The Role of Thermalizing and Non-thermalizing Walls in Phonon Heat Conduction along Thin Films

TL;DR

This study investigates how thermalizing and non-thermalizing boundary conditions affect phonon heat conduction in thin films, revealing differences in transient behavior and challenging assumptions in existing models.

Contribution

It provides a detailed analysis of boundary scattering effects using spectral Boltzmann transport equations, highlighting the unphysical nature of thermalizing boundaries in transient regimes.

Findings

Steady state transport aligns with Fuchs-Sondheimer theory regardless of boundary thermalization.

Transient decay rates differ significantly between thermalizing and non-thermalizing walls.

Thermalizing boundary condition is unphysical due to heat flux conservation violation.

Abstract

Phonon boundary scattering is typically treated using the Fuchs-Sondheimer theory, which assumes that phonons are thermalized to the local temperature at the boundary. However, whether such a thermalization process actually occurs and its effect on thermal transport remains unclear. Here we examine thermal transport along thin films with both thermalizing and non-thermalizing walls by solving the spectral Boltzmann transport equation (BTE) for steady state and transient transport. We find that in steady state, the thermal transport is governed by the Fuchs-Sondheimer theory and is insensitive to whether the boundaries are thermalizing or not. In contrast, under transient conditions, the thermal decay rates are significantly different for thermalizing and non-thermalizing walls. We also show that, for transient transport, the thermalizing boundary condition is unphysical due to violation of heat flux conservation at the boundaries. Our results provide insights into the boundary scattering process of thermal phonons over a range of heating length scales that are useful for interpreting thermal measurements on nanostructures.