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

The thermal conductivity (k) of semiconducting nanomaterials is controlled by the geometry-dependent phonon boundary scattering mean free path (Λ_Bdy). Here, we use phonon ray tracing simulations to study phonon backscattering and geometry-dependent Λ_Bdy in recently fabricated coaxial cylindrical nanowires. We use simulated average transmissivity t to calculate Λ_Bdy via a Landauer-Bttiker formalism. For a fixed smaller cylinder diameter (D₁) and cylinder length ratio, we find that Λ_Bdy of periodic nanowires can be maximized or minimized via geometric control of the pitch (p) and larger cylinder diameter (D₂). Saturated phonon backscattering for small pitch ratio (p_r) nanowires causes a minimum in Λ_Bdy/D₁ at p_r near unity, while the maximum in Λ_Bdy/D₁ for large p_r nanowires can be understood by a simple thermal resistor model for two individual nanowires in series. Combining our Λ_Bdy calculations with analytical phonon dispersion and bulk scattering models, we predict that k of periodic silicon nanowires with fixed D₁ can be tuned by up to 34% in the boundary scattering dominated regime by modifying D₂ and p. These results provide insight into phonon backscattering mechanisms in periodic nanomaterials, and can be used to model future experiments on coaxial cylindrical nanowires.