Phonon transport across nano-scale curved thin films

Abstract

Phonon transport across the curve thin silicon film due to temperature disturbance at film edges is examined. The equation for radiative transport is considered via incorporating Boltzmann transport equation for the energy transfer. The effect of the thin film curvature on phonon transport characteristics is assessed. In the analysis, the film arc length along the film centerline is considered to be constant and the film arc angle is varied to obtain various film curvatures. Equivalent equilibrium temperature is introduced to assess the phonon intensity distribution inside the curved thin film. It is found that equivalent equilibrium temperature decay along the arc length is sharper than that of in the radial direction, which is more pronounced in the region close to the film inner radius. Reducing film arc angle increases the film curvature; in which case, phonon intensity decay becomes sharp in the close region of the high temperature edge. Equivalent equilibrium temperature demonstrates non-symmetric distribution along the radial direction, which is more pronounced in the near region of the high temperature edge.