Phonon focusing and temperature dependences of the thermal conductivity of silicon nanowires

The influence of phonon focusing on the anisotropy and temperature dependences of the thermal conductivity of silicon nanowires (NWs) has been studied using the three-mode Callaway theory. The calculated temperature dependences of the thermal conductivity of silicon NWs with diameters above 50 nm agree well with experimental data in the 20–300 K range. The temperatures of transitions from the boundary-scattering to volume-relaxation mechanisms are determined. Variation of the thermal conductivity anisotropy depending on temperature is analyzed. The free paths of phonons with various polarizations in the boundary scattering regime in silicon NWs significantly differ and depend to a considerable degree on the phonon focusing. The free paths reach maxima in the directions of phonon focusing and exceed values for other oscillatory modes. However, in the isotropic medium model, the phonon free paths for various polarizations coincide and are fully determined by the geometric parameters of NWs.