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A widely used term, “photocatalysis”, generally addresses photocatalytic (energetically downhill) and photosynthetic (energetically uphill) reactions and refers to the use of photonic energy as a driving force for chemical transformations, i.e., electron reorganization to form/break chemical bonds. Although there are many such important reactions, this contribution focuses on the fundamental aspects of photocatalytic water splitting into hydrogen and oxygen by using light from the solar spectrum, which is one of the most investigated photosynthetic reactions. Photocatalytic water splitting using solar energy is considered to be artificial photosynthesis that produces a solar fuel because the reaction mimics nature’s photosynthesis not only in its redox reaction type but also in its thermodynamics (water splitting: 1.23 eV vs glucose formation: 1.24 eV). To achieve efficient photocatalytic water splitting, all of the parameters, though involved at different time scales and spatial resolutions, should be optimized because the overall efficiency is obtained as the multiplication of all these fundamental efficiencies. The purpose of this Review is to provide the guidelines of a concept, “photocatalysis by design”, which is the opposite of “black box screening”; this concept refers to making quantitative descriptions of the associated physical and chemical properties to determine which events/parameters have the most impact on improving the overall photocatalytic performance, in contrast to arbitrarily ranking different photocatalyst materials. First, the properties that can be quantitatively measured or calculated are identified. Second, the quantities of these identified properties are determined by performing adequate measurements and/or calculations. Third, the obtained values of these properties are integrated into equations so that the kinetic/energetic bottlenecks of specific properties/processes can be determined, and the properties can then be altered to further improve the process. Accumulation of knowledge ranging in fields from solid-state physics to electrochemistry and the use of a multidisciplinary approach to conduct measurements and modeling in a quantitative manner are required to fully understand and improve the efficiency of photocatalysis.
General Strategy for Improved Photosynthetic Reactions
A photocatalyst is a substance that absorbs photons and generates excited states, which then cause photophysical and photochemical processes as they return to their original ground states. (1) Photocatalyst materials can consist of additional catalytic components, often called cocatalysts, that catalyze electrochemical redox reactions. (2) Such an electrocatalyst is often essential to the photocatalyst (photon absorber) because its surface is not typically designed to catalyze redox reactions unless the reaction is an outer-sphere electrochemical reversible reaction. The time scale of electrocatalysis during the photocatalytic process is sufficiently longer than the time scales of photophysical or photochemical processes; (3) in many photocatalytic reactions, the photocatalysis can thus be considered to be electrocatalysis where electrocatalyst components induce the redox reactions driven by the potential shifts caused by the photocatalyst (photon absorber). Photocatalysis eventually builds an electromotive force (emf), a difference in chemical potentials or Fermi levels, to enable electrocatalysis. (1) This emf transient charging at electrocatalytic sites is indeed required for water-splitting photocatalysts because both the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) require multiple electron transfer reactions at the active species and thus a relatively slow process compared to prior photophysical processes.
One may consider the difference between a photocatalyst (photon absorber and electrocatalyst) and a device that consists of a photovoltaic and an electrolyzer (PV + E). Making hydrogen by PV + E technology is still more expensive than using natural gas reforming. (4, 5) A large number of elementary events are common; however, the photocatalyst may induce charge separation utilizing an electrocatalyst–semiconductor interface and a solid–liquid junction directly, (1) potentially skipping the p–n junctions in solid–solid structures. This is the major driving force of cost reduction in photocatalytic system compared to PV + E system. Photocatalytic materials also do not require the wiring of a PV (but instead require the collection of produced gases). On the other hand, in a PV + E configuration, separating the functions of photovoltaic current generation (PV) and electrocatalysis (E) is easily optimizable for these two separate components, and PV + E systems are therefore expected to produce higher efficiencies than photocatalyst systems. (6) To combine these systems, PV material can be immersed into aqueous solution, (7-9) which allows the material to avoid a detrimental temperature increase (because of the water) and the resultant efficiency loss. There is a significant chance, however, that the PV material corrodes because the water itself is corrosive and even worse at extreme pH values; additionally, fewer photons are expected to be absorbed when the PV is in water because, besides photon loss due to reflection by the water, the absorption coefficient of water is nonzero especially beyond 600 nm. (10) Lewis recently reviewed the future possibilities for solar energy conversion technology in industry and academia. (5) Practical use of either of these systems requires future efforts: PV + E prices must be decreased by engineering or some technical advancement that produces a reasonable device and system, and the photocatalytic efficiency of photocatalysts must be improved without forgetting a final, scaled-up reactor design. Recently, immobilization of photocatalyst powder in sheets for use in overall water splitting was demonstrated, (11) but the overall efficiency of this catalyst remains low, predominantly because of inefficient charge separation by the photocatalyst materials. Collective efforts are needed to address these complex issues in clearly desired solar energy conversion technology.
