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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.
Image KpUPq

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.

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Next: 6.2 Thermoelectric Figure of Merit Up: 6. Thermoelectric Figure of Merit of Ultra-Narrow Silicon Nanowires Previous: 6. Thermoelectric Figure of Merit of Ultra-Narrow Silicon Nanowires   Contents
H. Karamitaheri: Thermal and Thermoelectric Properties of Nanostructures