We present a novel approach for computing the surface roughness-limited thermal conductivity of silicon nanowires with diameter $D<100\mathrm{nm}$. 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 $\Delta$ and autocovariance length $L$. Using a full phonon dispersion relation, we find a quadratic dependence of thermal conductivity on diameter and roughness as $(D/\Delta {)}^2$. 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 $2\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at room temperature in rough-etched 50 nm silicon nanowires.

• Received 24 November 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.125503