## 3 Results
Therefore, power factors (\(\sigma S^{2}\)) also show no increase with the addition of NbTe\({}_{2}\) at all compositions (inset of Figure 3d). Figure 2: Schematic of energy band diagrams of the samples at the heterointerfaces between Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\) and the secondary phase: (**a**) NiTe\({}_{2}\) and (**b**) NiTe\({}_{2}\). Figure 4 shows the results from the Hall measurement (Hall carrier concentration, \(n_{\rm H}\), and Hall mobility, \(\mu_{\rm H}\)) and the Pisarenko plots at room temperature [14; 15; 19]. In Figure 4a, no clear relationship between \(n_{\rm H}\) and \(\mu_{\rm H}\) is seen, while the \(n_{\rm H}\) does not change for NiTe\({}_{2}\)-added samples in the range of 9.5 \(\times\) 10\({}^{18}\)-9.6 \(\times\) 10\({}^{18}\) cm\({}^{-3}\). Figure 4b shows a Pisarenko plot (\(S\) as a function of \(n_{\rm H}\)) with the effective mass \(m^{\star}\) of 0.5 \(m_{0}\), 0.55 \(m_{0}\), and 0.6 \(m_{0}\) shown as lines, based on Equation (1). \[S = \frac{8\pi^{2}k_{B}^{2}}{3e^{h2}}\Big{(}\frac{\pi}{3n}\Big{)}^{2/3}m^{ \star}T \tag{1}\]  
where \(h\) is the Planck constant, \(k_{\rm B}\) is the Boltzmann constant, \(e\) is the elemental electric charge and \(n\) is the carrier concentration. The gradual increase in \(m^{\star}\) is clearly shown as \(x\) increased for NiTe\({}_{2}\)-added samples (Figure 4b), although the noticeable decrease in \(n_{\rm H}\) is not seen (Figure 4a). As \(n_{\rm H}\) could vary for various reasons, the systematic increase in the \(m^{\star}\) would suggest the presence of the carrier filtering effect due to the energy barrier of 0.26 eV (Figure 2a) as the density of interfaces between NiTe\({}_{2}\) and the matrix increases; for instance, the simultaneous increase in \(\sigma\) and \(S\) in NiTe\({}_{2}\)-added samples (\(x\) = 0.01 compared to \(x\) = 0 of Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\)(NiTe\({}_{2}\))\({}_{x}\)). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase Segregation** & **Properties** &
\begin{tabular}{c} **Work Function (\(\Phi\)) or** \\ **Electron Affinity (\(\chi\)) and Band Gap (\(E_{\rm g}\))** \\ \end{tabular} \\ \hline NbTe\({}_{2}\) & Metallic & \(\Phi\) = 4.62 eV \\ NiTe\({}_{2}\) & Metallic & \(\Phi\) = 4.44 eV \\ (Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\)) & Semiconducting & \(E_{\rm g}\) = 0.2 eV, \(\chi\) = 4.50 eV \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Work function (\(\Phi\)) for NbTe\({}_{2}\) and NiTe\({}_{2}\), and electron affinity (\(\chi\)) and band gap (\(E_{\rm g}\)) for (Bi\({}_{0.5}\)Sb\({}_{1.5}\))Te\({}_{3}\). Figure 3: Temperature dependence of (**a**,**c**) the electrical conductivity and (**b**,**d**) the Seebeck coefficient for Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\)(NiTe\({}_{2}\))\({}_{x}\) (\(x\) = 0, 0.003, 0.01) and Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\)(NbTe\({}_{2}\))\({}_{x}\) (\(x\) = 0, 0.005, 0.01). Inset graphs in (**b**,**d**) exhibit the power factors of the samples. Figure 4c shows that the \(n_{\rm H}\) of Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\)(NbTe\({}_{2}\))\({}_{x}\) (\(x\) = 0, 0.005, 0.01) gradually decreased with \(x\); the \(n_{\rm H}\) values of 9.5 \(\times\) 10\({}^{18}\), 9.0 \(\times\) 10\({}^{18}\), and 8.7 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) for \(x\) = 0, 0.005, and 0.01, respectively. In contrast, the, \(\mu_{\rm H}\) increased gradually with increasing \(x\), leading to values of 314, 327, and 343 cm\({}^{2}\)/Vs for \(x\) = 0, 0.005, and 0.01, respectively. However, no change in \(m^{\star}\) was shown. It seems that there is less carrier filtering influence on these samples due to the smaller barrier height (Figure 2b).