Non-monotonic dependence of the current density on the thickness of the photoactive layer

We have developed a mathematical model able to predict the dependence of the current density, j0, in the dc limit, on the thickness of a photoactive semiconductor layer, d, in contact with an electrolyte. The model considers the application of an external bias. The theoretical analysis has been done by means of a diffusive model, where the excess of charges moves by diffusion in the presence of a generation term, due to the incident light, and a recombination term, proportional to the excess of charge carriers. We show that a non-monotonic dependence of j0 vs. d is expected. For small d, the photocurrent density is proportional to d and the proportionality constant is related to both the attenuation of the light in the photoactive semiconductor layer and to the applied potential. In the opposite limit of large d, the current tends to a constant value that is dependent on both the light intensity and the applied bias. Our theoretical predictions are in qualitative agreement with the experimental data reported in literature for BiVO4 films. © 2017 Elsevier B.V.