Introduction: Errare humanum est

Titanium dioxide, tin dioxide, and zinc oxide are among the generic materials, which triggered the success of semiconductor photo/electrochemistry in the mid of the twentieth century. Studies of these three n-type semiconductors revealed fundamental and practical incentives, which comprised, inter alia, development of photocatalysis, photovoltaics (dye-sensitized and perovskite solar cells), generation of solar fuels from abundant resources (water, N2, or CO2), and fabrication of Li-batteries. According to Web-of-Science, investigations of these three materials currently produce about 130 scientific documents per day! Such an information overload is also responsible for inconsistent data, oversimplifications, and conflicting interpretations.

Disclosing pitfalls in textbooks and scientific papers is an unrewarding job, like writing a negative referee’s report or expelling a student from an exam. In all cases, the reviewer or examiner must convincingly articulate his/her arguments, as people usually do not protest positive evaluation, but do reject critical assessments. Yet, making errors in research and teaching/learning is very natural and omnipresent. (The trial/error is a strategy, not a disgrace.) The author of this article also made many mistakes in his research; some examples are listed at the end of this paper.

There are several good reviews on the properties and applications of oxide semiconductors. We can mention, e.g., the special issue of Chem.Rev [1] and the “coming-soon” book [2]. Consequently, there is no reason to write yet another text of this kind. My review is focused on open questions and problematic issues in the field, i.e., it is selective rather than comprehensive. I did my best to avoid subjective assortment of these topics, but it may happen that others are allergic to different glitches. In any case, my paper endeavors to highlight questionable issues and to aid students and teachers of electrochemistry.

Band structure and water splitting

Chemistry in general and electrochemistry in particular investigate the valence electrons in molecules (highest occupied molecular orbital, HOMO) and solids (valence band maximum, VBM). Photo(electro)chemistry pushes these electrons towards LUMO (lowest unoccupied molecular orbital) or CBM (conduction band minimum). Figure 1 shows the basic scheme of energy levels in n-doped semiconductors. Though it looks trivial, there are entries, which deserve attention. Due to n-doping, which is typical for TiO2, SnO2, and ZnO, the Fermi level (EF) is upshifted towards the vicinity of CBM. Strictly speaking, the terms “Fermi energy” and “Fermi level” (electrochemical potential of electrons, µe) are not synonyms [3], but in the context of this article, we can omit subtle differences of both quantities. The offset of the Fermi level from energy of the conduction band minimum (ECBM) is:

$${\zeta }_{\mathrm{nb}}=\frac{{k}_{\mathrm{B}}T}{e}\mathrm{ln}\left(\frac{{N}_{\mathrm{C}}}{{N}_{\mathrm{D}}}\right)$$

kB is the Boltzmann constant, T is temperature, e is electron charge, ND is the concentration of donors, and NC is the effective total concentration of conduction-band states at CBM:

$${N}_{C}=2{\left(\frac{2\pi {m}^{*}{k}_{\mathrm{B}}T}{{h}^{2}}\right)}^{3/2}$$

h is the Planck constant, and m* is the reduced mass of electron. (Eq. 1 is valid if all the donors are ionized, which is a reasonable assumption in most cases.) Table 1 lists the selected characteristics of TiO2 (anatase, rutile), SnO2, and ZnO, which are relevant to the follow-up discussion. The quoted numbers are just typical estimates from various values in literature.

Fig. 1
figure 1

Scheme of energy levels and the corresponding derived quantities for n-doped semiconductors. CBM and VBM are conduction band minimum and valence band maximum, respectively. The position of Fermi level is EF. IE is the ionization energy, EA is electron affinity, φ is work function, and EBG is the band gap. EVAC is the reference energy of an electron at rest in vacuum

Table 1 Selected characteristics of TiO2 (anatase, rutile), SnO2, and ZnO. The average values of Vfb were determined from the Gaussian fits of histograms of the flatband potential distribution compiled from literature (see Fig. 4 and ref. [16] for details)

Titanium dioxide has four naturally occurring phases: tetragonal rutile and anatase, orthorhombic brookite, and a quite rare monoclinic TiO2(B). Furthermore, there are at least seven additional synthetic polymorphs of TiO2. Rutile is reported to be the thermodynamically stable form of TiO2. However, if the crystal dimensions drop below ca. 10–20 nm, anatase becomes the stable polymorph of TiO2. This is reminiscent of the allotropic forms of carbon, where thermodynamic stability of diamond/graphite, reportedly flips too in the nano-world [4].

Figure 2 shows the calculated positions of CBM/VBM for eight common titania polymorphs related to the position of the redox potentials of H+/H2 and O2/H2O [5]. A prototype diagram of this kind (quoting experimental data for TiO2, SnO2, ZnO, GaAs, GaP, CdSe, CdS, and SiC) was presented in 1975 by Gleria and Memming [6]. The motivation for comparing the band edges with electrochemical potentials of water is obvious: if these redox potentials are located at positions, which are inside the band gap, the direct photoelectrolysis of water is possible without external bias. More specifically, the bias-free photoelectrolysis of water requires that the conduction band minimum (CBM) is higher than the energy corresponding to the H+/H2 redox potential, and the valence band maximum (VBM) is lower than that of the O2/H2O redox potential.

Fig. 2
figure 2

Positions of conduction band (CB) and valence band (VB) calculated by density functional theory (DFT) for eight different TiO2 polymorphs. (The α-PbO2 (columbite)-type phase of titania is sometimes labeled TiO2(II) or α-TiO2.) The positions are referenced to the e-vacuum scale (left axis) and to the scale of standard electrochemical potentials (vs. SHE; right axis). The band positions are compared with the levels corresponding to redox potentials of H+/H2 and O2/H2O in aqueous medium at pH≈0. Adapted with permission from [16]. Copyright (2015) American Chemical Society

The discovery of “bias-free” electrolysis of water at a photoexcited rutile single crystal anode and Pt-cathode is habitually credited to Fujishima and Honda [7], despite Boddy [8] published a very similar work four years before this seminal paper appeared. (In fact, 5 years, if we count the Dallas Meeting of the Electrochemical Society in 1967.) Another problem of this famous work is the suspected omission of “chemical bias” originating from the pH-gradient in the cell. In fact, rutile appears to have too low CBM to split water effectively (cf. Fig. 2 and ref. [9] for detailed discussion).

