Phonon Transport in Silicon Thin Film: Effect of Temperature Oscillation on Effective Thermal Conductivity

Abstract

In this article, we consider phonon transport in thin silicon film and examine the influence of temporal oscillation of the temperature heat source on the phonon transport. We solve the frequency-dependent transient two-dimensional Boltzmann equation numerically to observe the quasi-ballistic effects of the phonons on the film effective thermal conductivity. Temperature oscillation at different periods is incorporated at the bottom face of the film as a heat source. The size of the temperature source is varied by introducing the spatial Gaussian distribution along this face. In order to assess the phonon distribution in the film, we introduce the equivalent equilibrium temperature. We determine the effective thermal conductivity of the film and analyze its variation due to the different periods of the temperature oscillation and the Gaussian parameters. It is found that reducing the period of the temperature oscillation lowers the effective thermal conductivity of the film, which is more pronounced for low Gaussian parameters. In this case, the quasi-ballistic behavior of phonons contributes adversely to the effective thermal conductivity of the film.

Keywords:

• phonon transport
• thin silicon film
• size effect
• thermal conductivity