Influence of Heat Source Size on Phonon Transport in Thin Silicon Film

Energy transfer is mainly governed by the phonon transport in dielectric films. The polarization and dispersion of the phonons alter the thermal resistance of the film as the film size becomes comparable to the mean path of the substrate material. This is because of the quasi-ballistic behavior of the transport characteristics. In this case, the ballistic phonons do not undergo scattering in the film while suppressing the thermal resistance increase across the film. In the present study, the quasi-ballistic phonon transport and the effect of heat source size on the phonon transport characteristics are investigated in the two-dimensional silicon film. The heat source is located at one edge of the film while other edges assumed to be at uniform temperature. Since the Knudsen number is small (~1), the Boltzmann transport equation is solved numerically, incorporating the polarization and dispersion of phonons, to obtain phonon intensity distribution in the film. Equivalent equilibrium temperature is introduced to assess the phonon intensity distribution in the film. The transient behavior of the phonon transport is incorporated in the analysis to predict the time to reach steady state value of equivalent temperature in the film. It is found that the size of the heat source has a significant effect on the phonon transport in the film. The effective thermal conductivity reduces significantly as the heat source size reduces.