Network of flatband solar cells as a model for solid-state nanostructured solar cells

Nanostructured solar cells are too complex for standard modeling. Here, we decouple the effects at a microscopic (nm) scale from those at a macroscopic (μm) scale. The three-dimensional nanoporous geometry is simplified to a quasiperiodic nm-scale ordering of “unit cells,” each consisting of a ${\mathrm{TiO}}_2$ sphere and its $p$ -semiconductor or $\mathrm{dye}\mathrm{/p}$ -conductor shell. It is shown that, due to the periodic boundary conditions, such a unit cell is essentially field free; it is called here a “flatband cell.” The band diagram, including possible discontinuities, the Fermi levels, carrier density and recombination (interface and bulk) of these flatband cells is given accurately by a back-of-the-envelope calculation, as confirmed by numerical simulation. The unit cells are connected in a one-dimensional electrical network, which also accounts for the transport effects in the porous ${\mathrm{TiO}}_2$ network and for the contact effects at the electrodes. Results for solid-state nanostructured cells are: the interconnection geometry is disadvantageous for the open circuit voltage $V_{\mathrm{oc}};$ it is tolerant to moderate resistance in the $\mathrm{n-}{\mathrm{TiO}}_2$ network, but not to resistance in the $p$ -conductor.