Maximizing and minimizing the boundary scattering mean free path in diameter-modulated coaxial cylindrical nanowires

Abstract

The thermal conductivity (k) of semiconducting nanomaterials is influenced by the geometry-dependent phonon boundary scattering mean free path (ΛBdy). Although prior work has calculated ΛBdy of periodically corrugated rectangular nanowires and used these results to study phonon backscattering in nanomaterials, ΛBdy remains unknown for recently fabricated periodic coaxial cylindrical nanowires. Here, we use phonon ray tracing simulations to comprehensively study the effect of geometric parameters on ΛBdy in coaxial cylindrical nanowires. We find that for a fixed smaller cylinder diameter (D1) and cylinder length ratio, ΛBdy of periodic nanowires can be maximized or minimized via geometric control of the pitch (p) and larger cylinder diameter (D2). Our simulations show that saturated phonon backscattering for small pitch ratio (pr) nanowires gives rise to a minimum in ΛBdy/D1 at pr near unity, while the maximum in ΛBdy/D1 for large pr nanowires can be understood using a simple thermal resistor model for two individual nanowires in series. Combining our ΛBdy calculations with analytical phonon dispersion and bulk scattering models, we predict that k of periodic silicon nanowires with fixed D1can be tuned by up to 34% in the boundary scattering dominated regime by modifying D2 and p and that variations as large as 135% can be observed in the normalized thermal conductance. Our results provide insight into geometry-dependent phonon backscattering and can be used to predict k of periodic cylindrical nanowires over a range of temperatures and geometric lengthscales.