Coupled multi-physics modeling can reveal new insights into the processes that govern the performance and degradation of photoelectrodes under varying operation conditions [1]. While many subprocesses have been studied to a great extent, a unified model for PEC device operation is still a work in progress [2]. For example, recent studies use simplified models for the charge transport in the semiconductor [3] or neglect the electrolyte species transport [4]. Also, charge transfer theory at the semiconductor-electrolyte junction (SCEJ) coupled to the solid and liquid has been seldom investigated [5]. Furthermore, the modeling of (time-dependent) degradation through (electro-)chemical corrosion has been initiated recently yet with simplified charge transfer and neglected species transport [6].

Herein, new physics relevant for photoelectrode operation have been included to predict the performance and stability of photoelectrode material systems. Transport of electrons and holes in the semiconductor were modeled with Poisson-drift-diffusion equations including carrier generation and recombination terms. Special attention was put on the surface recombination by trap states. Band edge unpinning was introduced through surface state (dis-)charging, which allowed to study a surface state-passivating co-catalyst. Transport of species in the electrolyte was modeled in a multi-modal manner including diffusion, drift in electric field and drift in boundary layer flow. Charge transfer modeling at the SCEJ based on Marcus Theory was implemented to study simultaneously multiple redox reactions of different energetics and kinetics. Degradation was modeled as competition between charge transfer to electrolyte species and charge capture by surface bonds with time-dependent photoelectrode dissolution.

A BiVO₄ photoanode with CoPi co-catalyst for water splitting served as case study for model validation and demonstration. Parameters of the SCEJ and charge transfer were determined through first principle calculations and with dedicated experiments. Voltammograms were used for validation by variation of operational conditions (pH, temperature and irradiance) and its effect on, otherwise, inaccessible material properties was assessed by sensitivity analysis. Voltammograms showed a mild pH-dependence resulting from changes in the surface state charging and electrolyte species concentrations. Under concentrated sunlight (> 10 kW m^-2), a cathodic shift in the onset potential was observed, dependent on surface state charging and recombination. The effect of mass transport limitation on the photocurrent caused by sluggish species near the SCEJ was also quantified. A photocurrent dependence on the illumination direction (front vs. back), typical for BiVO4 due to limited majority carrier transport, was confirmed in the model. The dissolution-based degradation model was able to capture characteristics of the photocurrent decrease experimentally observed in BiVO4 photoanodes.

In-depth parametric studies on photoelectrode operation (including degradation) were conducted with a coupled multi-physics model. The model has capabilities to be expanded to include multiple dimensions and complex photoelectrode structures to provide more insights into the heterogeneity and local variation of operation condition in a photoelectrochemical device or component. Moreover, additional degradation mechanisms, e.g. surface passivation, will permit stability studies of a broad range of photoelectrode materials.