Main

Suppose one desires to identify a semiconductor material that can photoreduce a species with a formal reduction potential ε°′. Such a reduction could be a one-electron transfer for application in organic synthesis, environmental remediation or solar energy conversion, or a kinetically complex multi-electron transfer as in the reduction of H2O or H+ to H2 fuel. A typical starting point would be to consult a photoelectrochemistry review article for the band-edge positions of semiconducting materials relative to the vacuum energy level and/or standard hydrogen electrode energy level, typically in an aqueous electrolyte1,2,3,4. With the knowledge that bandgap photoexcitation creates electron–hole pairs that relax/thermalize to the band edges before interfacial electron transfer occurs, an inspection of the tabulated conduction-band-edge energy (Ec) relative to −qε°′ would allow one to predict whether a given semiconductor was appropriate for the desired reaction (the variables used in this contribution are defined in Table 1). One might also conclude that interfacial electron transfer from the semiconductor into solution would not occur at all if −qε°′ > Ec, that is, if the reduction potential lies above the conduction-band energy. These ideas are misleading and are often not the limiting property for photoelectrochemical devices and particulate photocatalysts. Distinct rate processes developing excess charge, described in this Perspective, can move the tabulated Ec value relative to the −qε°′ without a chemical transformation. A reduction potential that falls outside the semiconductor bandgap may impact the current–voltage behaviour and voltage-dependent interfacial kinetics, but does not in fact preclude facile electron transfer.

Table 1 Definitions of the variables used in this Perspective
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Tabulated band-edge positions are poor indicators of interfacial redox chemistry because they are not singular parameters—they are sensitive to the chemical environment and surface chemistry and are modulated by interface electrostatics. The free energies of non-equilibrium electronic charge carriers (for example, the hole and electron quasi-Fermi levels) in a semiconductor, at steady state and under illumination, determine their ability to drive overall reactions and perform chemical work5. The degree to which the quasi-Fermi levels split under illumination, in turn, depends on the kinetics of charge transfer; that is, the surfaces or interfaces acting as charge-carrier-selective contacts, not on the absolute band-edge energies. In this Perspective, we discuss the origins of the common misconception that absolute band edges are critical and illustrate the underlying design principles for improved materials and interfaces, operative charge-separation/collection mechanisms and stabilization strategies at semiconductor/electrolyte interfaces.

Governing equations

The purpose of this section is to show how the band-edge positions are not the critical parameters for the selection of semiconductors because they shift in response to carrier accumulation and surface chemistry. Consider a semiconductor without dopants and without interfacial electric fields at equilibrium (that is, the so-called flat-band condition). With generality to molecular, particulate and bulk semiconductor photoabsorbers, we can write the following equilibrium expressions for a pair of redox reactions (either outer-sphere one-electron reactions or multi-step electron-transfer reactions) that include both electrons (\(e^-_{{\rm{cb}}}\)), holes (\(h^+_{{\rm{vb}}}\)), and O (oxidized) and R (reduced) species, with the specific charge not included for simplicity of notation:

$${\nu }_{1}{e}_{{{\rm{cb}}}}^{-}+{{\rm{O}}}_{1}\mathop{\rightleftharpoons}\limits^{{k}_{1,{{\rm{et}}}}}_{{k}_{1,{{\rm{et}}}}^{{\prime}}}{{\rm{R}}}_{1},\,{\nu }_{1}{h}_{{{\rm{vb}}}}^{+}+{{\rm{R}}}_{1}\mathop{\rightleftharpoons}\limits^{{k}_{1,{{\rm{ht}}}}}_{{k}_{1,{{\rm{ht}}}}^{{\prime} }}{{\rm{O}}}_{1}$$
(1)
$${\nu }_{2}{e}_{{{\rm{cb}}}}^{-}+{{\rm{O}}}_{2}\mathop{\rightleftharpoons}\limits^{{k}_{2,{{\rm{et}}}}}_{{k}_{2,{{\rm{et}}}}^{{\prime} }}{{\rm{R}}}_{2},\,{\nu }_{2}{h}_{{{\rm{vb}}}}^{+}+{{\rm{R}}}_{2}\mathop{\rightleftharpoons}\limits^{{k}_{2,{{\rm{ht}}}}}_{{k}_{2,{{\rm{ht}}}}^{{\prime} }}{{\rm{O}}}_{2}$$
(2)

