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

## TL;DR

This paper introduces a novel spectral phonon transport simulation method based on the Boltzmann equation to accurately predict the thermal conductivity of dielectric materials like silicon at various length scales.

## Contribution

The paper develops a new computational approach using a Self-Adjoint Angular Flux formulation and Richardson iteration for spectral phonon transport simulations, enhancing prediction accuracy.

## Key findings

- Accurate thermal conductivity predictions for silicon at room temperature.
- Effective modeling of spectral phonon interactions and disorder effects.
- Validation of the method across multiple length scales.

## 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.