Monte Carlo simulation of diffusive-to-ballistic transition in phonon transport

Heat conduction properties in Si nanostructures are analyzed using a Monte Carlo method developed for solving the phonon Boltzmann transport equation. The thermal resistances are evaluated for the systems with various sizes, and the transition from the diffusive to the ballistic heat conduction are investigated. We compare the two different phonon dispersion models (the realistic dispersion relation based on the adiabatic bond charge model and the analytically approximated model), and it is shown that the correct implementation of the phonon dispersion relation is essential to accurately simulate the quasi-ballistic heat conduction properties, which becomes obvious in the structures smaller than the phonon mean free path.