Phonon ballistic-diffusive heat conduction in silicon nanofilms by Monte Carlo simulations

Abstract

Abstract An efficient Monte Carlo (MC) method on the basis of introducing a model of phonon scattering processes is proposed to simulate the ballistic-diffusive heat conduction in silicon nanofilms. The calculated thermal conductivity of nanofilms agrees with the experimental data, which is indicative of the validity of our simulations. The boundary temperature jump caused by the effects of phonon ballistic transport is observed by the MC technique. It is found that the boundary temperature jump increases with the Knudsen number (Kn). Theoretical models for predicting the boundary temperature jumps are also derived from the phonon Boltzmann transport equation. Model 1 is derived based on the acoustically thin approximation (Kn ≫ 1), whereas model 2 is obtained by the diffusive approximation (Kn ≪ 1). Furthermore, we derive model 3 in the intermediate region by an empirical way i.e. averaging model 1 and model 2. The theoretical models agree well with the MC simulations in different regions.