  Band convergence is considered a clear benefit to thermoelectric performance
because it increases the charge carrier concentration for a given Fermi level,
which typically enhances charge conductivity while preserving the Seebeck
coefficient. However, this advantage hinges on the assumption that interband
scattering of carriers is weak or insignificant. With first-principles
treatment of electron-phonon scattering in
CaMg$_{2}$Sb$_{2}$-CaZn$_{2}$Sb$_{2}$ Zintl system and full Heusler
Sr$_{2}$SbAu, we demonstrate that the benefit of band convergence can be
intrinsically negated by interband scattering depending on the manner in which
bands converge. In the Zintl alloy, band convergence does not improve weighted
mobility or the density-of-states effective mass. We trace the underlying
reason to the fact that the bands converge at one k-point, which induces strong
interband scattering of both the deformation-potential and the polar-optical
kinds. The case contrasts with band convergence at distant k-points (as in the
full Heusler), which better preserves the single-band scattering behavior
thereby successfully leading to improved performance. Therefore, we suggest
that band convergence as thermoelectric design principle is best suited to
cases in which it occurs at distant k-points.
