Ballistic-Diffusive Approximation for Phonon Transport Accounting for Polarization and Dispersion

A ballistic-diffusive approximation to the Boltzmann transport equation is developed for describing phonon transport in semi-conductors and dielectrics. The model incorporates the effects of phonon dispersion and polarization by considering longitudinal, transverse and optical branches. Each branch is divided into frequency bands, and scattering between branches and bands is incorporated subject to conservation rules. The phonon energy in each band is divided into a boundary and a medium component, with the latter being computed using a diffusion approximation. The approximation is shown to work well by comparing its predictions to exact solutions as well thermal conductivity measurements for bulk silicon.