1.1.

Basic Working Principle of Photoelectrochemical Cells

Photoelectrochemical water splitting into hydrogen and oxygen is thermodynamically an up-hill process with the free-energy barrier of $G=+237\mathrm{kJ}/\text{mole}$ or $E_0=1.23\mathrm{eV}$ under standard conditions. The photoelectrolysis of water consists of five main steps, as depicted in Fig. 1: (1) absorption of photons with energy greater than the bandgap of the semiconductor, (2) photogeneration of electron–hole pairs, (3) band bending at the semiconductor–electrolyte interface leading to separation of charge carriers, (4) diffusion of charge carriers toward the semiconductor–electrolyte interface, and (5) redox reaction involving charge carriers and solution species (oxidation of water to ${\mathrm{O}}_2$ and reduction of water to ${\mathrm{H}}_2$). Additionally, the protons are transported across the electrolyte through proton permeable membranes and the electrons travel to the external circuit to complete the process. The overall solar splitting of water involves two half reactions taking place at the photoanode and photocathode simultaneously. For a PEC system comprising an $n$-type photoanode and $p$-type photocathode material, the two half reactions in alkaline media ($\mathrm{pH}=14$) can be expressed as follows:

Fig. 1

Schematic representations of (a) the band diagram of PEC in which both the photoanode and the photocathode have the required ideal band positions for spontaneous water splitting. The total photovoltage generated is large enough to split water and to overcome the electrochemical overpotentials ${\eta }_{\mathrm{ox}}$ and ${\eta }_{\text{red}}$ for the oxidation and reduction of water, respectively. Note that the energy scale is $V$ versus NHE at $\mathrm{pH}=14$. The two types of PEC configurations: (b) dual stack and (c) dual side-by-side.

1.2.

Structural Properties of Spinel Ferrites

Spinel ferrites are ternary transition metal oxides which are represented by a general formula ${\mathrm{M}}_x{\mathrm{Fe}}_{3-x}{\mathrm{O}}_4$, where M refers to the divalent metal ions ($\mathrm{M}=\mathrm{Ni}$, Co, Zn, Ca, Mg, Mn, and so on). They are best known as magnetic materials and photocatalysts, with the most common photocatalytic application being the degradation of pollutants.^12,24 The structure of spinel ferrites is derived from the mineral spinel, ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, by replacing the trivalent Al atom with ${\mathrm{Fe}}^{3+}$ and Mg atom by other divalent metal ions.

In the spinel ferrites, the oxide anions are arranged in a cubic close-packed lattice and the cations M and Fe occupy two different crystallographic sites, namely, the tetrahedral (A) and octahedral (B) sites.²⁵ The cubic unit cell consists of 56 atoms, 32 oxygen anions, and 24 cations, 8 of them occupying tetrahedral sites and the other 16 being located at the octahedral sites. Although the charges of M and Fe in the prototypical spinel structure ($x=1$) are $+2$ and $+3$, respectively, other combinations are also possible. The type and the distribution of the divalent metal cations govern the final ferrite structure and dictate the chemistry of ferrites. The main factors governing the preference of the individual ions for the two crystallographic sites are the ionic radii and coordination chemistry of the ions. For example, ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Cd}}^{2+}$ preferentially occupy the tetrahedral sites, whereas ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Cr}}^{3+}$ have strong preference for octahedral sites. When the tetrahedral sites are occupied by divalent metal ion ${\mathrm{M}}^{2+}$ and the octahedral sites by ${\mathrm{Fe}}^{3+}$, the resulting ferrites are called normal spinels (e.g., ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$) [Fig. 2(a)]. If the ${\mathrm{Fe}}^{3+}$ cations fully occupy the tetrahedral sites and octahedral sites are occupied evenly by ${\mathrm{M}}^{2+}$ and ${\mathrm{Fe}}^{3+}$, this leads to an inverse spinel [Fig. 2(b)]; examples of these classes include but are not limited to ${\mathrm{Fe}}_3{\mathrm{O}}_4$, ${\mathrm{NiFe}}_2{\mathrm{O}}_4$, and ${\mathrm{CoFe}}_2{\mathrm{O}}_4$. However, there exists a certain degree of inversion in most ferrites which is determined by the fraction of ${\mathrm{M}}^{2+}$ ions in the octahedral sites.

Fig. 2

Crystal structures of spinel ferrites: (a) normal spinel, (b) inverse spinel, and (c) orthorhombic each demonstrating the three crystallographic sites.

Thus, in general, the spinel ferrites can be represented by ${[{\mathrm{M}}_{1-y}{\mathrm{Fe}}_y]}^{\mathrm{A}}{[{\mathrm{M}}_y{\mathrm{Fe}}_{2-y}]}^{\mathrm{B}}{\mathrm{O}}_4$, where the superscripts A and B identify the tetrahedral and octahedral sites, respectively, and $y$ corresponds to the degree of inversion ($0\le y\le 1$). Mixed spinel structures are reported for Mn ferrites and Mn-Zn ferrites. Some spinel ferrites, such as ${\mathrm{MgFe}}_2{\mathrm{O}}_4$, ${\mathrm{CaFe}}_2{\mathrm{O}}_4$, and ${\mathrm{BaFe}}_2{\mathrm{O}}_4$, are known also to form orthorhombic phases [Fig. 2(c)].^26–28 Other ferrites, such as ${\mathrm{CuFe}}_2{\mathrm{O}}_4$, form crystalline solids with cubic or tetragonal unit cells depending on the synthetic conditions.²⁹

Ferrites are regarded to be chemically and thermally stable in aqueous systems.¹⁵ Considering the Pourbiax diagrams, most ferrites are stable in the alkaline or near neutral media in which most PEC investigations are carried out, however, they suffer from corrosion in acidic media.^30,31 Most of them are semiconductors with bandgap energies allowing the excitation by visible light and possess energetic positions of the conduction and the valence band suitable for either reduction of protons and/or oxidation of water (Fig. 3). The theoretical and experimental bandgap energies $E_{\mathrm{g}}$ are presented in Table 1, and the energetic positions of the valence band $E_{\mathrm{VB}}$ and the conduction band $E_{\mathrm{CB}}$ of some simple ferrites are shown in Fig. 3. The variation of ${\mathrm{M}}^1$, ${\mathrm{M}}^2$, $x$, and $y$ in ${\mathrm{M}}_x^1{\mathrm{M}}_y^2{\mathrm{Fe}}_{3-x-y}{\mathrm{O}}_4$ is known to affect the resistivity (conductivity),^41–44 the optical properties (reflectivity), bandgap energy, and the $p/n$-type behavior^45,46 of the semiconductor. Also, the ability to catalyze thermal reactions is affected by the chemical nature and the magnitude of x present in an ${\mathrm{M}}_x{\mathrm{Fe}}_{3-x}{\mathrm{O}}_4$ compound.^47,48

Fig. 3

Band positions of spinel ferrites in contact with aqueous solution referenced with NHE ($\text{right}\mathrm{pH}=14$ and $\text{left}\mathrm{pH}=0$) relative to the standard potentials for the reduction and oxidation of water. Note that the variations of the band positions for some of the spinel ferrites data were collected from references cited in this article.

