Thermoelectric properties of highly doped n-type polysilicon inverse opals

Nanostructured single-crystal silicon exhibits a remarkable increase in the figure of merit for thermoelectric energy conversion. Here we theoretically investigate a similar enhancement for polycrystalline silicon inverse opals. An inverse opal provides nanoscale grains and a thin-film like geometry to scatter phonons preferentially over electrons. Using solutions to the Boltzmann transport equation for electrons and phonons, we show that the figure of merit at 300 K is fifteen times that of bulk single-crystal silicon. Our models predict that grain boundaries are more effective than surfaces in enhancing the figure of merit. We provide insight into this effect and show that preserving a grain size smaller than the shell thickness of the inverse opal increases the figure of merit by as much as 50% when the ratio between the two features is a third. At 600 K, the figure of merit is as high as 0.6 for a shell thickness of 10 nm. This work advances the fundamental understanding of charge and heat transport in nanostructured inverse opals.