Prediction of reduced thermal conductivity in nano-engineered rough semiconductor nanowires

We explore phonon decay processes necessary to the design of efficient rough semiconductor nanowire (NW) thermoelectric devices. A novel approach to surface roughness-limited thermal conductivity of Si, Ge, and GaAs NW with diameter D < 500 nm is presented. In particular, 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 Δ and autocovariance length L. Using a full phonon dispersion relation, the thermal conductivity varies quadratically with diameter and roughness as (D/Δ)². Computed results are in agreement with experimental data, and predict remarkably low thermal conductivity below 1 W/m/K in rough-etched 56 nm Ge and GaAs NW at room temperature.