Phonon transport and equivalent equilibrium temperature in thin silicon films

Phonon transport in dielectric film depends on phonon polarization and their frequencies. This requires the solution of frequency-dependent Boltzmann equations for energy transport in dielectric films. In the present study, a frequency-dependent solution of the Boltzmann equation is obtained for a two-dimensional silicon film, and variation of equivalent equilibrium temperature in the film is presented. The influence of film width on phonon transport in the film is examined. The comparison of equivalent equilibrium temperature obtained from the frequency-dependent and -independent solutions is also presented. It is found that ballistic phonons suppress equivalent equilibrium temperature increase in the film. Two-dimensional phonon transport reduces to one-dimensional transport in film as the film width increases to more than twice of the film thickness.