Lattice Thermal Conductivity in Nanowires: Coupling the Bechmann–Kirchhoff Boundary Scattering Model With a Monte Carlo Framework

Abstract

In this article, the effect of rough surface on phonon transport has been studied for silicon nanowire structures. The diffusive boundary scattering has been treated using the Beckmann–Kirchhoff (B-K) surface roughness scattering (SRS) model, considering the effect of roughness height, correlation length, phonon wavelength, and incident/reflected angles. The model is more comprehensive and accurate than the conventional approaches, where surface roughness is usually modeled based on experimental fitting parameters or only phonon wavelength. The B-K SRS model has been integrated within a particle-based Monte Carlo phonon transport (MCPT) simulator to study the thermal conductivity of different nanowire structures. The simulator is benchmarked against the experimental data for both bulk and nanowire devices. The reduction of thermal conductivity in nanowires as a function of the degree of roughness has been discussed. It is found that for a 70-nm-width, 6- $\mu \text{m}$ -long silicon structure, using 2.3-nm roughness height and 8.9-nm correlation length, 89% reduction in thermal conductivity occurs at 300 K. The sensitivity of the developed simulator with varying degree of roughness and the effect of SRS on different phonon spectral branches have been studied. These observations can be useful in designing materials with low thermal conductivity for thermoelectric cooling applications.