Marcus theory shows how the standard electron-transfer rate constant for an outer-sphere redox reaction (that is, where electron transfer is across the double layer) can be expressed in terms of the energy difference between the band edge and redox energy6,7. While in some (ideal) cases Marcus theory describes the kinetics of electron transfer from a semiconductor to molecular acceptors8,9, photochemical fuel-forming reactions do not generally proceed as purely outer-sphere reactions, but instead involve catalytic species and mechanistic steps with inner-sphere intermediates (that is, species that may interact in the strong-coupling limit)10. Furthermore, band-edge positions are generally unknown under the experimental conditions of interest as they are not singular parameters. Ab initio calculations can provide a guide, but are limited in that they assume an atomic-scale structure and termination of the active surface and interface solvent/double-layer structure that is typically experimentally unknown. Predicting rate constants for practically relevant photoelectrochemical processes thus remains a major challenge.

The free energy of charge carriers in a semiconductor is described by their electrochemical potential (\({\bar{\mu }}_{i}^{\alpha }\)). In general, assuming thermal equilibrium, for species i in phase α:

$${\bar{\mu }}_{i}^{\alpha }={\mu }_{i}^{\alpha }+{z}_{i}F{\phi }^{\alpha }=\left({\mu }_{i}^{0\alpha }+{RT}\;{\mathrm{ln}}{\,a}_{i}^{\alpha }\right)+{z}_{i}F{\phi }^{\alpha }={N}_{a}{\left(\frac{\partial G}{\partial {N}_{i}}\right)}_{T,P,N_{j\ne i}}$$
(3)

Under illumination, one can separate the electrochemical potential of conduction band electrons from valence band holes. In semiconductor physics, these quantities are termed the electron and hole quasi-Fermi levels (Efn and Efp, respectively). Although quasi-Fermi levels are understood for populations of electronic charge carriers, the concept applies in the ergodic limit to individual species11. For example, if a semiconductor particle is sufficiently small so that there are few excited carriers, the time-averaged behaviour is equivalent to the ensemble average across many particles, and energies can be described in terms of the quasi-Fermi level. Regardless of the band-edge position under the flat-band condition, the quasi-electrochemical potentials of conduction-band electrons and valence-band holes in the photoabsorber (\({\bar{\mu }}_{{\rm{n}}}^{{\rm{absr}}}\) and \({\bar{\mu }}_{{\rm{p}}}^{{\rm{absr}}}\), respectively) will tend towards equilibrium, transferring charge according to equations (1) and (2), or via the recombination of electrons and holes at the surface and within the bulk of the photoabsorber. To drive an overall uphill (∆Grxn > 0) chemical reaction with light, the quasi-Fermi-level splitting (Efn − Efp) must be greater in magnitude than ∆Grxn under steady-state reaction conditions (and relevant species activities at the surface). Differences between Efn and Efp beyond this minimum energy value are needed due to associated kinetic (catalytic) and mass-transport energy losses.

Semiconductor/liquid junctions

Next consider a wide-bandgap (Eg ≈ 3–4 eV) semiconductor particle with a conduction band energy (or equivalently potential, which is the energy per charge on the relevant reference scale) that is not high enough to drive the hydrogen evolution reaction (that is, not reducing enough to drive the reduction of H2O or H+ to form H2) but a valence band energy that is substantially below (that is, more oxidizing) the reversible oxygen reduction potential (Fig. 1). Under illumination, a small photoexcited carrier concentration (n′ and p′) is needed to produce the minimum thermodynamically required difference between \({\bar{\mu }}_{{\rm{n}}}^{{\rm{absr}}}\) and −\({\bar{\mu }}_{{\rm{p}}}^{{\rm{absr}}}\) to drive water splitting because of the low equilibrium concentrations of holes and electrons (neq and peq) in a wide-bandgap semiconductor. The total free energy available to drive chemical reactions is given by the difference between the electron and hole quasi-Fermi levels (or equivalent electrochemical potentials) according to equation (4).

