Ineffectiveness of energy filtering at grain boundaries for thermoelectric materials

We use a one-band effective mass model within the Landauer formalism to investigate the influence of double Schottky barriers on the thermoelectric coefficients. It is assumed that these double Schottky barriers arise due to trapping states in grain boundaries. Such barriers can cause an energy filtering effect, which is widely believed to advance thermoelectric efficiencies. We show that for low doping concentrations the Seebeck coefficient is indeed increased due to energy filtering effects, whereas the electric conductivity is strongly decreased. The resulting power factor is also decreased. For higher doping concentrations, which are necessary for large electric conductivities and thus reasonable ZT values, the double Schottky barriers are very small and have therefore an insignificant impact on the thermoelectric parameters. Consequently, there is no significant influence of grain boundaries on ZT values due to additional electrostatic barriers. This does not preclude that other mechanisms at grain boundaries, such as additional scattering due to disorder, can have a positive impact on the power factor.