Diagrams showing CBM/VBM of common semiconductors appear in almost every textbook or review article dealing with semiconductor electrochemistry, and in many special papers, too. It should be noted that authors often omit citation to where the band energies come from. (The pioneering paper [6] is a rare exception to this rule.) Though being so popular, these diagrams are also sources of numerous problems.

The first issue is the energy scale: physicists use the energy of electron at rest in vacuum (EVAC) as their reference zero (Figs. 1 and 2, left axis). Electrochemists use the standard hydrogen electrode (SHE) as their reference zero (Fig. 2, right axis). These two scales are difficult to interrelate, even if we forget that energy and potential are different physical quantities. Furthermore, the relation of both scales requires adopting the concept of “absolute electrode potential,” which, for fundamental reasons, cannot be expressed accurately. A practical way-out is the IUPAC recommendation by Trasatti [10], to use the value of − 4.44 ± 0.02 eV for the absolute potential of SHE at 298.15 K. However, others quote different numbers, e.g., − 4.5 eV [3]. Eventually, students are confused by the fact that a downshift of an energy level in the physical scale means an upshift in the electrochemical scale (cf. the arrows in Fig. 2).

Another formal flaw is that some authors (including the pioneers [6]) used the normal hydrogen electrode (NHE), instead of SHE for indexing their band diagrams. Though the difference between SHE and NHE is small (≈5.7 mV), we should avoid NHE because it is not a recognized electrochemical standard [11]. Particularly in the discussion of water splitting, a practical reference system is the so-called reversible hydrogen electrode (RHE). The potential of RHE is:

$${V}_{\mathrm{RHE}}={V}_{0}+\frac{RT}{F}\mathrm{ln}\frac{{a}_{{\mathrm{H}}^{+}}}{({p}_{\mathrm{H}2}/{p}_{0}{)}^{1/2}}\cong -0.059\cdot \mathrm{pH}\hspace{1em}[\mathrm{V}]$$

V0 is the standard potential of H+(aq)/H2(g) redox couple (defined as 0.000 V at all temperatures), R is the gas constant, F is Faraday constant, aH+ is the activity of H+(aq), pH2 is the fugacity of H2(g), and p0 is the standard pressure (1 bar). For a detailed discussion of SHE and RHE see [12]. The RHE scale is useful, e.g., for presenting the flatband potential, Vfb which is equivalent to the Fermi level position at zero band bending (EF,fb):

$${E}_{\mathrm{F},\mathrm{fb}}= -{\varphi }_{\mathrm{fb}}=e{V}_{0}^{\mathrm{SHE}}-{eV}_{\mathrm{fb} }={E}_{\mathrm{CBM}}-{\xi }_{\mathrm{nb}}$$

V0SHE is the potential of SHE in the absolute scale; V0SHE ≈ − 4.44 V [13]. The entry φfb is the work function derived from the flatband potential (also called “electrochemical work function”) [14]. There is a common mistake in the literature that electrode potentials on the RHE scale are recalculated to the absolute scale using the − 4.44 V value. This is valid only if the experiment was carried out at pH 0; at another pH, one must properly recalculate from RHE to SHE (Eq. 3). The second problem associated with Eqs. 3 and 4 is that the electrochemical work function, φfb should be correctly calculated for pH corresponding to the point of zero-charge of the given semiconductor (Table 1) [15]. This is a non-trivial task, because the Vfb = Vfb(pH) function is complicated and material-specific (see below and Table 1).

Considering Eq. (3), one could argue that positioning the energy level of H+/H2 above CBM could be simply carried out by decreasing the pH. However, the idea of “pH engineering” is a bit problematic. The band edges (CBM/VBM) are reported to move with pH in the same way, due to the acidobasic equilibria (protonation/hydroxylation) at the oxide semiconductor surfaces.

The assumption of parallel Nernstian shifts of CBM/VBM and hydrogen (oxygen) redox potentials may or may not be true. Patel et al. [16] showed that there are semiconductor electrodes, such as ZnO thin films, whose CBMs/VBMs are virtually pH-independent. (This work actually analyzed flatband potentials, not CBMs, but both quantities differ just by a constant, ζnb.) The physical reason for this anomaly has not yet been clearly elucidated; one hypothesis is based on the finding that the abundant crystal face (0001) on ZnO (wurtzite) can be capped either by O atoms or Zn-atoms, and this induces a varying surface polarity [16].

Yet another fundamental problem of the energy diagrams (Figs. 1 and 2) is that the CBM, VBM, and work functions are trivially regarded as material constants, independent of experimental or theoretical techniques used for their determination. However, this is not true. A standard technique to measure work function and VBM is the ultraviolet photoelectron spectroscopy (UPS) and X-ray photoelectron spectroscopy (XPS) in ultrahigh vacuum. Actual experimental values, e.g., for the work function of the TiO2 anatase (001) surface, fluctuated between 3.61 and 6.76 eV depending on details of sample cleaning and pretreatment [17]. The chaos is further boosted in polycrystalline samples. For instance, Zhu et al. [18] positioned the CBM of polycrystalline rutile slightly below that of anatase, contradicting most UPS/XPS works of others [19,20,21].

Mansfeldova et al. [15] revisited the problem by using several experimental methods for testing of four different TiO2 surfaces, viz. anatase (101), anatase (001), rutile (001), and brookite (100). Figure 3 shows example data for anatase and rutile. In accord with the “mainstream” literature, rutile had smaller work function than anatase from UPS. This finding was reproduced by the near-ambient-pressure (NAP) UPS in the presence of 0.5 mbar of H2O (g), by Kelvin probe measurements in ambient air, and by the flatband potentials in acetonitrile electrolyte solution. But in contrast to aprotic medium, the φfb of rutile was larger than that of anatase in an aqueous electrolyte solution (Fig. 3).