$${\frac{F}{q}\left({E}_{{{\rm{fn}}}}-{E}_{{{\rm{fp}}}}\right)}=\frac{F}{q}{E}_{{\rm{g}}}+{RT}\;{\mathrm{ln}}\frac{{n}^{{\prime} }{p}^{{\prime} }}{{N}_{{\rm{C}}}{N}_{{\rm{V}}}}={RT}\;{\mathrm{ln}}\frac{{n}^{{\prime}}{p}^{{\prime} }}{{{n}_{i}}^{2}} > \Delta {G}_{{\rm{rxn}}}\,(+\, \Delta {G}_{{\rm{losses}}})$$
(4)

where ni is the intrinsic carrier concentration ∆Grxn and ∆Glosses are the molar free energy of the reaction and that lost to the environment leading to inefficiency. Note that equation (4) does not include variables associated with the kinetics of the electron-transfer reactions or the absolute band-edge positions.

Fig. 1: Interface energies and reactions.
figure 1

a, Excess charge-carrier-density plots (left) and band diagrams (right) for an n-type semiconductor in depletion, accumulation and inversion due to equilibration with a contacting phase (for example, redox species). b, Depleted photoabsorber particle (site 2) driving misaligned half reactions under illumination (simulated one-dimensional COMSOL Multiphysics model, ND = 1014 cm−3, length = 1 µm, and disparate electron-transfer (et) and hole-transfer (ht) rates at the electron- and hole-selective contacts, respectively). Accumulated surface electrons (site 1) pull up the photoabsorber energy levels relative to \({q}\varepsilon_{{{\rm{O}}}_{1}/{{\rm{R}}}_{1}}\) by an electrostatic potential energy q∆ϕedl, allowing photoexcited electrons to drive a reduction reaction on the semiconductor surface whose energy is out of the bandgap. c, Possible facet-dependent oxidation and reduction kinetics and rate equations quantifying charge-carrier selectivity, as discussed in the text.

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How can both electrons and holes transfer if the conduction-band-edge energy is not high enough to drive the reaction? Consider the following qualitative picture. The kinetics of hole transfer from semiconductor to solution species initially will be fast as the valence band holes are quite oxidizing, while electrons transfer slowly. This will lead to a build-up of negative electron charge on/in the semiconductor, which is equivalent to an applied negative bias that raises the electron quasi-Fermi level and eventually the band edges, increasing the reducing power of the photoexcited electrons. This process will occur until the rates of both hole and electron transfer are equal (at steady state). If the semiconductor particle is already doped n-type, as most metal oxides used in water splitting are12,13,14,15, this negative charging under photoexcitation is termed majority carrier accumulation (electrons in an n-type semiconductor). The same phenomena can occur with the addition of excess minority carriers (holes in an n-type semiconductor), which is called inversion. The excess mobile carriers reside close to the surface of the semiconductor, typically within the first few atomic layers, as required by Gauss’s law (Fig. 1a). This analysis assumes that there is no chemical change (for example, cation intercalation/deintercalation, changing surface termination or surface oxidation) that modifies the surface electrochemical potential without requiring the development of excess space charge—such processes can also play an important role in dictating interfacial energetics16,17,18.

Experimental data support the qualitative picture outlined above19,20,21,22. Grimm et al. showed systematic control of the interface photovoltage in H- and CH3-terminated crystalline p-Si and n-Si photoelectrodes, governed by the reversible potential of the solution redox couple (Fig. 2a)22. These surfaces have low defect densities, with nearly every Si surface atom chemically terminated. If the redox potential of the solution was outside the bandgap of Si (that is, under flat-band conditions), the interface was driven into either inversion, where the minority carrier concentration at the surface exceeds that of the majority carriers in the semiconductor bulk, or accumulation, where excess majority carriers are at the surface23. Inversion creates the functional equivalent of a buried junction, leading to high photovoltages, while accumulation leads to an Ohmic contact between the solution and semiconductor.

