Low-Variance Monte Carlo Simulation of Thermal Transport in Graphene

Abstract

ue to its unique thermal properties, graphene has generated considerable interest in the context of thermal management applications. In order to correctly treat heat transfer in this material, while still reaching device-level length and time scales, a kinetic description, such as the Boltzmann transport equation, is typically required. We present a Monte Carlo method for obtaining numerical solutions of this description that dramatically outperforms traditional Monte Carlo approaches by simulating only the deviation from equilibrium. We validate the simulation method using an analytical solution of the Boltzmann equation for long graphene nanoribbons; we also use this result to characterize the error associated with previous approximate solutions of this problem.