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

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.