PEC measurements

The photocurrent (j) vs. potential (U) voltammograms are shown in Fig. 1a; the measurements were done under white light-emitting diode (LED) illumination of 80 mW cm−2 (see Methods section for details) at H 2 O 2 concentrations ranging from 0 to 500 mM in alkaline solution (1 M NaOH in deionized water). The photocurrent density, j, is the current measured under illumination after subtraction of the dark current (at the same potential), divided by the aperture area of the PEC cell. At low H 2 O 2 concentrations (5 mM), the photocurrent voltammograms display three regions distinguished by their slope, i.e., weak increase in j with increased U up to point (i), rapid increase from point (i) to point (ii), and moderate increase from point (ii) onwards. At higher H 2 O 2 concentrations (10 mM) j increases almost linearly with U, indicating that the flux of photo-generated holes arriving at the surface is proportional to the applied potential. To distinguish the bias-dependent interfacial charge transfer at the photoanode|electrolyte interface from the bias-dependent hole flux from the bulk to the surface, the photocurrent voltammograms were normalized by the photocurrent obtained at the highest H 2 O 2 concentration (500 mM), for which the surface reaction no longer limits the photocurrent27. The normalized photocurrent voltammograms are depicted in Fig. 1b. They display an unexpected non-monotonous behaviour at low H 2 O 2 concentrations (from 1 to 5 mM) wherein the normalized photocurrent first increases at low potentials, secondly decreases at moderate potentials, thirdly exhibits a steep rise at the onset potential around 1.1 V RHE , and finally converges with the water photo-oxidation current at about 1.5 V RHE .

Fig. 1 Photocurrent voltammograms and intensity-modulated photocurrent spectra at varied H 2 O 2 concentrations. a Photocurrent density as a function of the applied potential under white LED illumination (80 mW cm−2) at different H 2 O 2 concentrations as indicated in the legend. b Normalized photocurrent voltammograms obtained by dividing the photocurrent voltammograms in a by the photocurrent measured at [H 2 O 2 ]= 500 mM, j 500 . Bottom IMPS spectra correspond to: (i) [H 2 O 2 ]=0 mM, U= 1.05 V RHE , (ii) [H 2 O 2 ]=0 mM, U= 1.25 V RHE , (iii) [H 2 O 2 ]= 5 mM, U= 1.05 V RHE , (iv) [H 2 O 2 ]= 5 mM, U= 1.25 V RHE , (v) [H 2 O 2 ]= 500 mM, U= 1.05 V RHE , (vi) [H 2 O 2 ]= 500 mM, U=1.25 V Rhe Full size image

To shed more light into the photocurrent behaviour at different H 2 O 2 concentrations, IMPS measurements were carried out at potentials and H 2 O 2 concentrations marked by points (i) to (vi) in Fig. 1a, b. The IMPS spectra of the complex photocurrent admittance, Y(ω) = j(ω)/Φ(ω), where ω is the ac frequency and Φ is the light intensity, display two main features: upper (positive imaginary part) and lower (negative imaginary part) semicircles. The diameter of a lower semicircle corresponds to hole flux to the surface, whereas the diameter of the upper semicircle corresponds to surface recombination39. In the absence of H 2 O 2 in the electrolyte, the upper semicircle at low potentials (point (i)) is large, indicating strong surface recombination. Notably, the Y(ω) vanishes when ω → 0, indicating that all photo-generated holes arriving at the surface recombine with electrons such that an increase in light intensity does not lead to an increase in photocurrent. At higher potentials (point (ii)), the upper semicircle shrinks, indicating lower surface recombination as usually observed in haematite photoanodes in alkaline solution (without H 2 O 2 ) at high potentials39. The spectra obtained at a high H 2 O 2 concentration (500 mM, points (v) and (vi)), display only the lower semicircle, whereas the upper semicircle disappears both at low and high potentials. This indicates that at high concentrations, H 2 O 2 serves as an effective hole scavenger that suppresses surface recombination as expected27. However, at a low H 2 O 2 concentration (5 mM, points (iii) and (iv)) surface recombination is strong at low potentials (point (iii)) and is suppressed at higher potentials (point (iv)), similarly to the situation without H 2 O 2 (points (i) and (ii), respectively). These analogies indicate that in points (iii) and (iv), Y(ω) is dominated by water photo-oxidation rather than by H 2 O 2 photo-oxidation. This implies that at low H 2 O 2 concentrations, the photocurrent below the onset of water photo-oxidation is limited by the supply of H 2 O 2 to the surface.

