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6.2.3 Diffusive Thermoelectric Figure of Merit

Figure 6.5: The ZT figure of merit for (a) $ n$ -type and (b) $ p$ -type 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. In the calculation of the power factor electron-phonon plus electron-boundary scattering is considered. In the calculation of the thermal conductivity phonon-phonon and phonon-boundary scattering are considered, but in this case the boundary is assumed to be fully diffusive. The dotted lines in (a) show for reference the $ ZT$ when only electron-phonon and phonon-phonon scattering is considered as in Fig. 6.2-a.
Image ZTP0

This improvement in the power factor further proves the point that boundary scattering is more effective in reducing the thermal conductivity than reducing the power factor. As a result, phonon engineering techniques that cause additional reductions in the thermal conductivity could provide improvements of $ ZT$ , despite the consequent reduction in the electrical conductivity. For example, in the case of a fully diffusive boundary for phonons, either by special engineering of the roughness [148,149,21], by decorating the surfaces with various species [150,59,151], or by modulating the nanowire's diameter [124], the $ ZT$ performance could be increased. This is illustrated in Fig. 6.5, showing $ ZT$ for the same nanowires as before in Fig. 6.3, but now we assume a fully diffusive boundary for phonons, e.g. the specularity parameter is set to $ p=0$ for all wavevectors. In this case, $ ZT$ is increased to values close to $ ZT\sim 1.3$ for both $ n$ -type and $ p$ -type nanowires (in the best cases). This is almost a factor of $ 2\mathrm{X}$ improvement compared to the case we present in Fig.6.3 where we employ the $ q$ -dependent specularity parameter $ p(q)$ , rather than fully diffusive boundaries for all phonons.


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Next: 7. Summary and Conclusions Up: 6.2 Thermoelectric Figure of Merit Previous: 6.2.2 Electron versus Phonon Transports in Rough Nanowires   Contents
H. Karamitaheri: Thermal and Thermoelectric Properties of Nanostructures