Review of Multiscale Simulation in Submicron Heat Transfer

Over the last decade, interest in the simulation of micro- and nano-scale heat transfer has lead to the development of a variety of models and numer-ical methods for phonon transport in semiconductors and dielectrics. These models span direct simulation using molecular dynamics, a range of mod-els of varying fidelity based on the Boltzmann transport equation, as well as simpler hyperbolic extensions to the classical Fourier heat conduction equa-tion. The paper reviews the basics of phonon transport in crystals, available models for phonon transport, as well as numerical methods for solving the equations resulting from these models. Recommendations are made for fu-ture work. 1 Nomenclature £ interatomic distance £¥¤§¦¨£¥ © ¡ center and neighbor discrete coefficients volumetric specific heat �� � energy density density of states for polarization � angular average of energy density phonon distribution function equilibrium distribution function interatomic force between atoms � and � reciprocal lattice vector number of atoms per unit volume Planck constant thermal conductivity Boltzmann constant wavenumber wave vector domain length