  We propose a new method for accurately calculating electrical transport
properties of a lightly-doped thermoelectric material from density functional
theory (DFT) calculations, based on experimental data and density functional
theory results for the corresponding undoped material. We employ this approach
because hybrid DFT calculations are prohibitive for the large supercells
required to model low dopant concentrations comparable to those achieved
experimentally for high-performing thermoelectrics. Using zinc antimonide as
our base material, we find that the electrical transport properties calculated
with DFT and Boltzmann transport theory exhibit the same trends with changes in
chemical potential as those computed with hybrid DFT, and propose a fitting
algorithm that involves adjusting the computed Fermi energy so that the
resulting Seebeck coefficient trends with temperature match experimental
trends. We confirm the validity of this approach in reproducing the
experimental trends in electrical conductivity and Seebeck coefficient versus
temperature for Bi-doped $\beta-$Zn$_4$Sb$_3$. We then screen various
transition metal cation dopants, including copper and nickel, and find that a
Cu dopant concentration of 2.56% in Zn$_{39}$Sb$_{30}$ exhibited a 14% increase
in the thermoelectric power factor for temperatures between 300-400 K. We thus
propose that transition metal dopants may significantly improve the
thermoelectric performance of the host material, compared to heavy and/or
rare-earth dopants.