Table 1

PEC performances of ferrite-based photoelectrodes.

2.1.

p-Type Spinel Ferrites

As with many other materials investigated for photoelectrochemical reduction of water, spinel ferrites are also studied as photocathodes for HER. In order to reduce protons to ${\mathrm{H}}_2$, the conduction band edge of the photocathode must be more negative than the hydrogen redox potential. Considering the band diagrams in Fig. 3, most of the spinel ferrites meet this criterion, however, only $p$-type ${\mathrm{CaFe}}_2{\mathrm{O}}_4$,^{36–38,55–59} ${\mathrm{CoFe}}_2{\mathrm{O}}_4$,³⁹ and ${\mathrm{NiFe}}_2{\mathrm{O}}_4$⁴⁰ have been studied in PECs. Furthermore, the mechanism of HER is pH dependent; in acidic media, the reaction mainly involves proton reduction while the reduction of water to hydroxide ions is the primary route in alkaline solutions. Hence, PEC studies involving spinel ferrites are preferably conducted in neutral or basic solutions, as most spinel ferrites are not stable in acidic media.

One of the most investigated $p$-type ferrite is ${\mathrm{CaFe}}_2{\mathrm{O}}_4$. Matsumoto et al.⁵⁵ reported a $p$-type ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ for the photoelectrochemical reduction of water. The ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ electrodes are prepared as pressed pellets and sintered at 1200°C followed by oxidation under ${\mathrm{O}}_2$ at 1000°C. The ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ photocathode exhibits $p$-type behavior from Mott–Schottky analysis. However, the cathodic photocurrent for HER is negligibly low and when the electrode is coupled with an $n$-type ${\mathrm{Zn}}_{1.2}{\mathrm{Fe}}_{1.8}{\mathrm{O}}_4$, photoelectrolysis of water without external bias results in an STH conversion efficiency of $<0.01\%$. Matsumoto⁴⁹ summarized his results on ferrites and other oxide semiconductors, compiled data on the bandgap, and formulated an empirical relation between the bandgap, the conduction band edge, and the valence band edge.

Cao et al.³⁶ have investigated the visible light-induced water splitting reaction employing a $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ photocathode. The photocathodes have been fabricated by depositing ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ thin films on fluorine-doped tin oxide (FTO) coated glass employing a pulsed laser deposition method. A hydrogen evolution rate of $\sim 4.8\mu \mathrm{mol}{\mathrm{m}}^{-2}{\mathrm{h}}^{-1}$ was observed under visible light irradiation (300 W Xe) using a Pt metal electrode without applying any additional bias. In a three-electrode configuration, a cathodic photocurrent was observed at values more negative than $+0.64\mathrm{V}$. A photocurrent density of $-0.117\mathrm{mA}{\mathrm{cm}}^{-2}$ at $-0.06\mathrm{V}$ was reported as being significantly larger than the values reported by Matsumoto et al.^55,56 for metal-loaded ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ photoelectrodes, probably due to shorter electron transfer distances in the thinner films and higher electric conductivity.³⁶

Furthermore, Ye et al. have compared the photoelectrochemical properties of $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$, $n\text{-}{\mathrm{ZnFe}}_2{\mathrm{O}}_4$, $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4/n\text{-}{\mathrm{ZnFe}}_2{\mathrm{O}}_4$, and multiple $p\text{-}n$ junction ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ photoelectrodes. The electrodes have been prepared by a pulsed laser deposition method using ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ and ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ pellets as the targets and FTO as the substrate. The authors observed a photocathodic current assigned to the reduction of water on a single-layer $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ thin film, and a photoanodic current due to the oxidization of water on a single-layer $n\text{-}{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ thin film. An $\mathrm{FTO}/{\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{CaFe}}_2{\mathrm{O}}_4$ photoelectrode exhibited a negative photocurrent and a positive open circuit photovoltage ($+0.025\mathrm{V}$, $\lambda =430\mathrm{nm}$, $118\mu \mathrm{W}{\mathrm{cm}}^{-2}$) indicating that this electrode with a $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ layer at the surface contacting the electrolyte acts as a photocathode. The photovoltage generated in such a system is controlled by the built-in junction potential (determined by the number of junctions) and the open circuit voltage (controlled by the type of semiconductor in contact with the electrolyte), as illustrated in Figs. 4(a) and 4(b). Investigating the photoelectrochemical properties of four multiple-junction $\mathrm{FTO}/{({\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{CaFe}}_2{\mathrm{O}}_4)}_x$ photoelectrodes with the same single-layer thickness of 10 to 15 nm, but with an increasing number of layers $x$ ($x=10$, 15, 20, and 25), has a remarkable effect on the photocurrent density and the onset potential was observed. The 20-junction photoelectrode showed the highest photocurrent density ($-0.025\mathrm{mA}{\mathrm{cm}}^{-2}$ at $+0.4\mathrm{V}$) and the most positive onset potential ($+1.3\mathrm{V}$) of all four samples [Fig. 4(c)]. Furthermore, the 20-junction photoelectrode-based PEC exhibited a high open circuit photovoltage of up to $+0.97\mathrm{V}$, which was much higher than that for a cell having a single junction photoelectrode exhibiting only an open circuit photovoltage of $+0.13\mathrm{V}$.⁵⁸

Fig. 4

(a) Band structure of ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ junction immediately after light irradiation. (b) Band structure of ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ junction under the light irradiation after reaching steady-state conditions. In both cases, the $V_{\mathrm{oc}}^{\prime }=V_{\mathrm{oc}}+V_{pn}$. (c) $J-V$ curves of different multilayer $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4/n\text{-}{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ junction electrodes (0.1 M ${\mathrm{Na}}_2{\mathrm{SO}}_4$, 500 W Xe lamp). Reprinted with permission from Ref. 52. © American Chemical Society 2013.

The quantum efficiency of a pristine $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ electrode was found to be relatively low, which is presumably due to the poor mobility of the photogenerated charge carriers.⁵⁶ Therefore, efforts have been made to improve the conductivity of ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ electrodes by doping the material. Doping with Na and Mg was performed by Matsumoto et al. yielding oxides of the type ${\mathrm{Ca}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Mg}}_y{\mathrm{O}}_4$. The authors suggested that as the ionic radii of ${\mathrm{Na}}^{+}$ and ${\mathrm{Mg}}^{2+}$ are similar to ${\mathrm{Ca}}^{2+}$ and ${\mathrm{Fe}}^{3+}$, respectively, ${\mathrm{Na}}^{+}$ will substitute for ${\mathrm{Ca}}^{2+}$ and ${\mathrm{Mg}}^{2+}$ will replace ${\mathrm{Fe}}^{3+}$. This will create acceptor levels in the bandgap leading to higher electronic conductivity; however, the reported photocurrents are still very small. The authors suggested that the formation of oxygen vacancies at higher amounts of Na ($x>0.2$) lead to the decrease of conductivity, but the formation of oxygen vacancies is not supported experimentally. In an attempt to improve the low quantum efficiency for the light-induced water splitting reaction, Sekizawa et al. have prepared various metal-doped ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ electrodes by radio frequency magnetron cosputtering onto glass substrates coated with antimony-doped tin oxide (ATO) followed by postannealing at a low temperature. However, the doping metals were aggregated in the films after annealing as revealed by scanning transmission electron microscopy. Doping of ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ with Au and Ag resulted in an enhancement of the photocurrent without affecting the $p$-type conductivity. Doping with Ag resulted in an improvement of the carrier mobility together with a red-shift of the photoabsorption. Ag-doped ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ showed a 23-fold higher photocurrent than undoped ${\mathrm{CaFe}}_2{\mathrm{O}}_4$.⁵⁹ It is worth mentioning that the enhanced photoresponse may originate from the dopant metals (Ag, Au, Cu/CuO) as they are known as HER cocatalysts.

