The trap-limited diffusivity of electrons in nanoporous semiconductor networks permeated with a conductive phase

The transport of photogenerated electrons in nanocrystalline semiconductor networks permeated with a conducting phase is studied, with a particular emphasis on dye-sensitized nanoporous TiO₂ solar cells. We extend the classical approach to the trap-limited mobility according to specific features of the nanoporous configuration: electron transport by diffusion, the capacitive behavior of the nanoporous film and the possible bandshifts due to the charging of surface states. We show that the trap-limited diffusivity, as measured by small-signal techniques, is proportional to the ratio of the conduction-band capacitance and the trap capacitance. These capacitances are defined in terms of a pseudopotential related to the chemical energy of the free electrons, in order to account for possible band unpinning. Several specific distributions of bandgap states are investigated. The dependence of the trap capacitance on the number of free electrons takes the general form C_trap = An^1-a, where 0 ≤ a ≤ 1 depends on the distribution of the traps. The trap-limited diffusivity depends on the number of free electrons as D_n = Bn^a, and D_n also shows a power-law dependence with the light intensity. We describe the correlation of the electron conductivity with the photovoltage in the solar cell and the photon irradiation intensity.