Silicon Thin Film Thermal Conductivity in Ballistic and Diffusive Regimes Predicted by Molecular Dynamics

Abstract

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 relationship and the Stillinger-Weber interatomic potential. Film thicknesses range from 2 to 220 nm and temperatures from 300 to 1000 K. In this range of temperatures, the relation between the phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (≫ ds) to the diffusive, bulk-like regime (≪ ds). We show that equilibrium molecular dynamics and the Green-Kubo relationship can be applied to the study of the thermal conductivity of thin films in the ballistic, transitional and diffusive regimes. When the film is thin enough, the thermal conductivity becomes orthotropic and decreases 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 theory, the predicted out-of-plane thermal conductivity varies linearly with the film thickness and is temperature-independent for temperatures near or above Debye’s temperature. This paper was also originally published as part of the Proceedings of the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems.