Onset of non-diffusive phonon transport in transient thermal grating decay

TL;DR

This paper theoretically investigates the decay of sinusoidal temperature perturbations in dielectrics, revealing how long mean free path phonons influence thermal relaxation at micron-scale grating periods, especially in silicon.

Contribution

It provides an analytical model for phonon transport in transient thermal grating decay, highlighting the onset of non-diffusive effects for long MFP phonons at micron scales.

Findings

Ballistic phonons' contribution to thermal conductivity is suppressed at micron scales.

Significant reduction in effective thermal conductivity in silicon at 10 micron grating periods.

Analytical expression for thermal grating relaxation rate derived.

Abstract

The relaxation of a spatially sinusoidal temperature perturbation in a dielectric crystal at a temperature comparable to or higher than the Debye temperature is investigated theoretically. We assume that most phonons contributing to the specific heat have mean free path (MFP) much shorter than the thermal transport distance and can be described by the thermal diffusion model. Low-frequency phonons that may have MFP comparable to or longer than the grating period are described by the Boltzmann transport equation. These low-frequency phonons are assumed to interact with the thermal reservoir of high frequency phonons but not with each other. Within the single mode relaxation time approximation, an analytical expression for the thermal grating relaxation rate is obtained. We show that the contribution of "ballistic" phonons with long MFP to the effective thermal conductivity governing the grating decay is suppressed compared to their contribution to thermal transport at long distances. The reduction in the effective thermal conductivity in Si at room temperature is found to be significant at grating periods as large as 10 microns.