Fig. 3
figure 3

The experimental work functions for single crystal surfaces determined by ultraviolet photoelectron spectroscopy (UPS), Kelvin probe (KP), near-ambient pressure UPS (NAP-UPS), and by Mott-Schottky plots from electrochemical impedance spectra (EIS) measured in acetonitrile or aqueous electrolyte solutions. TiO2(A) is anatase (101) face (red points); TiO2(R) is rutile (001) face (black points). Data reprinted with permission from [15]. Copyright (2021) American Chemical Society. The previously published plot is here updated by new data for SnO2 (cassiterite) (001) (blue stars) [23, 25] and for ZnO (wurtzite) [14, 24]. Brown hexagons are for the Zn-terminated (0001) face and yellow hexagons for the O-terminated (\(000\overline{1}\)) face

Deak et al. [22] proposed that flipping of the band alignment of anatase/rutile in aqueous electrolyte solution is caused by dissociative adsorption of water (cf. right part of Fig. 3). The histogram of work functions is updated for SnO2 (cassiterite) (001) and for ZnO (wurtzite) from other works [14, 23,24,25]. Specifically, for ZnO, we can distinguish slightly different values for the O-terminated and Zn-terminated (0001) faces [14].

The crucial information is that the work functions and the corresponding CBMs fluctuate over a range of more than 1 eV, even on the well-defined single crystal surfaces, depending on experimental techniques and the actual sample environment. This makes an appeal for cautious discussion of these energy levels in textbooks and special papers. Also, care should be taken when using, e.g., tabled data from various handbooks. The only quantity, which is robust enough (i.e., the “true” material constant), is the band-gap, EBG (Table 1). It is conveniently measured by a Tauc plot or by an electrochemical Tauc plot (for details, see [26]).

Determination of flatband potential and donor concentration by Mott-Schottky analysis

The flatband potential, Vfb can be determined by various spectro/photo/electrochemical techniques [16, 27], but the so-called Mott-Schottky analysis is surely the most popular one. It is based on the measurement of potential-dependent capacitance (C) at a semiconductor/electrolyte solution interface. In one single experiment, we get two useful parameters: the flatband potential and the concentration of majority charge carriers, i.e., donors in the case of n-type semiconductors, ND. The Mott-Schottky equation for this interface reads:

$$\frac{1}{{C}^{2}}=\left(\frac{2}{e{{\varepsilon }_{0}{\varepsilon }_{\mathrm{r}}N}_{\mathrm{D}}}\right)\left({V}_{\mathrm{app}}-{V}_{\mathrm{fb}}-\frac{{k}_{\mathrm{B}}T}{e}\right)+\frac{1}{{C}_{\mathrm{H}}^{2}}$$

ε0 is the permittivity of free space, εr is the dielectric constant (Table 1), and Vapp is the applied potential. The Helmholtz capacitance, CH, is assumed to be of the order of tens of µF/cm2. It is often supposed to be much larger than the space-charge capacitance, thus causing negligible contribution to Eq. 5. This may or may not be true.

The overall capacitance, C, is determined by electrochemical impedance spectroscopy (EIS). The simplest variant, which is embedded in software of some potentiostats with frequency–response analyzers, is the calculation of C at a fixed circular frequency, ω. Other frequencies will give, almost always, different C values, and this leads to a conceptually problematic finding of frequency dispersion of Mott-Schottky plots [28]. The dispersion is sometimes discussed in terms of “structural perfection” of the semiconductor, but this perception is questionable, too. One could ask: why the Vfb and ND values of good samples should be frequency-dependent?

A straightforward way out is the fitting of the complete impedance spectrum, determined at all used frequencies, to certain Randles-type equivalent circuit. The constant phase element (CPE) is usually preferred over a simple capacitor particularly for polycrystalline thin films (for an overview of equivalent circuits see [29, 30]; for a general discussion of CPE, see [31]). The impedance of CPE equals [15, 23, 31]:

$${Z}_{\mathrm{CPE}}={B}^{-1}{(i\omega )}^{-\beta }$$

B (admittance pre-factor) and β are the frequency-independent parameters of the CPE. The interfacial capacitance, C is then calculated from:

$$C=\frac{{({R}_{\mathrm{CT}}\cdot B)}^{1/\beta }}{{R}_{\mathrm{CT}}}$$

RCT is the charge-transfer resistance, which is deconvoluted from the EIS fitting, too. The measurement must be carried out on well-defined surfaces, ideally on single crystal electrodes. (In this case, the use of CPE (Eqs. 6 and 7) seems to be overestimated, but CPE converts to a pure capacitor for β = 1.) Polycrystalline electrodes (e.g., thin films on substrates) are also acceptable, provided they are free from pinholes. This can be simply checked by voltammetric blocking tests [23, 32,33,34,35]. On the other hand, porous electrodes, such as nanospheres [36] nanorods [36, 37] or nanotubes [16] are, in general, too complicated (if not inapplicable) for the Mott-Schottky analysis. Theoretical treatment was pioneered by Bisquert et al. [36] and Peter et al. [37]; general discussions were presented by Sivula [38] and Hankin et al. [30]. In certain cases (e.g., in amorphous thin films), the single-frequency impedance could still provide useful information [39], but the deconvolution of a complete EIS-spectrum is generally preferable for high-quality crystalline thin films and single crystal electrodes [30].

Strictly speaking, the assumption about the overall perfection of single crystal electrodes is unfaithful, too. For instance, the TiO2 (anatase) single crystal is usually purchased, while manufacturers cut it from natural minerals. These, of course, contain impurities, such as Fe. Iron tends to segregate upon thermal treatment, up to even overgrowth of iron oxide on the TiO2 surface [40]. The laboratory growth of sufficiently large anatase single crystal is uneasy and time-consuming [41]. Furthermore, the synthesis requires an addition of structure-directing impurities (Al, Nb) in concentrations ≈0.2% [40, 41]. Eventually, the crystal is not “atomically flat,” but can contain terraces [42].

Patel et al. [16] compiled flatband potentials in aqueous media (505 values for TiO2, 97 values for SnO2, and 223 values for ZnO). A striking output from their analysis is the huge spread in the literature data (Fig. 4). For instance, the flatband potentials for TiO2 varied over a range as large as > 1.5 V (Fig. 4b), clearly documenting that some values are false. Indeed, the distribution for TiO2 is narrowed by eliminating data for anatase nanotubes, which are principally unsuitable for these studies (see above and Fig. 4d). The width of the depletion layer (W) on a flat n-type semiconductor surface equals:

Fig. 4
figure 4

Histograms of the flatband potential distribution and the corresponding Gaussian fits (if relevant) for a single crystals TiO2 (anatase, rutile) and ZnO (wurtzite), b different phases of TiO2 in all morphologies, c all forms of SnO2, and d TiO2 as in chart (b), but without anatase nanotube data points. Reprinted with permission from [16]. Copyright (2022) AIP Publishing

$$W={\left(\frac{2{\varepsilon }_{0}{\varepsilon }_{\mathrm{r}}}{e{N}_{\mathrm{D}}}\right)}^{1/2}{\left({V}_{\mathrm{app}}-{V}_{\mathrm{fb}}-\frac{{k}_{\mathrm{B}}T}{e}\right)}^{1/2}$$

Table 1 compiles the limiting values (Wlim) calculated for ND = NC and for the applied potential of 1 V referenced to Vfb (the band bending). The calculated values for TiO2, SnO2, and ZnO are from 3 to 21 nm (Table 1). This is the minimum film thickness to fully accommodate the space charge layer, thus allowing for an unperturbed measurement of EIS. Yet, the penetration of the depletion layer into the substrate can sometimes be traced on good-quality films [34].

The space-charge layer thickness is conceptually related to the Debye length (LD) which is a distance over which the charge carriers screen the local electrical field:

$${L}_{\mathrm{D}}={\left(\frac{{\varepsilon }_{0}{\varepsilon }_{\mathrm{r}} {{k}_{\mathrm{B}} T}}{{e}^{2}{N}_{\mathrm{D}}}\right)}^{1/2}$$

For low-doped spherical nanoparticles, the Debye length, LD, is much larger than the particle radius, i.e., the band-bending is unlikely. This is further complicated in mesoporous thin films, used, e.g., in dye-sensitized (Grätzel) solar cells [43, 44], in which nanoparticles interconnect and the electrolyte solution resides in mesopores. Bisquert et al. [36] provided rationale for negligible band bending in this case. Hence, the mesoporous film is yet another system, in which the Mott-Schottky analysis fails for principal reasons [45].

Incorrect flatband potentials are not the only issue of the Mott-Schottky plots. The analysis of otherwise good samples (e.g., non-porous thin films) tends to overestimate the donor densities as compared, e.g., to Hall-effect measurements [32]. More specifically, the NC calculated from Eq. 2 (Table 1) gives the upper estimate of ND assuming the semiconductor is still non-degenerated. The limiting value means that the Fermi level coincides with CBM (ζnb = 0).

Values of ND exceeding NC would indicate a degenerated semiconductor, which is hardly the case in most studies. For instance, SnO2 thin films do not show any metal-like electrochemistry (like, e.g., the F-doped SnO2, FTO), but instead—a perfectly rectifying behavior [23, 32, 33]). This contradiction is implicitly present in many literature values of ND [16, 38]. Another point to highlight is that the flatband potential provides the position of the Fermi level (Eq. 2) not the conduction band edge. This mistake appears frequently in the literature (for collection of papers infected by this error, see [16]).

Calculation of work functions and band edges by DFT

Most DFT (density function theory) calculations are made for perfect single crystals surrounded by vacuum, which is usually not articulated in the specific works. Calculations of two interacting phases [20, 46], non-stoichiometric surfaces [47], small nanocrystals [48], or crystals interacting with, e.g., water [22] are less often encountered in the literature. (Strictly speaking, the oxide semiconductors used in electrochemistry are hardly stoichiometric at all; the n-doping is often attributed to a small oxygen deficiency, e.g., TiO2-x; x ≈ 0.01.) Theoretical modelling by Zhang and Dong [20] revealed that the interface itself can reverse the CBM alignment of the coupled and isolated TiO2 phases. Analogously, Ko et al. [48] predicted that the CBM alignment of anatase/rutile will flip for nanocrystals below ≈15 nm in size.

Calculations for “ideal” conditions and bulk crystals systematically put the CBM of TiO2 (anatase) slightly below that of rutile (as in Fig. 2). This prediction is confirmed by a majority of UPS/XPS experiments, which are usually, but not necessarily always, made in ultrahigh vacuum [15, 17, 21]. Resolving the controversy about band alignment between anatase and rutile TiO2 would require computational modelling of more realistic systems, ideally a semiconductor surface contacting an electrolyte solution. Unfortunately, treatment of this electrochemical interface is beyond the capabilities of the current super-computers.

A drastic simplification of the Helmholtz layer by just two monolayers of water molecules provides a model, which can be reasonably treated by DFT calculations. Interestingly, the flipping of CBM positions in TiO2 anatase/rutile is confirmed even by this primitive model. More specifically, the electrochemical interface composed of an anatase (101) surface covered by one monolayer of dissociated water and one monolayer of molecular water above it (cf. Fig. 3) provides a plausible computational background for the CBMs flipping [22].

Photoelectrochemistry: beyond the Gärtner-Butler model

Theory of electron transfer at the semiconductor/electrolyte solution interface was developed in 1959–1966 by W.W. Gärtner and H. Gerischer, and later updated by M. A. Butler. It has been very useful and didactically rewarding, as it elegantly explained photoelectrochemical reactions occurring on semiconductor electrodes, illuminated by photons with energies larger than EBG. The model elucidates why and how the faradaic processes are driven by the electron/hole separation (exciton dissociation) in the built-in electrical field of the space-charge layer and the subsequent drifting of photoholes to the interface (Fig. 5a).

Fig. 5
figure 5

Band bending and charge carrier dynamics at the photoexcited semiconductor contacting electrolyte solution. Red dashed arrows indicate recombination. a The exciton dissociation occurs exclusively in the built-in electrical field of the depletion layer (thickness W). b The exciton dissociation occurs also outside the depletion layer. Some photogenerated holes are transported towards the interface by diffusion. Lp is the hole diffusion length. Reprinted with permission from [93] Copyright (2016) American Chemical Society. c Scheme of a photoelectrochemical cell under illumination. The quasi-Fermi levels of electrons and holes are annotated as εFC and εFV, respectively. They merge and align with the respective Fermi levels of the metallic contacts at both terminals of the cell. Vph is the photovoltage. Reprinted with permission from [51]. Copyright (2022) the Royal Society of Chemistry

More precisely, in addition to the holes generated inside the space charge region, the classical model also considered holes in the close vicinity of the depletion layer. These holes can still reach the interface by diffusion, and contribute to the photocurrent at a probability P(x):


x is distance from the interface, and Lp is the hole diffusion length. Within this approximation, the photocurrent on thin-film electrodes does not saturate, when the film thicknesses exceed the depletion layer width, W (see Eq. 8), but at the thicknesses exceeding the photon-attenuation depth. It is defined as a thickness, at which the optical density of 1 (i.e., 90% light absorption) is achieved for incident photons [49]. This diffusion-drift model is schematized in Fig. 5b.

In the last decade, additional studies have shown that the diffusion-drift model was still not sufficient for description of some systems. For instance, ZnO thin-film electrodes exhibited photocurrents, which did not saturate for film thicknesses equal to the photon attenuation depth, but increased further in thicker films [49]. The deviation was attributed to the long-range backward diffusion of excitons. This effect is important for semiconductors with large exciton binding energies (such as ZnO; ≈60 meV), but small for semiconductors with weakly bond excitons (e.g., TiO2 and Fe2O3) [49]. (Note, however, a conflicting work about TiO2 anatase single crystal and nanoparticles [50]).

Recently, Schleuning et al. [51] presented yet another concept to account for deviations from the Gärtner-Butler model. Figure 5c shows a scheme of the full photoelectrochemical cell for water splitting. This model highlights the role of electron- or hole-selective contacts, which actually control the photovoltage, Vph. In other words, the gradient of quasi-Fermi levels of electrons and holes is the fundamental driving force for these photoelectrochemical reactions. Moreover, many devices operate without any significant built-in electric fields (e.g., dye-sensitized solar cells; see below).

Applications: photocatalysis and superhydrophilicity

Titania is the key material for photocatalysis, and it has been intensively debated how the band structure influences its activity. In general, rutile is regarded better reductant, and anatase is a better oxidant in photocatalytic reactions [52]. This resonates with the smaller work function of rutile, which is observed in majority of experiments and calculations (see Figs. 2 and 3 and discussion thereof). The photocatalytic applications often favor mixed-phase TiO2 (anatase/rutile) composites, from which the P25 (Degussa/Evonik) is surely the most popular benchmark material. A systematic study by Yaemsunthorn et al. [52] confirmed that the anatase/rutile composites exhibit synergistic effects in photocatalysis, as compared to pure phases.

The simplest explanation of this synergy follows from the band alignment at the interface (Fig. 6) [53]. It provides additional driving force for exciton dissociation, in which the photoexcited electrons are pushed towards the CBM of anatase and photoholes towards the VBM of rutile. Nevertheless, other factors need to be considered, too. They comprise efficiency of charge separation, lifetime of photogenerated charges, light absorption, redox characteristics, porosity, surface area, and the specific reaction/s, for which the photocatalyst is optimized [52].

Fig. 6
figure 6

Proposed band alignment for the rutile and anatase forms of TiO2 considering the direct (3.8 eV) and indirect (3.2 eV) band gaps for anatase. Data reprinted with permission from [53]. Copyright (2016) American Chemical Society

The second issue, which is often ignored, is the flipping of flatband potentials (CBM positions) at the aqueous electrochemical interfaces [15]. A rare exception to this rule is the work of Nosaka and Nosaka [53]. They proposed that the Vfb for anatase, measured by Mott-Schottky plot, is related to the minimum direct band gap of ≈3.8 eV (Fig. 6). The direct CBM is hit, if the EIS-measurement sweeps potentials from lower to higher values. This explanation would elegantly address the contractions, even quantitatively: Fig. 6 confirms that the direct CBM of anatase is by 0.2 eV above the CBM of rutile. Nevertheless, this idea still requires experimental verification, whether or not the scan direction is really that important. Another objection is that the reference studies were made on high-quality single crystals, but photocatalysts are usually imperfect materials, up to suspended nanoparticles, which are outside any electrochemical control. Small nanoparticles and interacting phases can exhibit different anatase/rutile alignment, too [20, 46, 48].

The synergic effect, which improves the photocatalytic activity of TiO2, can be, however, detrimental in other applications, such as in cosmetics and cotton textiles [54]. For instance, larger toxicity of mixed-phase TiO2 manifests itself by enhanced injury of human skin during sunlight exposure, which is proven by both in vitro and in vivo experiments [54].

The photoinduced wettability of the TiO2 surface (“superhydrophilicity”) is another issue in photocatalysis. Since its discovery in 1997, it generated significant experimental and theoretical efforts, aiming at explanation of this spectacular effect. It manifests itself as perfect spreading of water droplets over photo-treated titania, which attain, eventually, a contact angle close to 0° [55]. Various practical applications of the TiO2-coated glass, e.g., for antifogging windows and mirrors, are at hand.

The effect was attributed to structural changes of the TiO2/H2O interface, re-arrangement of hydrogen bonds, H2O-clusters etc. XPS and IR-spectroscopy supported a partial photocatalytic removal of hydrocarbon impurities, too [55]. Nevertheless, a subsequent work by Diebold et al. [56] elegantly clarified, that the UV-induced superhydrophilicity in ambient environment is actually caused by selective adsorption/photodegradation of airborne carboxylic acids, rather than by structural modifications of the TiO2 surface. This approach elucidated also the reverse dark reaction, which is hard to understand in terms of the water rearrangement on the surface.

Applications: dye-sensitized (Grätzel) solar cell

The discovery of a dye-sensitized solar cell (DSSC) [57], also called the Grätzel cell, triggered significant scientific and industrial efforts during the last three decades [43, 58]. The record efficiency of DSSCs is currently 15.2% [58]. All the discussed oxide semiconductors (TiO2, SnO2, ZnO) are useful as the photoanode materials, but the nanocrystalline TiO2 (anatase) in mesoporous thin film clearly dominates. The photoanode is sensitized to visible light by a suitable dye, which is interfaced to an electrolyte redox mediator. The latter serves for reductive regeneration of the dye, which becomes oxidized after electron injection from LUMO into the CBM of TiO2 (Fig. 7). The open circuit photovoltage (VOC) of the solar cell under sunlight equals:


nph is the number of photogenerated electrons in a semiconductor, and Mredox is the standard redox potential of the mediator. The open-circuit photovoltage is then determined from the difference between the maximum achievable quasi-Fermi level of electrons in the semiconductor film (the sum of the first two terms in Eq. 11) and the redox potential of the mediator (the third term in Eq. 11). Typical mediators are:

