  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.
