3.1.1.3 Thermoelectric Figure of Merit

Figure 3.6: Ballistic thermoelectric figure of merit as a function of ribbon's width and temperature.

After calculating the ballistic electrical and thermal parameters, one can evaluate the thermoelectric figure of merit using the Eq. 2.1. The $ZT$ values are shown in Fig. 3.6 for the ribbon's widths between $1\mathrm{nm}$ and $6~\mathrm{nm}$ and temperature up to $750~\mathrm{K}$ . By increasing the ribbon's width, $ZT$ decreases drastically. It is due to the fact that the lattice thermal conductance strongly increases with $W$ , whereas the power factor slightly increases. On the other hand, for a given ribbon's width, $ZT$ peaks both at very low and very high temperatures. At high temperature, the contribution of the second conduction subband results in a high power factor. On the other hand, the lattice thermal conductance strongly decreases with temperature, whereas the power factor can be kept by adjusting the Fermi energy. As a result, a high value of $ZT$ can be obtained at very low temperature as well, although the $ZT$ value is smaller than $0.3$ for various ribbons and temperatures.