In a series of papers, Ida et al.^37,38,57 reported the light-induced water splitting employing $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$-based cathode coupled with different $n$-type semiconductors. In their first report, a suspension of presynthesized $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ powder was coated on a Pt substrate and annealed at 1100°C to 1200°C.³⁸ The sample annealed at 1200°C resulted in a flat, well-adhered crystalline film of $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ oriented in (320) and (420) planes. Under illumination (500 W Xe lamp), the PEC consisting of $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ and an $n\text{-}{\mathrm{TiO}}_2$ photoanode generated a photovoltage of 0.97 V and short-circuit photocurrent density of $0.22\mathrm{mA}{\mathrm{cm}}^{-2}$, respectively. The obtained photovoltage is close to the difference between the two onset potentials of $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ (0.31 V) and $n\text{-}{\mathrm{TiO}}_2$ ($-0.75\mathrm{V}$). The authors demonstrated generation of hydrogen under irradiation with visible light without applying a bias, however, the stoichiometric ratio ${\mathrm{H}}_2/{\mathrm{O}}_2$ was an order of magnitude different than the expected value of 2. The slow rate of ${\mathrm{O}}_2$ generation is accounted for from the weak absorption of ${\mathrm{O}}_2$ on ${\mathrm{TiO}}_2$ and slow water oxidation kinetics (indicating the need for an OER catalyst). The PEC configuration, the band diagram, and the amounts of gases generated as a function of time in this study are presented in Fig. 5.

Fig. 5

(a) Reaction and band model in PECs using $p$-type and $n$-type semiconductor electrodes. (b) Current–potential curve of a photocell with $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ ($2{\mathrm{cm}}^2$) and $n-{\mathrm{TiO}}_2$ ($0.5{\mathrm{cm}}^2$) electrodes and model structure of measurement cell and (c) amount of hydrogen and oxygen gases generated from the photocell short-circuited by connecting the $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ and $n\text{-}{\mathrm{TiO}}_2$ electrodes as a function of illumination time. Measurements were carried out in 0.1 M NaOH (aq) under illumination (500 W Xe lamp). Reprinted with permission from Ref. 48. © American Chemical Society 2010.

Later, the same authors reported the presence of the ${\mathrm{Ca}}_2{\mathrm{Fe}}_2{\mathrm{O}}_5$ impurity phase in the $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$, enhancing the short circuit photocurrent density ($0.55\mathrm{mA}{\mathrm{cm}}^{-2}$) and slightly increasing the photovoltage (1.09 V).³⁷ Additionally, the ${\mathrm{O}}_2$ formation is enhanced, decreasing the ${\mathrm{H}}_2/{\mathrm{O}}_2$ ratio to 3.7, which is, however, still higher than the theoretical value of 2. $n$-ZnO was also tested as a photoanode together with $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ and a photovoltage of 0.82 V was generated. When employing this PEC for unbiased water splitting, only ${\mathrm{H}}_2$ gas was detected.⁵⁷ The photodissolution of $n$-ZnO is partly responsible for the absence of ${\mathrm{O}}_2$ gas, but there is no obvious correlation between the amount of dissolved ${\mathrm{Zn}}^{2+}$ ions and the ${\mathrm{H}}_2$ gas evolved (which is much higher than the ${\mathrm{Zn}}^{2+}$ ion concentration detected).

Very few additional spinel ferrites other than $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ are studied as photoathodes. Yang et al. have investigated the photoelectrochemical performance of porous ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ nanosheets on FTO. The electrodes have been prepared from an aqueous solution of Co and Fe nitrate through a template-free electrochemical deposition followed by a heat treatment at 933 K. The electrodes exhibited only a small cathodic photocurrent of $\sim 0.3\mu \mathrm{A}{\mathrm{cm}}^{-2}$ in 0.1 M aqueous ${\mathrm{Na}}_2\mathrm{S}$ solution at zero bias voltage under visible light illumination ($\lambda \ge 390\mathrm{nm}$, $30\mathrm{mW}{\mathrm{cm}}^{-2}$).³⁹

The photoelectrochemical properties of $p\text{-}{\mathrm{NiFe}}_2{\mathrm{O}}_4$ pellets prepared by sintering sol–gel synthesized particles at 850°C were investigated by Rekhila et al. The open-circuit voltage of and short-circuit current of a two electrode configuration consisting of Pt and $p\text{-}{\mathrm{NiFe}}_2{\mathrm{O}}_4$ in a 0.5 M KCl cell were reported to be 0.43 V and $0.71\mathrm{mA}{\mathrm{cm}}^{-2}$ under irradiation with visible light ($50\mathrm{mW}{\mathrm{cm}}^{-2}$). A photon-to-electron conversion efficiency of 0.28 was calculated. However, corrosion of the semiconductor electrode was observed under illumination as well as in the dark.⁴⁰

Considering the bandgaps presented in Fig. 3, less attention is given for other $p$-type ferrites (${\mathrm{CoFe}}_2{\mathrm{O}}_4$, ${\mathrm{NiFe}}_2{\mathrm{O}}_4$, ${\mathrm{CuFe}}_2{\mathrm{O}}_4$) and more tests and investigations are still required. Sometimes, even the fundamental optical properties are controversial. For example, most report the optical indirect bandgap of ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ as 1.3 to 1.4 eV,^62,63 but Xiong et al. reported a bandgap much lower than these values (0.8 eV).⁶⁴ In the authors’ opinion, one of the main reasons is that these $p$-type ferrites are known to exist in a completely or partially inverted spinel structure.^24,63 Such a degree of inversion should be well controlled and require a rational design of synthetic strategy to accurately determine the optical properties and to enhance the PEC performance. In addition, they are prone to photocorrosion particularly in acidic media, which can be alleviated by applying suitable protective layers (${\mathrm{TiO}}_2$, ${\mathrm{Al}}_2{\mathrm{O}}_3$).

2.2.

n-Type Spinel Ferrites

The photoelectrochemical oxidation of water to ${\mathrm{O}}_2$ requires an $n$-type semiconductor with the valence band located more positive than the ${\mathrm{H}}_2\mathrm{O}/{\mathrm{O}}_2$ oxidation potential (1.23 V versus NHE). In contact with an aqueous electrolyte, such a semiconductor results in an upward band bending which drives the holes toward the surface leading to the oxidation of water to ${\mathrm{O}}_2$. Additionally, good electrical properties and stability under water oxidation conditions are needed. Among the spinel ferrites, $n\text{-}{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ is the promising candidate and is the only $n$-type photoanode material reported for PEC application.

