4.1 Silicon Nanowires

Numerous studies can be found in the literature regarding the thermal conductivity of silicon nanowires [98,99,100,101,102]. The effects of different scattering mechanisms, i.e. surface roughness scattering, mass doping, phonon-phonon scattering, and phonon-electron scattering have been investigated by several authors [103,104,105,106]. In these works, it is demonstrated that the thermal conductivity in ultra-narrow silicon nanowires drastically degrades once the diameter of the nanowire is reduced below $50~\mathrm{nm}$ , or when scattering centers are incorporated. For even smaller nanowire diameters, i.e. below $10~\mathrm{nm}$ , the effect of confinement could further change the phonon spectrum significantly, and provide an additional mechanism in the reduction of the thermal conductivity [107]. This could provide additional benefits to the thermoelectric figure of merit $ZT$ . In this section, we employ the modified valence force field method [45] to address the effect of structural confinement on the phonon dispersion, group velocity and ballistic thermal conductance of ultra-narrow silicon nanowires of diameters below $10~\mathrm{nm}$ . We consider different transport orientations, and different cross sectional sizes (square cross sections $W=H$ ).