Effect of cross-sectional geometry on thermal conductivity of Si1−xGex nanowires

Abstract

By incorporating the direction-dependent phonon-boundary scattering from the surface of the nanowires with different cross-sectional shapes into the linearized phonon Boltzmann transport equation, we theoretically investigate the effect of cross-sectional geometry on the thermal conductivity of [Formula: see text] nanowires. It is demonstrated that the surface-to-volume ratio (SVR) is a universal gauge for both pure silicon nanowires (SiNWs) and silicon–germanium nanowires (SiGe NWs), and the thermal conductivity of nanowires decreases monotonically with the increase of SVR. We also find that the thermal conductivity of high-frequency phonons in nanowires is more strongly SVR dependent than that of low-frequency phonons, and the thermal conductivity of high-frequency phonons is severely suppressed by alloy scattering, therefore the SVR dependence on thermal conductivity of [Formula: see text] NWs decreases with the increase of Ge atom concentration [Formula: see text] [Formula: see text]. These findings are useful for understanding and tuning the thermal conductivity of nanowires by geometry.