PhonoMC: Occupation-based deviational Monte Carlo for phonon transport with temperature-dependent scattering

Abstract

Nanoscale self-heating involves phonon transport across confined geometries, material interfaces, and temperature fields over which the scattering rates can vary substantially. We develop PhonoMC, an occupation-based deviational Monte Carlo method for solving the phonon Boltzmann transport equation within the relaxation-time approximation. A fixed equilibrium state is retained as the deviational reference, while the local temperature reconstructed from the represented energy is used to evaluate mode-dependent scattering rates. Collisions are updated with a separately determined relaxation temperature to conserve energy over each time step, and prescribed lattice heating is introduced by changing carrier occupations rather than continuously adding computational particles. For cross-plane transport through a 100-nm Si film, the deviational formulation reproduces the full-population heat flux while reducing its standard deviation by a factor of approximately 3.3 at \(ΔT=100\)~K with \(10^5\) carriers. In contrast, keeping the scattering rates fixed at 300~K overestimates the heat flux by 23.7\% at \(ΔT=250\)~K. Calculations of Si thin films distinguish finite-length effects from surface-scattering suppression, and Si/3C-SiC bilayers are used to examine interfacial thermal resistance. The method is further applied to localized heating in FinFET-like structures, where replacing the lower Si substrate with higher-conductivity 3C-SiC leads to a higher hotspot temperature because of the additional resistance associated with the confined Si region and the Si/SiC interface. These results show that a fixed deviational reference can be combined with local temperature-dependent scattering and sustained heat deposition in a mode-resolved Monte Carlo description of nanoscale thermal transport.