Interpretation of the time constants measured by kinetic techniques in nanostructured semiconductor electrodes and dye-sensitized solar cells

The processes of charge separation, transport, and recombination in dye-sensitized nanocrystalline TiO2 Solar cells are characterized by certain time constants. These are measured by small perturbation kinetic techniques, such as intensity modulated photocurrent spectroscopy (IMPS), intensity modulated photovoltage spectroscopy (IMVS), and electrochemical impedance spectroscopy (EIS). The electron diffusion coefficient, D-n, and electron lifetime, tau(n), obtained by these techniques are usually found to depend on steady-state Fermi level or, alternatively, on the carrier concentration. We investigate the physical origin of such dependence, using a General approach that consists on reducing the general multiple trapping kinetic-transport formalism, to a simpler diffusion formalism, which is valid in quasi-static conditions. We describe in detail a simple kinetic model for diffusion, trapping, and interfacial charge transfer of electrons, and we demonstrate the compensation of trap-dependent factors when forming steady-state quantities such as the diffusion length, L-n, or the electron conductivity, sigma(n).