Universal curve of optimum thermoelectric figures of merit for bulk and low-dimensional semiconductors

Analytical formulas for thermoelectric figure of merit and power factor are derived based on the one-band model. We find that there is a direct relationship between the optimum figures of merit and the optimum power factors of semiconductors despite of the fact that the two quantities are generally given by different values of chemical potentials. By introducing a dimensionless parameter consisting of optimum power factor and lattice thermal conductivity (without electronic thermal conductivity), it is possible to unify optimum figures of merit of both bulk and low-dimensional semiconductors into a single universal curve that covers lots of materials with different dimensionalities.