Fig. 7
figure 7

a Cyclic voltammograms in dichloromethane electrolyte solution; from top to bottom: Cu(tmby)2+, ditto upon addition of ferrocene (Fc, red dashed), ND-dye (blue), ditto upon addition of ferrocene (blue dashed), mixture of ND + Cu(tmby)2+ + Fc (magenta). The last voltammogram (black) is for the ND-dye adsorbed on the TiO2/FTO electrode. For recalculation, the Fc+/Fc potential was set to 0.624 V vs. SHE. b Schematic diagram of the energy levels of TiO2, ND-dye, and three typical redox mediators. c The formula of ND-dye and photograph of ND@TiO2/FTO electrodes with the dye in in the ground state (orange, bottom) and after the electrochemical oxidation (black, top). Adapted with permission from [62]. Copyright (2018) John Wiley and Sons

$${{\mathrm{I}}_{3}}^{-}+2{\mathrm{e}}^{-}\to 3\mathrm{I}^{-}\;{M}_{redox}=0.35\ \mathrm{V}$$
$${[\mathrm{Co}{\left(\mathrm{bpy}\right)}_{3}]}^{3+}+{\mathrm{e}}^{-}\to {[\mathrm{Co}{\left(\mathrm{bpy}\right)}_{3}]}^{2+}\;{M}_{redox}=0.56\ \mathrm{V}$$
$${\mathrm{Cu}{(\mathrm{tmby})}_{2}}^{2+}+{\mathrm{e}}^{-}\to {\mathrm{Cu}{(\mathrm{tmby})}_{2}}^{+}\;{M}_{redox}=0.87\ \mathrm{V}$$
$${\mathrm{Cu}{(\mathrm{dmby})}_{2}}^{2+}+{\mathrm{e}}^{-}\to {\mathrm{Cu}{(\mathrm{dmby})}_{2}}^{+}\;{M}_{redox}=0.97\ \mathrm{V}$$

bpy is the 2,2′-bipyridine, tmby is the 4.4′,6,6'-tetramethyl-2,2′-bipyridine, and dmby is the 6,6′-dimethyl-2,2′-bipyridine. Mediators beyond I3/I were developed in parallel with novel donor-π-acceptor dyes (such as ND in Fig. 7). This allows enhancement of VOC of the solar cell (Eq. 11 and Fig. 7). The Mredox is theoretically limited only by the redox potential of the dye’s ground state (≈1 V vs. SHE). Interestingly, the driving force for dye regeneration can be as small as ≈0.1–0.2 V in certain Cu2+/+-mediated DSSCs (cf. Figure 7 and [58, 59]).

The second possible strategy for boosting VOC is the upshift of the quasi-Fermi level of the semiconductor photoanode. It can be achieved by electrolyte additives [60] or by engineering of the semiconductor’s CBM [61]. Unfortunately, most additives have detrimental effect on the ionic diffusion and charge-transfer rate at the counter-electrode, specifically for the Cu2+/+-mediators, and this problem is yet to be solved [60]. The other issue is the ubiquitous uncertainty in the position of Fermi level of the semiconductor (cf. Figure 3). The value in Fig. 7 is just a guess (− 0.5 V vs. SHE in the electrochemical scale, translating into the work function of ≈3.9 eV [62,63,64]). The experimental φfb for single crystal anatase (101) face is about 3.8 eV (for acetonitrile electrolyte solution; Fig. 3), but a more authentic measurement at polycrystalline thin film anatase in the DSSC-electrolyte solutions yielded values from 4.16 to 4.27 eV [33].

Figure 7 also demonstrates the frequent error of using the redox potentials of dyes in solution instead of the redox potentials of dyes adsorbed on the TiO2 photoanode. The difference could even generate a curious conclusion about “negative driving force” for dye regeneration. For instance, the standard redox potential of ND-dye in solution is 0.87 V (by coincidence identical to the Mredox of Cu(tmby)22+/+), but the correctly measured value for ND@TiO2 is 1.05 V (Fig. 7a). This approach obviously removes the misconception of zero or negative driving force. In any case, the high open-circuit photovoltages of ca. 1.1 V are now achievable in DSSCs. They are well comparable to those of the best performing perovskite solar cells [63].

Applications: perovskite solar cells

Perovskite solar cell (PSC) has demonstrated an unprecedented efficiency jump from 3.8% in the pioneering work in 2009 to the current values exceeding 26% [65], which already attack the Shockley-Queisser limit. PSC is sometimes called the “young sister” of dye-sensitized solar cell to highlight their similar principles [44]. While electrochemistry is a key methodology in DSSCs [44], and the first PSCs were actually pure electrochemical (liquid-junction) devices, this strategy soon became a dead end in PSC [65]. In fact, the key discovery behind the boom of PSC was a replacement of liquid electrolyte solutions by a solid hole-conductor. This finding was made in 2012 independently and almost simultaneously by four prominent scientists in DSSC research, viz. Grätzel and Park [66] and Snaith and Miyasaka [67]. We should note that the replacement of liquid electrolyte solutions by a solid hole-conductor was known long before the “PSC-era.” It was actually used in the solid-state DSSC, which was discovered by Grätzel el al. [68] in 1998.

PSC can be schematized as a diode, in which the light absorber (the generic material is CH3NH3PbI3 perovskite) is sandwiched between an electron-selective contact (TiO2, SnO2, or ZnO) and the hole-conductor capped by a hole-selective contact. Hence, the architecture of PSC can be conceived as a prototypical p-i-n solar cell, in which the intrinsic semiconductor, i.e., perovskite (i), is positioned between the n-/p-selective contacts. The first and still the top successful hole conductor is N2,N2,N2′,N2′,N7,N7,N7′,N7′-octakis(4-methoxyphenyl)-9,9′-spiro-bi[9H-fluorene]-2,2′,7,7′-tetramine (abbreviated spiro-OMeTAD) (see Fig. 8a). It was brought to the field from the solid-state DSSCs, but initially from the light-emitting diodes [68]. Another promising hole conductor is CuSCN [65, 69].

