6. Thermoelectric Figure of Merit of Ultra-Narrow Silicon Nanowires

Thermoelectric materials based on nanostructured and low-dimensional silicon have attracted a significant attention after recent experiments indicated that they can provide a large $ZT$ figure of merit [20,17,142]. Although bulk silicon has $ZT_{\mathrm{bulk}} \sim 0.01$ , the $ZT$ of silicon nanowires with side lengths scaled down to $\sim 50~\mathrm{nm}$ was experimentally demonstrated to be $ZT_{\mathrm{NW}} \sim 0.5$  [20,17]. A similar observation was made in silicon nanomeshes of features sizes $\sim 55~\mathrm{nm}$  [142]. This remarkable improvement in the $ZT$ was a result of a significant suppression in the thermal conductivity $\kappa_{\mathrm{ph}}$ , whereas the electronic power factor was not changed significantly compared to the bulk material. The measurements to date were performed in nanowires or nanomeshes of feature sizes of several 10s of nanometers [20,17,142]. Whether this trend continues, or even improves, when the nanowire diameters are reduced in the sub-ten nanometer regime still needs to be shown. The initial theoretical studies proposed that the performance can be improved once the channels are truly one-dimensional, or if the channel bandstructure is properly optimized [9,143]. On the other hand, at the sub-ten nanometer scale, the electronic mobility is severely degraded due to enhanced electron-phonon interaction and stronger surface roughness scattering (SRS) [143]. It still needs to be shown if this reduction would offset the performance improvement achieved through the reduction of thermal conductivity.

In this chapter, we compute the room temperature thermoelectric figure of merit $ZT$ in ultra-narrow silicon nanowires using atomistic simulations. The role of transport orientations and diameter on the thermoelectric power factor of nanowires using atomistic bandstructure simulations has been recently studied [143]. Using the thermoelectric power factor of Ref. [143] (Figs. 3c and 7c of Ref. [143]) and the calculated thermal conductivity, as in Chapter 5, we estimate the $ZT$ figure of merit for $n$ -type and $p$ -type cylindrical nanowires of various transport orientations.