two Temperature model, providing new expressions for energy transfer rates in nanoscale metals.

Findings

Surface phonon energy transfer rate is an order of magnitude less than bulk.

Extended model accounts for surface geometry constraints.

Quantitative expressions for electron-surface phonon interactions.

Abstract

The Two Temperature model of M I Kaganov, I M Lifshitz and L V Tanatarov (Sov. Phys. JETP 4, 173 (1957)) about relaxation between electrons and bulk phonons is extended to the case of surface phonons. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. The new feature added is the geometric constraint of surface phonons. We obtain expressions for the energy transfer rate from degenerate hot electrons to surface-phonons, which is order of magnitude less than that for the bulk.