Fig. 8
figure 8

a Molecular formula of spiro-OMeTAD. b Cyclic voltammogram in dichloromethane electrolyte solution of spiro-OMeTAD on FTO electrode (dashed black curve) and on FTO coated with thin-film of TiO2 made by atomic layer deposition (ALD, the film thickness is indicated in annotations). The red curve is for the 6-nm TiO2 film after its calcination at 500 °C, 1 h in air. Thermal treatment causes cracking of the film and re-appearance of voltammetric features of spiro-OMeTAD. Potentials are referenced against the Ag-wire pseudo-reference electrode. Reprinted with permission from [62]. Copyright (2018) John Wiley and Sons

As in DSSCs, titania thin-film is still the material of the first choice for fabricating the electron-selective layer. In addition to single-phase titania layers, also double layers, e.g., anatase/rutile were employed [18]. The motivation was a better band alignment of CBMs, but this idea is a bit problematic (vide infra). Furthermore, the cited work [18] reports on a curiously opposite anatase/rutile CBM stacking, conflicting most other works [15, 19,20,21, 52, 53]. The electron-selective (blocking) layers for DSSC/PSC are tested for their pinhole-free texture. This is mandatory not only for Mott-Schottky analyses (see above) but also for preventing the contact of the negative terminal (FTO) with the electrolyte mediator or hole conductor. The spiro-OMeTAD can also serve as a suitable redox probe, i.e., an alternative to the common Fe(CN)63−/4−. Figure 8b demonstrates a perfectly rectifying behavior of ultrathin TiO2 layers made by atomic layer deposition (ALD). Unfortunately, these layers are sensitive to cracking upon heat treatment [34, 70].

Some authors prefer SnO2 for the e-selective transport layers in PSC. They do not crack upon calcination [32] and have ca. 100-times larger electron mobility [71]. Also the larger EBG of SnO2 (Table 1) improves stability against photodegradation under solar light [72]. The quantum dot-SnO2 provides still larger EBG of ≈4 eV, thanks to quantum-size effect. This is beneficial for improved electron capture and stability [73].

It is tempting to discuss the open-circuit photovoltage of PSC in terms of the electronic band diagrams. More specifically, some authors tried to compare the CBM/VBM of perovskite (e.g., − 3.93/ − 5.49 eV, respectively, for CH3NH3PbI3) with the VBM of hole conductor (e.g., − 5.2 eV for spiro-OMeTAD) and the CBMs of the electron-selective contacts (TiO2, SnO2, or ZnO; Table 1). The motivation was optimization of the PSC by conduction-band engineering of the electron selective layers, either single-phase or double-phase (e.g., TiO2(A)/TiO2(R) or TiO2/SnO2) [18, 61, 65, 74]. Though the idea looks rational, and works reasonably well in the case of DSSCs (cf. previous chapter and Fig. 7), it is quite questionable in PSCs. In fact, the open-circuit photovoltages of PSCs employing TiO2, SnO2, or ZnO as the e-selective contacts are all about the same (around 1.1 V), despite the CBM of SnO2 is markedly lower [65, 71]. Obviously, there must be other factors, beyond the band alignment, which control the photopotential of PSC.

For instance, the often-ignored interface between the transparent conductive oxide (e.g., FTO) and e-transport layer (TiO2, SnO2, ZnO…) deserves attention. Walter et al. [75] investigated the parasitic Schottky junction at this interface, which is responsible for conductance loses (TiO2 was quite susceptible to this problem). Unfortunately, the discussion requires quantification of the Fermi level misalignment between, e.g., TiO2 and FTO, which is a thorny issue (cf. Figure 3).

Applications: Li-batteries

SnO2 and ZnO are attractive materials for the negative electrode of Li-battery, thanks to their large charge capacity. It corresponds to the conversion reactions:

$${\mathrm{SnO}}_{2}+4{\mathrm{Li}}^{+}+{4\mathrm{e}}^{-}\to \mathrm{Sn}+2 {\mathrm{Li}}_{2}\mathrm{O}\;[711\ \mathrm{mAh}/\mathrm{g}]$$
$$\mathrm{Sn}+{\mathrm{xLi}}^{+}+{\mathrm{xe}}^{-}\rightleftarrows {\mathrm{Li}}_{\mathrm{x}}\mathrm{Sn}\;[\le 783\ \mathrm{mAh}/\mathrm{g};\ \mathrm{x}\le 4.4]$$
$$\mathrm{ZnO}+2{\mathrm{Li}}^{+}+{2\mathrm{e}}^{-} \rightleftarrows \mathrm{Zn}+{\mathrm{Li}}_{2}\mathrm{O}\;[658\ \mathrm{mAh}/\mathrm{g}]$$
$$\mathrm{Zn}+{\mathrm{xLi}}^{+}+{\mathrm{xe}}^{-} \rightleftarrows \mathrm{Zn}+{\mathrm{Li}}_{2}\mathrm{O}\;[\le 329\ \mathrm{mAh}/\mathrm{g};\ \mathrm{x}\le 1]$$

The conversion reactions are hardly understood in terms of the electronic band structure. On the other hand, TiO2 (in all its naturally occurring forms, i.e., anatase, rutile, brookite, and TiO2(B)) is active in the topotactic Li-accommodation:

$${\mathrm{TiO}}_{2}+\mathrm{x }\left({\mathrm{Li}}^{+}+{\mathrm{e}}^{-}\right)\to {\mathrm{Li}}_{\mathrm{x}}{\mathrm{TiO}}_{2} \left[168\ \mathrm{ mAh}/\mathrm{g\ for\ x}=0.5\right]$$

The coefficient x varied from 0.1 to 1 for different titania phases [76], but x≈0.5 is most often encountered in the literature. At this point, we can make two terminological notes:

  1. 1.

    The accommodation of lithium in host structures is termed either “insertion” or “intercalation” (from the Latin verb intercalare, used originally for adding extra month, mensis intercalaris, into the Roman calendar). The IUPAC recommendation from 1995 [77] reserved the term “intercalation” for lithium storage in laminar host structures. None of TiO2 polymorphs has layered structure, hence, the term “insertion” is preferable. Nevertheless, the next IUPAC recommendation from 2007 [78] provided softer coding, which allowed the term “intercalation” for any one-, two-, or three-dimensional hosts. Hence, the wording “intercalation into TiO2” is acceptable, though many authors insist traditionally on the term “insertion.”

  2. 2.

    The battery community ubiquitously uses the term anode for what is properly named the “negative electrode” (and conversely, the term cathode for the “positive electrode”). These terms are actually slang words. After all, we teach students that the anode is where the oxidation occurs, and this electrode is negative during both charging and discharging, but it is an anode only during the discharge. (At charging it is, technically, a cathode, i.e., a reduction reaction occurs.)

