MCBTE: A variance-reduced Monte Carlo solution of the linearized Boltzmann transport equation for phonons

TL;DR

MCBTE introduces a variance-reduced Monte Carlo method for solving the linearized Boltzmann transport equation for phonons, enabling detailed transient and steady-state thermal transport analysis in nanostructured materials.

Contribution

It presents a novel, portable Monte Carlo algorithm that efficiently models phonon transport with variance reduction, integrated with first-principles and empirical data.

Findings

Accurately models ballistic and quasi-ballistic thermal transport.

Provides detailed frequency-resolved thermal conductivity analysis.

Achieves near-linear parallel scalability.

Abstract

MCBTE solves the linearized Boltzmann transport equation for phonons in three dimensions using a variance-reduced Monte Carlo solution approach. The algorithm is suited for both transient and steady-state analysis of thermal transport in structured materials with size features in the nanometer to hundreds of microns range. The code is portable and integrated with both first-principles density functional theory calculations and empirical relations for the input of phonon frequency, group velocity, and mean free path required for calculating the thermal properties. The program outputs space- and time-resolved temperature and heat flux for the transient study. For the steady-state simulations, the frequency-resolved contribution of phonons to temperature and heat flux is written to the output files, thus allowing the study of cumulative thermal conductivity as a function of phonon frequency or mean free path. We provide several illustrative examples, including ballistic and quasi-ballistic thermal transport, the thermal conductivity of thin films and periodic nanostructures, to demonstrate the functionality and to benchmark our code against available theoretical/analytical/computational results from the literature. Moreover, we parallelize the code using the Matlab Distributed Computing Server, providing near-linear scaling with the number of processors.