As recently emphasized by Osterloh, (12) photosynthetic reactions (ΔG > 0) require detailed photon management and charge separation, in contrast to photocatalytic reactions (ΔG < 0), whose performance is most sensitive to surface area. Basing the selection of materials for photon absorption (photocatalyst) solely on their bandgap and electrocatalyst, often called the cocatalyst, is not enough to result in high photocatalytic efficiency. We will review that defect density, carrier concentrations, and interfaces (metal, semiconductor, electrolyte, etc.) strongly influence efficiency, even when the same materials are used. This fact is widely known, yet there is no consensus as to how to evaluate these properties and consequences. In addition to the use of disparate reporting protocols, (13-23) this discrepancy is the reason why every research article reports different efficiencies even when the same composition of photocatalyst is used. For instance, there are multiple methods to prepare photocatalyst materials, (24) but they result in different photocatalytic performances because unquantifiable or difficult-to-measure properties vary. (25) Photocatalysis research is becoming largely arbitrary because of an infinite number of variables, for example, different precursors, synthesis protocols, annealing, pre/post-treatment, and addition of small quantities of dopants/impurities/additives (often unconsciously); it is very difficult to reproducibly make photocatalysts. In a specific operation, one may want to concretely determine how overall efficiency is improved by a particular “quantity”. (25) There are excellent review articles concerning photocatalyst and photoelectrochemical reactions: many focus on various materials and techniques of characterization. (26-45) This Review is specifically targeted to developing a guideline as to what fundamental key parameters improve photocatalytic efficiencies, regardless of the photocatalyst material. It is time to integrate advanced modeling into the design of photocatalyst materials. Without these efforts, photocatalytic research remains abstract, unestablished, and unquantifiable.
Consolidation of Chemical Potentials and Fermi Levels
The basic concept of photocatalysis relies on the same protocol as all types of catalysis research: a description of chemical potentials of electrons, or Fermi levels. A strong connection between solid-state chemistry and physical chemistry, or photophysics and electrocatalysis, is the accurate description of chemical potentials of electrons in various substances (metals, semiconductors, redox ions in the solution, etc.) at thermodynamic equilibrium or under steady-state illumination. The concepts of the chemical potentials of electrons in metals to semiconductor is well described in an excellent book by Sato. (46) Each elementary step/event in “catalysis” including photocatalysis, in terms of thermodynamics and kinetics, becomes quantitatively describable if we have tools to appraise the chemical potentials of electrons, especially reactive ones, in molecules, nanoparticles, and solids (catalyst materials) and in both reactants and products during (photo)catalysis. Work functions of metals, Nernstian redox potentials of molecules/ions, and Fermi levels or flatband potentials of semiconductors are useful statistical measures of energy equilibrium and flow, although overlapping reactive energy states in solids and interfaces makes determining the value of these potentials difficult. Recent advances in solid-state physics and chemistry establishes reasonable theories that can measure (estimate) or calculate such energy levels and their densities of state. This estimate, consisting of a large number of quantifiable parameters, (25) can ideally be used to predict overall photocatalytic efficiency, even without experiments. It is thus possible to determine which parameter is most influential in improving overall efficiency. This strategy is one step forward to “photocatalysis by design”—the design of systems to reach a target by altering specific parameters rather than randomly screening materials.
