Theoretical Investigation on Interfacial-Potential-Limited Diffusion and Recombination in Dye-Sensitized Solar Cells

The electron diffusion and recombination limited by interfacial potential in dye-sensitized solar cells are theoretically investigated within a potential barrier model. The dependence of diffusion coefficient D and recombination rate K on various parameters is examined. The D and K exhibit electron density dependence with three distinct regions: (i) constant region, (ii) linear region, and (iii) nonlinear region when the quasi-Fermi energy level sweeps from the lower-energy side to the conduction band edge. For a dye-sensitized solar cell operated at normal conditions, a linear-density-dependent expression for D or K is a reasonable approximation. The diffusion coefficient D in a temperature range of 200–400 K exhibits thermally excited behavior as D ∼ exp(− E act / k B T ) when the potential barrier width W is large enough (∼4 nm) and the corresponding activation energy E act is independent of quasi-Fermi energy level or electron density. The diffusion coefficient D shows linear dependence on particle size. The recombination rate K shows more complicated size dependence due to the competition between the pure size effect and the local electric field effect. When the quasi-Fermi energy level approaches the conduction band edge, the K increases significantly with size due to the shrinkage of the potential barrier on the interface. Because of the local electric field generated by excess electrons accumulated in nanoparticles, the recombination rate K is approximately proportional to 1/ε r (ε r is relative dielectric constant of interface layer). This implies a way to suppress recombination by controlling the dielectric property of the interface layer. The interfacial-potential-limited diffusion and recombination are beneficial supplements to the well-established mechanisms, such as localized-state-limited diffusion (trapping and detrapping effect), chemical-reaction-limited recombination, etc., and is helpful for us to understand the operating mechanism in dye-sensitized solar cells.