Chemical Diffusion Coefficient of Electrons in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells

Abstract

The properties and physical interpretation of the electron diffusion coefficient, D n, observed in nanostructured semiconductors and dye-sensitized solar cells by small perturbation electrical and electrooptical techniques are investigated. The chemical diffusion coefficient is defined as the product of a thermodynamic factor (that accounts for the effect of nonideal statistics in a gradient of chemical potential) and a jump diffusion coefficient (that depends on average hopping distances and rates). The thermodynamic and kinetic similarities, as well as the differences, between interacting ions in the lattice and electrons in nanostructured semiconductors are discussed. From these considerations, the chemical diffusion coefficient of electrons for multiple trapping transport in nanoporous dye solar cells can be calculated indirectly, and the results are in agreement with the reduction of the kinetic-transport equations in the quasistatic approximation. The chemical diffusion coefficient in several models for electrons is discussed: for a wide but stationary distribution of sites energies, giving the Fermi-level dependent D n [Fisher et al. J. Phys. Chem. B 2000, 104, 949] and for the enhancement of the diffusivity by effect of electrostatic shift of energy levels [Vanmaekelbergh et al. J. Phys. Chem. B 1999, 103, 747]. This last model is shown to correspond to the mean-field approximation to interaction in a lattice gas. A general expression containing all of these cases is provided, and several important consequences of the distinction between macroscopic diffusion and single particle random walk are pointed out.