Chapter 1: Concepts of Photoelectrochemical Energy Conversion and Fuel Generation

Photoelectrochemical energy conversion dates back to the seminal work of Fujishima and Honda, who demonstrated light-induced water splitting¹  183 years after van Trostwijk and Deiman first split water using electricity in 1789.²  Although photoeffects at the electrolyte contact were observed as early as 1835 by Becquerel,³  energy conversion at the interface with electrolytes was preceded by the development of solid state photovoltaic solar cells.^4,5  In 1975, Gerischer published the concept of formation of rectifying junctions between semiconductors and redox electrolytes,⁶  thereby providing the conceptual and scientific basis for already ongoing, as well as for subsequently pursued, work.⁷  The first efficient and, in part, stable photoelectrochemical solar cells were developed by the Bell Laboratories group of Heller.^8,9  The initial realization of half cells focused on the photovoltaic mode of energy conversion, but was followed rather soon by the first efficient light-induced hydrogen evolution at an InP photocathode.¹⁰ 

As stability was recognized early as a serious issue for these systems, which operate at a reactive solution junction, a framework for assessing the underlying thermodynamic stability was introduced by Gerischer and Wrighton.^11,12  It was noted that semiconductors that exhibit both cathodic and anodic thermodynamic stability did not exist. Accordingly, the issue of materials development and optimization, as well as the search for corrosion protection schemes, dominated the field from early on. However, the issue of stability seriously compromised technological developments and the hitherto only example of a technically realized photoelectrochemical solar cell is the dye sensitized cell introduced by O'Reagan and Graetzel.¹³  Despite its limitations and the considerable struggle for increased robustness while maintaining sufficiently high efficiency,¹⁴  this success was instrumental for the next phase of development in the field: the attempt to arrive at an integrated water splitting system, sometimes referred to as the artificial leaf.¹⁵  Worldwide activities in this direction began more than a decade ago and culminated, in part, in the foundation of the Joint Center for Artificial Photosynthesis (JCAP), a United States Department of Energy (US DOE) Energy Innovation Hub, located in California.¹⁶ 

The Energy Innovation Hubs (or, Hubs for short) were the brainchild of former DOE Secretary Steven Chu and were originally modelled after the Bell Laboratory R&D approach, where work on fundamental and use-inspired research, devices, and applications existed alongside efforts dedicated to prototype development with deployment to industry, integrated in single facilities.¹⁷  Consequently, the Hubs have been conceptualized to enable developments that reach a similar breadth in pursued projects and, as such, are highly multidisciplinary in an unprecedented manner within the sphere of publically funded research. Figure 1.1 shows a comparison of the different Hubs (including the Joint Bioenergy Institute (JBEI)), their approximate technological readiness, and the respective funding programs. JCAP, in its first phase of funding, spanned the largest range of activities: from basic to applied research, from fundamental understanding and discovery to the realization and scale-up of functional water splitting prototypes. In contrast to many of the other Hubs, with topics closely linked to existing industries, at JCAP's inception, no trained work force or industry existed in the field of photoelectrochemical water splitting.

In the following sections, we give an overview and background on photoelectrochemistry and light-induced energy conversion at the electrolyte contact, with an emphasis on water photolysis. This will allow the readers to follow most of the more expert-level chapters in this book without having to resort extensively to overview articles and the seminal papers in the respective fields.

Semiconductors are characterized by an absolute energy gap, where thermal excitation of electrons from the valence band to the conduction band results in a conductivity that depends on temperature and the energetic width of the bandgap. Doping with foreign atoms allows the conductivity to be tuned over a potentially broad range if the energy levels of the dopants, E_D,A, are located close enough to the band edges. In this case, thermal excitations of electrons from E_D (donors) to the conduction band of an n-type semiconductor or from the valence band to E_A (acceptors) in a p-type semiconductor increases the majority carrier concentration and thus the conductivity. For an n-type semiconductor, the conductivity is given by σ=e n μ, and increases as the carrier concentration in the conduction band, n, is increased for a given mobility, μ. The semiconductor Fermi level, E_F, is given by the electroneutrality condition and can be expressed by the relation of the donor doping concentration, N_D, and the effective density of states at the conduction band edge, N_CB, which defines the energetic distance of E_F from the conduction band edge, E_CB:

for n-type semiconductors; accordingly, the Fermi level for p-type semiconductors, with acceptor doping concentration N_A, is located above the valence band maximum according to (Figure 1.2):

The Fermi level is an electrochemical potential and is the sum of a concentration and an electrical term, i.e. of the chemical potential μ and the Galvani potential φ:

The Galvani term arises because equilibria between charged phases are considered and the depletion of, for example, electrons on one side of a contact results in its positive charging, whereas the electron-receiving phase will be negatively charged. The energetic position of the Fermi level (or electrochemical potential) in two phases that are contacted defines the flow of charges upon contact formation. The phase with larger electrochemical potential (¹E_F>²E_F or ¹μ*>²μ*) will provide the electrons during contact formation. This charge exchange continues until the redistribution of charges is compensated by the built-up electrical field. Accordingly, both phases are charged. For an asymmetric semiconductor p–n junction in which the n-type doping concentration is higher than the p-type doping concentration, an energy schematic is shown in Figure 1.3.

