Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the Lattice Boltzmann Method applied to phonon transport. The discrete Lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path, and that the thermal energy transport process is characterized by the propagation of multiple, superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray Lattice Boltzmann Method.
Lattice Boltzmann method for the fractional advection-diffusion equation
