Thermoelectric Power Factor Enhancement in Tetrahedrites

We report a strategy for power factor enhancement of the thermoelectric properties of Cu$_{12}$Sb$_{4}$S$_{13}$ tetrahedrites. Our previous strategy to improve the figure of merit in tetrahedrites was to reduce the electronic thermal conductivity at the expense of reducing the power factor by replacing monovalent Cu with divalent Zn or Fe. Here, we substitute S with Se, which is isovalent with S and therefore does not induce a doping effect. However, we observe a reduction in electronic resistivity in Cu$_{12}$Sb$_{4}$S$_{13-x}$Se$_{x}$ without affecting the thermopower, which leads to at least a 20{\%} enhancement in power factor. Furthermore, the substitution of S with Se causes a reduction in the lattice thermal conductivity via a solid solution effect, keeping the total thermal conductivity unchanged. Density Functional Theory (DFT) calculations indicate a narrowing of the band gap in Cu$_{12}$Sb$_{4}$Se$_{13\, }$relative to the sulfide; however, DFT also shows that the pure selenide is not thermodynamically stable. But Cu$_{12}$Sb$_{4}$S$_{13-x}$Se$_{x}$ single phase materials may be synthesized up to at least x $=$ 3. We believe this strategy will introduce additional degenerate energy levels near the top of valence band. Further studies should be performed to investigate the optimal Se concentration and its effect on figure of merit.