The transition from H 2 O 2 -limited photocurrent at low potentials to H 2 O 2 -independent photocurrent at high potentials implies a competition between H 2 O 2 photo-oxidation and water photo-oxidation for the available holes, surface reaction sites and intermediate species33. To test this hypothesis, we examine the effect of light intensity, which controls the photo-generation rate of excess charge carriers (holes), at a low H 2 O 2 concentration of 2.5 mM. The results are shown in Fig. 2. The pronounced nonlinear behaviour observed at high light intensities becomes linear as the light intensity is decreased. This shows that at low light intensity, the photo-generation rate is low enough to enable hole scavenging even at low H 2 O 2 concentrations. Another observation that supports our hypothesis is the saturation of the photocurrent density with increasing light intensities at potentials lower than 1.1 V RHE , which indicates that the photocurrent is limited by H 2 O 2 rather than by the flux of photo-generated holes.

Fig. 2 Photocurrent voltammograms under different illumination intensities. For all measurements H 2 O 2 concentration is at 2.5 mM Full size image

Modelling of the reaction kinetics

The experimental results presented in the previous section suggest that the fate of the photo-generated holes arriving from the bulk (where they are created) to the surface of the photoanode (where they vanish) involves different possible paths: H 2 O 2 photo-oxidation, water photo-oxidation and recombination with electrons (surface recombination). The competition between these paths depends on control parameters such as the H 2 O 2 concentration, light intensity and applied potential, thereby affecting the photocurrent. In order to understand the mechanisms of the respective reactions and the competition between them that determines the fate of the photo-generated holes, and thereby the performance of the photoanode, we construct a kinetic model. Our model extends the water photo-oxidation mechanism presented by Zandi and Hamann26 and Zandi and co-workers40, by adding additional steps that account for H 2 O 2 photo-oxidation. The model yields kinetic equations, which we solve numerically in order to analyse the fate of the photo-generated holes as a function of the control parameters, aiming for qualitative agreement between the calculations and the experimental results in the entire parameter space examined. Since we aim for qualitative rather than quantitative agreement, our model is not so sensitive to the selection of the parameters (rate constants) in the kinetic equations, unlike multi-parametric fitting that aims for quantitative agreement by fitting the unknown parameters to reproduce the experimental results precisely. Instead, the essence of our model is in capturing the nonlinearity of the PEC kinetics that gives rise to the non-trivial behaviour observed in the experimental results presented in Figs. 1, 2. Therefore, the model depends on the phenomenological structure of the nonlinear kinetic equations rather than on the parameters within those equations.

We start with the widely accepted model of water photo-oxidation mechanism on haematite in alkaline solution26,40,41:

(1)

(2)

(3)

(4)

(5)

where boxed ( ) species correspond to surface intermediates and k i are the respective rate constants. The reaction path from steps (1) to (5) is illustrated on the left side of Fig. 3. According to this mechanism, the water photo-oxidation current is given by the net summation of all the reaction rates, that is, the sum of the forward charge transfer rates (steps (1) and (3)–(5)) minus the backward reaction rate (step (2)). When both reactions (1) and (2) occur successively, their combination forms effectively a surface recombination step. It is noteworthy that steps (1)–(5) give rise to a set of linear kinetic equations, see Model equations and numerical computations in Methods.