Whereas for solid state devices, contact and equilibrium formation is rather straightforward and has a long history,^18,19  the establishment of equilibria at the semiconductor–electrolyte junction was less explored. In fact, the first observation of light-induced water splitting with TiO₂¹  can be viewed as an empirical result since a conceptual basis for operation had not yet been developed. The fundamental concept uses the definition of the solution redox potential according to the Marcus–Gerischer theory,^20–22  the consideration of the interface between a semiconductor and a redox solution, and the partition of the contact potential difference between electrolyte and semiconductor. The redox potential or energy has been derived using the picture of fluctuating energy levels for electrons on ions in (aqueous) solution. The influence of a polar solvent such as water on the electronic levels is basically twofold: first, the solvent becomes polarized due to the charged ions, resulting in an altered electronic energy on the ion upon formation of the solvation shell; second, the thermal fluctuation of the dipoles at a given temperature induces a type of ‘breathing’ of the solvation shell on the timescale of nuclear motion, e.g. picoseconds,²³  which results in a fluctuation of the electron energy around its most likely value. The derivation of the concept was classical in its early version^20–22  and advanced later^24,25  and the solvation shell can be viewed as a type of quantum confinement of the ion with periodic fluctuation of its size. Based on a harmonic oscillator approximation, Gerischer developed the occupation probability, w^G(E), for oxidized and reduced ionic species in solution as

Eqn (1.3) describes a Gaussian behavior of the energy levels on the ion. The thermal fluctuation shifts the electronic energy from its equilibrium values E_ox or E_red for the oxidized or reduced species, respectively, to a value E. The reorganization energy, λ, is the energy needed to change the nuclear configuration of the solvent from the donor to the acceptor state or vice versa. Another picture is to envisage an outer sphere charge transfer of an electron from the solid to the oxidized state of the redox couple, for example, Fe$aq3+$, which, as an ultrashort tunneling process, occurs without structural changes in solution (Franck Condon principle²⁶ ). On mostly a ps timescale, the CT process is followed by relaxation of the nuclear coordinates from the acceptor state to the donor state in solution, and the corresponding free energy change E_ox−E_red is 2λ.

For contact formation, the equilibrium potential of the redox couple in solution has to be considered; it is given by the condition D_Ox(E)=D_Red(E), where D denotes the density of electronic states on the ions. The functional dependence of D(E) is defined by w^G(E) and the concentration of the respective species in solution: D_R,O=c_R,O w$R,OG$(E). The situation is graphically depicted in Figure 1.4 where the electron energy relations also include the semiconductor at flatband condition, i.e. before contact formation and without surface states. The main parameter that defines the formation of the junction is the contact potential difference (CPD), i.e. the energetic difference between the electrochemical potential in solution and in the semiconductor, hence CPD=E_F−E_R,O. In the simplest case, one can approximate the potential distribution across the junction by considering the respective capacitance in each phase; in semiconductors, C=ε ε₀/W where the space charge layer width is given by W=(2εε₀V_bi/qN)^1/2 and depends on the dopant concentration (N), the built-in voltage, V_bi, and the static dielectric constant ε. For non-degenerately doped semiconductors, typical space charge layer widths are in the range between 100 nm and 1 μm. The corresponding space charge layer capacitance is of the order of 10 nF. The Helmholtz double layer capacitance for solutions with ionic strength around 0.1–1 M is about 1–3 μF,²⁷  i.e. larger by a factor of ∼100. The relative voltage drop on either side of the junction is V=Q (1/C_HH+1/C_sc) and the larger part of the CPD drops across the semiconductor surface, forming a space charge layer.

Figure 1.5 depicts the situation shown in Figure 1.4 after contact formation. Equilibrium is established by equalizing the electrochemical potentials on both sides of the junction, E_F=E_R,O. In this ideal case (absence of surface states, non-degenerate semiconductor, moderate built-in voltage), most of the CPD drops within the semiconductor, exhibiting a linear-parabolic behavior with distance, x, below the surface. The figure also shows a small potential drop in the HHL, which has been included for clarity. Depending on the doping level of the semiconductor (which in turn changes the capacitance) the branching between semiconductor band bending eV_bb and HHL potential eV_HH changes. Increased doping reduces eV_bb relative to eV_HH, and vice versa. The energetic situation shown represents a rectifying contact.

In its functional behavior, the dark current at the redox–electrolyte junction resembles that of a Schottky diode.¹⁸  However, the factors/parameters that determine the current are considerably different from the thermionic emission model²⁸  of a metal–semiconductor junction. Although one sometimes encounters the expression ‘Tafel equation for semiconductors’ for the corresponding characteristic, this is seriously misleading because the Tafel equation is an approximation of the Butler–Volmer equation²⁹  for larger overpotentials. However, the Butler–Volmer equation has been derived for the metal–electrolyte case, where the total potential drops across the HHL, resulting in an electrochemical Stark effect where the potential alters the energetic position of an activated complex (transition state theory³⁰ ). The charge transfer is adiabatic and the tunneling probability for outer sphere processes is 1 in the Butler–Volmer approach.

In the case of semiconductors, the distance dependence of the tunneling process cannot be neglected since the charge transfer reaction is not based on the potential-induced alteration of the energy of the transition state. The dark forward current for an n-type semiconductor is given by

which gives an exponential increase of the cathodic dark current j$dC$(V_a) with applied voltage. This similarity in behavior has led to the confusion of the concepts of adiabatic and diabatic electron transfer at the electrode–electrolyte phase boundary.³¹  The fundamental differences between the two approaches are contained in the rate constant for the cathodic (forward) reaction, k^C. Whereas it carries the potential dependence of the reaction in the activated complex theory framework that leads to the Butler–Volmer equation for metal–electrolyte systems, it is ideally potential-independent for the semiconductor case. The potential dependence is given by the surface concentration of electrons, n_s. k$0C$ contains a term that includes the tunneling probability for electron transfer summed over all distances.³²  Since the potential drop in the HHL can moderately change with applied potential, the rate constant is also a function of V. In the (typical) case when surface states are present, the according capacitance depends on their density of states and, for a high density, a substantial part of the CPD drops across the HHL, resulting in a mixed situation where n_s=n_s(V_a) and k^C=k^C(V_a).

The reverse current from the electrolyte to the semiconductor (anodic component) is, in this ideal consideration, potential independent and has the same value as the forward current without applied voltage, j₀, although the transfer mechanism is different. Accordingly, the total current at the semiconductor–electrolyte junction follows the functional behavior of the well-known relation for rectifying junctions:³³ 

The parameters j₀ and in eqn (1.5) represent different charge transfer processes in the forward and reverse directions. In the reverse (anodic) process, the reservoir of the electrons on the solvated ions differs from the Boltzmann term for the surface electron concentration of the semiconductor and the current, , is given by

where N_CB denotes the effective density of states in the semiconductor conduction band.

