Thermoelectric Properties of Cu$_{12}$Sb$_{4}$S$_{13}$ and Derivatives

The room-temperature Seebeck coefficient and resistivity of thin film variants of the mineral tetrahedrite Cu$_{12}$Sb$_{4}$S$_{13}$ and its derivatives were measured. In bulk form, tetrahedrite has shown promise as a good thermoelectric material. Thin films of Cu$_{12-x}$M$_{x}$Sb$_{4}$S$_{13\, }$(M $=$ Cu, Zn) were produced by e-beam deposition, and we also produced films with a second metal on the Cu site. The Seebeck coefficients ranged from 10 to 113 $\mu $V/K and the resistivity from 8 to 50 m$\Omega $cm. Together, these values yield power factors S$^{2}$/$\rho $ ranging from 10$^{-7}$ to 10$^{-4}$ W/mK$^{2}$, approaching the range of their bulk counterparts at the upper end. As a comparison, the power factors for $n$- and $p$-doped silicon were measured and compared to published values. For both $p$-Si and $n$-Si, the power factor was 3.0$\cdot$10$^{-3}$ W/mK$^{2}$.