Numerical simulations of time-dependent 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 first gray dispersion and then nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that a transition from diffusive to ballistic energy transport is found as the characteristic length of the system becomes comparable to the phonon mean free path. The methodology is used in representative microelectronics applications covering both crystalline and amorphous materials including silicon thin films and nanoporous silica dielectrics. Size-dependent thermal conductivity values are also computed based on steady-state temperature distributions obtained from the numerical models. For each case, reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values. Overall, simulations that consider phonon dispersion yield results more consistent with experimental correlations.