Fig. 3 Schematic illustration of water (left) and H 2 O 2 (right) photo-oxidation reaction paths in alkaline solution. The former follows steps (1) to (5), whereas the latter follows steps (6) to (8) combined with step (1). In addition, the red arrow denotes the recombination reaction (2) Full size image

Next, incorporating the H 2 O 2 photo-oxidation reaction requires accounting for the following observations: (a) At low and intermediate potentials, the photocurrent depends on the H 2 O 2 concentration, whereas at high potentials it coincides with the water photo-oxidation current (without H 2 O 2 ), see Fig. 1a, b. This suggests that the H 2 O 2 photo-oxidation reaction competes with the water photo-oxidation reaction33. (b) Comparison of the IMPS spectra in points (i) and (iii) in Fig. 1 shows a deviation of the upper semicircle from a perfect shape in the presence of H 2 O 2 in the electrolyte, which suggests that the H 2 O 2 photo-oxidation reaction competes with the recombination reaction (step (2)). (c) Since the stable surface intermediate in the water photo-oxidation reaction is Fe = O26,40,41, it is expected that the competing step in the H 2 O 2 photo-oxidation reaction should involve Fe = O intermediates. (d) In the presence of H 2 O 2 in the electrolyte the photocurrent at low potentials is due to H 2 O 2 photo-oxidation rather than water photo-oxidation. Under these conditions, the Fe = O intermediates are short-lived and the stable surface species is Fe-OH26. Thus, for H 2 O 2 photo-oxidation to occur, an adsorption step that involves the long-lived Fe-OH species is expected to precede the step in which the adions interact with the Fe = O intermediates, as suggested in (c).

Accordingly, we postulate that the water photo-oxidation reaction (steps (1)–(5)) is complemented by the following steps to account for the H 2 O 2 photo-oxidation reaction:

$${\mathrm{H}}_2{\mathrm{O}}_2 + {\mathrm{OH}}^ - \to {\mathrm{HOO}}^ - + {\mathrm{H}}_{\mathrm{2}}{\mathrm{O,}}$$ (6)

(7)

(8)

Step (6) describes the deprotonation reaction of H 2 O 2 in the alkaline solution31, which occurs spontaneously since a pK a of 11.7 for H 2 O 2 deprotonation42 yields [HOO−]/[H 2 O 2 ]≃100 at pH = 13.6. Due to the fast nature of deprotonation reactions, step (6) is expected to occur much faster than the other steps, thus it does not affect the overall kinetics. Its product, HOO−, is postulated to weakly (physically) adsorb to Fe-OH surface sites in the next step, as described in step (7), in accordance with (d) above. Empirical evidence supporting this adsorption step was obtained by infrared spectroscopy (see Supplementary Figure 1 and related discussion in the Supplementary Information). It is also supported by previous works showing the adsorption of (non-deprotonated) H 2 O 2 to Fe-OH surface sites in haematite43 (and similarly in other transition metal oxides44). Finally, step (8) postulates that the adsorbates from step (7) are oxidized by photo-generated holes coupled with proton transfer to adjacent Fe = O surface intermediates that were produced in step (1) of the water photo-oxidation reaction. Thus, step (8) represents a concerted interaction between two different surface species, one from the water photo-oxidation reaction and the second from H 2 O 2 adsorption. It couples both reactions and gives rise to nonlinearity in the kinetic equations that depend on the concentration of the respective species (see Model equations and numerical computations in Methods for details). It is noted that the exact molecular identity of the surface species involved in the reaction is beyond the scope of this work, and it remains to be verified by spectroelectrochemical studies45. However, this specific detail is not crucial to the results that follow, and alternative surface species may be considered without affecting the qualitative results of the analysis. The salient point is that the H 2 O 2 photo-oxidation reaction mechanism involves a concerted interaction of two surface sites, as in LH reactions, consuming two holes and yielding an oxygen molecule. The postulated reaction path is schematically illustrated on the right side of Fig. 3.

To uncover the nonlinear nature of the elementary steps in the water and H 2 O 2 photo-oxidation reactions that result in the measured non-monotonic photocurrents for certain H 2 O 2 concentrations (see Fig. 1), we derive kinetic equations (see Model equations and numerical computations in Methods for details) and supplement them by the hole flux from the surface to the electrolyte that is given by the sum of the forward chemical reactions (1), (3)–(5), and (8):

