Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation

Abstract

Quasiballistic heat transfer occurs when there is a temperature gradient over length scales comparable to phonon MFPs. This regime has been of interest recently because observing quasiballistic transport can lead to useful information about phonon mean free paths (MFPs), knowledge of which is essential for engineering nanoscale thermal effects. Here, we use the Boltzmann transport equation (BTE) to understand how observations of quasiballistic transport can yield information about MFPs. We solve the transient, one-dimensional, frequency-dependent BTE for a double layer structure of a metal film on a substrate, the same geometry that is used in transient thermoreflectance experiments, using a frequency-dependent interface condition. Our results indicate that phonons with MFPs longer than the thermal penetration depth do not contribute to the measured thermal conductivity, providing a means to probe the MFP distribution. We discuss discrepancies between our simulation and experimental observations which offer opportunities for future investigation.

Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate

“…23 We find that both the heater size and the spacing between neighboring heaters have strong impact on the transport regime. Our results also show that the degree of ballistic thermal transport depends on what is measured: for the peak temperature rise, the ballistic effect diminishes as the heaters get closer, while for the peak-valley temperature difference, ballistic effect increases.…”

“…2(a)), V is the phonon group velocity,  is the gray phonon lifetime, and 0 () x, y, t I is the equivalent equilibrium phonon intensity used to resolve the spatial and temporal temperature distribution. 23,28 In the definition of the phonon intensity I,  The numerical technique has been thoroughly described elsewhere 4 and is briefed here.…”

Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport

“…The numerical details concerning the dispersion and relaxation times are the same as those described in our recent work [21]. Only phonon-phonon scattering is considered for simplicity.…”

Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations

“…21 Cruz et al used ab-initio calculations in an attempt to explain a modulation frequency dependence of thermal conductivity in TDTR. 23 Heat transport in the crossplane direction in TDTR experiments has been studied by numerically solving the 1D Boltzmann transport equation (BTE) 22 and by using a two-channel model of the BTE. 25 While radial quasiballistic transport due to variation of the pump size in TDTR experiment has been studied as an example of the Monte Carlo method, 24,26 there has been no systematic investigation of radial quasiballistic transport in TDTR.…”

“…19 Quasiballistic transport has been studied using simulation with a variety of techniques. [20][21][22][23][24][25] Ezzahri and Shakouri used a Green's function formulation to examine electronic ballistic transport. 21 Cruz et al used ab-initio calculations in an attempt to explain a modulation frequency dependence of thermal conductivity in TDTR.…”