Monte Carlo Study of Non-diffusive Relaxation of A Transient Thermal Grating in Thin Membranes

TL;DR

This study rigorously analyzes how boundary scattering affects non-diffusive thermal relaxation in thin membranes using multidimensional phonon Boltzmann equations, revealing limitations of existing models and aligning simulations with experimental data.

Contribution

It provides a comprehensive multidimensional analysis of thermal relaxation in membranes, highlighting the failure of simplified models and validating spectral Boltzmann simulations against experiments.

Findings

Gray Boltzmann simulations show existing models fail for membranes with thickness comparable to phonon MFP.

Spectral Boltzmann simulations yield effective thermal conductivities matching experimental results.

Boundary scattering significantly influences non-diffusive thermal relaxation in nanostructured membranes.

Abstract

The impact of boundary scattering on non-diffusive thermal relaxation of a transient grating in thin membranes is rigorously analyzed using the multidimensional phonon Boltzmann equation. The gray Boltzmann simulation results indicate that approximating models derived from previously reported one-dimensional relaxation model and Fuchs-Sondheimer model fail to describe the thermal relaxation of membranes with thickness comparable with phonon mean free path. Effective thermal conductivities from spectral Boltzmann simulations completely free of any fitting parameters are shown to agree reasonably well with experimental results. These findings are important for improving our fundamental understanding of non-diffusive thermal transport in membranes and other nanostructures.