  We present a new Monte Carlo method for obtaining solutions of the Boltzmann
equation for describing phonon transport in micro and nanoscale devices. The
proposed method can resolve arbitrarily small signals (e.g. temperature
differences) at small constant cost and thus represents a considerable
improvement compared to traditional Monte Carlo methods whose cost increases
quadratically with decreasing signal. This is achieved via a control-variate
variance reduction formulation in which the stochastic particle description
only solves for the deviation from a nearby equilibrium, while the latter is
described analytically. We also show that simulating an energy-based Boltzmann
equation results in an algorithm that lends itself naturally to exact energy
conservation thereby considerably improving the simulation fidelity.
Simulations using the proposed method are used to investigate the effect of
porosity on the effective thermal conductivity of silicon. We also present
simulations of a recently developed thermal conductivity spectroscopy process.
The latter simulations demonstrate how the computational gains introduced by
the proposed method enable the simulation of otherwise intractable multiscale
phenomena.
