Surface scattering analysis of phonon transport in the quantum limit using an elastic model

TL;DR

This paper analyzes how surface roughness affects phonon energy transport and thermal conductance in mesoscopic elastic beams, revealing mode-dependent power law scattering effects in the quantum limit.

Contribution

It introduces a full 3D elasticity model to study surface scattering effects on phonons, providing new insights into mode-dependent power laws and thermal conductance reduction.

Findings

Power law dependence of scattering coefficients varies with mode.

Surface roughness significantly reduces thermal conductance.

High-frequency scattering becomes dominant at mode onset frequencies.

Abstract

We have investigated the effect on phonon energy transport in mesoscopic systems and the reduction in the thermal conductance in the quantum limit due to phonon scattering by surface roughness using full 3-dimensional elasticity theory for an elastic beam with a rectangular cross-section. At low frequencies we find power laws for the scattering coefficients that are strongly mode dependent, and different from the $\omega^{2}$ dependence, deriving from Rayleigh scattering of scalar waves, that is often assumed. The scattering gives contributions to the reduction in thermal conductance with the same power laws. At higher frequencies the scattering coefficients becomes large at the onset frequency of each mode due to the flat dispersion here. We use our results to attempt a quantitative understanding of the suppression of the thermal conductance from the universal value observed in experiment.