Quasiballistic phonon transport from first principles

Abstract

At short length scales phonon transport is ballistic: the thermal resistance of semiconductors and insulators is quantized and length independent. At long length scales, on the other hand, transport is diffusive and resistance arises as a result of the scattering processes experienced by phonons. In many cases of interest, however, these two transport regimes coexist. Here we propose a first-principles approach to treat quasiballistic phonon transport where diffusive and ballistic phonons receive separate theoretical treatments. Partitioning the overall phonon population for a given transport length is performed examining the mean free paths obtained from the solution of the Boltzmann transport equation and allowing only diffusive phonons to participate in anharmonic phonon-phonon scattering processes. We present results for Si and diamond, discussing the crossover from ballistic to diffusive transport as the length scale and/or the temperature increases and compute the relative contribution of ballistic and diffusive phonons to the thermal conductance in each transport condition.