Modeling quasi-ballistic transient thermal transport with spatially sinusoidal heating: a McKelvey-Shockley flux approach

Abstract

Ballistic phonon effects, arising on length scales comparable to the mean-free-path, result in non-diffusive heat flow and alter the thermal properties of materials. Simple theoretical models that accurately capture non-diffusive transport physics are valuable for experimental analysis, technology design, and providing physical insight. In this work, we utilize and extend the McKelvey-Shockley (McK-S) flux method, a simple and accurate framework, to investigate ballistic effects in transient phonon transport submitted to a spatially sinusoidal heating profile, simulating a transient thermal grating. We begin by extending a previous McK-S formulation to include inelastic scattering, then obtain an analytical solution in the single phonon energy case (gray approximation), and after show how this approach can readily support a full phonon dispersion and mean-free-path distribution. The results agree with experimental data and compare very well to solutions of the phonon Boltzmann transport equation in the diffusive and weakly quasi-ballistic transport regimes. We discuss the role of ballistic and non-equilibrium physics, and show that inelastic scattering is key to retrieving the heat equation solution in the diffusive limit. Overall the McK-S flux method, which takes the form of a diffusion-like equation, proves to be a simple and accurate framework that is applicable from the ballistic to diffusive transport regime.

9 pages, 5 figures

References in corpus (10)

• Direct Measurement of Room Temperature Non-diffusive Thermal Transport Over Micron Distances in a Silicon Membrane
• A new regime of nanoscale thermal transport: collective diffusion counteracts dissipation inefficiency
• Thermal Transport at the Nanoscale - A Fourier's Law vs. Phonon Boltzmann Equation Study
• Steady-State Heat Transport: Ballistic-to-Diffusive with Fourier's Law
• A Simple Boltzmann Transport Equation for Ballistic to Diffusive Transient Heat Transport
• Monte Carlo Study of Non-diffusive Relaxation of A Transient Thermal Grating in Thin Membranes
• Multidimensional quasiballistic thermal transport in transient grating spectroscopy
• Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations
• Variational Approach to Solving the Spectral Boltzmann Transport Equation in Transient Thermal Grating for Thin Films
• Compact models for multidimensional quasiballistic thermal transport