Successful photocatalysis requires that charged-up electrocatalysts are maintained at the potentials where steady-state redox reactions occur. A scheme can be derived, on a scale of the chemical potential of electrons (and holes), that visualizes the ideal energy transfer (and loss) that occurs during sequential photocatalytic processes. Figure 1 describes an example of the use of a single semiconductor powder as a photocatalyst that is decorated with HER and OER electrocatalysts on the surface, in an attempt to achieve overall water splitting. The process is initiated with photon absorption, as depicted in the middle of Figure 1. Upon light absorption, an excited hole and electron are generated in the valence band and conduction band, respectively, on the femtosecond time scale. (47) After rapid relaxation to the edges of their respective bands in femto- to picoseconds, an exciton (electron–hole pair) is separated into free carriers and the semiconductor-catalyst interface guides the electron and hole to the HER and OER catalysts, respectively, generally in nano- to microseconds. (47) Substantial losses of potentials are expected at the interface (“interfacial loss”) and may originate from entropic contributions of electrons (48-50) and interfacial potential barriers that are generated by inadequate alignment. Successful electron/hole transfer to the electrocatalyst shifts the potentials either negatively or positively at transient time on the millisecond to second time scales, and then maintain steady-state potentials that are allowed to drive steady-state electrochemical redox reactions to produce H2 and O2. (47) The solution properties may influence the overall performance by limiting the mass transfer of the reactant ions. How can we draw this type of scheme for every photocatalyst? What properties are involved that determine such potentials at each event? Can we identify the bottleneck that limits the overall efficiency? In the next section, the selected key parameters as well as photocatalysis events that occur at different time scales are identified.
List of Properties Involved in Photocatalytic Water Splitting
The primary effort of this Review focuses on discussing the fundamental parameters that are involved in photocatalytic water splitting and their quantitative measurement using powdered semiconductor material (the concept can be applied to other photocatalysis as well). Photocatalysis for water splitting indeed involves a complex series of photophysical and electrocatalytic processes. (25) The processes involved in photocatalytic reactions are divided into the following six components:
Mass transfer of reactants and products
Events 3 and 4 can occur simultaneously and coherently, but are separated here for convenience. Figure 2 shows this six-gear concept, which represents the photocatalytic water-splitting process sequentially occurring at different time scales. (25) Photon absorption initiates nonequilibrium photophysical and photochemical processes. The photon absorption generates an exciton, that is, excitation of an electron in the valence band (VB) or the highest occupied molecular orbital (HOMO) to the conduction band (CB) or the lowest unoccupied molecular orbital (LUMO). (47) The probability to occupy such states are predominantly determined by the electronic structure (local displacement of atoms) of the semiconductor. This femtosecond process is followed by relaxation of the electron and the hole to the bottom of the CB and the top of the VB, respectively, on a similar time scale. (47) Next, the exciton (electron–hole pair) is generally separated after overcoming the exciton binding energy determined by the electronic structure; this structure should guide the excited electron and hole (polaron) to move independently, being influenced by their effective masses. The combination of carrier diffusion and transport effectively utilizes the introduced interfaces (i.e., potential differences) and successful charge transfer typically in microseconds to the electrocatalysts decorated on the surface needs to occur. Because the kinetics of electrocatalysis are unfortunately sluggish compared to the prior events, such electrocatalytically active species will be charged either negatively or positively and drive electrocatalytic redox reactions on a time scale typically longer than microseconds. (47) The key is that most of the semiconductor and electrocatalytic properties and measures of efficiency at each stage are listed separately and are quantitatively measurable by using various characterization and kinetics measurements. Once a material is synthesized, these properties and efficiencies are quantified so that the bottleneck of the process is identified, leading to improved overall efficiency. A previous report describes the associated equations and measurement protocols in more detail. (25) This contribution aims to emphasize the most influential key components in determining overall photocatalytic efficiency.
Quantification of Key Properties Relevant to Photocatalytic Water Splitting
When solar energy conversion is the primary concern, analysis of the solar spectrum provides useful information regarding theoretical maximum efficiency. The solar-to-hydrogen (STH) conversion efficiency is defined by the H2-energy generated divided by the entire solar irradiance. Using the NREL standard spectrum of AM 1.5G, (51) integration of UV photons accounts for a maximum of 3.3% STH efficiency. Including light from the UV to the visible (to 600 nm) results in a maximum theoretical STH efficiency of 17.8%, while up to 800 nm results in >35% (using a single semiconductor). Analysis of the solar spectrum reveals that development of a visible-light-responsive photocatalyst material is essential to achieving substantial solar energy conversion. (52) A representative scheme for various visible light responsive materials is shown in Figure 3, which is taken from the review paper by Sivula and van de Krol. (45) The bandgap of the materials is minimum thermodynamic requirement for high-efficiency photocatalysis; however, the shape of conduction and valence bands are unique to each electronic structure, and densities of state typically become very weak at band edges (bands are not rectangular as depicted in Figure 3).
