Monte Carlo simulation of phonon ballistic diffusive heat conduction in silicon nanofilm

Abstract

A Monte Carlo (MC) method is proposed by establishing a new model of phonon scattering processes with random sampling according to a scattering probability function. The MC scheme is used to simulate steady and transient ballistic-diffusive heat conduction in silicon nanofilm. In the MC simulations, we trace the phonon bundles that emit into media from the boundaries, and obtain the temperature profiles through statistics of the distribution of phonon bundles. It is found that the size effect of phonon transport leads to a boundary temperature jump which increases with the Knudsen number increasing. The thermal conductivity of the silicon nanofilm is calculated and the results suggest that nanofilm thermal conductivity increases with film thickness increasing, which is in good agreement with the experimental data as well as the results from the theoretical model. The temperature profiles vary with time in the transient simulations, which shows that the heat wave is related to not only time scale but also spatial scale. When the spatial scale becomes smaller, the ballistic transport is more dominant, which leads to stronger heat waves.