Cross-plane phonon transport in thin films

We predict the cross-plane phonon thermal conductivity of Stillinger-Weber silicon thin films as thin as 17.4 nm using the lattice Boltzmann method. The thin films are modeled using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. We use this approach, which considers all of the phonons in the first Brillouin-zone, to assess the suitability of common assumptions. Specifically, we assess the validity of: (i) neglecting the contributions of optical modes, (ii) the isotropic approximation, (iii) assuming an averaged bulk mean-free path, and (iv) the Matthiessen rule. Because the frequency-dependent contributions to thermal conductivity change as the film thickness is reduced, assumptions that are valid for bulk are not necessarily valid for thin films.