It is obvious that if no photons are absorbed, no photocatalysis occurs. The initial step of photocatalysis is unambiguously the absorption of a photon and exciton generation by the photon absorber. Once the photocatalyst material is chosen for investigation, it is crucial to identify its electronic structure (displacements of the atoms or a crystal structure), which in turn determines the densities of the relevant energy states. Commonly, photon flux of incident light, I0, commonly lead to the following relationships:(1)where A% is absorptance, the ratio of the absorbed to incident electric field, and T, Rs, S, Rd are lights that are transmitted, specularly reflected, forward-scattered, and backscattered, respectively. (53) Most importantly, the absorption coefficient, α(λ), an indicator of how far photons of a particular wavelength can penetrate before it is absorbed by the material, can be measured or calculated as a function of wavelength. (25, 27) It also determines important absorption properties such as the bandgap, band positions (flatband potentials), and the direct/indirect nature of light absorption. The absorption spectra indicate the consequences of bandgap excitation, d–d transitions, phonon absorptions, and excitations associated with defect states. (53) To practically measure absorption coefficients, the single crystal thin-film configuration of semiconductors provides a more precise description because contribution of scattering is minimized and the film thickness is well-defined. (54) From transmittance, T, and reflectance, R, (55) values, we obtain α for the film thickness, d, when Re–αd ≪1: (56)(2)The number of electron–hole pairs that are generated per photon striking the semiconductor as a function of depth, x, and wavelength, λ, is described using the generation rate, G, per geometric area. After considering Rayleigh and Mie scattering by the powder, which depend on the size of the particle, (57) and reflection and transmission by the medium with distinct refractive indices, (58) the Beer–Lambert law approximation leads to (59, 60)(3)where I0 is photon flux of irradiated light per geometric area. From this equation, it is thus obviously essential to obtain photon flux densities by irradiance measurements. Other intrinsic parameters can then also be quantified: for example, the refractive index, n; the extinction coefficient, κ(λ); and the dielectric constant, εr, which can be divided into contributions from the electronic density, ε∞, and from the motion of ions in the material, εvib; εr = ε∞+ εvib. (61) Methods to obtain these properties can be found in the literature. (25)
Once the absorption coefficient is obtained, we obtain the absorption depth, which is a useful measure how far light can penetrate into a material before being absorbed; the absorption depth can be determined by simply taking the inverse of the absorption coefficient α. (25) The absorption depth, together with scattering and reflection, is critical to deciding how thick a photocatalyst film or suspension should be or how many semiconductor particles are required to be able to report a useful photocatalytic efficiency. To be able to compare photocatalytic performances from different laboratories, the maximum photon absorption should be achieved by a photoreactor that is used to obtain an “optimal rate” that is not perturbed by the amount of photocatalyst used. (20) Absorption coefficients of typical direct bandgap semiconductors fall into the range of 1 × 104 – 1 × 106 cm–1, equivalent to absorption depths of 1000–10 nm. A typical indirect bandgap semiconductor, Si, possesses a typically low absorption coefficient of 1 × 103 – 1 × 105 cm–1, corresponding to absorption depths of up to a few micrometers for visible light (400–800 nm). (62) We emphasize that the density of state (DOS) is the primary criterion to select a semiconductor for photocatalysis. Essentially, the Franck–Condon principle (63, 64) suggests that the displacement of atom positions does not change upon photon absorption and that accurate determination of a local crystal structure (Brillouin zone) with an appropriate consideration of spin–orbit coupling predominantly determines these optoelectronic properties. Recent advances in density functional theory (DFT) calculations give quite accurate and reliable estimates of the electronic structures and resultant DOS of semiconductors with a given crystal structure. (61) When new photovoltaic and photocatalytic materials are developed, it is recommended that the accurate crystal structure (e.g., via Rietveld refinement), which dictates the electronic structure and resultant optoelectronic properties, be determined.
As mentioned, single-crystal thin films are preferred in measurements of optoelectronic properties because of minimized contribution of scattering and diffuse reflection. It is also noted that the Kubelka–Munk function, (65) used in diffuse reflectance spectroscopy equipped with an integrating sphere, is a useful tool for measuring the absorption properties of powder samples. However, use of this function often leads to an exaggerated interpretation of the absorption intensity, especially when close to bandgap. One must consider that near band edges, absorption coefficients can be exceptionally low, which is not obvious from the spectra plotted using a Kubelka–Munk function. The absorption spectra and the Kubelka–Munk function also contain quantitative information, where a value of zero is especially meaningful. When impurities are present in the system, nonzero absorption data reflects not only that the spectrum does not purely represent the desired compound or material but also the extent of dopant or metallic character; therefore, do not forget to plot zero in absorption spectra or Kubelka–Munk function. The impurity energy levels beyond the bandgap energy also empirically follow the Ulbach rule, (66) which can be additionally considered to quantify the absorption properties of the semiconductors.
