Random walk models of charge transfer and transport in dye sensitized systems

Abstract

Electron transport in porous, nanocrystalline metal oxide electrodes exhibits many features typical of dispersive transport in disordered semiconductors. This disorder can be attributed to energetic disorder in localized electron transport sites, or ‘trap’ sites. A numerical model based upon the continuous-time random walk (CTRW) is introduced to describe electron dynamics. The model is applied primarily to explain the stretched-exponential kinetic shape and strong bias dependence of optically observed recombination of electrons with photo-oxidized dye molecules, with the conclusion that recombination is limited by electron diffusion through a distribution of trap states. Analogous experimental and modelling studies of the functionally important back reaction between electrons in the metal oxide and oxidized species in the redox couple indicate that this recombination pathway is also dominated by trap-limited electron diffusion. The model predicts that such dispersive charge transport should be observed only on time scales shorter than the release time from the deepest trap, and this feature is used to explain the transition from fast, dispersive recombination kinetics slow and monoexponential behaviour in the presence of a slow (>10 ms) process limiting interfacial electron transfer. It is shown how transient optical measurements combined with modelling can be used as a probe of local electron dynamics, using inter-particle electron transport as an example. Finally, the application of random walk methods to simulation of device current–voltage characteristics is discussed.