4.2 Silicon Thin Layers

In this section, the effects of confinement and orientation on the phonon transport properties of ultra-thin silicon layers of various surface and transport orientations are investigated. Figure 4.7 shows the geometrical cross sections of the thin-layers considered. The layers have $\{100\}$ , $\{110\}$ , $\{111\}$ , and $\{112\}$ surface orientations. In all cases, we consider the $x$ -axis to be parallel to the $\textless 110\textgreater$ orientation, and define the angle $\theta$ of the transport direction counter-clockwise from the $x$ -axis. Below, a complete analysis is presented by calculating the phononic properties and thermal conductance as a function of the angle $\theta$ for the four surface orientations mentioned. The layer thickness $H$ varies from $1$ to $16~\mathrm{nm}$ . The phononic dispersion, density of states, ballistic transmission, and effective group velocity of the different structures are calculated.

Figure 4.7: The atomistic structure of the cross sections of the different thin silicon layers investigated (a) $\{100\}$ , (b) $\{110\}$ , (c) $\{111\}$ , and (d) $\{112\}$ surface. In all cases the $x$ -axis is along the $\textless 110\textgreater$ transport direction. Transport orientations $\theta$ varies between 0 and $\pi$ .