A compact heat transfer model based on an enhanced Fourier law for analysis of frequency-domain thermoreflectance experiments

TL;DR

This paper introduces a compact heat transfer model based on an enhanced Fourier law that effectively analyzes frequency-domain thermoreflectance experiments by considering both diffusive and quasi-ballistic phonon channels, revealing limitations in current experimental approaches.

Contribution

The paper develops a minimal-parameter heat transfer model incorporating an enhanced Fourier law with two phonon channels, improving analysis of FDTR data and highlighting limitations in extracting MFP accumulation functions.

Findings

The model accurately explains FDTR data with fewer parameters.

FDTR experiments have limitations in deriving bulk MFP accumulation functions.

The quasi-ballistic phonon channel is effectively modeled using spherical harmonic expansion.

Abstract

A recently developed enhanced Fourier law is applied to the problem of extracting thermal properties of materials from frequency-domain thermoreflectance (FDTR) experiments. The heat transfer model comprises contributions from two phonon channels; one a high-heat-capacity diffuse channel consisting of phonons of mean free path (MFP) less than a threshold value, and the other a low-heat-capacity channel consisting of phonons with MFP higher than this value that travel quasi-ballistically over length scales of interest. The diffuse channel is treated using the Fourier law, while the quasi-ballistic channel is analyzed using a second-order spherical harmonic expansion of the phonon distribution function. A recent analysis of FDTR experimental data suggested the use of FDTR in deriving large portions of the MFP accumulation function; however, it is shown here that the data can adequately be explained using our minimum-parameter model, thus highlighting an important limitation of FDTR experiments in exploring the accumulation function of bulk matter.