6.1 Thermal Conductivity

Figure 6.1: The thermal conductivity for silicon nanowires versus diameter at $T=300~\mathrm{K}$ . Results for nanowires in the $\textless 100\textgreater$ (blue-circle), $\textless 110\textgreater$ (red-square), and $\textless 111\textgreater$ (green-triangle) orientations are shown. Solid symbols: Results when only phonon-phonon scattering is included. Empty symbols: Results when phonon-phonon and phonon-boundary scattering are included.

The thermal conductivity of silicon nanowires versus diameter is shown in Fig. 6.1 for nanowires in the $\textless 100\textgreater$ (blue lines), $\textless 110\textgreater$ (red lines), and $\textless 111\textgreater$ (green lines) transport orientations. With solid symbols we show the phonon-phonon scattering-limited thermal conductivity, whereas with empty symbols the thermal conductivity additionally includes phonon-boundary scattering. Several interesting observations can be made here. First, there is a significant anisotropy in the thermal conductivity, with the $\textless 110\textgreater$ nanowires having the highest conductivities in the entire diameter range, also in agreement with other theoretical studies [111]. Second, the phonon-phonon scattering-limited thermal conductivity (solid symbols) is reduced by a factor of $\sim 5\mathrm{X}$ from to the bulk value which is $140~\mathrm{W/mK}$ . This indicates the strong influence of phonon confinement. Third, phonon-boundary scattering has a quite strong influence, reducing the thermal conductivity by another factor of $\sim 5\mathrm{X}$ , limiting the thermal conductivity to values below $10~\mathrm{W/mK}$ in the entire diameter range, irrespective of transport orientation.

This strong reduction of the thermal conductivity is the main reason for the improved thermoelectric performance in nanostructures. Phonon-boundary scattering is the main reason for that reduction, although phonon confinement also contributes to $\kappa_{\mathrm{ph}}$ reduction. For nanowires with ultra-narrow diameters, however, the electrical conductivity is also strongly degraded by SRS, and it is yet not clear if rough boundaries can still provide a benefit to the $ZT$ . Below, we provide answers to this issue.