Prediction of thermal conductivity in dielectrics using fast, spectrally-resolved phonon transport simulations

Abstract

We present a new method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$) in materials, informed by ${ab\,initio}$ material property simulations. Using the Boltzmann transport equation in a Self-Adjoint Angular Flux formulation, we performed simulations in silicon at room temperatures over length scales varying from 10 nm to 10 $\mu$m and report temperature distributions, spectral heat flux and thermal conductivity. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. In this method, a closure term is introduced to the transport equation which acts as a redistribution kernel for the total energy bath of the system. This term is an effective indicator of the degree of disorder between the spectral phonon radiance and the angular phonon intensity of the transport system. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations.