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We present a new Monte Carlo method for obtaining solutions of the Boltzmannequation for describing phonon transport in micro and nanoscale devices. Theproposed method can resolve arbitrarily small signals (e.g. temperaturedifferences) at small constant cost and thus represents a considerableimprovement compared to traditional Monte Carlo methods whose cost increasesquadratically with decreasing signal. This is achieved via a control-variatevariance reduction formulation in which the stochastic particle descriptiononly solves for the deviation from a nearby equilibrium, while the latter isdescribed analytically. We also show that simulating an energy-based Boltzmannequation results in an algorithm that lends itself naturally to exact energyconservation thereby considerably improving the simulation fidelity.Simulations using the proposed method are used to investigate the effect ofporosity on the effective thermal conductivity of silicon. We also presentsimulations of a recently developed thermal conductivity spectroscopy process.The latter simulations demonstrate how the computational gains introduced bythe proposed method enable the simulation of otherwise intractable multiscalephenomena.

Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations