  Complex electronic band structures, with multiple valleys or bands at the
same or similar energies can be beneficial for thermoelectric performance, but
the advantages can be offset by inter-valley and inter-band scattering. In this
paper, we demonstrate how first-principles band structures coupled with
recently developed techniques for rigorous simulation of electron-phonon
scattering provide the capabilities to realistically assess the benefits and
trade-offs associated with these materials. We illustrate the approach using
n-type silicon as a model material and show that intervalley scattering is
strong. This example shows that the convergence of valleys and bands can
improve thermoelectric performance, but the magnitude of the improvement
depends sensitively on the relative strengths of intra- and inter-valley
electron scattering. Because anisotropy of the band structure also plays an
important role, a measure of the benefit of band anisotropy in the presence of
strong intervalley scattering is presented.