Surface states are ubiquitous at semiconductor interfaces. One distinguishes between intrinsic surface states that arise from the termination of the solid in one direction and extrinsic ones, which result from surface interactions, such as exposure to atmospheres, as well as contact to other solids and to liquids. The capacitance of surface states depends on their density and can substantially exceed that of the space charge layer. In that case, with a surface state DOS in the range above 10¹³ cm⁻² eV⁻¹, the semiconductor behaves in a hybrid manner: it shows partial or complete Fermi level pinning (FLP).³⁴  Partial FLP exemplifies the situation most clearly: the total CPD now drops across both the HHL and the semiconductor space charge region because the potential drops follow the capacitance relationship. Complete FLP is typically observed for a DOS>10¹⁴ cm⁻² eV⁻¹. Figure 1.6 depicts the situation for partial FLP where the CPD is split between a drop in the HHL and in the space charge region. Applying a positive potential will then increase both the HHL potential drop and that of the space charge. In that case, the band edges shift and the band bending increases but the applied potential only partially increases the semiconductor band bending.

In cases where the energetic overlap between the semiconductor band edges and the DOS of the redox couple is small, the explanation of the experimental results has to invoke the participation of surface states in the charge transfer process.^35,36  The overall transfer process consists of (i) transport of carriers in the semiconductor bands to the surface, (ii) inelastic transfer of carriers from the bands to surface states and (iii) the charge transfer to the oxidized redox species (see blue arrows in Figure 1.6). It becomes obvious from the figure that the overlap with the DOS of the oxidized redox species is increased, resulting in higher currents. In this scenario, eqn (1.4) and (1.5) have to be modified in two ways: first, the electron flux to the surface is given by

where the terms N$te$, σ_n and v$thCB$ denote the trap density of empty surface states, the electron capture cross section (ranging from 10⁻¹² cm² for Coulomb attraction to 10⁻¹⁸ cm² for repulsion), and the thermal velocity of electrons in the conduction band (typically 10⁶–10⁷ cm s⁻¹), respectively. Second, the charge transfer process to the redox species does not follow the ideal non-adiabatic behavior. Here, theoretical development is needed that connects adiabatic and diabatic electron transfer processes in relation to the surface state density.

Figure 1.7 shows the influence of an applied negative potential on the energetic relations at the semiconductor–electrolyte contact based on the schematic presented in Figure 1.6. One observes that a forward (negative) voltage results in a reduction of the semiconductor band bending and, also in a reduced potential drop within the HHL. Accordingly, the band edges shift upward. In this situation, the overlap between the redox DOS and the conduction band minimum is reduced and processes via surface states gain more importance due to the Gaussian reduction of the DOS with a linear shift of the semiconductor energy levels.

Up to this point, the fundamental interfacial properties of semiconductors in contact with electrolyte, as well as corresponding dark charge transfer characteristics, have been presented. Before discussing redox reactions at illuminated semiconductor interfaces, we provide a general overview of the various types of charge-separating semiconductor junctions and how they are commonly assembled into integrated solar fuels systems.

Semiconductor light absorbers lie at the heart of integrated solar fuel generators, though a wide range of different internal configurations for generating photovoltage and photocurrent are used in practice. These include both solid–solid photovoltaic junctions and solid–liquid photoelectrochemical junctions. Figure 1.8 gives a general overview of semiconductor-based rectifying junctions. Further below, the scope will be extended to address the taxonomy of solar energy converting solid–liquid junctions which are represented by two examples in Figure 1.8. Schottky solar cells are limited in their efficiency due to light attenuation by the metal, where sheet resistance, metal thickness, and absorption length have to be balanced. Recently, however, ultra thin graphene sheets have been used as metallic front contact in an efficient Schottky cell configuration.³⁷  The typical example of a pn homojunction cell is the classical crystalline Si solar cell³⁸  that has been introduced in 1954.⁵  Heterojunction solar cells, where the semiconductors are made from different materials, are typically found in thin film solar cells, such as the ternary chalcopyrite-based material class that includes the more recently developed kesterites.^39,40  The exploitation of the electron excess energy, which otherwise is lost by thermalization, is pursued by structures with dual or multiple absorbers where the respective energy gaps are chosen to optimize the efficiency. These tandem cells or multi-junction cells generate higher voltages and the maximum attainable photocurrent is given by a judicious balance between energy gap, absorption behavior and thickness of the subcells (absorbers) of the stack. Due to the increase in photovoltage, such structures have become increasingly interesting for application in light-induced water splitting.^41–44  Since multi-junction solar cells, if monolithically integrated, need tunnel junctions between their component cells, the preparation of devices with more than three absorbers is challenging. In particular, abrupt junction doping profiles have to be established, which imposes stringent demands on materials control at highly doped interfacial regions. Another approach uses the spectral splitting method where the incoming solar light is split into a multitude of spectral beams that each illuminate a solar cell, optimized for the given spectral irradiation.⁴⁵  These multi-terminal devices operate as solar concentrators.⁴⁶ 

Photoelectrochemical solar cells are, in principle, based on the formation of a rectifying junction between a semiconductor and a redox electrolyte. Both photovoltaic, i.e. current generating, and photoelectrosynthetic cells, which can generate fuels (e.g. H₂), have been realized^41–44,47  and their details will be discussed below.

The dye sensitization cell can be viewed as a hybrid as its function is based on the asymmetry of the chemical potential for charge carriers between a dye on the surface of a large energy gap semiconductor and the host semiconductor, where a depletion region (band bending) exists. The original work and most of the subsequent research has been done on Ru-dyes on TiO₂.^13,48  The redox reaction replenishes the oxidized dye, whose excited electron has been injected into the substrate. While dye sensitized cells have most commonly been investigated for the production of electrical power, dye sensitized photoelectrochemcial cells, in which catalysts are incorporated into the device, are actively investigated for direct fuels generation.⁴⁹  However, these intriguing systems, as well as many elaborate molecular architectures, lie outside the scope of the current volume.