Systematic investigation of the photoelectrochemical activity ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ was reported by Tahir and Wijayantha³³ and Tahir et al.⁶¹ The electrodes were prepared by aerosol-assisted chemical vapor deposition (AACVD) of alcoholic solutions of a bimetallic precursor ($[{\mathrm{Fe}}_2{(\mathrm{acac})}_4{({\mathrm{dmaeH}}_2)}_2][{\mathrm{ZnCl}}_4]$) on FTO. The thickness, morphology, and nanostructure of the electrode were controlled by altering the solvent for dissolution of the bimetallic precursor and physical deposition parameters.^33,61 The photocurrents were found to be dependent on the solvent, as well as on the deposition temperature and the deposition time. A maximum photocurrent density of $0.35\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 V versus RHE was obtained with a ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ electrode synthesized using a 0.1 M solution of the bimetallic precursor in ethanol, the optimum deposition temperature of 450°C, and a deposition time of 35 min. This electrode showed an incident-photon-to-electron conversion efficiency of 13.5% at 350 nm and an applied potential of 1.23 V versus RHE.³³ In the AACVD process, the aerosol droplet size (controlled by the solvent) and the enthalpy of combustion determine the decomposition pathway (homogeneous versus heterogeneous), thus varying the methanol/ethanol ratio of the solvent resulted in a change in the texture of the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ electrode. A compact ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ film composed of hexagonal like particles was obtained in pure methanol, but the structure transformed in to porous ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ nanorod films when ethanol was used as the solvent. Intermediate structures were obtained by varying the methanol/ethanol ratio. The textured electrodes exhibited a significantly higher photocurrent under AM1.5 illumination compared to their compact counterparts. The authors attributed this behavior to the improved collection of the photogenerated minority carriers at the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/\text{electrolyte}$ interface as the average feature size gradually decreased from $\sim 500\mathrm{nm}$ (methanol) to $\sim 100\mathrm{nm}$ (ethanol).⁶¹

In general, ferrites as photoelectrodes need high temperatures to crystallize ($>1000°\mathrm{C}$). This limits the choice of support materials and poses a critical challenge to maintain the desired electrode material properties such as surface area and porosity. Recently, Kim et al. introduced a hybrid microwave annealing (HMA) postsynthetic heat treatment with graphite powder as the susceptor being compatible to most transparent conducting glasses. They treated solution processed $\beta$-FeOOH nanorods with a Zn nitrate solution and obtained ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ nanorods after thermal treatment at 550°C for 3 h. Some unwanted ZnO on the nanorods was removed in NaOH. Subsequently, the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ nanorods were subjected to a second heating step at 800°C (20 min) or to HMA (5 min) to increase the crystallinity. The HMA-treated ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ nanorods exhibited at 1.23 V versus RHE (1 M NaOH) and AM 1.5G illumination a photocurrent of $0.240\mathrm{mA}{\mathrm{cm}}^{-2}$, which was a 10- to 15-fold increase in comparison to conventional thermally treated electrodes and was stable for at least 3 h. The authors claimed that stoichiometric amounts of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ can be measured with Faradaic efficiencies (= actual gas evolution rate/rate expected from current) of 90% to 100%. The improved performance after the HMA treatment was attributed to better crystallinity and reduced surface defects as evinced by electrochemical impedance spectroscopy.⁶⁵ Extending their work, the same authors recently reported the influence of the composition of the annealing atmosphere on the photoelectrochemical behavior of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ (Fig. 6).³⁴ ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ nanorod films were first treated at 800°C (20 min in air) followed by a mild temperature treatment at 200°C (2 h) either under vacuum, air, or hydrogen atmosphere. The hydrogen and vacuum post-thermal treatment enhanced the photoactivity about 20-fold [Fig. 6(b)]. The increased activity is attributed to oxygen vacancies created in the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ lattice due to the limited oxidation environment as proven by O 1s XPS. Optimal oxygen vacancy concentrations increase the majority carrier density and lead to improved charge separation. The highest photocurrent was observed for the hydrogen treated sample, $0.320\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 V versus RHE under AM 1.5G illumination. The authors suggested two types of mechanisms of how the lattice O ($O_L$) is replaced by oxygen vacancies (${\ddot{V}}_O$) under controlled hydrogen and vacuum atmosphere [Fig. 6(a)]. In hydrogen atmosphere, the $O_L$ reacts with ${\mathrm{H}}_2$ and leaves the lattice as water molecules:

Fig. 6

(a) Schematic representation of different mechanisms of generating oxygen vacancies by post-treatments under hydrogen or vacuum conditions, (b) $J-V$ characteristics of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ photoanodes before and after post-treatment [hydrogen (H), vacuum (V), and atmospheric air (A)] under AM 1.5G illumination ($100\mathrm{mW}{\mathrm{cm}}^{-2}$) in 1 M NaOH electrolyte ($\text{scan rate}=10\mathrm{mV}{\mathrm{s}}^{-1}$). Reprinted with permission from Ref. 60. © Royal Society of Chemistry 2015.

In general, for most iron based $n$-type semiconductor oxide materials, the diffusion length of the minority carrier is very short leading to an inherently high charge recombination rate, which limits the efficiency of the PECs. Several strategies to address this issue were developed including nanostructuring^33,61,65 and doping.⁵⁹ Another attractive nanostructuring strategy is to use a structured transparent conductive oxide current collector to capture and tunnel the photogenerated electrons readily while the large interfacial area allows efficient transfer of the holes to the solution. This strategy was recently demonstrated for ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ decorated Al-doped ZnO (AZO) nanowire films.³² The Al:ZnO nanowires were grown on FTO substrate hydrothermally at 88°C and treated with an ethanolic solution of ${\mathrm{FeCl}}_3$. Subsequent annealing at 550°C leads to ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$-coated Al:ZnO nanowires [Figs. 7(a)–7(d)]. Depending on the time of ${\mathrm{FeCl}}_3$ exposure, the nanowires can be converted to nanotubes due to the dissolution of Al:ZnO in acidic ${\mathrm{FeCl}}_3$ solution. The photoanode shows outstanding photoelectrochemical performance with low onset potential (0.38 V versus RHE) with a photocurrent density of $1.72\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 V versus RHE [Fig. 7(e)]. The synergy of high conductivity of Al:ZnO, the nanowire morphology for charge separation, and the visible light absorption of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ coating are attributed to be responsible for the high photoelectrochemical performance.

Fig. 7

SEM images of (a) 0.5% AZO and 0.5% AZO–ZFO with treatment times of (b) 1 min, (c) 3 min, (d) 7 min, (e) LSV plots of 0.5% AZO and 0.5% AZO–ZFO photoanodes under chopped illumination and (e) the corresponding ABPE plots. Insets show the schematic illustration of morphology evolution for the AZO and AZO–ZFO composite photoanodes with different treatment times. Reprinted with permission from Ref. 61. © Royal Society of Chemistry 2016.

