Utilizing Band Diagrams To Interpret the Photovoltage and Photocurrent in Photoanodes: A Semiclassical Device Modeling Study

Abstract

The photovoltage and photocurrent both serve as important design metrics when assessing the performance of photoanodes within photoelectrochemical cells. However, to date, wide disagreement persists (even in the recent literature) regarding how the photovoltage should be physically interpreted; this lack of consensus is further coupled to physical interpretations of the photocurrent. In this work, we utilize state-of-the-art device modeling to help clarify the physical origins of both the photovoltage and photocurrent in photoanodes. Our methodology is based on directly solving the governing electron and hole continuity equations, coupled self-consistently with Poisson’s equation, with appropriate boundary conditions. Through a systematic examination of a model photoanode, hematite, we correlate directly measurable current–voltage characteristics with operational band diagrams. It is shown that, by directly mapping specific operating points of either equal current or equal voltage (both illuminated and in the dark) to band diagram plots, one is able to obtain substantial insights into the physical nature of both the photocurrent and photovoltage. Throughout this analysis, the fundamental distinction between electrostatic and electrochemical perturbations under arising illumination is underscored. By aiding the community-wide effort to arrive at a consensus on these concepts, we aim to further enable the design of higher-efficiency photoanodes.

Characterizing photocatalysts for water splitting: from atoms to bulk and from slow to ultrafast processes

“…284 Photovoltage, flat band potential and photocurrent are important measures when designing water splitting catalysts. Yet, there is still a lack of consensus regarding their physical interpretation, 285 and uncertainties when determining these values at nanostructured materials. 286 Metal nanosheets containing d 0 transitions metals such as titanates, niobates and tantalates are usually n-type semiconductors with adequate light adsorbing, electron accepting, and electron transfer mediating properties.…”

Evolution of Surface Oxidation on Ta3N5 as Probed by a Photoelectrochemical Method

“…In the simulation results, the coupled Poisson-continuity equations were numerically solved with appropriate boundary conditions. − In photocatalytic systems, such as Ta 3 N 5 , the steady-state electron and hole continuity equations can be expressed in the form where annihilated and generated electrons/holes are captured through the recombination ( R n, p ) and generation ( G n, p ) rates. − A detailed discussion on the recombination and generation terms applied can be found in refs., , a short summary of the recombination and generation terms can be found in the supporting information. Here, J n and J p represent the electron and hole current, respectively, throughout the Ta 3 N 5 electrode, and q is the elementary charge.…”

“…Here, J n and J p represent the electron and hole current, respectively, throughout the Ta 3 N 5 electrode, and q is the elementary charge. The continuity equations were only solved inside the electrode, as conduction bands are not formed in the liquid where ionic charge transport dominates. ,, In this regard, appropriate boundary conditions must be applied at both the electrode bulk and liquid interface, respectively. Deep within the Ta 3 N 5 electrode, the carrier concentration was set equal to the bulk values (forming Dirichlet boundary conditions for electrons and holes), whereas Neumann boundary conditions were applied at the semiconductor–liquid interface because of the electron ( J n | int ) and hole ( J p | int ) current transfer expressions , Here, n s and p s are, respectively, surface electron and hole concentration; n s0 and p s0 are the corresponding surface electron and hole concentrations in equilibrium; v t, n and v t, p are the electron and hole transfer velocities (essentially rate terms).…”

“…Poisson’s equation was solved self-consistently with the continuity equations because of the coupling between the electrostatic potential and carrier concentrations. − , Fundamentally, the potential (ϕ) present in the entire span of the Ta 3 N 5 -liquid junction arises from interactions between the charges inside Ta 3 N 5 (ρ sc ) and those in the liquid (ρ L ). It can be expressed in the form where ε represents the spatially varying dielectric constant across the entire system.…”

“…To solve Poisson’s equation, electrostatic boundary conditions must also be appropriately set. Dirichlet boundary conditions were implemented in the bulk of the liquid, whereas a floating potential Neumann boundary condition was applied in the bulk of the semiconductor to capture the photovoltage. , Further details concerning the computational methodology can be found in the extensive discussions provided in refs. , …”