A classification of photoelectrochemical solar cells can be developed by assessing the location of the rectifying junction with respect to the electrolyte. Figure 1.9 presents an overview of some hitherto considered systems. Since the rectifying junction is the ‘engine’ of a solar cell, its formation and its position within the solar energy converting structure is of interest, in particular because (photo)corrosion processes at the reactive electrolyte interface can seriously limit the device performance. Therefore, the displacement of the active junction away from the electrolyte boundary can protect this junction. Additional protection against decomposition can be achieved by interfacial layers and also by compact and surface covering electrocatalyst films if the catalysts are stable in the respective electrolyte. Naturally, these interfaces and interfacial films affect the interfacial energetics and, in particular, the energy band alignment.⁵⁰ 

Figure 1.9(a) shows the formation of a rectifying junction between a redox solution and an n-type semiconductor. The half cell is protected by a passivation layer and for photoelectrocatalysis applications, electrocatalysts reside at the electrolyte boundary. Without catalysts, a classical photoelectrochemical junction would exist.⁶  However, the presence of the metallic catalyst can alter the rectification properties. Rectification can depend on the size and thickness of the catalyst layer. The influence of smaller catalytic deposits (nano-particle layers) on the junction energetics is a topic of ongoing investigation. In Figure 1.9(b), the photovoltage is generated between an asymmetrically doped n⁺- and a p-type semiconductor (see perpendicular dashed lines that indicate the space charge layer extension) in a photocathode heterojunction structure (compare also Figure 1.8). The contact of the catalyst/n⁺–p structure to the electrolyte has been assumed to be ohmic.

Approaches that generate higher photovoltages are pursued because of the efficiency limitation for single junction photocatalysis cells: for unassisted efficient water splitting with a photocurrent of >10 mA cm⁻², the thermodynamic value of 1.23 V has to be exceeded substantially because of reaction and working overpotentials. Considering radiative recombination in the Shockley–Queisser detailed balance limit,⁵¹  the minimum photovoltage that has ideally to be generated is ∼1.6 V.⁵²  For the oxygen evolution reaction (OER), a 4-electron transfer process, an additional potential of 0.3–0.4 V is needed to sustain the current density. Including a series of additional loss processes, the photovoltage of an efficient system should be ∼2.2 eV, which places the maximum power point close to 2 V for a system with high fill factor. The resulting solar-to-hydrogen (STH) efficiency using a single semiconductor light absorber is then limited to a theoretical efficiency of 15.1% for 1 sun (AM 1.5G spectrum) illumination.⁵²  The theoretical approach includes reflection losses and absorption by the (metallic) highly active electrocatalyst. Systems with more than a single absorber are employed to achieve high photovoltages while maintaining rather large photocurrents. For generality, a corrosion protection interlayer (labeled PL) has been included in Figure 1.9(a), (b), (d) and (e). It has become a standard approach in the search for more robust systems. For oxide covered surfaces (Figure 1.9(c), (e)) the use of a larger energy gap transition metal oxide (TMO) as front absorber layer is assumed to provide some protection.

Adding another absorber layer on top of, for example, a Si or GaAs pn junction, can result in a sufficiently increased photovoltage. Such a structure has been drawn in Figure 1.9(c) where an n-type material, such as TiO₂, WO₃ or BiVO₄ is deposited onto a pn junction. The contact layer provides tunneling and recombination of the light-induced excess electrons with the holes from the underlying pn junction. These devices are presently limited to rather low efficiency values due to the large energy gap of the typically employed absorber materials.⁵³  The search for better suited materials uses combinatorial approaches and first advances have been made.⁵⁴  Whereas in Figure 1.9(b), the rectifying junction is removed from the electrolyte interface, the top absorber in Figure 1.9(c) can form a photoelectrochemical cell (depending on the equilibrium condition of the metallic catalyst) coupled to a buried junction, i.e. the pn-junction in its interior. If the catalyst is energetically ‘coupled’ to the semiconductor, the structure can be considered a hybrid PEC and pn junction cell.

The dual tandem structure (Figure 1.9(d)) gains its power from the combination of two buried pn-junction solar cells with four space charge regions. Only the larger extended space charge layers contribute notably to the total achievable photovoltage because the systems are asymmetrically doped, as also shown in Figure 1.3. The use of p–i–n (or n–i–p) semiconductor structures has become a standard whenever the product of excess carrier lifetime, τ, and mobility, μ is small.⁵⁵  Such a condition results in a minority carrier diffusion length of L=(D τ)^1/2, where D=(kT/q) μ, that is small compared to the photon absorption length of x_α=3α⁻¹ (x_α>L). By creating systems in which the electric field extends throughout the intrinsic part of the semiconductor, transport of photogenerated carries occurs via drift and charge extraction competes favorably with bulk recombination processes. This concept has been originally employed to develop efficient solar cells with amorphous silicon.⁵⁶  The p–i–n design is shown in Figure 1.9(e). Such cell structures have been used to develop efficient water photolysis systems. The photoactive junctions are removed from the electrolyte contact and such devices represent buried junction photocatalysis cells. Figure 1.9(f) shows the equivalent structure of Figure 1.9(c) for a dual tandem junction. Here again, the system is of hybrid nature, consisting of a buried and a possible semiconductor–redox electrolyte junction.

A variety of architectures have been used to assemble semiconductor light harvesting elements into integrated solar fuels generators. A comprehensive treatment is given in the chapter by Xiang et al. Here, a major consideration is the geometric placement of not just the semiconductor but also the ion-conducting membrane. As described in the chapter by Miller and Houle, such membranes are essential elements that separate generated products, while allowing transport of ions between the catholyte and anolyte. Product separation ensures reduced back reaction rates (i.e. oxygen reduction and hydrogen oxidation), which are loss processes in solar water splitting devices, and ensures that pure product streams with no explosive mixtures are created. In Figure 1.10, two examples of geometries for monolithic integration into a solar fuels device (i.e., an “artificial leaf”) are depicted. The structures have been modeled to obtain the dimensions necessary to minimize losses due to ion transport, membrane conductivity, and motion of light-induced carriers.⁵⁷  For photocurrents of 10 mA cm⁻², corresponding to 12.3% STH efficiency (see Section 1.4 and eqn (1.16) below), the dimensions of the louvered design are: 1.5 cm absorber length and a membrane (Nafion) height of 4 mm.

