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We develop a computational framework, based on the Boltzmann transportequation, with the ability to compute the thermal transport in nanostructuredmaterials of any geometry using as the only input the bulk thermal conductivityaccumulation function. The main advantage of our method is twofold. First,while the scattering times and dispersion curves are unknown for mostmaterials, the phonon mean free path distribution can be directly obtained byexperiments. As a consequence, a wider range of materials can be simulated thanwith a frequency-dependent approach. Second, when phonon dispersions areavailable from first principles calculations, our approach allows one toinclude easily the whole Brillouen zone in the calculations withoutdiscretizing the phonon frequencies for all polarizations, reducingconsiderably the computational effort. Furthermore, after deriving theballistic and diffusive limits of our model, we develop a multi-scale schemethat couples phonon transport across different scales, enabling efficientsimulations of materials with wide phonon mean free path distributions. Afterwe validate our model against the frequency-dependent approach, we apply themethod to porous silicon membranes and find good agreement with experiments onmesoscale pores. By enabling the investigation of thermal transport inunexplored nanostructured materials, our method has potential to advancehigh-efficiency thermoelectric devices.

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