Phonon-boundary scattering in nanoporous silicon films: Comparison of Monte Carlo techniques

The thermal conductivities of silicon thin films with periodic pore arrays (i.e., nanoporous films) and square silicon nanowires are predicted at a temperature of 300 K. The bulk phonon properties are obtained from lattice dynamics calculations driven by first-principles calculations. Phonon-boundary scattering is included by applying three Monte Carlo-based techniques that treat phonons as particles. The first is a path sampling technique that modifies the intrinsic bulk mean free paths without using the Matthiessen rule. The second uses ray-tracing under an isotropic assumption to calculate a single, mode-independent boundary scattering mean free path that is combined with the intrinsic bulk mean free paths using the Matthiessen rule. The third modifies the ray-tracing technique to calculate the boundary scattering mean free path on a modal basis. For the square nanowire modeled using isotropic ray-tracing, the maximum mean free path is comparable to the wire width, an unphysical result that is a consequence of the isotropic approximation. Free path sampling and modal ray-tracing produce physically meaningful mean free path distributions. The nanoporous film thermal conductivity predictions match a previously measured trend, suggesting that coherent effects are not relevant to thermal transport at room temperature. A line-of-sight for phonons in the nanoporous films is found to change how thermal conductivity scales with porosity.