The Li-insertion, like any cathodic dark reaction on n-type semiconductors, proceeds at potentials ≤ Vfb, when the host material is in the accumulation (quasi-metallic) regime. From the known values of Vfb in Li-containing aprotic medium (Fig. 3) this prediction is correct, at least qualitatively: the difference in formal potentials of Li-insertion into anatase/rutile is about 0.38 V for single crystal electrodes and about 0.5 V for polycrystalline titania [42, 76, 79, 80]. Nevertheless, the assumption that the Li-insertion into TiO2 is triggered at Vfb is incorrect. In fact, big overvoltages downshift the onset potentials for Li-insertion by hundreds of mV [42, 76, 79, 80].

On the other hand, this reasoning works surprisingly well, if TiO2 (anatase) is employed as an additive for the cathode of the Li-sulfur battery. Zlamalova et al. [79] confirmed that the reduction of S8 on anatase starts at 2.1 V vs. Li+/Li. This agrees perfectly with the Vfb measured in the same electrolyte solution, indicating negligible overvoltage of this reaction.

The majority of works on the Li/titania deal with anatase [61, 71, 76, 79,80,81,82,83,84,85]. Attention is paid to kinetic analysis [82, 83], distinction of insertion and (pseudo)capacitive phenomena [84], crystal-face specific Li-insertion activity [42], in situ Raman spectroelectrochemistry with isotopic labeling (16/18O, 6/7Li) [85] up to fabrication of anodes for practical Li-ion batteries [76]. It has been long speculated that small particle size of nanocrystalline anatase is responsible for improved kinetics of Li-storage, but Dahlman et al. [82] showed recently that the situation is more complex. According to their study, the Li-insertion rates depend on the applied overpotential, electrolyte concentration, and initial state of charge. Recently, Tetteh et al. [83] reported on fast Li-storage in a 50 nm sized anatase particle. More precisely, the x-value of ≈0.3 (Eq. 14) was achieved by cyclic voltammetry at 0.1 V/s scan rate (corresponding to C-rate above 100 C).

Errors by the author: some examples (out of many)

In 1993, I co-authored a textbook “Principles of Electrochemistry” [86], which unfortunately, contains many errors discussed above. More specifically, this book presents: (i) the problematic diagram of electronic bands (p. 398, Fig. 5.59), (ii) the oversimplified model of a semiconductor/electrolyte interface (p. 399, Fig. 5.60), (iii) the wrong scheme of dye-sensitized solar cells with band bending in the semiconductor photoanode (p. 404, Fig. 5.63). In the same year, we reported on quantum-size effects in “anatase nanoparticles” having dimensions as low as ≈1 nm [87]. Since the lattice constant (c) of anatase is ≈0.94 nm, one could ask a provocative question, whether our TiO2 particle was still a “crystal?”.

In 2004, we observed two extra peaks (called S-peaks) in the cyclic voltammograms of Li-insertion into anatase, synthesized by hydrothermal growth, and attributed it to a quantum-size confinement in titania nanosheets [88] or to surface charging in well-organized anatase nanostructures [89]. Both ideas were totally wrong; the correct explanation was that the S-peaks were signatures of a monoclinic phase, TiO2(B), which we had overlooked [90].

In 2012, we found that the open-circuit photovoltage of a DSSC employing (001)-oriented anatase TiO2 was by 45 mV larger, than that of the reference cell with ordinary (101)-anatase [91]. The enhancement was attributed to a negative shift in flatband potential. This reasoning was questionable with respect to the poorly defined Vfb in nanoporous materials. The story was revisited [92], and the effect was elucidated by differences in lifetime and diffusion coefficients of electrons. Furthermore, we sometimes used the oversimplified Mott-Schottky plot at single frequency for characterization of anatase single crystals [41, 42].

In 2017, we reported on “metal-like” Ta-doped TiO2 (anatase) exhibiting quasi-reversible cyclic voltammograms of Fe(CN)63−/4− and dimethylviologen redox couples like on FTO [81]. This assumption failed for Ru(bpy)33+/2+, which was idle on a Ta:TiO2 electrode. Similar behavior was observed for ALD-grown SnO2. It provided a rectifying (semiconductor-like) interface for Fe(CN)63−/4− in the as-received (quasi-amorphous) state, but metal-like electrochemistry after the calcination-driven crystallization; Ru(bpy)33+/2+ was electrochemically silent at both electrodes [32]. We proposed an explanation based on a ≈0.5 eV downshift of the Fermi level upon thermal crystallization, which was hopefully correct for SnO2, but hardly applicable for ALD-TiO2 which did not show any marked changes upon thermal treatment [23]. Hence, our “discovery” of a metallic transparent titania electrode remains elusive.


Some technical and formal ambiguities in semiconductor electrochemistry are outlined in this review. Its principal motivation is not the criticism of errors, but to aid students and teachers of electrochemistry. Selected examples of challenging issues are:

  1. (i)

    Determination of flatband potentials and donor concentrations by Mott-Schottky analysis, particularly for nanotextured materials. Huge spread of literature data of flatband potentials of TiO2, SnO2, and ZnO. Unrealistically high concentrations of the majority charge carriers, which can even wrongly predict degenerated semiconductors.

  2. (ii)

    Calculation of work functions and band edges by DFT and ignoring the effects of sample environment, and/or defects in real crystals.

  3. (iii)

    Measurement of work functions and band edges by a single experimental technique only (e.g., by photoelectron spectroscopy, Kelvin probe, or by electrochemistry). Disregarding the inherently poor reproducibility of the values from each individual technique.

  4. (iv)

    Transposition of these problematic data, both theoretical and experimental, into discussions of water splitting, solar fuel generation, solar cells, and Li-ion batteries.

  5. (v)

    The endless contradictory debate about CBM stacking in titania anatase/rutile and its impact to photocatalysis. The elucidation of synergic effects in mixed-phase photocatalysts (e.g., P25).

  6. (vi)

    Application of the Gärtner-Butler model for carrier dynamics in a semiconductor photoanode, disregarding, e.g., the gradient of electrochemical potentials as the driving force for e/h+ separation.

  7. (vii)

    The “superhydrophilicity” in UV-irradiated titania appears to be caused by selective adsorption/photodegradation of airborne carboxylic acids, rather than by structural modifications of the TiO2 surface.