# Na-Doping Effects on Thermoelectric Properties of Cu\({}_{2-x}\)Se Nanoplates
## 3 Results and Discussion
Figure 5 shows the electrical and thermal properties of SPSed bulk pellets of nanowire, nanoplate, and Na-doped Cu\({}_{2-x}\)Se nanoplate, and compared to that of bulk Cu\({}_{1.75}\)Se sample [32]. For all of the samples, with the increase of the temperature, the electrical conductivity decreases, indicating a degenerated semiconductor behavior, shown in Figure 5a. The electrical conductivity of SPSed bulk pellets of nanowire is relatively lower than those of the other two samples, which is mainly due to the presence of point defects and dislocations by Cu vacancies in the pellet along with lower symmetry. Compared to the bulk, the undoped Cu\({}_{2-x}\)Se nanoplates exhibited a similar electrical conductivity. It is observed that a Na doped Cu\({}_{2-x}\)Se nanoplate sample shows lower electrical conductivity than a Cu\({}_{2-x}\)Se nanoplate sample. The reason for this may be the reduction of the carrier concentration by Na-doping. Figure 5b shows the temperature dependences of the Seebeck coefficients. All samples possess a positive Seebeck coefficient in the measured temperature range. This means that the Cu\({}_{2-x}\)Se samples exhibit p-type conduction and the majority carriers are holes, which is consistent with the Hall measurements. It can be seen that the Seebeck coefficients increase from 10 to 70 \(\upmu\)V/K with increasing temperature. It is observed that Na doped Cu\({}_{2-x}\)Se nanoplate sample shows a slightly higher Seebeck coefficient than that of the undoped Cu\({}_{2-x}\)Se nanoplate sample. This result can be attributed to the lower carrier concentration by Na doping. Based on the results of the electrical conductivity and the Seebeck coefficient, the power factor (_PF_) of all of the samples can be calculated according to the equation _PF_ = \(\sigma\)_S_\({}^{2}\). As shown in Figure 5c, the power factor increases as temperature increases due to the increased values of Seebeck coefficients. Because of a high electrical conductivity, the maximum power factor of the undoped Cu\({}_{2-x}\)Se nanoplate  
Figure 4: (a) X-ray photoelectron spectroscopy (XPS) survey spectra, and high-resolution XPS spectra of (**b**) Na; (**c**) Cu; and (**d**) Se ions of SPSed Na-doped Cu\({}_{2-x}\)Se sample. is 6.5 \(\upmu\)W/cmK\({}^{2}\) (at \(\sim\)673 K). A Na-doped Cu\({}_{2-\chi}\)Se nanoplate has a slightly lower PF when compared to the Cu\({}_{2-\chi}\)Se nanoplate. The peak PF values of 3.9 \(\upmu\)W/cmK\({}^{2}\) (at \(\sim\)673 K) was observed for the Na-doped Cu\({}_{2-\chi}\)Se nanoplate. This lower PF is mainly owing to the lower electrical conductivity of Na-doped Cu\({}_{2-\chi}\)Se nanoplate samples. As shown in Figure 5d, the thermal conductivity of all of the samples decreased gradually with increasing temperature. Owing to the \(\upalpha\)-\(\upbeta\) phase transition in Cu\({}_{2-\chi}\)Se compounds, an anomalous behavior of thermal conductivity is observed near 373 K [35]. The thermal conductivities of the Na-doped Cu\({}_{2-\chi}\)Se samples are lower than that of the undoped Cu\({}_{2-\chi}\)Se nanoplate sample. The total thermal conductivity (\(\kappa_{tot}\)) is the sum of two contributions, one from the charge carriers (\(\kappa_{dec.}\)), and the other from the lattice vibrations (\(\kappa_{latt. }\)), (\(\kappa_{tot}\) = \(\kappa_{dec.}\) + \(\kappa_{latt.}\)). Here \(\kappa_{dec.}\) is estimated by the Wiedemann-Franz relationship, \(\kappa_{dec.}\) = \(L_{0}\sigma T\), where \(L_{0}\) is the Lorenz number, \(\sigma\) is the electrical conductivity and \(T\) the absolute temperature. The value of Lorenz number (\(L_{0}\) = 1.5 \(\times\) 10\({}^{-8}\) W\(\Omega\)/K\({}^{2}\)) [35] for Cu\({}_{2-\chi}\)Se is used to estimate \(\kappa_{dec.}\). The \(\kappa_{latt. }\) values are calculated by subtracting \(\kappa_{dec.}\) from \(\kappa_{tot}\), present in Figure 5d. The \(\kappa_{latt. }\) values of undoped and Na-doped Cu\({}_{2-\chi}\)Se at 300 K are \(\sim\)3.03 W/m\(\cdot\)K and \(\sim\)0.83 W/m\(\cdot\)K, respectively.