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 10 nm.
Highlights
Boundary scattering of thermal phonons in thin solid films is typically analyzed using FuchsSondheimer theory, which provides a simple equation to calculate the reduction of thermal conductivity as a function of the film thickness
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 10 nm
Thermal transport in thin solid films with thicknesses from tens of nanometers to micrometers is a topic of considerable importance,1–4 with such films being used in applications ranging from quantum well lasers to lighting with light-emitting diodes lighting
Summary
Boundary scattering of thermal phonons in thin solid films is typically analyzed using FuchsSondheimer theory, which provides a simple equation to calculate the reduction of thermal conductivity as a function of the film thickness. 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 10 nm.
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