Thermal phonon boundary scattering in anisotropic thin films

TL;DR

This paper generalizes the Fuchs-Sondheimer theory to account for anisotropic phonon dispersion, revealing that graphite retains high in-plane thermal conductivity even at nanometer-scale thicknesses.

Contribution

It introduces a new model for boundary scattering in anisotropic materials, improving predictions for thermal conductivity in thin films like graphite.

Findings

Isotropic Fuchs-Sondheimer overestimates boundary scattering in graphite.

Graphite maintains high in-plane thermal conductivity at nanometer-scale thickness.

Anisotropic dispersion significantly affects phonon boundary scattering predictions.

Abstract

Boundary scattering of thermal phonons in thin solid films is typically analyzed using Fuchs-Sondheimer theory, which provides a simple equation to calculate the reduction of thermal conductivity as a function of the film thickness. However, this widely-used equation is not applicable to highly anisotropic solids like graphite because it assumes the phonon dispersion is isotropic. Here, we derive a generalization of the Fuchs-Sondheimer equation for solids with arbitrary dispersion relations and examine its predictions for graphite. We find that the isotropic equation vastly overestimates the boundary scattering that occurs in thin graphite films due to the highly anisotropic group velocity, and that graphite can maintain its high in-plane thermal conductivity even in thin films with thicknesses as small as ten nanometers.