Onset of size effects in lattice thermal conductivity and lifetime of low-frequency thermal phonons

Abstract

ABSTRACTThe onset of size effects in phonon-mediated thermal transport along a thin film at temperatures comparable or greater than the Debye temperature is analyzed theoretically. Assuming a quadratic frequency dependence of phonon relaxation rates in the low-frequency limit, a simple closed-form formula for the reduction of the in-plane thermal conductivity of thin films is derived. The effect scales as the square root of the film thickness, which leads to the prediction of measurable size-effects even at “macroscopic” distances ~100 μm. However, this prediction needs to be corrected to account for the deviation from the ω−2 dependence of phonon lifetimes at sub-THz frequencies due to the transition from Landau-Rumer to Akhiezer mechanism of phonon dissipation.