Exciton Binding Energy
After successful photon absorption and the resultant exciton generation, electron–hole pairs (67) are to be separated to generate excited electrons and holes (free carriers), or otherwise to recombine easily. The next criterion for selection of a photocatalyst is the exciton binding energy, which represents the energy required to ionize an exciton from its lowest energy state. (68) For a Mott–Wannier-type exciton, the 1s state energy, E1, of an exciton described by the Bohr theory is the exciton binding energy, Rex, and it can be described as(4)where εr is a relative permittivity or dielectric constant, m* is the reduced effective mass of the electron (n)–hole (p) system (), e is the elemental charge, and h is Planck’s constant. (61) A database containing these parameters for a large number of typical semiconductors is already available. (69) The benchmark energy value is that of thermal energy (25 meV at room temperature), (61) and the efficient separation of excitons requires that the binding energy be lower than this value. For Mott–Wannier excitons, the typical binding energy is less than 10 meV, and the exciton radius is ∼10 nm. For Frenkel excitons, such as carbon nitride, these values can be greater than 1 eV and ∼1 nm. (70) Such a high exciton binding energy necessitates charge separation at the molecular level, similar to the case of bulk heterojunctions of organic semiconductors. The key properties that affect the values of the exciton binding energy are the effective masses and dielectric constant. The effective masses of the electron and hole are determined by the curvature of the electronic structure in the conduction and valence bands, respectively. The electronic dielectric constant is also predominantly determined by the electronic structure of a given material. High dielectric materials, such as perovskite structures, are typically excellent photocatalysts. Currently, DFT calculation can estimate exciton binding energies and effective masses as well as different crystal orientations at high accuracy; typically, high distortion creates an anisotropic electronic field upon exciton generation, and this field assists charge separation. (36)
For successful photocatalysis, the generated free carriers are transferred to redox-active sites on the catalyst surfaces (or to the back contact, in the case of photoelectrochemistry). The next useful parameter is the minority carrier lifetime, τ, which is another intrinsic indicator of whether a semiconductor material can be an effective photocatalyst. Generally, the recombination can occur through the following mechanisms; “surface” recombination, “bulk” Shockley–Read–Hall (defects) (srh), (71, 72) the band-to-band radiative (bbr), and the band-to-band Auger (bba), (73) and more; the lifetime of which are reciprocally correlated:(5)Once the carrier lifetime is obtained, recombination rate can be estimated, depending on the recombination models. Essentially, the generation rate will be canceled out by the recombination rate to leave the effective carrier rates for electrocatalysis. (25) The carrier lifetime also gives the minority carrier diffusion length, L, representing the average distance that the excess minority carrier travels from where it was generated to where it is annihilated.(6)where Dc is the diffusion coefficient of the carriers, which will be described more in details in the following section. The comparison of this value with the particle size of the photocatalyst or the film thickness of the photoelectrode is critical in designing the photon absorber. (74)
An empirical expression between carrier lifetime and dopant concentration was reported by Law et al. for indirect bandgap Si (Figure 4), but it describes very interesting trend as a function of dopant concentration. (75) Two types of srh and bba recombinations are integrated into this model:(7)where τ0 is the low-concentration lifetime, ND is the doping carrier concentration, Nref is the roll-off concentration, and CA is the Auger coefficient. From this analysis, it is obvious that the carrier lifetime increases as the doping level decreases, i.e., the more intrinsic semiconductor generally has longer carrier lifetimes. This parameter is primarily associated with bulk recombination that originates from the srh process and impurity concentrations (and therefore, strictly speaking, the descriptor is not the carrier concentration alone). The GaAs semiconductor shows a similar trend. (76) Relatedly, the surface treatment (etching or shell formation) of single-crystal surfaces substantially improves the minority carrier lifetime, as measured by time-resolved photoluminescence, or the photoconductivity lifetime, as measured by terahertz photoconductivity. Examples of this behavior include that of well-investigated photovoltaic semiconductors such as CdTe, (77, 78) InP, (79) and GaAs. (80)
In the case of powder samples or nanostructured architectures, whose surface contributions are large relative to that of the bulk, the surface states largely influence the minority carrier