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Phonon transport across silicon thin film pair with minute gap (Casimir limit) between the films 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 film pair. Since the gap size is minute (Casimir limit), the radiative energy transport between the edges of the film pair is incorporated. In addition, phonon transmission and reflection 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 film pair. Increasing gap size enhances temperature difference between the edges of the gap; in which case, the effect of phonon transmittance is more significant on the temperature difference than that corresponding to the radiation heat transfer due to Casimir limit.

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