  To increase the performance of thermoelectric materials, the electronic
parameters in the figure of merit must be improved. In this paper, we use full,
numerical band structures and solve the Boltzmann equation in the relaxation
time approximation using energy-dependent scattering times informed by first
principles simulations. By varying the strength of the electron-phonon coupling
or the lattice thermal conductivity, we compute the thermoelectric figure of
merit, zT, vs. a generalized thermoelectric quality factor. More than a dozen
different complex electronic structures are examined. Surprisingly, we find
that at a given quality factor, none provides a better figure of merit than
that of a material with a simple, parabolic band and acoustic deformation
potential scattering. A qualitative argument for this unexpected finding is
presented. This apparent universal behavior suggests that even for complex
electronic band structures, the thermoelectric figure of merit depends solely
on the ratio of electrical to thermal conductivity; the Seebeck coefficient and
Lorenz number need not be considered. This observation should simplify the
search for promising new materials, but if exceptions to this behavior can be
identified, new paths for increasing thermoelectric material performance will
open up.