Although most approaches are based upon planar structures for reasons of simplicity and processing, three-dimensional structures can offer considerable advantages by providing a larger interfacial area for catalysis, allowing decoupling of light absorption and charge transfer length scales, and enabling advanced photon management strategies. In Figure 1.11, a microwire design is shown where radial carrier collection occurs. Light absorption, parallel to the rod axis, is orthogonal to carrier separation. An asymmetric pn junction of Si is used that generates ∼0.6 V photovoltage. To overcome the limit of 1.23 V for water splitting, the TMO is deposited onto its surface and needs to supply a voltage of at least 1 V in the ideal case discussed above. For TiO₂, the observed photovoltage exceeds 1.6 V. The structure thus shows unassisted water splitting albeit with reduced efficiency.⁵⁸  It should be noted that this design uses majority carrier electrons from n-Si to reduce water and light-induced minority carriers from the TMO for oxidation. The indium tin oxide interlayer (ITO) functions as a tunnel junction where the majority electrons from the TMO recombine with the minority holes from n-Si. An energy band schematic is shown in Figure 1.11.

We now turn from device architectures to the internal processes that govern the function of light harvesting elements of integrated solar fuels generators, beginning with light absorption and extending to redox reactions at solid–liquid interfaces.

Semiconductors are generally classified as either indirect or direct according to the nature of optical transitions across their fundamental energy gaps. The terminology for direct and indirect transitions results from consideration of the alignment of the conduction band minimum and valence band maximum in reciprocal space, i.e. in electron k-space. Direct transitions are typically shown as vertical transitions in the reduced zone scheme and are associated with high oscillator strength, leading to large absorption coefficients. It can be shown that, for nearly free electrons, the absorption coefficient near the fundamental absorption edge is given by⁵⁹ 

Thus, a plot of [α(ω)ħω]²versus the photon excitation energy, ħω, gives a linear relationship and allows extrapolation of the energy gap of the respective semiconductor.

For indirect transitions, the conduction band minimum and valence band maximum lie at different positions in k-space. Therefore, energy and momentum conservation dictates that optical transitions across the fundamental energy gap must include additional momentum sources, e.g. phonons, that, depending on their wave vector, k_ph, and their nature (optical, acoustic) vary in energy. Accordingly, both the phonon energy and momentum have to be considered in these transitions and one obtains

The photon energy dependence of the absorption coefficient can be determined for free-electron like semiconductors in the effective mass approximation.⁶⁰  The energy bands are represented by parabolae, where the crystal potential enters via the effective mass. The curvature of the parabola is given by the effective mass, leading to expressions such as heavy and light holes (in GaAs, for example). The energies in k-space assume a spheroidal shape since E=ħ²k²/2m* (m* effective mass). Integration over initial and final states and including the electron-phonon interaction yields, for indirect transitions:⁵⁹ 

Note, that the pre-factor A in eqn (1.8), which is on the order of 10⁴, is approximately 5×10² times larger than B* (for example, when comparing the absorption coefficients of the indirect semiconductor Ge with that of the direct band gap material GaAs).

In some materials, optical transitions are forbidden for k=0 due to selection rules,⁶¹  such as for s→d (Δl=2) excitations, which, however, become allowed for k≠0 for hybridized bands that can be described by s, p and/or d band contributions. Such transitions are termed forbidden direct and the photon energy dependence of the absorption coefficient in such cases is given by

More generally, the wavelength or photon energy dependence of the absorption coefficient is evaluated using a Tauc plot⁶²  according to the following equation:

where m=½, 2, 3/2 and 3, depending on whether the excitation leads to a direct, indirect, forbidden direct, or forbidden indirect transition. The constant C* contains the refractive index, the dc conductivity extrapolated to T=0 K, the vacuum velocity of light, and the extent of the band tailing, a deviation from the idealized picture of a perfect semiconductor crystal, which plays a prominent role in disordered materials such as amorphous silicon.

With the advent of amorphous semiconductors for solar applications, the concepts developed for crystalline solids with 3D periodic atomic arrangement do not always apply and a modified formalism has been developed to describe absorption behavior.⁶³  It accounts for low energy transitions that involve defect states, given by an exponential behavior with photon energy that extends over several orders of magnitude of the absorption coefficient, along with a higher energy component with α∼(hν−E_g)². The determined optical gap and the mobility edge, where carrier transport is notable, differ in amorphous semiconductors. One observes that the absorption coefficient of amorphous hydrogenated silicon (a-Si : H) is significantly higher than the crystalline (c-Si) form, allowing the fabrication of thin film and tandem solar cells.⁶⁴ 

We consider, for example, Figure 1.5 under illumination. The energetic situation is depicted in Figure 1.12 where the redox energy is indicated without the DOS of the redox couple constituents. It is assumed that the CPD drops exclusively across the semiconductor space charge layer. Hence, the band bending eV_bb equals the CPD (Figure 1.5). Following photonic excitation (process 1), the light-induced excess carriers either rapidly thermalize (process 2) or, if generated very close to the surface, are transferred as hot carriers. The electrons (process 3) and holes (process 6) drift in the electric field of the space charge region. Outside W, the electrons and holes diffuse in the neutral regions of the absorber (process 4). The excess holes, which are minority carriers for an n-type semiconductor, drift to the surface (process 6) where they are transferred to the reduced species of the redox couple in an outer sphere tunneling charge transfer (process 7). The arrow indicating the hole transfer to E_R,O (labeled 5) is an often-found but somewhat misleading graphic representation of the light-induced excess carrier hole transfer. The electron transfer occurs from the reduced part of the redox couple to the surface. Here, we depict a situation where holes at the valence band edge become neutralized by electron transfer (iso-energetic tunneling from E_R to the semiconductor). In the simplest approximation, the light-induced current density can be written as the product of the number of absorbed photons (hν>E_g) with A=1−R (reflectivity):

In this simple approximation, the photocurrent–voltage characteristic assumes the shape of the dark j–V curve.

