Computational techniques for simulation of sub-micron thermal conduction

Sub-micron heat conduction in dielectrics can be analyzed using the phonon Boltzmann Transport Equation (BTE) in the relaxation time approximation. The paper describes the development of unstructured finite volume numerical techniques to address the BTE. Spatial, angular, spectral and temporal discretization procedures are described. The performance of sequential solution procedures for the BTE is compared to that of a point-coupled algorithm called the coupled ordinate method (COMET). The sequential algorithm is shown to perform well for low acoustic thicknesses, but is quickly exceeded in performance by COMET as the acoustic thickness is increased. The proposed numerical schemes are applied to a variety of sub-micron conduction problems, both unsteady and steady. Favorable comparison is found with the published literature and with exact solutions.