$$\begin{array}{l}k_1p_4\theta _{{\mathrm{Fe}} {{-}} {\mathrm{OH}}}\sigma _{\mathrm{h}} + k_2p_4\theta _{{\mathrm{Fe}} \,=\, {\mathrm{O}}}\sigma _{\mathrm{h}} + k_3p_4\theta _{{\mathrm{Fe}} {{-}} {\mathrm{OOH}}}\sigma _{\mathrm{h}} + k_4p_4\theta _{{\mathrm{Fe}}}\sigma _{\mathrm{h}}\\ \quad \quad \quad \quad \quad +\, k_6\theta _{{\mathrm{Fe}} {{-}} {\mathrm{OH}} \cdots {\mathrm{OOH}}}\theta _{{\mathrm{Fe}} \,=\, {\mathrm{O}}}\sigma _{\mathrm{h}} = p_1,\end{array}$$ (9)

where p 1 is the hole flux from the surface to the electrolyte46, which in general depends on the illumination intensity and potential, and p 4 is the OH− concentration in the electrolyte, which depends on the electrolyte composition, θ x is the fractional surface coverage of species x, and σ h corresponds to the surface density of holes at reacting sites. It is useful to regard eq. 9 as the charge conservation constraint46. In addition to the charge conservation constraint, we also employ a standard surface site conservation constraint:

$$\theta _{{\mathrm{Fe}} {\mbox{-}} {\mathrm{OH}}} + \theta _{{\mathrm{Fe}} \,=\, {\mathrm{O}}} + \theta _{{\mathrm{Fe}} {\mbox{-}} {\mathrm{OOH}}} + \theta _{{\mathrm{Fe}}} + \theta _{{\mathrm{Fe}} - {\mathrm{OH}} \cdots {\mathrm{OOH}}} = 1.$$ (10)

Next, we define the normalized photocurrent that is related to the flux of holes across the surface (p 1 ) minus the flux of holes consumed by the surface recombination reaction (step (2)):46

$$\frac{j}{{j_{\mathrm{max}}}} = 1 - \frac{{k_{ - 1}\theta _{{\mathrm{Fe}} \,=\, {\mathrm{O}}}p_2}}{{p_1}}.$$ (11)

where p 2 is the electron density at the surface. We emphasize that this form regards only the reaction kinetics at the surface and it does not account for bulk processes that control the hole flux to the surface. From experiments, it is evident that p 1 is often potential dependent, but the dependence is relatively weak. For instance, in the results presented in Fig. 1 the dependence is essentially linear (see j 500 in Fig. 1). In contrast to p 1 , p 2 displays strong dependence on the applied potential, p 2 ∝exp(-φ), where φ is dimensionless potential (see Model equations and numerical computations in Methods section for details). Thus Eq. (11) comprises an empirical normalization by p 1 (similarly to the normalization by j 500 in Fig. 1b). Notably, the shape of the calculated voltammograms of the normalized photocurrent is essentially robust with respect to the potential dependence of p 1 , as shown here by comparing Fig. 4a, b in which p 1 is taken to be linearly proportional to U or independent of U, respectively. This implies a generic mechanism that is hidden in this physicochemical process that we unfold, in what follows, by using a bifurcation theory via keeping p 1 as constant for simplified analysis purposes, \(p_1 = p_1^{\mathrm{c}}\).

Fig. 4 Numerically computed normalized photocurrent voltammograms at different H 2 O 2 concentrations (p 3 ). All the observables are dimensionless. The photocurrents are calculated for two cases in which p 1 is a with linear dependence on the applied potential, or b constant (see text and Model equations and numerical computations in Methods section for details) Full size image

The qualitative similarity between the calculated curves in Fig. 4 and the experimental results in Fig. 1b is clearly evident. Specifically, the calculated curves capture the non-monotonous behaviour of the normalized photocurrent at low H 2 O 2 concentrations and potentials below the onset of water photo-oxidation, and the convergence of the photocurrent at high potentials towards the water photo-oxidation limit. It is noted that the non-monotonous behaviour displayed by the cyan (p 3 = 0.01) curve in Fig. 4 emerges from the nonlinearity in the kinetic equations, as a result of the concerted interaction of two different surface sites as in step (8) above.