The photocurrent–voltage curve shown in Figure 1.13 follows from the simple superposition principle where the dark current density and the light-induced component have opposite signs j_Ph(V)=j_D(V)−j_L j_ph(V)=j_D(V)−j_L using eqn (1.4) and (1.5):

In this simplest picture of the voltage dependence of the photocurrent for a rectifying junction, one subtracts the light-induced current j_L (eqn (1.12)) from the dark current–voltage curve j_D(V) as shown in Figure 1.13. The main solar cell parameters are included in the figure; the output power P is defined by the largest rectangle in the fourth quadrant of the j–V diagram. It is given by the current and voltage at the maximum power point, which is defined by d(  j_PhV)/dV=dP/dV=0. The open circuit voltage, V_oc, is obtained for j_Ph=0 or j_D=−j_L. The latter defines the short circuit current at V=0. The solar-to-electrical conversion efficiency is given by

where the fill factor ff defines the rectangularity of the photocurrent–voltage characteristic: ff=(  j_MP · V_MP)/(  j_SC · V_SC). The open circuit voltage is obtained from the condition j_Ph=0 in eqn (1.13):

Hence, in this simple approximation, the photovoltage varies logarithmically with the light intensity I(x), where x denotes the direction perpendicular to the surface as shown in Figure 1.12, because j_L is proportional to I(x).

In Section 1.2, we discussed junctions for photoelectrochemical energy conversion (Figure 1.9) and related devices (Figures 1.10 and 1.11). Here, we present the governing equations for combined photovoltaic–electrocatalyst systems and derive their basic behaviour. Water dissociation is characterized by a thermodynamic energy threshold as mentioned above in Section 1.2.2. The according voltage is given by V₀=−ΔG⁰/nF with ΔG⁰=ΔH⁰−TΔS⁰ which yields for the water splitting reaction H₂O→H₂+½O₂ a voltage of V₀=−1.23 V at 25 °C for pH 0. Hence, in contrast to solid state photovoltaics, a minimum voltage is necessary to achieve water dissociation into hydrogen and oxygen gas. This cut-off affects the achievable solar-to-hydrogen conversion efficiency and, besides stability issues, puts an additional constraint on the materials selection. Materials such as hematite are characterized by a comparably low theoretical water photolysis efficiency.

The low overpotentials selected in Figure 1.14 are given by the activation overpotential and the reaction overpotential which is defined by the current passed at the respective heterogeneous catalysts. It has been established in benchmarking studies to use a current density of 10 mA cm⁻² since a photocurrent of 10 mA cm⁻² has been considered a norm for efficient PEC water splitting. Overvoltages of 0.4 V as shown in Figure 1.14 result from highly active electrocatalysts, such as Pt for the hydrogen evolution reaction (HER) and RuO₂, IrO₂, or NiFeO_x for the oxygen evolution reaction (OER). Catalyst activities are typically described in the form of so-called Volcano plots, where either the exchange current density (see below) or the reaction overpotential is plotted versus the metal_hydrogen bond energy (HER) or versus the standard enthalpy change from lower to higher oxide MO_x→MO_x+1, as introduced by Trasatti.⁶⁶ 

Currents at metallic electrocatalysts have been described by the Butler–Volmer equation.^29,67  This equation is based on the transition state theory,³⁰  where the activated complex between the initial and the final state of an electrochemical reaction becomes voltage dependent due to the high electric field in the compact Helmholtz layer at the metal/electrolyte interface. The current–voltage behaviour is characterized by the anodic and cathodic reaction branches. At low overpotentials, the Butler–Volmer behaviour is linear with potential. For increased potential, one branch dominates, described by the Tafel approximation that shows an exponential increase of the current.⁶⁸  This increase is defined by the exchange current density,⁶⁹  a measure of the kinetic activity of a material in a given electrolyte.

Solar-to-fuel efficiency can be defined for the two basic situations, i.e. when solar testing is performed with half-cells under applied bias or for unassisted water splitting. For integrated solar hydrogen generators, in which spontaneous overall water splitting occurs without external electrical power applied, the solar-to-hydrogen (STH) efficiency is calculated by the limiting (thermodynamic) voltage for water splitting V_H2=1.23 V:

where j_op denotes the operating current density of the device, V_H2 is the thermodynamically defined voltage of 1.23 V, I is the incident light power density, and f_FE the faradaic efficiency. If, for instance, side reactions, related to (photo)corrosion are present, the faradaic efficiency drops below 1.

For half cells, operating with applied potential, the achieved conversion efficiency can be described by the energy saved due to illumination, compared to the unassisted case⁷⁰ 

V_a is the voltage applied between the hydrogen evolving (photo)cathode and the oxygen evolving (photo)anode and j_MP denotes the photocurrent measured at the maximum power point.

The photocatalytic current j_op, j_MP in eqn (1.16) and (1.17) can be calculated for both a pn junction with deposited electrocatalysts^71,72  and tandem junctions.⁵²  The according photocurrent–voltage characteristics are written in inverted form with V(j) to allow analytic representation. The expression for the total voltage of the system V(j) (eqn (1.18)) combines the catalytic dark current, described by the Tafel approximation of the Butler–Volmer equation for cathodic currents with the light-induced part of the photocurrent, j_L, of a diode

Here, the dark current j_0,PV corresponds to the reverse saturation current of a Schottky diode or a pn junction, n_d is the junction ideality factor that extends the description of the photocurrent to behavior beyond purely thermionic emission; α_C, n_e and j_0,cat denote the cathodic charge transfer coefficient, the number of transferred electrons and the exchange current density of the metal–electrolyte junction. R_s is the total series resistance that is used as a floating parameter to simulate experimental systems.

