Nanostructure thermal conductivity prediction by Monte Carlo sampling of phonon free paths

We propose a method by which the thermal conductivity of a nanostructure with arbitrary geometry can be predicted through Monte Carlo sampling of the free paths associated with phonon-phonon and phonon-boundary scattering. The required inputs are the nanostructure geometry and the bulk phonon frequencies, group velocities, and mean free paths. The method is applied to a thin film in the in-plane and cross-plane directions and to a polycrystalline bulk material. For the film, a faster approach to the bulk thermal conductivity is found compared to predictions made using the Matthiessen rule with the bulk mean free path and an average phonon-boundary scattering length.