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The addition of porosity to thermoelectric materials can significantlyincrease the figure of merit, ZT, by reducing the thermal conductivity.Unfortunately, porosity is also detrimental to the thermoelectric power factorin the numerator of the figure of merit ZT. In this manuscript we derivestrategies to recoup electrical performance in nanoporous Si by fine tuning thecarrier concentration and through judicious design of the pore size and shapeso as to provide energy selective electron filtering. In this study, weconsidered phosphorus doped silicon containing discrete pores that are eitherspheres, cylinders, cubes, or triangular prisms. The effects from these poresare compared with those from extended pores with circular, square andtriangular cross sectional shape, and infinite length perpendicular to theelectrical current. A semiclassical Boltzmann transport equation is used tomodel Si thermoelectric power factor. This model reveals three key results: Thelargest enhancement in Seebeck coefficient occurs with cubic pores. Thefractional improvement is about 15% at low carrier concentration ($< 10^{20}\\mathrm{1/cm^3}$) up to 60% at high carrier population with characteristiclength around $\sim 1\ \mathrm{nm}$. To obtain the best energy filtering effectat room temperature, nanoporous Si needs to be doped to higher carrierconcentration than is optimal for bulk Si. Finally, in $n$-type Sithermoelectrics the electron filtering effect that can be generated withnanoscale porosity is significantly lower than the ideal filtering effect;nevertheless, the enhancement in the Seebeck coefficient that can be obtainedis large enough to offset the reduction in electrical conductivity caused byporosity.

Mitigating the Effect of Nanoscale Porosity on Thermoelectric Power Factor of Si