Lattice-Boltzmann modeling of sub-continuum energy transport in Silicon-on-Insulator microelectronics including phonon dispersion effects

Numerical simulations of time-dependent energy transport in semiconductor thin films are conducted by using the Lattice-Boltzmann method applied to phonon transport. The discrete Lattice-Boltzmann method is first derived from the continuous Boltzmann transport equation, where nonlinear phonon dispersion relations are used to find frequency-dependent phonon velocities for longitudinal acoustic phonons. A Silicon-on-Insulator (SOI) transistor is modeled as a thin film of silicon, with a hotspot simulated by imposing a heat generation term in a localized region of the computational domain. Results indicate that a transition from diffusive to ballistic energy transport is found as the characteristic length of the thin film becomes comparable to the phonon mean free path. This transition is present in heat conduction in thin films as well as in the transient thermal response of SOI transistors. Steady-state temperature distributions are then used to calculate size-dependent thermal conductivity values in silicon thin films.