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Multiscale Phonon Conduction in Nanostructured Materials Predicted by Bulk Thermal Conductivity Accumulation Function

We develop a computational framework, based on the Boltzmann transport equation, with the ability to compute the thermal transport in nanostructured materials of any geometry using as the only input the bulk thermal conductivity accumulation function. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with a frequency-dependent approach. Second, when phonon dispersions are available from first principles calculations, our approach allows one to include easily the whole Brillouen zone in the calculations without discretizing the phonon frequencies for all polarizations, reducing considerably the computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multi-scale scheme that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon mean free path distributions. After we validate our model against the frequency-dependent approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has potential to advance high-efficiency thermoelectric devices.