4. Ballistic Thermal Properties of Silicon-Based Nanostructures

Low dimensional silicon materials, such as nanowires and ultra-thin layers have demonstrated record low thermal conductivities of $1-2~\mathrm{W/mK}$ , reaching the amorphous limit. This resulted in $ZT$ values close to $ZT\sim 0.5$ , a large improvement compared to bulk silicon with $ZT_{\mathrm{Bulk}}\sim 0.01$  [17,20]. Although the two order of magnitude reduction in the thermal conductivity is attributed to boundary scattering of phonons, an additional reduction can be achieved from changes in the phonon mode structure due to geometrical confinement. In this chapter, the effect of confinement and orientation on the phonon transport properties of silicon-based nanostructures of various surface and transport orientations are investigated. To this aim, the density of states, the transmission function, the sound velocity, and the ballistic thermal conductance of silicon-based ultra-thin layers and narrow nanowires are extracted. The lattice dynamics is, here, modeled by the modified valence force field method and the ballistic Landauer transport formalism is employed to calculate the thermal conductance.