On the applicability of the single parabolic band model to advanced thermoelectric materials with complex band structures

Due to the complex interplay between composition, synthesis parameters and the performance of thermoelectric materials, the optimization of thermoelectric materials needs to be complemented by modelling. A relatively simple and thus popular approach is the so called single parabolic band model, which allows for an efficient optimization of the material properties and a benchmarking of different materials based on relatively few, well available experimental results. As complex band structures are common for high performance materials, single parabolic band modelling is also employed with apparent success for material systems where the underlying assumptions are not well fulfilled. In order to assess the validity of a single parabolic band analysis for such systems, the thermoelectric properties for two model systems are calculated: one with a single band that is twofold degenerate and one with a light and a heavy band. Even if the density of states masses and the scattering potentials are kept identical, the transport properties and in particular the Hall coefficients differ significantly, which leads to an incorrectly determined carrier concentration. As the carrier concentration is the base for the single parabolic band analysis, all the quantities obtained from it (optimum carrier concentration, effective mass, deformation potential) are determined incorrectly as well.