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

TL;DR

This paper introduces a new method to calculate how surface roughness affects the thermal conductivity of silicon nanowires smaller than 100 nm, showing good agreement with experiments and predicting very low thermal conductivity in rough nanowires.

Contribution

It develops a frequency-dependent phonon scattering model based on surface roughness parameters and full phonon dispersion, providing accurate predictions of thermal conductivity in silicon nanowires.

Findings

Thermal conductivity scales quadratically with diameter and roughness.

Model matches experimental data across various diameters and temperatures.

Predicts extremely low thermal conductivity (~2 W/m·K) in rough 50 nm silicon nanowires.

Abstract

We present a novel approach for computing the surface roughness-limited thermal conductivity of silicon nanowires with diameter D < 100 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 W.m^{-1}.K^{-1} at room temperature in rough-etched 50 nm silicon nanowires.