Fig. 2: Accumulation, depletion and inversion at photochemical junctions.
figure 2

a, The absolute value of Voc (|Voc|) measured for n- and p-type H- and CH3-terminated Si with corresponding error bars as a function of the reducing power of the A/A– redox couple in the electrolyte, (εeff(A/A−); data from ref. 22) that is aligned with the absolute energy scale and the differential capacitances in b. The solid lines are a guide to the eye and show the trends. Here, Voc was directly measured from the semiconductor against a Pt electrode poised at the Nernstian potential of the solution (ε(A/A−)) and plotted against the effective solution potential (εeff(A/A−)), normalizing the minority-carrier acceptor concentration to 10 mM. The regions highlighted in blue and red correspond to strong inversion for n-type Si (dopant density of 3 × 1015 cm−3) and p-type Si (dopant density of 8 × 1016 cm−3), respectively. b, Semiconductor differential capacitance (Csem) for p-type Si (top) and n-type Si (bottom) at 295 K, taken from the calculated space-charge density26, as a function of band bending (∆ϕsem). The vertical asymptotes correspond to flat-band potentials. Csem values have been plotted using the same dopant density as used by Grimm et al.22 A double-layer capacitance (Cedl) of 10 µF cm−2 is shown as an approximate reference for relative voltage drops (∆ϕedl and ∆ϕsem). The expected high-frequency dark response in the inversion region is shown by a dashed line when the rate of generation of the minority carrier at the surface is low.

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While the regenerative photoelectrochemical cell architecture used by Grimm et al. has only one electrochemically active semiconductor interface, the demonstration of large (bulk-recombination-limited) photovoltages with solution potentials outside the absolute-energy limits of the Si bandgap is conceptually the same as the picture for the hypothetical wide-bandgap semiconductor described above. For example, the difference between the H- and CH3-terminated surfaces leads to a systematic shift in the band-edge positions of ~0.4 V due to changes in the interface dipole. Regardless, there is no change in the maximum interface photovoltage or the ability to drive any given redox reaction irrespective of the reaction’s redox potential24. The relative positions of the solution reduction potential/energy and the band edge energy positions do not determine the photochemical reactions that photoexcited carriers can drive. In fact, the highest photovoltages were observed for a p-Si photoelectrode in contact with a redox couple, dimethylcobaltocene (Fig. 2a), whose reduction potential close to −1 V versus the saturated calomel electrode (SCE) is much more negative than the conduction band edge (at flat band) for Si at about −0.6 V versus SCE25,26. The absolute conduction band energy/potential value is irrelevant for determining which reductions p-Si can drive due to, in this case, carrier inversion. Evidence for inversion has been reported at photoelectrochemical interfaces via near-surface channel conductance measurements27, photocapacitance28 and infrared spectroscopy29.

In the absence of other observations, the data in Fig. 2a could also be explained by densities of surface states that prevent larger degrees of band bending and high photovoltages (that is, surface-state-induced Fermi-level pinning)30,31. However, near-surface channel conductance measurements on some of the systems are inconsistent with this possibility27. Nevertheless, when large densities of surface states do cause Fermi-level pinning, the resultant photoelectrode behaviour is like that of a buried junction or a photoelectrode in inversion—the photovoltage is independent of the redox potential of the solution and the absolute band-edge energies remain irrelevant with respect to which reactions can be driven.

The data in Fig. 2a come from measurements of the semiconductor operating under accumulation, depletion, or inversion conditions, which can be understood with equivalent-circuit models. At semiconductor/liquid junctions, the simplest model consists of two capacitors, one representing the charge stored in the semiconductor space charge region (Csem) and the other the Helmholtz double layer (Cedl). More complex models that include a diffuse layer, interfacial surface states and other corrections can also be used3, but they are not needed to illustrate accumulation, depletion and inversion conditions. The absolute electrostatic potential drops across the space charge region (∆ϕsem) and double layer (∆ϕedl) are inversely related to their relative capacitances by the conservation of charge (equation (5)), where equilibration of the surface electrochemical potential sets the degree of band bending and therefore the potential dropped in the semiconductor (∆ϕsem; Fig. 2b).

$$\frac{{\Delta \phi }_{{\rm{sem}}}}{{\Delta \phi }_{{\rm{edl}}}}=\frac{{C}_{{\rm{edl}}}}{{C}_{{\rm{sem}}}}$$
(5)

The surface charge and Csem depend on the applied potential in a manner that can be calculated from carrier statistics and Poisson’s equation26, but the key point is that the magnitudes of the potential drops in each region depend on both Csem and Cedl. The value of ∆ϕ is thus larger across the region with the smaller capacitance between Csem and Cedl. Simply, the smaller capacitance reflects where the electrostatic potential change is larger. Plots of measured capacitance as a function of electrode potential may thus illustrate when accumulation or depletion conditions are operative, but such data are rarely reported, presumably due to the presence of surface states32.

