Doping optimization for the power factor of bipolar thermoelectric materials

Bipolar carrier transport is often a limiting factor in the thermoelectric efficiency of narrow bandgap materials at high temperatures due to the reduction in the Seebeck coefficient and the introduction of an additional term to the thermal conductivity. Using the Boltzmann transport formalism and a two-band model, we simulate transport through bipolar systems and calculate their thermoelectric transport properties: the electrical conductivity, the Seebeck coefficient and the thermoelectric power factor. We present an investigation into the doping optimisation of such materials, showing the detrimental impact that rising temperatures have if the doping (and the Fermi level) is not optimised for each operating temperature. We also show that the doping levels for optimized power factors at a given operating temperature differ in bipolar systems compared to unipolar ones. We show finally that at 600 K, in a bipolar material with bandgap approximately that of Bi2Te3, the optimal doping required can reside between 10% and 30% larger than that required for an optimal unipolar material depending on the electronic scattering details of the material.