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

•Demonstrate an approach to phonon transport that bridges the gap between nanoscale and microscale, enabling fast simulation of problems on domains from 10 nm to 10 μm.•Self-Adjoint formulation of the Boltzmann transport equation for phonons allows for efficient simulations using widely available linear algebra solvers.•New closure term, which acts as a source term for the phonon Boltzmann transport equation and preserves conservation of energy.•Novel material property discretization consistent with angular discretization of the transport system. We present a new method for predicting effective thermal conductivity (κeff) 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 μm 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.