A Comparative Study of Submicron Phonon Transport Using the Boltzmann Transport Equation and the Lattice Boltzmann Method

Abstract

The subcontinuum energy transport mechanism in solids can be explained by the Lattice Boltzmann Method (LBM), a discrete representation of the Boltzmann Transport Equation (BTE). The present study focuses on a detailed comparison of the LBM and BTE. Results reveal that at continuum scale, the LBM follows the BTE almost precisely. However, as the device dimensions are reduced, approaching the ballistic limit, the LBM deviates from the BTE results in terms of thermal property estimation. The inherent nonisotropic lattice configuration has a dominant contribution to the performance of the LBM. A threshold length scale is also proposed for successful implementation of the LBM solver.