Transient Effects of Phonon Transport in Two-Dimensional Silicon Film

Abstract

Energy transport in silicon film takes place through a phonon transport, which is important in cooling applications of photonic devices. Since the energy transport is transient, the transient effect should be considered in the analysis. In the present study, phonon transport in the two-dimensional silicon film with transient effect is considered. The Boltzmann transport equation is solved numerically with the appropriate boundary conditions to compute equivalent equilibrium temperature in the film. The difference between equivalent equilibrium temperature in one- and two-dimensional films is demonstrated, and the time required to attain a steady state temperature in the film is established. The findings revealed that the time required to reach steady temperature is faster in the vicinity of the high temperature edge of the film than that corresponding to the low temperature edge. Equivalent equilibrium temperature for one-dimensional film is slightly lower than its counterpart corresponding to two-dimensional film during the time period t ≤ 30 ps; however, as the heating period progresses, this becomes the opposite.