An energy band schematic of a combined PV-electrocatalyst structure is shown in Figure 1.15. Here, quasi-Fermi levels (QFL) are used to show the operation condition at the maximum power point where, according to Figure 1.13, the voltage V_MP can be large and close to V_oc for systems with large fill factors. QFLs describe the stationary energy content of the system due to the light-induced excess carrier concentration with n*(x,hν)=n₀+Δn(x,hν). The latter term denotes the excess carrier concentration that depends on a spatial coordinate because of the absorption profile and the subsequent carrier diffusion. QFLs ((x)) can be schematically derived from the exponential Boltzmann distribution of the carrier concentration (eqn (1.1) and (1.1a)) by replacing N_D and N_A by n*(x,hν) and p*(x,hν), respectively:

Eqn (1.19) yields

The difference between QFLs for electrons and holes at the surface is the maximum attainable photovoltage, hence

Figure 1.16 shows a half cell where the photocurrent–voltage characteristics of a photovoltaic pn junction and that of the pn junction modified with an electrocatalyst are compared. The exponential onset of the photocurrent near V_oc (blue curve) is due to the (exponential) Tafel behavior of the electrocatalyst and indicates an electrocatalytically limited system. This limitation depends on the interplay of electrocatalytic exchange current density and Tafel slope, as well as on the photodiode fill factor and the total device current. One notes a shift of the MPP to lower potentials and slightly lower currents for the catalyst loaded device. This shift is caused by the subtraction of the catalytic overvoltage from the quasi-Fermi Level splitting in the PV diode. Hence, the operating voltage is reduced and, for systems with low fill factor, the corresponding photocurrent is also lowered. In the example presented here, the fill factor is rather large, which results in only a small lowering of j_ph. Upon inclusion of a series resistance, an efficient p–InP half cell with a thin film epitaxial (111) : (2×4)-oriented absorber could be modelled.⁷¹ 

High efficiency unassisted water splitting has been reported for several device structures. Photoanode⁷³  as well as photocathode^42–44  designs have been realized. The photoactive core of these systems is a photovoltaic ‘buried’ tandem junction. Here, we provide a brief introduction to one such system, as well as a description of its functional characteristics and limiting efficiencies. Details and device related considerations can be found in the chapters by May et al. and by Xiang et al.

We consider tandem structures as shown in Figure 1.9(d), (e) and visualized in Figure 1.10. Figure 1.17 shows a design where the dual tandem consists of np junctions, formed between the higher doped n⁺ regions and the p-type absorber. Here, a fully immersed artificial leaf is displayed, although without passivation layers and membrane. The ‘engine’ of the cell is the PV tandem, where carrier separation occurs. Energetic alignment with the electrocatalysts depends on their size, thickness, and distribution. For small deposit amounts (ultrathin layers or island formation), the energetics are dominated by the semiconductor.⁷⁴ 

The maximum theoretical efficiencies achievable at the electrolyte contact with such systems has been calculated recently.^52,75  In Figure 1.18 theoretical efficiencies under realistic conditions with respect to the system components are displayed for a dual PV tandem structure coupled to electrocatalysts. Efficiencies have been calculated using the STH relationship of eqn (1.16). The maximum STH efficiency is reached for a tandem structure with E$g(1)$ (bottom subcell)=0.95 eV and E$g(2)$ (top cell)=1.60 eV.

Analytically, the current–voltage characteristic of integrated catalyst–tandem structures can be developed based on eqn (1.18) by expanding to a variable number of photodiodes and including two catalysts, for the anodic and cathodic reactions. The photoelectrochemical device output voltage, V_PEC, can then be written as

with the requirement that V_PEC>V$0rxn$ in order for the reaction to proceed; V$0rxn$ denotes the thermodynamic value of the reaction and V_S the IR drop in the solution. Please note that for these ideal considerations, recombination terms have not been included. The individual PV tandem component voltage includes a factor that describes the optical transmission of the electrocatalyst because, in the integrated design, one catalyst layer will be on the illuminated side. The factor describes the light attenuation due to (often metallic) absorption by the catalyst. The first term of eqn (1.18) becomes

For the overvoltages, we use the expression from the Butler–Volmer equation instead of the Tafel approximation and include a surface area factor, f_sa, that modifies the catalytic exchange current density (c, a denote cathodic and anodic branches)

With eqn (1.22) one obtains the analytic expression for the output voltage of the coupled tandem-electrocatalyst device using α=0.5

Figure 1.19 shows the calculated behavior of a dual tandem (i=2) for the ideal case (f_T=1, f_sa =1 and external radiative efficiency (ERE) 1 (see ref. 52)) and in the more realisitc scenario f_T=0.9 and ERE=10⁻³ have been assumed. Further parameters regarding energy gaps and exchange current densities of the catalysts are given in the figure caption.

Reducing the transmission by 10% lowers the short circuit current by this amount and, accordingly a logarithmic reduction of the photovoltage in addition to the influence of the external radiative efficiency is noted. For complete transmission and optimized surface area, the tandem should reach its maximum performance. In real systems, however, the parameters are interlinked: for 100% transmission, the catalyst coverage must be minimized, which results in a low value for f_sa (eqn (1.24)). For increased f_sa, the transmission typically decreases. Judicious choice of catalyst nano- and microtopography on the surfaces, however, can result in higher transmission than in planar structures.⁷² 

The present costs of the tandem cores demand alternatives. For application of III–V semiconductors, epitaxial lift-off and spalling techniques can alleviate the situation.^76,77  The also costly material use of scarce noble metal catalysts can be reduced by advancing the design of earth abundant core–noble metal shell strutures, which has already found considerable attention in fuel cell research and development.⁷⁸ 

To have potential for making an impact on renewable energy conversion technologies, integrated solar water splitting devices must be simultaneously efficient, stable, and capable of being produced at scale. While impressive advances have been made with tandem photovolatic elements directly coupled to catalysts (see above), the III–V semiconductor material stacks used for these demonstrations remain expensive. Furthermore, corrosion protection strategies based on conformal coating of chemically sensitive semiconductors have allowed remarkable progress in recent years, but such interfaces are delicate and, for photoanode operations, have been limited to very small electrodes because of an increased probability for pinhole formation. For these reasons, the most robust protected photoelectrodes are limited to those, like silicon, that self-passivate.⁷⁹  Considerable current research is focused on reducing the cost of III–V tandems, as well as on improving the reliabiltiy of corrosion protection schemes. However, the discovery and development of thin film photoelectrodes that can be inexpensively produced and are intrinsically stable under reaction conditions remains a grand challenge in the field of artificial photosynthesis.

