Review of diffusion models for charge-carrier densities in dye-sensitized solar cells

Originated in 1991 by O'Regan and Grätzel, dye-sensitized solar cells (DSSCs) provide alternative solutions for renewable energy problems. Earlier mathematical models for DSSCs are based on junction solar cells, which was first studied by Chapin et al in 1954. These equations were derived from Shockley's work on modelling semiconductors in the late 1940s. However, it was pointed out by Cao et al and Gregg that diffusion model is more suitable for modelling DSSCs. Since the study by Södergren in 1994, the diffusion model has become prevalent in literature and the development of this model by including additional equations to incorporate electrolyte concentrations, time dependence for charge carrier densities and nonlinear diffusivity has shown to capture more complex processes of charge transport within DSSCs. In this paper, we review the development of the diffusion model for the charge carrier densities in a conduction band of DSSCs.