Model for lattice thermal conductivity of clamped and free surface cylindrical nanowires.

Abstract

A model for the prediction of thermal conductivities of cylindrical nanowires (NWs) is presented. The model is based on the solution of the Boltzmann equation within the relaxation time approximation. Silicon (Si) NWs with clamped and free surface boundary conditions are considered, where the phonon group velocities were obtained from elasticity theory. Surface roughness is also modelled through the use of a specularity parameter. Calculations were carried out on NWs of diameter 10 and 22 nm for both clamped and free surface boundary conditions. The thermal conductivity of the NWs is found to be about two orders of magnitude lower than that of bulk Si. The significant drop in the thermal conductivity from its bulk value is ascribed to enhanced phonon boundary scattering and to phonon spectrum modification. The accuracy of the developed theory is demonstrated with reference to reported experimental measurements on individual Si NWs. It is found that the thermal conductivity of a free surface NW is larger than that of a clamped surface NW, and we predict an increase of approx. 100percent at 300 K for the 10 nm wire as the boundary conditions are changed from clamped to free. We suggest using the observed surface effect for thermal current modulation with piezoelectric cladding materials.