An anisotropic full Brillouin zone model for the three dimensional phonon Boltzmann transport equation

A model and associated numerical method are presented for simulation of heat transport at the microscale via the solution of the three dimensional phonon Boltzmann Transport Equation (BTE). In small domains, the full Brillouin Zone has a finite number of vibrational modes, as determined by Born von-Karman boundary conditions. As a result of this discreteness, the present method allows for general crystal anisotropy and finite dimensional effects that naturally permit anisotropic thermal transport and energy flow. The method is shown and verified using analytical solutions for isotropic flows. Then numerical experiments are performed to calculate temperature and energy in a fin field effect transistor made of a cubic crystalline material. The anisotropic thermal conductivity and the consequences on thermal fields are calculated. The differences between an isotropic solution and the anisotropic model are shown to be significant with differences in the temperatures approximately 10%. At larger scales, where scattering effects dominate, differences in the solutions become smaller and macroscopic isotropy is recovered due to the cubic symmetry of the material.