Temporal evolution of the electron diffusion coefficient in electrolyte-filled mesoporous nanocrystalline TiO 2 films

Abstract

Electron transport in electrolyte-filled mesoporous TiO 2-based solar cells is described quantitatively from the perspective of the continuous-time random walk model. An analytical expression is derived for the time-dependent diffusion coefficient of electrons, which transforms at a characteristic (Fermi) time from strongly time-dependent values (dispersive transport) at short times to relatively time-independent values (nondispersive transport) at long times. At short times, the diffusion coefficient displays a power-law behavior with time. The timescale for the diffusion coefficient to reach its steady-state value is substantially longer than the Fermi time. The Fermi time and the steepness of the distribution of waiting times associated with trap sites have a strong influence on both the steady-state diffusion coefficient of electrons and on the dispersiveness of electron transport. At short timescales, ionic drag, associated with the ambipolar effect, slows electron transport through the TiO 2 matrix, whereas at steady state, transport is trap limited. Decreasing the electron density lowers the steady-state limit of the diffusion coefficient and increases the timescale over which transport is dispersive.