Optimum band gap of a thermoelectric material

Transport properties of direct-gap semiconductors are calculated in order to find the best thermoelectrics. Previous calculations on semiconductors with indirect band gaps found that the best thermoelectrics had gaps equal to nkBT, where n=6-10 and T is the operating temperature of the thermoelectric device. Here we report similar calculations on direct-gap materials. We find that the optimum gap is always greater than 6kBT, but can be much larger depending on the specific mechanism of electron scattering.