Mesoscale modeling of phononic thermal conductivity of porous Si: interplay between porosity, morphology and surface roughness

In this work we compute the effective thermal conductivity of porous Si by means of the phonon Boltzmann transport equation. Simulations of heat transport across aligned square pores reveal that the thermal conductivity can be decreased either by increasing the pore size or decreasing the pore spacing. Furthermore, by including the surface specularity parameter we show that the roughness of the pore walls plays an important role when the pore size is comparable with the phonon mean free path, because to the increase in the surface-to-volume ratio. Thanks to these results, in qualitatively agreement with those obtained with Molecular Dynamics simulations, we gained insights into the scaling of thermal properties of porous materials and interplay between disorder at different length scales. The model, being based on a flexible multiscale finite element context, can be easily integrated with electrical transport models, in order to optimize the figure of merit ZT of thermoelectric devices.