## 3 Results and Discussion
### Transport Property Evaluation
The Lorenz number (\(L_{\text{o}}\)) for all compounds was calculated by using the following equations:  
\[L\ =\ \left(\frac{k_{B}}{e}\right)^{2}\left[\frac{(r+7/2)F_{r+5/2}(\xi)}{(r+3/2) F_{r+1/2}(\xi)}\ -\left(\frac{(r+5/2)F_{r+3/2}(\xi)}{(r+3/2)F_{r+1/2}(\xi)}\right)^{2}\right] \tag{3}\]  
where \(r\) is the scattering parameter, \(k_{B}\) the Boltzmann constant, \(e\) is the electron charge, and \(F_{n}\) (\(\xi\)) is the Fermi integral given by  
\[F_{n}(\xi)=\int_{0}^{\infty}\frac{\chi^{n}}{1+e^{\chi-\xi}}d\chi \tag{4}\]  
Here, \(\xi\), is the reduced Fermi energy that can be calculated from the Seebeck coefficient \(S\) and the scattering parameter \(r\) according to  
\[S=\mp\frac{k_{B}}{e}\frac{(r+5/2)F_{r+\frac{3}{2}}(\xi)}{(r+3/2)F_{r+\frac{1} {2}}(\xi)}\ -\ \xi \tag{5}\]  
We used parabolic band model and assumed the system to be highly degenerate and scattering is dominated by acoustic phonons. The calculated \(L_{\text{o}}\) numbers, along with the estimated \(\kappa_{\text{el}}\) and \(\kappa_{tot}\) for all samples are displayed in Table S2. Looking at the proportion of the \(\kappa_{\text{el}}\), the major part of \(\kappa_{tot}\) is dominated by electronic contribution in Bi\({}_{2}\)Te\({}_{3}\) and Bi\({}_{1.8}\)Sb\({}_{0.2}\)Te\({}_{3}\) samples, while \(\kappa_{\text{lat}}\) is predominant in thermal conductivity of Sb\({}_{2}\)Te\({}_{3}\) and Bi\({}_{0.5}\)Sb\({}_{1.5}\)Te\({}_{3}\). This might be due to either phonon-point defect scattering or phonon grain boundary scattering (due to nanosized grains). The negative value of \(\kappa_{\text{lat}}\) of Sb\({}_{2}\)Te\({}_{3}\) at room temperature is not realistic, which indicates that the parabolic band model may not be suitable for calculating \(L_{\text{o}}\) for this sample. In any case, it is important to see how \(\kappa_{\text{lat}}\) can strongly affect the transport properties and thus play a major role in enhancing the \(\mathbf{ZT}\) value for these compositions. Using all these transport parameters, the resultant figure-of-merit, \(\mathbf{ZT}\), has been estimated and the results are presented in Figure 3e, where a monotonic increase was observed for all samples by increasing temperature. Pure Bi\({}_{2}\)Te\({}_{3}\) and Sb\({}_{2}\)Te\({}_{3}\) samples show \(\mathbf{ZT}\) values around 0.5-0.6 at RT, reaching beyond unity around 440 K. From this point onwards, the trend in Sb\({}_{2}\)Te\({}_{3}\) is still linear while that of Bi\({}_{2}\)Te\({}_{3}\) bends downwards, mainly due to the increase in the thermal conductivity due to bipolar effect. Bi\({}_{2}\)Te\({}_{3}\) reached a \(\mathbf{ZT}\) of 1.04, while Sb\({}_{2}\)Te\({}_{3}\) reached to 1.20 at 440 K. The ternary phases where Bi and Sb are co-doped also showed favorable ZT values by increasing temperature, reaching about 0.75-0.90 at 523 K. The highest ZT of 1.37 is achieved for pure Sb\({}_{2}\)Te\({}_{3}\) sample at 523 K, likely due to its lower thermal conductivity that is suppressed by phonon point defect and phonon grain boundary scattering. Fine thermoelectric powders as presented here are very valuable resources in the field of large area and flexible hybrid thermoelectric materials research. Many of the published works on hybrids have relied on commercial powders for making their films where micron size Bi\({}_{2}\)Te\({}_{3}\) material is either exfoliated via sonication, or ball-milled to reduce the particle size to prepare a good polymer nanoparticle hybrid. We attempted to show the ease of integration of as-made Bi\({}_{2}\)Te\({}_{3}\) material with PVDF and made few hybrid films using doctor blading method (see Figure S8). Our results show that stable dispersions can be easily made and films with reasonable transport properties can be obtained. A typical output from this film is n-type Seebeck (S = \(-\)46.12 \(\mu\)V/K), and electrical conductivity of around 0.6013 S/m leading to a power factor of PF= \(1.284\times 10^{-3}\)\(\mu\)W/m\(K^{2}\) (see Figure S9).