Prediction of thermal conductivity of silicon nanowires via phonon Monte Carlo simulation: Exact treatment of cylindrical boundary

Various analytical and numerical simulation models have been proposed in the past to solve the Boltzmann Transport Equation in order to describe semi-ballistic phonon transport in silicon nanowires. One of which is the statistical method called the Monte Carlo simulation. Most of the available Monte Carlo models however, prefer the inclusion of cuboidal boundary by applying equivalent diameter to bypass the complication of tracking phonon ensembles at the curved boundary. We propose a Monte Carlo simulation for transient phonon heat transport in silicon nanowires which includes the effect of a fully diffusive cylindrical boundary for temperatures ranging from 50K to 300K. A comparison between the simulation results obtained from the cuboidal and cylindrical boundary is provided to assess validity of the former assumption. The thermal conductivities obtained from the simulation compares well with the experimental data obtained from the literatures for silicon nanowires of diameters 115nm, 56nm and 37nm.