Phonon transport characteristics across silicon thin film pair: Presence of a gap between the films

Abstract

Phonon transport across silicon thin lm pair with minute gap (Casimir limit) between the lms is studied. Phonon transport characteristics across the gap are examined for various gap sizes, and the transient solution of the frequency-dependent Boltzmann transport equation is presented according to relevant boundary conditions incorporating the gap between the lm pair. Since the gap size is minute (Casimir limit), the radiative energy transport between the edges of the lm pair is incorporated. In addition, phonon transmission and re ection is introduced at the gap edges, thus satisfying energy conservation. The thermal conductivity predicted is validated through experimental data reported in the open literature. Predicted thermal conductivity data agree well with the experimental data reported in the open literature. Increasing gap size alters the phonon transport characteristics across the lm pair. Increasing gap size enhances temperature di erence between the edges of the gap; in which case, the e ect of phonon transmittance is more signi cant on the temperature di erence than that corresponding to the radiation heat transfer due to Casimir limit.