Simultaneously Solving the Photovoltage and Photocurrent at Semiconductor–Liquid Interfaces

Abstract

In this work, we present a general theoretical and numerical approach for simultaneously solving the photovoltage and photocurrent at semiconductor−liquid interfaces. Our methodology extends drift-diffusion methods developed for metal−semiconductor Schottky contacts in the device physics community into the domain of semiconductor− liquid "pseudo-Schottky" contacts. This model is applied to the study of photoelectrochemical anodes, utilized in the oxidative splitting of water. To capture both the photovoltage and photocurrent at semiconductor−liquid interfaces, we show that it is necessary to solve both the electron and hole current continuity equations simultaneously. The electron continuity equation is needed to primarily capture the photovoltage formation at photoanodes, whereas the hole continuity equation must be solved to obtain the photocurrent. Both continuity equations are solved through coupled recombination and generation terms. Moreover, to capture charge transfer at the semiconductor−liquid interface, floating (Neumann) boundary conditions are applied to the electron and hole continuity equations. As a model system, we have studied the illuminated hematite photoanode, where it is shown that our approach can capture band flattening during the formation of a photovoltage, as well as the photocurrent onset and saturation. Finally, the utility of this methodology is demonstrated by correlating our theoretical calculations with photocurrent measurements reported in the literature. In general, this work is intended to expand the scope of photocatalytic device design tools and thereby aid the optimization of solar fuel generation.

Plasmonic Photoelectrochemistry: In View of Hot Carriers

“…[ 34 ] This compensation diminishes the extent of band bending and increases Fermi level, causing OCP to move towards cathodic direction. [ 34–35 ] V ph (i.e., the OCP shift) is dictated by the split of Fermi level into quasi‐Fermi levels of electrons ( E Fn ) and holes ( E Fp ), where E Fp equilibrates with OH – /O 2 in the electrolyte (Figure 9b). [ 33,35 ] The above description is based on ideal conditions.…”

“…[ 34–35 ] V ph (i.e., the OCP shift) is dictated by the split of Fermi level into quasi‐Fermi levels of electrons ( E Fn ) and holes ( E Fp ), where E Fp equilibrates with OH – /O 2 in the electrolyte (Figure 9b). [ 33,35 ] The above description is based on ideal conditions. Experimentally observed V ph is usually smaller due to the presence of surface defects.…”

Charge Transport Phenomena in Heterojunction Photocatalysts: The WO3/TiO2 System as an Archetypical Model

“…A custom-made finite-difference (FD) numerical model was developed in order to discern charge transport and electrostatic properties within the WT heterojunction. 47 This model self-consistently solves the coupled Poisson-continuity equations (Eqs. 1-3):…”

A Review of Inorganic Photoelectrode Developments and Reactor Scale‐Up Challenges for Solar Hydrogen Production

“…Ways for avoiding major losses associated with suboptimal orientation of (photo)electroactive surfaces relative to each other, high material resistivity, and complications due to bubble evolution must be explored more proactively. Furthermore, reactor design should be supplemented with numerical models of: 1) Microkinetics – the prediction of photocurrent generated by a chosen combination of materials as a function of light intensity; [ 134,313,350–355 ] 2) macrokinetics – accounting for the spatial distributions of electrode kinetics, management of heat imparted by solar photons, changes in the chemical composition of the electrolyte, effect(s) of bubbles, product separation; [ 110,134,313,314,326 ] 3) systems model – for determining the BoP required to support the operation of the PEC reactor, including the means by which the H 2 product is collected and transferred to energy storage systems; [ 356,357 ] 4) technoeconomic model – for determining how cost‐effective the system is, given the combined set of parameters that characterize its performance (discussed in Section 5).…”