Bi-stability, competing kinetics and hysteresis

Analysis of the solutions shows that while for low H 2 O 2 concentrations there is only one solution (mono-stable regime), above a certain threshold concentration there is a limited potential range in which stable solutions coexist, as shown in Fig. 5a, c. The coexistence of stable solutions implies that hysteresis in the photocurrent should be expected in this range of potentials and H 2 O 2 concentrations. The hysteresis onset is at a generic cusp bifurcation47 (marked by Q c in Fig. 5a) in the two-parameter projection of the normalized photocurrent as a function of the potential (φ) and H 2 O 2 concentration (p 3 ), see Fig. 5a. The shaded region between the curves in Fig. 5a is where coexistence of bi-stable solutions exists. Above p 3 ≃ 0.144 (marked by the bold dashed line in Fig. 5a), although the coexistence persists, it cannot be observed experimentally because one of the stable solution branches spans the entire relevant potential range. In this case, an unstable solution connects the two stable solutions only at infinite potential, a known and universal (model independent) property of the cusp bifurcation47. Thus, our calculations predict a stable unique behaviour at low and high H 2 O 2 concentrations, whereas at intermediate concentrations bi-stable solutions and hysteresis are expected (in a certain potential range). It is noted that additional calculations (not shown here) demonstrate the same qualitative behaviour with similar features of hysteresis and multiplicity of solutions (i.e., bi-stable regimes) over a wide range of parameters spanning orders of magnitude of the respective rate constants, confirming the robustness of our model predictions. Moreover, the simple ER mechanism typically used to describe water photo-oxidation on haematite photoanodes24,25,34,35 cannot yield such hysteresis because it lacks nonlinearity in the kinetic equations of its elementary steps (see Model equations and numerical computations in Methods for details).

Fig. 5 Bi-stability and hysteresis. a Coexistence parameter space for the computed normalized photocurrent voltammograms showing the distinct regions of coexisting solutions. 2D projection of the manifold describing the computed normalized photocurrent voltammograms (j/j max ) as a function of the applied dimensionless potential (φ) and H 2 O 2 concentration (p 3 ), showing the coexistence (bi-stability) regime of the normalized photocurrent (the grey shaded area). The bold dashed line indicates the threshold between observable and non-observable hysteresis. b, c Simulated normalized photocurrent voltammograms at p 3 = 0.5 and 0.1, respectively. Solid lines indicate stable solutions, whereas dashed lines indicate unstable ones. The transition points from stable to unstable solutions and vice versa in b, c are, respectively, marked in a Full size image

The hysteresis predicted by the model calculations was validated by linear sweep voltammetry measurements, as shown in Fig. 6. Consistent with the model predictions, hysteresis was observed only at intermediate H 2 O 2 concentrations (5 mM; Fig. 6b) but not at low and high concentrations (Fig. 6a, c, respectively). The hysteresis mechanism is consistent with the proposed reaction path (Fig. 3) through examination of the potential dependence (and therefore dependence on the potential sweep direction) of the distinct surface species involved in the reaction. Specifically, we focus on the evolution of the Fe = O, Fe-OH, and Fe-OH···−OOH species. At low potentials, for example, U = 0.6 V RHE , the concentration of electrons at the surface is high (because the photoanode is donor-doped) and the recombination rate (step (2)) is fast, and therefore the surface is covered mostly by the long-lived Fe-OH and Fe-OH···−OOH species, whereas the short-lived Fe = O intermediates are minority species. Thus, the photocurrent at low potentials is dominated by the reaction path associated with the formation of Fe-OH···−OOH adions with increasing potentials, that is, in the 0.8 V RHE ≤ U ≤ 1.3 V RHE range, the electron concentration at the surface decreases due to band bending, thereby prolonging the lifetime of the Fe = O intermediates. Consequently, the surface concentration of Fe = O increases, leading to comparable contributions to the photocurrent from both the water and H 2 O 2 photo-oxidation reactions. At high potentials, U ≥ 1.3 V RHE , the surface recombination becomes negligible and the surface is covered mostly by long-lived Fe = O intermediates. If the potential is then swept in the opposite direction, that is from high to low potentials, the surface coverage of Fe = O decreases progressively. Unlike during the potential sweep from low to high potentials, the time scale that is required to form a significant coverage of Fe-OH···−OOH adions is much larger than in the reverse direction, consequently the H 2 O 2 photo-oxidation reaction dominates. Thus, the different time scales that are associated with the evolution of different surface intermediates are manifested as hysteresis in the case of H 2 O 2 photo-oxidation that involves concerted interaction of different intermediate specie.