Efficient calculations of the Mode-Resolved ab-initio thermal Conductivity in nanostructures

Abstract: First-principles calculations of thermal transport in homogeneous materials have reached remarkable predicting power. Modeling deterministically phonon transport in nanostructures, however, poses novel challenges; notably, it entails solving as many algebraic equations as the number of combinations of wave vectors in the discretized Brillouen and polarizations. We show that, within the relaxation time approximation of the Boltzmann transport equation (BTE), this issue is resolved by interpolating the phonon distributions in the vectorial phonon mean free paths (MFP) space. The coupling between structure and mode-resolved heat transport is investigated in terms of angular-resolved bulk thermal conductivity and phonon suppression function, the latter being associated primarily to the material's geometry. Our method, termed the anisotropic MFP-BTE (aMFP-BTE), allows for fast and accurate thermal conductivity calculations in nanomaterials regardless of the number of phonon branches and wave vectors. Furthermore, it naturally blends with first-principles thermal transport calculations, therefore allowing for multiscale, parameter-free simulations. We apply the aMFP-BTE to compute the mode-resolved effective thermal conductivity of porous Si membranes, achieving up to 50x speed with respect to the case with no interpolation. The proposed approach unlocks the engineering of novel nanostructures, with applications to thermoelectrics and heat management.