Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling

The lattice Boltzmann method (LBM) is used to investigate one-dimensional, multi-length and -time scale transient heat conduction in crystalline semiconductor solids, in which sub-continuum effects are important. The implementation of this method and its application to electronic devices are described. A silicon-on-insulator transistor subject to Joule heating conditions is used as a case study to illustrate the essence of the LBM. We compare our LBM results, for the diffusive to the ballistic transport regimes, with various hierarchical methodologies of heat transport such as the Fourier, Cattaneo, and ballistic-diffusive transport equations.