  Engineering materials to include nanoscale porosity or other nanoscale
structures has become a well-established strategy for enhancing the
thermoelectric performance of dielectrics. However, the approach is only
considered beneficial for materials where the intrinsic phonon mean free path
is much longer than that of the charge carriers. As such, the approach would
not be expected to provide significant performance gains in polycrystalline
semiconducting alloys such as $\mathrm{Si_xGe_{1-x}}$, where mass disorder and
grains provide strong phonon scattering. In this manuscript, we demonstrate
that the addition of nanoscale porosity to even ultrafine-grained
$\mathrm{Si_{0.8}Ge_{0.2}}$ may be worthwhile. The semiclassical Boltzmann
transport equation was used to model electrical and phonon transport in
polycrystalline $\mathrm{Si_{0.8}Ge_{0.2}}$ containing prismatic pores
perpendicular to the transport current. The models are free of tuning
parameters and were validated against experimental data. The models reveal that
a combination of pores and grain boundaries suppresses phonon conductivity to a
magnitude comparable with the electronic thermal conductivity. In this regime,
$ZT$ can be further enhanced by reducing carrier concentration to the
electrical and electronic thermal conductivity and simultaneously increasing
thermopower. Although increases in $ZT$ are modest, the optimal carrier
concentration is significantly lowered, meaning semiconductors need not be so
strongly supersaturated with dopants.