As a semiconductor electrode is biased into accumulation, the experimentally measured capacitance (Cexp) increases and saturates to the value of Cedl. In this condition, ∆ϕedl is larger than ∆ϕsem. That is, applying a bias to a semiconductor electrode in accumulation does not substantially move the (quasi-)Fermi levels relative to the band edges. Instead, the applied bias primarily shifts the band edges relative to a reference point in solution. Through equation (5), the quantity of charge from majority carriers (that is, ∆ϕsem × Csem) accumulated at the semiconductor surface must be counterbalanced exactly by the charge from ions in solution (that is, ∆ϕedl × Cedl) gathered at the interface. Physically, the availability of ions from solution at this location is limiting because the abundance of majority carriers from within the semiconductor at the surface is large in accumulation, that is, Cexp tends to Cedl.

In depletion, the opposite is true. Cexp tends to Csem because the total charge from the majority carriers in the semiconductor space charge region is much smaller than from the available ions in solution that could move to the interface. Correspondingly, ∆ϕsem is substantially larger than ∆ϕedl in depletion. This statement is equivalent to stating that the applied bias moves the (quasi-)Fermi levels relative to a reference point in solution, but the band-edge values are largely unchanged relative to that same reference point.

In accumulation, the interpretation of ∆ϕsem is straightforward. Csem is effectively independent of time/frequency because the equilibration of majority carriers from the bulk to the interface is fast on the relevant timescale of the impedance measurement. In inversion, the interpretation of ∆ϕsem is more nuanced. Csem can have a measurable time dependence as the supply of minority carriers to the surface depends on an interplay between the rate of thermal generation, drift, losses from recombination and consumption from interfacial processes. Accordingly, the measured capacitance–potential profile in inversion is a function of the frequency of measurement/observation (Fig. 2b, dashed versus solid line) and is strongly influenced by the operative kinetics of minority-carrier generation, transport, trapping and transfer33. This is why Mott–Schottky plots of impedance often remain linear in inversion at potentials well past the band edge and can make the increase in measured capacitance due to inversion difficult to observe32,34,35,36,37,38,39,40.

Nanoscopic and molecular systems

In a bulk semiconductor, the number of band-edge states is large compared with the number of carriers at the surface. Thus, the chemical potential at the surface does not change with the build-up of charge (that is, the activity term \({a}_{i}^{\alpha }\) for charge carriers in equation (3) becomes nearly constant and is unaffected by further changes in carrier density at the surface, as in a polarized metal electrode).

Nanoscopic and molecular systems show similar behaviour (Fig. 3), but there are differences. Semiconductor nanoparticles are typically (practically) undoped, that is, their size limits the number of atomic substitutions. Yet, under illumination, they can accumulate electrons or holes at steady state. In general, the rates of photochemical electron and hole transfer are not initially identical following illumination. When the system reaches steady state, by definition, the time derivatives of all concentrations are zero. This means that the concentrations of electrons and holes build up to different extents such that it is the rates of photochemical electron and hole transfer that are ultimately balanced. This process leads to a steady-state electrostatic potential developing across the nanoparticle/solution interface. This change in ∆ϕ moves the energies of the band edges relative to the solution reduction potential (or energy) for the reasons stated above. The steady-state electron and hole concentrations are thus defined by the reactant and product concentrations, charge-transfer rate constants and relevant generation/recombination mechanisms and rates.

