We determine how the natural distributions of phonon-phonon and phonon-boundary scattering free paths affect the prediction of thermal conductivity for thin films, nanowires, and porous nanofilms. Using Monte Carlo sampling, the effective mean free path for each phonon mode is calculated using a Poisson distribution for the phonon-phonon free path and assuming an equal probability of the phonon originating at any point in the nanostructure. We find our predictions to be consistent with an analytical result for the in-plane direction in the thin films, as opposed to the Matthiessen rule, which leads to an under-prediction by up to 10%. Furthermore, we are able to use our approach to predict the thermal conductivities of complex nanostructures, where correct application of the Matthiessen rule is challenging.

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