## 3 Results and Discussions  
Because of the anisotropic crystal structure of the Bi\({}_{2}\)Te\({}_{3}\)-based alloys, their electronic and thermal transport properties are strongly influenced by the measurement directions (00\(l\) orientation characteristics). To minimize this effect, we prepared the SPSed bulks with a similar 00\(l\) orientation by controlling the SPS conditions. As shown in Figure 1 (XRD patterns for the SPSed bulks of Cu\({}_{0.01}\)Bi\({}_{2\cdot x}\)Hf\({}_{x}\)Te\({}_{2.7}\)Se\({}_{0.3}\) (\(x\) = 0, 0.05, 0.075, 0.1, 0.125)), the 00\(l\) orientation, which can be denoted by a Lotgering factor \(f\) (\(f_{00l}\) = (\(p_{00l}\)-\(p_{0}\))/(1-\(p_{0}\)), where \(p_{00l}\) = \(\Sigma I_{00l}\)/\(\Sigma I_{hkl}\) and \(p_{0}\) = \(\Sigma I^{0}{}_{00l}\)/\(\Sigma I^{0}{}_{hkl}\) with \(I_{hkl}\) and \(I^{0}{}_{hkl}\) being the intensities of the (\(h\)\(k\)\(l\)) peaks for the textured and randomly oriented sample), for all samples are almost the same (\(f\) = 0.13-0.15). This suggests that the electronic and thermal transport parameters for these samples can provide reliable information to investigate the Hf-doping effect on the TE properties of Cu\({}_{0.01}\)Bi\({}_{2}\)Te\({}_{2.7}\)Se\({}_{0.3}\). It is noted that a single-phase without any Hf-related secondary phases is observed up to 5 at.% Hf-doped Cu\({}_{0.01}\)Bi\({}_{2}\)Te\({}_{2.7}\)Se\({}_{0.3}\); however, a small amount of Hf\({}_{3}\)Te\({}_{2}\) is observed in 6.25 at.% Hf-doped Cu\({}_{0.01}\)Bi\({}_{2}\)Te\({}_{2.7}\)Se\({}_{0.3}\). Peak positions in all samples are nearly constant due to the similar atomic radii of Bi (\(\sim\)230 pm) and Hf (\(\sim\)225 pm). Figure 1b shows the SEM image of the fractured surface of the SPSed Cu\({}_{0.01}\)Bi\({}_{1.9}\)Hf\({}_{0.1}\)Te\({}_{2.7}\)Se\({}_{0.3}\). The average grain size is about 10-20 \(\upmu\)m, and no inclusions and secondary phases were observed. Figure 2a shows the temperature dependence of \(\sigma\) for the SPSed bulks of Cu\({}_{0.01}\)Bi\({}_{2\cdot x}\)Hf\({}_{x}\)Te\({}_{2.7}\)Se\({}_{0.3}\). The measurement directions for \(\sigma\) and other parameters (\(S\) and \(\lambda\)) are illustrated in the inset of Figure 2a. The \(\sigma\) value of the pristine Cu\({}_{0.01}\)Bi\({}_{2}\)Te\({}_{2.7}\)Se\({}_{0.3}\) is \(\sim\)712 S cm\({}^{-1}\) at 300 K, and it gradually increases with an increasing Hf-doping content up to \(x\) = 0.1. This suggests that Hf is an effective doping element at the Bi-site to generate electron carriers. The decreased \(\sigma\) observed in Cu\({}_{0.01}\)Bi\({}_{1.875}\)Hf\({}_{0.125}\)Te\({}_{2.7}\)Se\({}_{0.3}\) is considered to be related to the generation of Hf\({}_{3}\)Te\({}_{2}\) owing to the solid solution limit of Hf at the Bi-site. Figure 1: (**a**) X-ray diffraction patterns of the spark plasma sintered (SPSed) Cu\({}_{0.01}\)Bi\({}_{2\cdot x}\)Hf\({}_{x}\)Te\({}_{2.7}\)Se\({}_{0.3}\) (\(x\) = 0, 0.05, 0.075, 0.1, 0.125) bulks in the planes perpendicular to the SPS press direction. (**b**) SEM image of the fractured surface of the SPSed Cu\({}_{0.01}\)Bi\({}_{1.9}\)Hf\({}_{0.1}\)Te\({}_{2.7}\)Se\({}_{0.3}\). On the other hand, \(S\) shows the trade-off relationship with \(\sigma\), as shown in Figure 2b. The calculated power factor (\(S^{2}\sigma\)) is shown in the inset of Figure 2b. The maximum power factor of \(\sim\)3.41 mW m\({}^{-1}\) K\({}^{-2}\) is obtained at 300 K in Cu\({}_{0.01}\)Bi\({}_{1.925}\)Hf\({}_{0.075}\)Te\({}_{2.7}\)Se\({}_{0.3}\), which is improved by \(\sim\)27% compared to that of the pristine Cu\({}_{0.01}\)Bi\({}_{2}\)Te\({}_{2.7}\)Se\({}_{0.3}\) (\(\sim\)2.68 mW m\({}^{-1}\) K\({}^{-2}\)). To clarify the electronic transport properties, we estimated the \(n_{\rm H}\) and \(\mu_{\rm H}\) at 300 K according to Hf-doping content (Figure 3a). The \(n_{\rm H}\) increases systematically with the increasing Hf-doping content up to \(x\) = 0.1, which suggests that Hf (Hf\({}^{\rm{++}}\)) is an effective doping element at the Bi (Bi\({}^{3+}\))-site to generate electron carriers.