Fig. 3: Band diagrams and photochemical charge accumulation in nanoscopic and molecular systems.
figure 3

a, Due to the kinetic limitations of either electron transfer (et) or hole transfer (ht), nanoparticles can accumulate either multiple electrons or holes, respectively, at steady state. This process leads to changes in the reducing or oxidizing power of the carriers associated with changes in electrostatic potential profiles. b, Molecular energy levels are typically well spaced, leading to changes in the reducing or oxidizing power of the ensemble via effects described by the Nernst equation and thus are more limited in range. c–e, Example band diagrams in the dark and under illumination for a photoelectrochemical junction in typical depletion conditions (c), with an inversion layer (d) and with a buried pn+ junction (e). Note that both the inversion layer and the buried junction can equivalently shift Ec and Ev relative to the solution redox potential, as in this example, due to an additional electric potential drop across the electrical double layer.

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For soluble molecular systems (M), the initial rates of electron and hole transfer will also not be identical in the ensemble of individual molecules. Molecular systems can thus also accumulate M− or M+ at steady state (representing an additional negative or positive charge on M, which may also be initially charged). This process shifts the Nernst potential of the redox solution containing the ensemble of molecules through a change in the activities:

$${{\varepsilon}}_{{{\rm{M}}}^{+}/{\rm{M}}}={{\varepsilon}}_{{{\rm{M}}}^{+}/{\rm{M}}}^{{\circ}}+\frac{{RT}}{{{\nu}_{{e}^{-}}}{F}}\mathrm{ln}\frac{{a}_{{{\rm{M}}}^{+}}}{{a}_{{\rm{M}}}}$$
(6)

and

$${{\varepsilon}}_{{\rm{M}}/{{\rm{M}}}^{-}}={{\varepsilon}}_{{\rm{M}}/{{\rm{M}}}^{-}}^{{\circ}}+\frac{{RT}}{{{\nu}_{{e}^{-}}}{F}}\mathrm{ln}\frac{{a}_{{\rm{M}}}}{{a}_{{{\rm{M}}}^{-}}}$$
(7)

We note that this is different from a semiconductor particle that can build up charge at one energy level (the band edge) as electronic states are closely packed in energy. In a molecule, the electronic states are usually widely spaced in energy and thus this is not generally possible. Hence, there is no mechanism to smoothly vary the electric potential term for molecular systems via a process analogous to accumulation or inversion in a semiconductor. Instead, changes in chemical potential dominate contributions to changes in free energy under photoexcitation. As such, the primary mechanism to change the oxidation or reduction strength of a specific molecular chromophore is to change the activity/concentration of the oxidized or reduced species.

The importance of charge-transfer kinetics and interface/contact selectivity

If band-edge energy positions (at flat band) do not matter much for semiconductor photoelectrochemistry, what does? Charge-transfer kinetics and interface charge-carrier selectivity are crucial. Consider a photoelectrode that has been fabricated to have a buried n+p junction, such as Pt/n+p-Si, and used as an efficient photocathode for photoelectrochemical H2 production (Fig. 3)4. The n+p junction is selective towards the collection of photoexcited electrons over holes because of the higher conductivity of electrons compared with holes in the n+ region41. Pt makes an Ohmic, unselective contact with the n+-Si surface (emitter) layer, but that is inconsequential to the system behaviour because the n+-Si layer is very thin and absorbs little light; the photocurrent is dominated by electron–hole pairs that separate at the n+p junction before reaching the Pt/n+-Si junction. The n+p junction here is functionally equivalent to the case of strong inversion. Such an interface can be contrasted with Pt/p-Si, which is not very selective towards electrons over holes because the relative lack of interfacial band bending leads to substantial surface hole concentrations and hole conductivity. In all these cases, the absolute band edges of the semiconductor are irrelevant to the ability of the photoelectrode to drive an efficient Faradaic reaction.

