Low-temperature electron-phonon heat transfer in metal films

TL;DR

This paper analyzes the electron-phonon heat transfer in thin metal films at low temperatures, deriving an explicit expression that explains experimental observations and highlights the role of specific acoustic modes.

Contribution

It provides a new explicit formula for electron-phonon heat transfer in quasi-two-dimensional metal films below the dimensional crossover temperature.

Findings

Heat transfer is dominated by Lamb's dilatational and flexural modes at low temperatures.

Derived formula matches experimental data for supported metallic films.

The model explains heat transfer behavior in films with different acoustic properties.

Abstract

We consider the deformation potential mechanism of the electron-phonon coupling in metal films and investigate the intensity of the associated heat transfer between the electron and phonon subsystems. The focus is on the temperature region below dimensional crossover $T<T^{\ast}$ where the thermally relevant vibrations are described in terms of a quasi-two-dimensional elastic medium, while electron excitations behave as a three-dimensional Fermi gas. We derive an explicit expression for the power $P\left( T\right) $ of the electron-phonon heat transfer which explains the behavior observed in some experiments including the case of metallic film supported by an insulating membrane with different acoustic properties. It is shown that at low temperatures the main contribution is due to the coupling with Lamb's dilatational and flexural acoustic modes.