Fermi level of surface states in TiO2 nanoparticles

We analyze the nonequilibrium steady-state statistics of electrons in nanoparticulate semiconductors containing a variety of electronic states in relation to applications in dye-sensitized solar cells and photocatalysis. The electrons trapped in surface states do not generally equilibrate to the free electrons' Fermi level, E-Fn. We show that a distinct Fermi level for surface states, E-Fs, can be defined consistently with Fermi-Dirac statistics, determining the surface states' occupancy far from equilibrium. The difference Delta = E-Fn - E-Fs depends on the rate constants for charge transfer and detrapping and can reach several hundred millielectronvolts. The E-Fs, becomes a key concept for the analysis of charge transfer and recombination kinetics in nanoparticulate semiconductors.