Recently, Hufnagel et al.³⁵ prepared mesoporous ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ thin films on a macroporous ATO scaffold using atomic layer deposition (ALD). The photoresponse of the electrodes was tested in three electrode PECs and the electrodes exhibited 4- to 5-fold higher photocurrent density ($0.26\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 versus RHE) compared to nonstructured ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ films prepared in a similar way ($0.05\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 versus RHE). Additionally, the authors show that such electrodes have more negative photocurrent onsets (0.9 V versus RHE) compared to reported values.³³

Spinel ferrites were recently investigated for construction of heterojunction electrodes to improve the photoelectrochemical performance of other widely used semiconductors. In this regard, heterojunction electrodes such as ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$,^66–68 ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$,^69,70 ${\mathrm{CaFe}}_2{\mathrm{O}}_4/\mathrm{TaON}$,⁷¹ and ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$⁷² as photoanodes for the OER were studied. Table 2 presents the PEC performance of ferrite heterojunction photoelectrodes. Borse et al. prepared ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ layers on stainless steel by depositing an aqueous solution of Zn and Fe salts employing a plasma spray method and investigated the photoelectrochemical activity of the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ electrode. Under simulated solar light (AM1.5G, $100\mathrm{mW}{\mathrm{cm}}^{-2}$) with a bias of 1.4 V versus RHE, a photocurrent of $0.1\mathrm{mA}{\mathrm{cm}}^{-2}$ is measured, which is fivefold higher than for pristine ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$. The authors also reported hydrogen production in a two electrode set-up employing graphite as the counter electrode. Again, the composite photoanode exhibited a significantly higher photoactivity than a bare ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ photoelectrode. The rates of HER at the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ and the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ photoanode were calculated to be 46.3 and $99.0\mu \mathrm{mol}{\mathrm{cm}}^{-2}{\mathrm{h}}^{-1}$, respectively, resulting in STH conversion efficiencies of 0.06 and 0.0125, respectively. However, no data were given for the formation of molecular oxygen. The results of electrochemical impedance spectroscopy evinced a significantly lower interfacial charge transfer resistance of the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ composite electrode than the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ electrode.⁶⁷

Table 2

PEC performance of ferrite based composite photoelectrodes.

${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanorod composite photoanodes have also been prepared using hydrothermally grown FeOOH nanorods and subsequent treatment with different concentrations of Zn precursor. After calcinations at 750°C, a ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ composite electrode was obtained.⁶⁸ The photocurrent density for the composite electrode was $0.44\mathrm{mA}{\mathrm{cm}}^{-2}$ at $\sim 1.2\mathrm{V}$ versus RHE, which was almost twice as high as that for a ${\mathrm{Fe}}_2{\mathrm{O}}_3$ electrode ($0.24\mathrm{mA}{\mathrm{cm}}^{-2}$). McDonald et al. employed the electrodeposition route and obtained photoelectrodes composed of an $\alpha \text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ (hematite) core and a ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ shell as confirmed by XRD.⁶⁶ The electrodeposited $\beta$-FeOOH films on FTO were converted into $\alpha \text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ by heat treatment and subsequent treatment with Zn-containing solution on top of $\alpha \text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ film yielded a Zn-rich top layer on $\alpha \text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ after annealing. The highest photocurrent was obtained with a composite electrode exhibiting a ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ ratio of 1. The increase in the photocurrent of the heterojunction electrodes compared to the bare $\alpha \text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ electrode was explained as being due to the enhanced electron hole separation at the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ interface. A further enhancement in photocurrent was obtained by a treatment of the composite electrodes with an ${\mathrm{Al}}^{3+}$ solution yielding thin layers of a solid solution (${\mathrm{ZnFe}}_{2-x}{\mathrm{Al}}_x{\mathrm{O}}_4$ or ${\mathrm{Fe}}_{2-x}{\mathrm{Al}}_x{\mathrm{O}}_3$) after heat treatment. With this, the number of surface states that serve as electron–hole recombination centers is probably reduced. But it was also observed that both the formation of a ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ layer and the incorporation of ${\mathrm{Al}}^{3+}$ into the surface made the surface less catalytic for the OER. However, when ${\mathrm{Co}}^{2+}$ was introduced into the surface of the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{Fe}}_2{\mathrm{O}}_3$ composite electrodes as oxygen evolution catalysts, the onset of the photocurrent was shifted to more negative voltage and the overall photocurrent was improved.⁶⁶ Furthermore, ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{TiO}}_2$ heterostructures are also prepared using a combination of solution-phase materials growth techniques and ALD.⁷³ The ${\mathrm{TiO}}_2$ nanowires were hydrothermally grown on FTO substrate and later infiltrated by Zn precursor using ALD. The ${\mathrm{ZnFe}}_2{\mathrm{O}}_4/{\mathrm{TiO}}_2$ composite electrodes show an enhanced visible light photoresponse compared to bare ${\mathrm{TiO}}_2$ photoelectrodes. The authors suggest that the extended visible light absorption by the ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$, the nanowire morphology of the ${\mathrm{TiO}}_2$, and favorable band edge positions are the main reasons for the increased photoresponse.

A related photoanode has been prepared by anisotropic growth of a $\beta$-FeOOH film on FTO from an aqueous solution containing Fe and Ca ions followed by two-step thermal annealing at 550°C and 800°C. The authors suggested that this procedure induces the formation of a $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4/n\text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ heterojunction photoanode. The presence of Ca in the ${\mathrm{Fe}}_2{\mathrm{O}}_3$ film, leading to the formation of ${\mathrm{CaFe}}_2{\mathrm{O}}_4$, has been proven by XPS measurements. Under illumination (AM 1.5G, $100\mathrm{mW}{\mathrm{cm}}^{-2}$), the heterojunction photoanode exhibits a photocurrent density of $0.53\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 V versus RHE, which is a 100% higher photocurrent response than that obtained using a bare $\alpha \text{-}{\mathrm{Fe}}_2{\mathrm{O}}_3$ electrode. Based on electrochemical impedance spectroscopy, the photocurrent enhancement has again been attributed to an enhanced charge carrier separation and a reduced resistance of the interfacial charge transfer between the electrolyte and the electrode.⁶⁹

Kim et al.^71,74 reported the preparation and characterization of $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ modified TaON and ${\mathrm{BiVO}}_4$ $p\text{-}n$ heterojunction photoanodes. Both $n$-type semiconductors are known to be suitable anode materials for solar-driven water splitting in PECs. The valence band of $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$ is more positive than the water oxidation potential, and both semiconductors TaON and ${\mathrm{BiVO}}_4$ form staggered relative band positions with the ferrite as required for an effective heterojunction photoanode. In both cases, $p\text{-}{\mathrm{CaFe}}_2{\mathrm{O}}_4$, which has been synthesized by a conventional solid state reaction, was deposited on top of the $n$-semiconductor/FTO electrode by electrophoresis. The pristine TaON electrode showed an anodic photocurrent density of $0.230\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 V versus RHE (0.5 M NaOH, $\lambda >420\mathrm{nm}$). The ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ layer on the surface of a TaON electrode resulted in a significant increase of the photocurrent density ($1.26\mathrm{mA}{\mathrm{cm}}^{-2}$). The observed photocurrent was found to be a result of overall water splitting yielding ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ in a ratio of 1.5, accompanied, however, by a deterioration of the TaON. Impedance spectroscopic analysis indicated that the formation of the heterojunction increased the photocurrent density by reducing the resistance of the charge carrier transport and, consequently, enhancing the electron–hole separation.⁷¹ Anodic photocurrents have likewise been observed for both ${\mathrm{BiVO}}_4$ and ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$ electrodes (0.5 M ${\mathrm{Na}}_2{\mathrm{SO}}_4$, AM 1.5G $100\mathrm{mW}{\mathrm{cm}}^{-2}$); the bare ${\mathrm{BiVO}}_4$ electrode showed a photocurrent density of $0.58\mathrm{mA}{\mathrm{cm}}^{-2}$ at 1.23 V versus RHE V while the ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$ heterojunction photoanode exhibited $0.96\mathrm{mA}{\mathrm{cm}}^{-2}$, comprising an increase of 65% over that measured at the ${\mathrm{BiVO}}_4$ electrode. The formation of the heterojunction was found to reduce the recombination of the photogenerated charge carriers on the electrode surface with little effect on bulk recombination as evinced by an investigation of the interfacial transfer of charge carriers using hydrogen peroxide as an electron donor.⁷⁴

