A theoretical investigation of ultrathin space charge layers in hematite photoelectrodes

Many efforts have been devoted to understand the hematite-electrolyte interface due to its potential application in the photoelectrocatalytic oxidation of water. This interface usually extends over lengths ranging from tens of nanometers to micrometers under water splitting conditions, therefore its realistic simulation via ab-initio calculations has been considered challenging. However, recent experiments measured space charge layers smaller ~10 Angstroms in highly doped nanostructured hematite photoanodes, which also displayed high photocurrent densities in water splitting experiments. We used a set of continuous equations based on the Poisson-Boltzmann distribution and the Stern model to investigate under which experimental conditions the space charge layer in hematite becomes ultrathin. In this regime, a considerable fraction of the potential drop across the interface is located in the Helmholtz layer, therefore we reported corrections to the Mott-Schottky equation that should be taken into account under these conditions. Using the continuous equations, we also examined the effect of the macroscopic properties provided by experiments on the microscopic state of the interface: we got access to the width of the space charge layer and the distribution of the electrostatic potential across the interface a function of the experimental conditions. We then used density functional theory (DFT) to get an atomistic insight of the space charge layer in the semiconductor, in systems ranging from the pristine stoichiometric surface, a surface with adsorbed hydroxyls, to Ti-doped slabs with doping densities of the order of ~10^{21} cm^{-3}. According to our analysis, space charge layers around 10 Angstroms must have been present also in other water splitting experiments with some of highest photocurrents registered. We observed that at high doping densities the inverse of the square of the capacitance should have a quadratic behavior close to flat-band conditions and a sub-linear behavior due to square-root-like corrections far from the flat-band potential. We used density functional theory to compute the band bending of the proposed atomistic models. The pristine stoichiometric and the hydroxylated undoped surfaces displayed band bendings of ~0.14 eV and ~0.49 eV, respectively. In the doped case, we found band bendings of ~0.07 eV and ~0.01 eV for the pristine and OH-terminated slabs, respectively. The latter band bendings corresponded to space charge layers extending in the sub-nanometer regime, according to the continuous equations. In the presence of doping, we found a qualitative and quantitative correspondence between the results provided by density functional and the continuous model. Contrary to the common picture of the electrochemical interface of a semiconductor and an electrolyte in water splitting experiments, where large space charge layers are present, the latter results give an insight of an unexpected regime of high photoelectrocatalytic efficiency in ultrathin space charge layers. Which in principle, are amenable to quantum mechanical ab-initio simulations. In this work we were able to describe the space charge layer of thin hematite slabs using DFT at an atomistic level.