Impact of Phonon-Surface Roughness Scattering on Thermal Conductivity of Thin Si Nanowires

Abstract

We present a novel approach for computing the surface roughness-limited thermal conductivity of silicon nanowires with diameter $D<100\text{ }\text{ }\mathrm{nm}$. A frequency-dependent phonon scattering rate is computed from perturbation theory and related to a description of the surface through the root-mean-square roughness height $\ensuremath{\Delta}$ and autocovariance length $L$. Using a full phonon dispersion relation, we find a quadratic dependence of thermal conductivity on diameter and roughness as $(D/\ensuremath{\Delta}{)}^{2}$. Computed results show excellent agreement with experimental data for a wide diameter and temperature range (25--350 K), and successfully predict the extraordinarily low thermal conductivity of $2\text{ }\text{ }\mathrm{W}\text{ }{\mathrm{m}}^{\ensuremath{-}1}\text{ }{\mathrm{K}}^{\ensuremath{-}1}$ at room temperature in rough-etched 50 nm silicon nanowires.