In the above demonstrated heterojunction electrodes, efficient charge separation is the key factor for improved photoelectrochemical activity. This is demonstrated in the energy diagrams of the composite electrodes in Fig. 8. The ferrites (${\mathrm{CaFe}}_2{\mathrm{O}}_4$ and ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$) have valence band energies located between the water oxidation potential and that of the valence band of the second semiconductor. Thus, holes generated at the more positive valence band are extracted to the ferrite valence band reducing bulk recombination and allowing successful injection of the holes to the electrolyte. On the other hand, as the conduction band of the ferrites is situated at a more negative potential, the photogenerated electrons will be easily transferred to the conduction band of the second semiconductor for collection at the back contact.

Fig. 8

Schematic representation of the band positions of heterojunction electrodes showing the flow of photogenertaed charge carriers: (a) the ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ /TaON/ ($p\text{-}n$ junction) and (b) the ${\mathrm{Fe}}_2{\mathrm{O}}_3/{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ ($n-n$ junction).

Furthermore, the modification of the heterojunction photoanodes by depositing OER cocatalysts results in higher photocurrent densities by decreasing the onset potential and facilitating the interfacial charge transfer. In this regard, “cobalt phosphate” (CoPi) is used widely as an OER catalyst.^75–78 For example, in the ${\mathrm{CaFe}}_2{\mathrm{O}}_4/\mathrm{TaON}$⁷¹ heterojunction electrode system, after deposition of CoPi and with an applied bias of 1.23 V versus RHE, ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ were generated with nearly of stoichiometric ratio of 2.1 ($123\mu \mathrm{mol}$ ${\mathrm{H}}_2$ and $59\mu \mathrm{mol}$ ${\mathrm{O}}_2$ were produced within 3 h of illumination with $\lambda \ge 400\mathrm{nm}$). The STH efficiency was 0.053% at 1.0 V versus RHE, but reached 0.55% when a PV device is coupled in tandem configuration (assuming the applied voltage is zero). However, the initial current decreased within 3 h to about 50%. The beneficial role of the CoPi cocatalyst was revealed by performing the gas evolution experiment with a ${\mathrm{CaFe}}_2{\mathrm{O}}_4/\mathrm{TaON}$ photoanode in the absence of CoPi. Under these experimental conditions, no constant photocurrent was obtained, the faradaic efficiencies decreased (50% to 70%), and the ${\mathrm{H}}_2/{\mathrm{O}}_2$ ratio became less than stoichiometric (1.51) due to the self-oxidation of TaON.⁷¹ Similar results have been obtained with ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$ composite photoanodes. In this case, the CoPi modified ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$ electrode exhibited a lower photocurrent density when compared to the ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$ heterojunction electrode, but an improved stability of the current density was observed indicating that the presence of the OER cocatalyst is beneficial for the stabilization of the ${\mathrm{CaFe}}_2{\mathrm{O}}_4/{\mathrm{BiVO}}_4$ heterojunction. The evolution of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ during the photoelectrochemical water splitting reaction was measured in a three electrode set-up in phosphate buffer ($\mathrm{pH}=7$) under applied bias. The total amounts of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ evolved within 2 h of illumination with visible light ($\lambda \ge 400\mathrm{nm}$) were 297 and $140\mu \mathrm{mol}$, respectively. The resulting ${\mathrm{H}}_2/{\mathrm{O}}_2$ ratio of 2.1 confirmed that the generation of the photocurrent was mainly due to the water splitting reaction. The Faradic efficiency during this reaction was reported to be about 78% to 88%. The photocurrent density was initially $\sim 4\mathrm{mA}{\mathrm{cm}}^{-2}$, but dropped rapidly during the first 30 min of illumination and decreased slowly afterward.⁷⁴

In general, the above few examples of spinel ferrite-based PECs demonstrated the attractive photoelectrochemical properties of these materials. The measured photocurrents of PECs with ferrite photoelectrodes are still low, but different strategies proved that higher photocurrents can be achieved. The main contributors for low photoelectrochemical performances are identified as (1) slow interfacial charge carrier transfer, (2) inherently high charge carrier recombination rates, and (3) loss of interfacial area due to the high thermal treatment. Strategies to address these bottle necks, including (1) nanostructuring, (2) forming heterojunction structures, (3) cocatalyst coating, and (4) control of the defect chemistry are shown to enhance the photoelectrochemical performance.

It is worth mentioning that the reported experimental band positions of some of the spinel ferrites related to HER and OER potentials are still arguable. Based on the energetic band diagrams of ferrites presented in Fig. 3, ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ and ${\mathrm{MgFe}}_2{\mathrm{O}}_4$ are, in principle, capable of producing hydrogen. However, to the best of the authors’ knowledge, there is no literature report proving this. For example, the reported flatband potentials of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ (0.6 to 0.8 V versus RHE)^33,35 suggest the conduction band lies slightly below the HER potential. We also found that the conduction band edge is slightly positive ($\sim 100\mathrm{mV}$) to that of the proton reduction potential, but we are still in the process of verifying this. Thus, more experimental investigations are required to refine the existing photoelectrochemical data. Furthermore, ${\mathrm{MgFe}}_2{\mathrm{O}}_4$ is also interesting for OER, but there are no reports except the fundamental investigation reported by Benco and Koffyberg.⁵² However, there are a few reports on photocatalytic ${\mathrm{H}}_2$ production using ${\mathrm{MgFe}}_2{\mathrm{O}}_4$ which to some extent show the potential of this material.^53,72

3.1.

