In-plane phonon transport in thin films

The in-plane phonon thermal conductivities of argon and silicon thin films are predicted from the Boltzmann transport equation under the relaxation time approximation. We model the thin films using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. The input required for the lattice dynamics calculations is obtained from interatomic potentials: Lennard-Jones for argon and Stillinger-Weber for silicon. The effect of the boundaries is included by considering only phonons with wavelengths that fit within the film and adjusting the relaxation times to account for mode-dependent, diffuse boundary scattering. Our model does not rely on the isotropic approximation or any fitting parameters. For argon films thicker than 4.3 nm and silicon films thicker than 17.4 nm, the use of bulk phonon properties is found to be appropriate and the predicted reduction in the in-plane thermal conductivity is in good agreement with results obtained from molecular dynamics simulation and experiment. We include the effects of boundary scattering without employing the Matthiessen rule. We find that the Matthiessen rule yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Our results show that the average of the bulk phonon mean free path is an inadequate metric to use when modeling the thermal conductivity reduction in thin films.