Historically, transition metal oxides have been considered as a promising class of materials for application as photoanodes. Indeed, the seminal experiment by Fujishima and Honda¹  was based on one such material, n-type TiO₂. While a variety of wide bandgap semicondctors, like TiO₂, exhibit the requisite stability and even desirable charge transport properties, their efficiencies are severly limited due to their transparency to photons that make up the majority of the solar spectrum (see Figure 1.14). On the other hand, numerous narrower bandgap transition metal oxides have been identified but these materials tend to suffer from optical absorption lengths that are significantly longer than their charge extraction lengths; the result is significant photocarrier recombination and poor overall efficiency. Nevertheless, considerable progress is being made on improving function of established materials, identifying new ones, and integrating such components into overall water splitting devices.

Among transition metal oxides, two materials—hematite (Fe₂O₃) and bismuth vanadate (BiVO₄)—have attracted considerable interest over the years. For the case of Fe₂O₃, the combination of a well-suited energy gap of 2.1 eV (Figure 1.14), high chemical stability, and very low prospective production costs are particularly alluring.⁸⁰  While it has long been known that the material possesses extremely short minority carrier diffusion lengths, on the order of 10 nm, significant progress has been made on creating nano- and meso-structured films with characteristic physical lengths that are well matched to charge transport lengths.⁸¹  The result has been a pronounced improvement in the attainable photocurrent.⁸⁰  The intrinsic stability of hematite, as well as methods for its controlled synthesis, has enabled mechanistic operando studies that reveal how competitions between photocarrier recombination and chemical reaction define efficiency, the chemical nature of accumulated holes on its surface affect water oxidation, how its electronic strucuture impacts the generation of mobile charge carriers at different photoexcitation energies, and integration of catalyst on the surface serves to passivate surface sites or improve catalysis.^82–86  These mechanistic insights provide a stronger framework for understanding function and limtiations of new materials, an endeavor that will be further aided by the unprecedented availability of such operando characterization methods.

In many respects, BiVO₄ is complimentary to Fe₂O₃ as a material for studying fundamental processes in transition metal oxide photoanodes and for developing generalizable strategies for improving function.⁸⁷  With an indirect bandgap of 2.5 eV,⁸⁸  it is naturally incompatible with high efficiency integrated solar fuels generators. However, it presently stands as the best performing transition metal oxide photoanode with achieved water splitting efficiencies near 5%, as shown in Figure 1.20.^89,90  Therefore, it deserves special attention for mechanistic understanding to guide discovery and aid in the evaluation of new semiconductors with smaller bandgaps and, thus, prospects for higher efficiency. In terms of electronic structure, BiVO₄ does not contain partially occupied d-orbitals, meaning that its bandgap does not arise specifically from electron correlation.⁹¹  This feature may prove important for understanding the relatively rapid progress towards high quantum efficiencies compared to Mott- and charge-transfer insulators⁹²  that describe a substantial fraction of recently identified, yet poorly performing, oxide semiconductors. On the other hand, it has been determined that both electrons and holes in the material self-trap to form small polarons that transport via thermally activated hopping with low mobilties.^93,94  The fact that charges can still be efficiently extracted points to the need for improved characterization of barriers to recombination associated with local structural distortions, as well as for understanding of interactions between polarons and both native and impurity defect states.⁸⁷  This example highlights that although polaronic conduction is not a desirable feature, it may not intrinsically exclude materials from use as high performance photoelectrodes.

As described in the Chapter by Eichhorn et al., stabiltiy of metal oxide semiconductors under reaction conditions cannot be assumed.⁹⁵  In addition to the Pourbaix stability, which describes the thermodynamiclly stable phases and ions as a function of electrochemical potential and pH, photocorrosion and kinetic processes can have a dramatic impact on the robust operation of light absorbers. For the case of BiVO₄, it has been found that in addition to vanadium leaching from the solid into solution, trapping of both electrons and holes at the surface can destabilize the lattice and promote photocorrosion.⁹⁵  While consideration of the Pourbaix diagram would suggest self-passivation by electochemically stable bismuth oxides, (photo)corrosion of BiVO₄ may leave a highly disorderd and atomically sparse layer that is kinetically hindered from transforming to a passivating stable surface layer.⁹⁵  Such an observation explains discrepencies in the literature regarding stability of BiVO₄, since different synthetic approaches may leave different surface compositions, including those with pre-formed stable passivation layers, which either favor or disfavor stabilization of the natively unstable BiVO₄.

Despite significant progress on improving photocurrent in visible light absorbing transition metal oxide semconductors, no demonstrations of integrated overall water splitting systems incorporating these materials with efficiencies exceeding 10% have been reported. In large part, this is because progress towards improved photovoltage in both Fe₂O₃ and BiVO₄ photoanodes has been slow. For the case of Fe₂O₃, the band edge energetics are not favorable for achieving low onset potentials for the oxygen evolution reaction. For the case of BiVO₄, future work should address the relative impacts of Fermi level pinning at surface defect states and energetic relaxation associated with formation of both electron and hole polarons, which would serve to reduce the effective bandgap of the material from the perspective of photovoltage.

The search for new materials that can replace Fe₂O₃ and BiVO₄ as workhorse photoanodes continues in parallel with developments in III–V based high efficiency systems. On the discovery front, theory has begun to make a significant impact in directing experiment, particularly with respect to high throughput surveys.^54,96  However, the discovery challenge remains great due to the strict combination of material properties that are simultansously desired. Identification of just one new material that possesses a bandgap in the range of 1.7–2.0 eV, favorable band edge positions for driving the desired reactions while generating maximum photovoltages, intrinsic (photo)chemical stability, defect tolerance, and long photocarrier diffusion lengths would represent a dramatic andvance on the path towards practical integrated solar fuels generators.

Decades of research into electrochemical, photovoltaic, and photoelectrochemical energy conversion provide the basis for modern sprints towards integrated, robust, and high efficiency solar fuels devices. This chapter presented a brief survey of some of the central concepts that underlie the function of these systems and their constituent components. In the remainder of this book, modern advances in the international solar fuels community, with an emphasis on how the Joint Center for Artificial Photosynthesis contributed to progress, are described.