Thermal transport across a pair of thin silicon films with the presence of minute vacuum gap: effect of film thickness on thermal characteristics

Abstract

Energy transport across a pair of thin silicon films with the vacuum gap at the films interface is studied. The Boltzmann transport equation is incorporated in the analysis and the solution for the transient frequency-dependent phonon distribution across the films pair is presented. To assess the phonon characteristics, equivalent equilibrium temperature is introduced, which resembles the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. Because the gap size is comparable to the mean free path of silicon, a near-field radiation heat transfer is incorporated across the film edges at the interface. The frequency cutoff method is used at the interface of the films and the phonons jump across the gap resembling the ballistic phonon contribution to the energy transport is accommodated. The thermal conductivity data predicted are validated with the data obtained from the previous study. The effect of near-field radiation heat transfer on temperature increase at the edges of the film, across the gap interface, is not considerable as compared to that corresponding to phonons transmitted across the gap. Increasing the first film thickness increases temperature difference across the gap, which is more pronounced for large gap sizes.