| Summary: | 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 Si<sub>x</sub>Ge<sub>1-x</sub>, where mass disorder and grains provide strong phonon scattering. In this manuscript, we demonstrate that the addition of nanoscale porosity to even ultrafine-grained Si<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.8</mn></mrow></msub></semantics></math></inline-formula>Ge<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.2</mn></mrow></msub></semantics></math></inline-formula> may be worthwhile. The semiclassical Boltzmann transport equation was used to model electrical and phonon transport in polycrystalline Si<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.8</mn></mrow></msub></semantics></math></inline-formula>Ge<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.2</mn></mrow></msub></semantics></math></inline-formula> 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, <i>ZT</i> can be further enhanced by reducing carrier concentration to the electrical and electronic thermal conductivity and simultaneously increasing thermopower. Although increases in <i>ZT</i> are modest, the optimal carrier concentration is significantly lowered, meaning semiconductors need not be so strongly supersaturated with dopants.
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