## 3 Results and Discussions  
Figure 1a shows the temperature dependence of the electrical resistivity and the Seebeck coefficient. The negative Seebeck coefficient indicates that the major carriers are electrons. As the amount of Ag is increased, the value of the electrical resistivity is increased. The absolute value of the Seebeck coefficient increased with Ag content. Both the increases in electrical resistivity and Seebeck coefficient  
with Ag may be attributed to a reduction in carrier concentration, because the electrical resistivity and the Seebeck coefficient are approximately proportional to \(n^{-1}\) and \(n^{-2/3}\), respectively [1]; this will be also supported by the measurement of the Hall coefficient. A reduction in electron concentration is responsible for an increase in electrical resistivity and Seebeck coefficient, which is generally acceptable for the transport properties within the considered carrier concentration in the Bi\({}_{2}\)Te\({}_{3}\)-related compounds [27]. The power factor (\(\alpha^{2}\)/\(\sigma\)) is shown in Figure 1b. It is well known that the values are dependent on the carrier concentration and show maximum values at the optimized concentration [1]. The maximum value of 1.73 mW/mK\({}^{2}\) was achieved in the 0.01 wt % Ag sample. Figure 2 shows the carrier concentration of samples as determined from the Hall coefficient (\(R_{H}\)) measurement. All of the Hall coefficient values were negative, which means electrons were the dominant carriers. The electron concentrations were evaluated using \(R_{H}=1/ne\), where \(n\) is the electron concentration and \(e\) is the charge of the electrons. As the amount of Ag increased, the electron concentrations decreased. Thus, the increases in electrical resistivity and Seebeck coefficient are due to the reduction in carrier concentration with Ag. Figure 1: The variation in electrical resistivity, Seebeck coefficient and power factor at room temperature with respect to the amount of Ag: (**a**) the electrical resistivity and Seebeck coefficient and (**b**) the power factor. Figure 2: Electron concentrations estimated from Hall coefficient as a function of Ag amount. In order to understand the origin of this reduction in electron concentrations, changes in the crystal structure that occurred with Ag doping were analyzed. Figure 3 shows the observed XRD and Rietveld refinement patterns of Bi\({}_{2}\)Te\({}_{3}\), and the refined structural parameters are shown in Table 1[28]. Even though Bi, Sb, Te, and Se atoms exist at the lattice sites, a refinement was performed for the hexagonal \(R\)-\(3m\) structure with Bi in the 6c (0, 0, z(Bi)) sites, Te(1) in the 3a (0, 0, 0) sites, and Te(2) in the 6c (0, 0, z(Te)) sites. The refined lattice parameters of both the a and c axes were smaller than those of Bi\({}_{2}\)Te\({}_{3}\), and this was attributed to the small amounts of Sb and Se substituted for Bi and Te, respectively. Because the covalent radius of Sb (139 pm) and Se (120 pm) is smaller than that of Bi (148 pm) and Te (138 pm), respectively, the lattice parameters will be decreased with Se [29]. The lattice parameters of the Ag-doped samples were also obtained with a Rietveld refinement and the results are shown in Table 2. The lattice parameters of the c-axis significantly increased with Ag, while the values of the a-axis were nearly the same. It should be noted that the covalent radius of Bi is significantly larger than that of Ag, resulting in a reduction of the lattice parameter if Ag is substituted for Bi. Thus, this anisotropic change and the increase in the lattice parameters indicate that Ag was not substituted for Bi. It is believed that Ag is located at the interstitial sites (0, 0, 0.5 in fractional coordinates) which are also known as van der Waals gaps, due to van der Waals bonding character between Te(2) and Te(2) atoms. In order to elucidate the Ag interstitial occupation, the formation energy of Ag in Bi\({}_{2}\)Te\({}_{3}\) and its structural properties were evaluated using first-principles calculations.