Electronic Structure of the Bulk

The effect of charge ordering in the octahedral sites of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ on their electronic structure was investigated using DFT+U.⁸² A precise description of charge ordering was found to be crucial in determining the bandgaps of the compounds. GGA+U calculations of the electronic structure of antiferromagnetic ${\mathrm{CaFe}}_2{\mathrm{O}}_4$ yield an indirect bandgap of $\sim 1.9\mathrm{eV}$.⁸³ The ionicity of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ has been determined using DFT calculations.⁸⁴ Furthermore, a new developed quantum mechanical estimation method for the ionicity of spinel ferrites has been proposed and tested. On the basis of this, the ionicities of the spinel ferrites ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Cu, Fe, Mn, Ni) were calculated. The electronic structure of ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ has been investigated using LSDA+U and hybrid-DFT in 2012.⁸⁵ According to the theoretical results, the system is an indirect gap material in one of the minority channels and slightly larger direct bandgaps can be found both in the minority and majority channels. The electronic structure of ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Ca, Mg, Zn) was investigated in a combined experimental and theoretical study.⁸⁶ The DFT calculations reveal that the M-ion controllably affects the density of states of the Fe d-orbitals near the Fermi level. The electronic structure of ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ was studied using GGA+U.⁸⁷ Taking the effect of spin arrangement on symmetry into account, ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ was classified as a semiconductor. The impact of cation distribution in ${\mathrm{CuFe}}_2{\mathrm{O}}_4$ on electronic structure and magnetic properties has been investigated by Feng et al.⁸⁸ The lattice structure was optimized on the GGA level and the electronic structure was calculated with GGA+U. The calculated density of states shows that the distribution of Cu ions significantly impacts the electronic structure. Multilayer bispinel composites, in which one member is ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the other is ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Mg, Mn, Ni), were modeled using GGA+U by Wells et al.⁸⁹ It was found that substitution of the transition metal sites in the supercell produces cation charge transfers and magnetization modulation. Band shifts and gap modulation were comparable to the chemically similar bulk compounds. Two different distributions for the octahedral-site cations in ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ and ${\mathrm{CdFe}}_2{\mathrm{O}}_4$ have been investigated using LDA and GGA, as well as LDA+U and GGA+U.⁹⁰ It was shown that a different octahedral-site distribution impacts the density of states as well as the bandgaps in both the normal and inverse spinel configurations of these compounds. Magnetic properties and the electronic structure of ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ have been studied using hybrid-DFT.⁹¹ The calculated density of states suggests that ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ is an insulator. The electronic structure of normal and inverse spinel ferrites ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Fe, Mn, Ni) was investigated by self-interaction corrected LSDA.⁹² For both structures, all studied compounds were found to be insulating but with smaller gaps in the normal spinel structure. The calculated spin magnetic moments and exchange splitting of the conduction bands were dramatically increased when moving from the inverse spinel structure to the normal spinel. A first principle investigation of the electronic structure of ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Fe, Mn, Ni) compares the performance of LSDA and LSDA+U.⁹³ For the LSDA+U approach, the charge ordering is stable in contrast to a metallic state given by the LSDA approach. Calculated x-ray absorption spectra as well as the x-ray magnetic circular dichroism spectra were in good agreement with the experiment. The electrical and magnetic properties of the normal and inverse spinel structures of ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ were calculated with DFT by Zuo and Vittoria.⁹⁴ The calculated bandgap suggests that ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ is a complex insulator, in contrast to earlier LSDA and GGA calculations which suggest a half-metallic behavior. ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ has been investigated theoretically at DFT level.⁹⁵ The calculated band structure shows a low carrier density half-metal in the fully ordered state, in contrast to experimental characterizations. The computations yield a strong coupling of the energy bands at the Fermi energy to the internal structural parameter $u$ as well as strong effects on the electronic structure upon partial interchange of Fe and Mn atoms.

Calculations of the K-edge x-ray absorption near-edge structure (XANES) in elemental iron and ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Mg, Mn, Ni, Zn) were carried out by Safontseva and Nikiforov.⁹⁶ It was shown that the Fe K-edge energy shift found experimentally occurs upon the transition from elemental iron to the spinel ferrites. This shift was demonstrated to be identically directed for ferrites with a normal and inverted spinel structure. A computational study of ferrimagnetic ${\mathrm{Zn}}_x{\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_2{\mathrm{O}}_4$ compounds using the pseudofunction method was carried out in 1996.⁹⁷ Substitution of Ni with Zn enhances the localization of the 3d states of Fe on the octahedral sites, so that the O 2p-Fe 3d hybridized states can be resolved into two distinct twofold and threefold features. Normal and inverse ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ was investigated with HF level of theory in 1996.⁹⁸ From Mulliken population analysis and net spin density distributions, it was concluded that the charge states of Mn and Fe in the ground state show no evidence of charge transfer leading to ${\mathrm{Fe}}^{2+}$ at A sites and ${\mathrm{Mn}}^{3+}$ at B sites in the inverse spinel structure ${\mathrm{AB}}_2{\mathrm{O}}_4$. An early computational study of the band structure and magnetic moments of ferrites ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Fe, Mn, Ni, Zn) on LSDA level⁹⁹ only covered the metallic, high-temperature phase in the case of $\mathrm{M}=\mathrm{Co}$, Fe, Mn, Zn. In contrast, ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ was described as an insulator.

Table 3 compares experimental bandgaps of selected ferrites with calculated values gained by different theoretical protocols. It is obvious that plain DFT without any further corrections systematically underestimates the bandgap of the considered systems. The theory states that using a self-interaction corrected or a hybrid DFT approach reduces the error. Using a DFT+U framework provides results that show good agreement with the experimental data. This is easily explained by the added potential U, which is an empirical parameter that can be explicitly chosen to fit the experimental bandgap. There is no universal choice for the U parameter.

Table 3

Comparison of experimental and calculated bandgap energies of some selected MFe2O4 spinel ferrites.

3.2.

Magnetic Properties

Since the magnetic structure of ferrites (strongly) affects the calculated bandgap,⁹² the magnetic properties also have to be taken into account when discussing electronic properties. The magnetic properties of ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Fe, Mn, Ni, Zn) were studied with DFT methods.¹¹⁸ The theoretically obtained magnetizations were consistent with experimental results in the absence of an external field. GGA+U was applied to investigate the electronic structure and magnetic properties of ${\mathrm{MnFe}}_2{\mathrm{O}}_4$.¹¹⁷ The calculations account for a cubic structure with ordered spins and insulating behavior. It was found that the high-spin state is favorable for the two cations Mn and Fe. The position of magnesium ions in ${\mathrm{Mg}}^{2+}$-doped lithium ferrite of the composition ${\mathrm{Li}}_{0.5-0.5x}{\mathrm{Mg}}_x{\mathrm{Fe}}_{2.5-0.5x}{\mathrm{O}}_4$ has been investigated by interatomic potential and DFT calculations.¹¹⁹ The lowest energy structure was found for ${\mathrm{Mg}}^{2+}$ ions evenly replacing ${\mathrm{Li}}^{+}$ and ${\mathrm{Fe}}^{3+}$ ions on octahedral sites. This occupation affects a decrease in magnetization for the ${\mathrm{Mg}}^{2+}$-doped ferrite relative to the undoped lithium ferrite. A computational study of the spinel ferrites ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ and ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ shows that LSDA+U and GGA+U allow for a good quantitative description of these materials.¹¹⁰ The effect of epitaxial strain on the magnetocrystalline anisotropy was investigated and the results are in good agreement with experimental observations. The structure of partially inverse spinel ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ as well as its electronic and magnetic properties has been investigated by the GGA+U approach.¹²⁰ It was found that the Co and Fe ions prefer their high-spin configurations with higher spin moments at octahedral sites. Certain investigated inversion degrees show half-metallic behavior.

3.3.

