Compact models for multidimensional quasiballistic thermal transport

TL;DR

This paper introduces a compact, physics-based model for multidimensional quasiballistic thermal transport that directly interprets experimental signals, bridging the gap between BTE solutions and conventional diffusive analyses.

Contribution

It develops a stochastic transport framework using an isotropic Poissonian process to characterize quasiballistic heat dynamics with a genuine thermal blueprint directly from measurements.

Findings

The spatial propagator serves as a true thermal blueprint of the medium.

The model accurately describes TTG and TDTR experimental data.

It provides a direct method to extract thermal properties from raw signals.

Abstract

The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. Experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive formalisms that merely extract "effective" Fourier conductivities. Here, we build upon stochastic transport theory to provide a characterisation framework that blends the rich physics contained within BTE solutions with the convenience of conventional analyses. The multidimensional phonon dynamics are described in terms of an isotropic Poissonian flight process with rigorous Fourier-Laplace single pulse response $P(\vec{\xi},s) = 1/[s + \psi(\| \vec{\xi} \|)]$. The spatial propagator $\psi(\|\vec{\xi}\|)$, unlike commonly reconstructed mean free path spectra $\kappa_{\Sigma}(\Lambda)$, serves as a genuine thermal blueprint of the medium that can be identified in compact form directly from raw measurement signals. Practical illustrations for transient thermal grating (TTG) and time domain thermoreflectance (TDTR) experiments on respectively GaAs and InGaAs are provided.