Analysis of the mechanisms of electron recombination in nanoporous TiO2 dye-sensitized solar cells.: Nonequilibrium steady-state statistics and interfacial electron transfer via surface states

Macroscopic assemblies of semiconductor particles, with dimensions in the nanometer range, permeated with a transparent conducting phase (nanoporous electrodes) show a useful behavior in applications such as photocatalysis and dye-sensitized solar cells. A fundamental event in dye-sensitized solar cells is the recombination of photoinjected electrons with acceptor species (ionic holes) in the electrolyte phase surrounding the nanoparticles. Intrinsic semiconductor surface states play an important role in this process, not only as electron traps but also as intermediate states for electron transfer to the electrolyte (interfacial recombination centers). To describe the electron lifetime of electron trapped at band gap surface states, the concepts developed in the early analysis of recombination processes in photoconductors, such as the demarcation level, are quite useful. However, in photoelectrochemical systems (dye-sensitized solar cell), holes can be identified with oxidized, electrolyte dissolved species so that a, new statistical analysis of the interfacial recombination process, considering the distribution of fluctuating, electrolyte energy levels, is required. Moreover, since in dyesensitized solar cells the quasi-Fermi level for electrons, E*(Fn) controls both the photovoltage and the rate of Fn electron transport through the porous network, it is of great significance to find a correlation between the traps occupancy and E*(Fn). We develop a consistent formulation that, fulfilling these requirements, allows to Fn deal with an arbitrary distribution of band gap surface states. Our analysis, which is based on those physical parameters describing the probability of electron transfer among band gap surface states, the conduction band, and electrolyte levels, allows macroscopic recombination time constants to be defined. The model considers different mechanisms for the transfer of photogenerated electrons from the semiconductor to empty electrolyte levels: direct electron transfer from conduction band states, indirect transfer of electrons trapped at monoenergetic, deep surface states, and indirect transfer of electrons trapped at an exponential distribution of band. gap surface states near the conduction band. The analysis shows the great influence of the distribution of electrolyte levels and band gap surface states on the electron recombination kinetics under open circuit conditions.