Structural and Thermodynamic Properties

A computational study of the inversion thermodynamics and electronic structure of (thio) spinels ${\mathrm{FeM}}_2{\mathrm{X}}_4$ (M: Co, Cr, Mn, Ni; X: O, S) was published in 2015.¹²¹ The analysis of the configurational free energies shows that ${\mathrm{FeCr}}_2{\mathrm{X}}_4$ and ${\mathrm{FeMn}}_2{\mathrm{S}}_4$ are fully normal, ${\mathrm{FeNi}}_2{\mathrm{X}}_4$ and ${\mathrm{FeCo}}_2{\mathrm{S}}_4$ are intermediate, and ${\mathrm{FeCo}}_2{\mathrm{O}}_4$ and ${\mathrm{FeMn}}_2{\mathrm{O}}_4$ are fully inverted. The calculations illustrate that ${\mathrm{FeCr}}_2{\mathrm{X}}_4$, ${\mathrm{FeMn}}_2{\mathrm{X}}_4$, ${\mathrm{FeCo}}_2{\mathrm{O}}_4$, and ${\mathrm{FeNi}}_2{\mathrm{O}}_4$ are half metals in the ferrimagnetic state when Fe is in tetrahedral positions. When M is filling the tetrahedral positions, the Cr-containing compounds and ${\mathrm{FeMn}}_2{\mathrm{O}}_4$ are shown to be half-metallic systems, whereas the Co and Ni spinels are shown to be insulators. Yao et al.¹¹⁶ investigated the structure and electronic properties of normal spinel ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ using GGA and LDA. They suggest that the GGA functional RPBE combined with ultrasoft pseudopotentials is a good method for predicting the crystal structure of the compound. The computational results indicate that ${\mathrm{ZnFe}}_2{\mathrm{O}}_4$ is a direct gap semiconductor and that there is a strong hybridization between the Fe 3d states and the O 2p states as well as between the Zn 3d states and O 2p states. DFT calculations at the GGA+U level were performed on ${\mathrm{AB}}_2{\mathrm{O}}_4$ (A: Fe, Ni, Zn; B: Fe, Cr) spinel oxides in order to determine thermodynamic properties.¹⁰¹ Calculated mixing energies quantitatively reproduce experimental data. Reactions leading to an excess of A or B, respectively, were found to be slightly exothermic in a number of spinel compounds. A set of effective chemical potentials (ECPs) that connect energies of ${\mathrm{MFe}}_2{\mathrm{O}}_4$ (M: Co, Fe, Ni, Zn) spinels and oxides calculated at 0 K from DFT to free energies at high temperature and pressure in the presence of water was derived and tested.¹⁰⁹ The ECPs were used to calculate free energies of low index stoichiometric surfaces of nickel ferrite in water, predicting surface denuding at high temperatures. A computational study compares the performance of GGA-DFT and hybrid-DFT (B3LYP) for the equilibrium structure of ${\mathrm{Fe}}_3{\mathrm{O}}_4$.¹⁰⁴ The ground state calculated by GGA-DFT is metallic with Fd-3m symmetry while the hybrid level of theory yields a charge ordered semiconducting state with P2/c symmetry. Phonon frequency calculations showed that charge ordering causes symmetry breaking of force constants on symmetry lowering from the cubic unit cell to the monoclinic unit cell.

3.4.

Surfaces and Adsorption

The structure, electronic properties, and energetics of the ${\mathrm{NiFe}}_2{\mathrm{O}}_4(001)$ surface and its interaction with water both in the absence and in the presence of surface oxygen vacancies have been studied using DFT+U.¹²² It was shown that water adsorbs dissociatively on the surface oxygen vacancies leading to the formation of surface hydroxyls. Furthermore, it was found that at high temperature, water desorbs leaving a surface containing oxygen vacancies. The reactivity of the ${\mathrm{NiFe}}_2{\mathrm{O}}_4(111)$ surface has been studied using DFT+U.¹²³ The surface reactivity is significantly higher in comparison with the ${\mathrm{Fe}}_3{\mathrm{O}}_4(111)$ surfaces. Dissociation of water was found to be highly favorable on the ${\mathrm{NiFe}}_2{\mathrm{O}}_4(111)$ surfaces. The activation barrier for the dissociation of a single water molecule was dependent on the termination of the surface. The electronic properties of ${\mathrm{CuFe}}_2{\mathrm{O}}_4$ and the adsorption behavior of an NO molecule on the ${\mathrm{CuFe}}_2{\mathrm{O}}_4$ (100) surface were studied using DFT+U.¹²⁴ The authors suggest that the ground state of ${\mathrm{CuFe}}_2{\mathrm{O}}_4$ bulk has an inverse spinel structure and is a magnetic semiconductor. The NO molecule prefers to adsorb on the top site of the Fe atom on the (100) surface, forming an N-Fe bond. DFT+U calculations of the adsorption behavior of Ni and Ti on the ${\mathrm{Fe}}_3{\mathrm{O}}_4(001)$ surface have been carried out by Bliem et al.¹²⁵ For both atoms, an incorporation in an octahedral Fe site of the force-relaxed ${\mathrm{Fe}}_3{\mathrm{O}}_4(001)$ surface is energetically favorable. Boron adsorption on an ${\mathrm{Fe}}_3{\mathrm{O}}_4(100)$ surface was studied by GGA calculations in 2015.¹²⁶ It was shown that B adsorption induces half-metallicity at the ${\mathrm{Fe}}_3{\mathrm{O}}_4(100)$ surface. The adsorption of group IV atoms (C, Si, Ge, Sn) on the ${\mathrm{Fe}}_3{\mathrm{O}}_4(100)$ surface has been investigated using GGA.¹²⁷ The results show that all these atoms prefer to bind on the surface oxygen atom, which has no tetrahedral Fe neighbor. The adsorption structures and energies of a single Au atom on six different terminations of the ${\mathrm{Fe}}_3{\mathrm{O}}_4(111)$ surface were computed using GGA+U.¹²⁸ It was found that the Au-atom adsorption energy decreases with increasing stability of the surface. Furthermore, the results indicate that the Au atom is reduced and has a negative charge on the iron-terminated surfaces, whereas it is oxidized and has a positive charge on the oxygen-terminated surfaces. Van Natter et al.¹²⁹ investigated with cluster models possible active sites on the (100), (110), and (111) surfaces of ${\mathrm{Fe}}_3{\mathrm{O}}_4$. Adsorption energies of oxygen adatoms located on exposed cation sites were calculated on hybrid-DFT (B3LYP) level of theory. The computed energies vary proportionally to the number of oxygen atoms missing from the normal octahedral coordination of the cation adsorption sites. A theoretical investigation of bare and water terminated ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ surfaces was carried out in 2014 using GGA+U.¹³⁰ It was found that surfaces that have more metal cations exposed are more stable. The most stable surfaces are shown to be along the (111) planes. Water adsorption on the ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ surfaces was found to be an exothermic process. In 2014, a DFT investigation of the ${\mathrm{NiFe}}_2{\mathrm{O}}_4(001)$ surface reported an overpotential of 0.42 V for the OER.¹³¹ It was concluded that Fe-doped $\beta$-NiOOH and ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ could be the phases responsible for the enhanced OER activity of ${\mathrm{NiO}}_x$ when it is doped with Fe.