In a simple model including carrier generation and interfacial charge transfer, Roe et. al. derived the limits on Voc ≤ (Efn − Efp)/q across a two-contact (photovoltaic or photochemical) device. The set of four rate equations for electron and hole partial currents, Jn(x) and Jp(x), at contacts x1 and x2 are given in Fig. 1 (ref. 42). The out-of-equilibrium surface electron and hole densities, \(\Delta n=({n}_{x}-{n}_{x}^{{{\rm{eq}}}})\) and \(\Delta p=({p}_{x}-{p}_{x}^{{{\rm{eq}}}})\), under illumination drive electron and hole partial currents. The magnitude of the current response is related directly to the kinetics of electron or hole transfer (k1,et or k1,ht) and local species concentrations or, similarly, the equilibrium-exchange-current densities (\({J}_{0{\rm{n}}}^{\,x}\) and \({J}_{0{\rm{p}}}^{\,x}\)). The terms \({J}_{0{\rm{n}}}^{\,x}\) and \({J}_{0{\rm{p}}}^{\,x}\) define (Efn – Efp)/q and Voc under steady-state illumination, and therefore the maximum free energy available to do work. Interfacial kinetics places limits on the maximum uphill chemical reaction that a photoabsorber can drive. This kinetic model applies identically to photoabsorbers beyond bulk semiconductors, including particulate photocatalysts, and could be adapted to molecular absorbers.

In particulate semiconductor photoelectrochemistry, the above considerations simultaneously apply to two spatially separated contacts on the same light-absorbing particle, with one contact selectively collecting electrons and the other holes43,44,45. The carrier selectivity of these contacts, along with the inherent properties of the semiconductor (mobility, lifetime, absorption coefficient), determine the ability of the semiconductor to drive any given photochemical reaction with a specific ∆Grxn. The measured absolute band-edge energies are of limited importance. Because many tests are carried out with sacrificial electron or hole acceptors (thus leading to the case where ∆Grxn is near zero or even negative and spontaneous without light), understanding of the underlying physics has often been obscured. One example of such a system is the black (defective) TiO2, which makes large amounts of H2 under illumination only in the presence of fast sacrificial hole acceptors, despite the likely low absolute energy of the conduction band defect states and probable lack of photovoltage generation46.

Corrosion and band edge energies

Gerischer proposed that semiconductors are inherently unstable in photoelectrochemical systems when the standard potentials for corrosion/decomposition are situated within the band edges47. For example, the anodic reaction CdS + 2h+ → Cd2+ + S has a standard potential more negative on an electrochemical scale than the valence band of CdS. As a result, n-CdS is thermodynamically unstable in water under illumination. However, this does not mean that n-CdS and other semiconductors with similar energetics cannot function meaningfully as photoelectrodes in water. The prolonged and stabilized operation of n-type CdS, ZnO, Cu2O, CdTe and metal dichalcogenide photoanodes in water has been achieved through the manipulation of interfacial kinetics in two ways. One strategy is to alter the electrolyte chemistry so that the redox reactions of interest greatly outpace the undesirable corrosion reactions for the flux of photogenerated carriers. Kinetic strategies that speed up the rate of productive reactions for electrons and holes through electrocatalysis will lower the steady-state population of electrons and holes at the surface (and quasi-Fermi-level splitting), also suppressing the competing corrosion reactions48. A second strategy is to coat the semiconductor surface with a protective thin film that specifically impedes corrosion/decomposition processes49,50,51. Such protective surface layers generally form a buried-junction-type structure where the charge-carrier selectivity of the passivating surface layer in contact with the bulk semiconductor controls the ability of the semiconductor to drive a specific reaction. We also note that because corrosion reactions take place on the semiconductor surface, and thus inside the electrical double layer, their relative potentials shift in the same way as the band-edge potential if the semiconductor moves into inversion or accumulation, that is, corrosion reactions are not outer-sphere processes.

Conclusion

We have clarified a common misconception of band-edge alignment with reduction potentials as a key material design principle for photocatalysts. Semiconductor absorbers can support excess charge densities where the kinetics of surface reactions will determine the resulting products. This clarification enables research of perhaps previously ignored materials and informs design principles for photocatalyst systems engineering for both one-electron redox reactions and more-complex multi-electron-transfer reactions (for example, H2 evolution, H2O oxidation and CO2 reduction). In multi-electron-transfer reactions, charge often accumulates at surface sites and how that charge is screened by electrolyte ions determines whether or not the apparent band edges shift with charge accumulation15. In the search for earth-abundant and efficient photocatalysts, the two primary materials properties of importance are sufficient optoelectronic properties of the absorber (optical absorption coefficient and free-carrier lifetime) and the ability to make both hole- and electron-carrier-selective contacts that connect the semiconductor with the catalytic sites that drive the oxidation and reduction half reactions of interest.