Semi-analytical model for the Seebeck coefficient in semiconductors with isotropic DOS given by a power function

The relations for the Seebeck coefficient in a semiconductor with the isotropic density of states given by a power function are introduced within the scope of a semi-analytical model, which is based on the theoretical relations given by the foundations of the semiconductor physics as well as on experimentally defined temperature dependences of various semiconductor characteristics, but does not include any adjustable parameters. Between those characteristics the major role plays the intrinsic carrier concentration. It was demonstrated that although the introduced model is based on the simplified Maxwell-Boltzmann statistic, it is not compromised by this choice. A comparison with experimental data for five different semiconductors proves its ability to provide reliable predictions over a wide range of parameters (temperature, dopant type and concentration) not only for non-degenerated wide bandgap semiconductors (Si, Ge) but also for InAs, which represents partly degenerated narrow bandgap semiconductors with a non-parabolic density of states. Even in the case of a HgCdTe, with its extremely narrow bandgap and complex temperature dependence of the carrier concentration, the model is in good agreement with experimental data. The semi-analytical nature of the introduced model and its dependence on the abundance and reliability of the used experimental data were discussed on the example of Bi2Te3. Although the relative deficiency and controversy of the experimental results in this case significantly impede the model’s applicability, it is still able to give at least qualitative predictions, which are nevertheless better than the results of the calculation of the thermopower from first principles. Being primarily addressed to the experimental community, the model provides simple relations in the case of the parabolic non-intrinsic semiconductor for thermoelectric voltage and for optimal dopant concentration for the thermogenerator within the known working temperature range, which can be useful in real-life ‘energy harvesting’ applications