In-plane and out-of-plane thermal conductivity of silicon thin films predicted by molecular dynamics

The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2 to 217 nm and temperatures from 300 to 1000 K. The relation between the bulk phonon mean free path (Lambda) and the film thickness (d(s)) spans from the ballistic regime (Lambda >> ds) at 300 K to the diffusive, bulk-like regime (Lambda << d(s)) at 1000 K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300 K. In the ballistic limit, in accordance with the kinetic and phonon radiative transfer theories, the predicted out-of-plane thermal conductivity varies linearly with the film thickness, and is temperature-independent for temperatures near or above the Debyes temperature.