Multiscale Lattice Boltzmann Modeling of Phonon Transport in Crystalline Semiconductor Materials

A coupled lattice Boltzmann (LB)–finite-difference (FD) method is used to solve for the heat transport in a two-dimensional domain. The LB method is used to capture relevant phonon physics near a microscopic heat-generation region by solving the Boltzmann transport equation, while a finite-difference model is used to capture the thermal transport at the macroscopic level. The coupling region between the LB and FD domains, which enables multiscale modeling, is discussed. The model is evaluated versus other numerical methods as well as experimental results. In all cases, the multiscale approach yielded results that were accurate to within the experimental uncertainty.