We report first principles LDA calculations of the electronic structure and thermoelectric properties of $beta $-Zn$_{4}$Sb$_{3}$. The material is found to be a low carrier density metal with a complex Fermi surface topology and non-trivial dependence of Hall concentration on band filling. The band structure is rather covalent, consistent with experimental observations of good carrier mobility. Calculations of the variation with band filling are used to extract the doping level (band filling) from the experimental Hall number. At this band filling, which actually corresponds to 0.1 electrons per 22 atom unit cell, the calculated thermopower and its temperature dependence are in good agreement with experiment. The high Seebeck coefficient in a metallic material is remarkable, and arises in part from the strong energy dependence of the Fermiology near the experimental band filling. Improved thermoelectric performance is predicted for lower doping levels which corresponds to higher Zn concentrations.
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