Phonon Transport in Silicon-Diamond Thin Film Pairs: Consideration of Thermal Boundary Resistance Due to Cutoff Mismatch and Diffusive Mismatch Models

Abstract

Thermal boundary resistance (TBR) generates a temperature drop across the interface of the thin film pairs, which in turn modifies the heat transport rates across the films. This effect magnifies for the dielectric films because of the boundary scattering of phonons during the energy transport. Therefore, investigation into TBR and phonon transport across thin film pairs becomes essential. In the present study, phonon transport across the silicon-diamond thin film pairs due to temperature disturbance is formulated using the first principle solution of the transport equation. The transient and frequency dependent solution of the Boltzmann transport equation is presented numerically for two-dimensional thin film pairs. The TBR at the interface of the thin film pairs is modeled incorporating the cutoff mismatch and diffusive mismatch models. It is found that the value of TBR predicted from the cutoff mismatch model agrees with the results reported in the open literature; in which case, the predictions of the cutoff mismatch model for the TBR are larger than those predicted from the diffusive mismatch model.