Lattice-Boltzmann finite-difference model with optical phonons for nanoscale thermal conduction
A recently developed multiscale model is used to study thermal conduction in silicon. In this work, the role of optical phonons is included in the nanoscale by introducing phonons with zero velocity in the lattice-Boltzmann domain. In the model, only the optical phonons are heated, and the energy transfer rate from optical to acoustic phonons is described with a relaxation time. As a test case, a nanoscale hot spot is introduced into the system, and thermal conduction to ambient medium is calculated. The results show a temperature step at the spot boundary, while elsewhere the results are identical to thermal diffusion. Optical phonons are seen to increase the spot boundary thermal resistance, which is also heavily dependent on the relaxation time of the optical-acoustic phonon scattering.
phonon boltzmann transport equation distribution function