  Advances in optimizing thermoelectric material efficiency have seen a
parallel activity in theoretical and computational advances. In the current
work, it is shown that the calculation of exact Fermi-Dirac integrals enables
the generalization of the Wiedemann-Franz law (WF) to optimize the
dimensionless thermoelectric figure of merit ZT. This is done by optimizing the
Seebeck coefficient, the electrical conductivity and the thermal conductivity.
In the calculation of the thermal conductivity, both electronic and phononic
contributions are included. The solutions provide insight into the relevant
parameter space including the physical significance of complex solutions and
their dependence on the scattering parameter r and the reduced chemical
potential.
