Thin film phonon heat conduction by the dispersion Lattice Boltzmann method. http://dx.doi.org/10.1115/1.2944249

Abstract

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
thermal conductivity when compared to bulk values, at a higher rate than what was
displayed by the Debye-based gray lattice Boltzmann method.