Monitoring interfacial electric fields at a hematite electrode during water oxidation

To understand the mechanisms of water oxidation on materials such as hematite it is important that accurate measurements and models of the interfacial fields at the semiconductor liquid junction are developed. Here we demonstrate how electric field induced second harmonic generation (EFISHG) spectroscopy can be used to monitor the electric field across the space-charge and Helmholtz layers in a hematite electrode during water oxidation. We are able to identify the occurrence of Fermi level pinning at specific applied potentials which lead to a change in the Helmholtz potential. Through combined electrochemical and optical measurements we correlate these to the presence of surface trap states and the accumulation of holes (h+) during electrocatalysis. Despite the change in Helmholtz potential as h+ accumulate we find that a population model can be used to fit the electrocatalytic water oxidation kinetics with a transition between a first and third order regime with respect to hole concentration. Within these two regimes there are no changes in the rate constants for water oxidation, indicating that the rate determining step under these conditions does not involve electron/ion transfer, in-line with it being O–O bond formation.

Electrode samples are mounted in a custom electrochemical cell ( Figure S2) that is 3D-printed in acrylonitrile butadiene styrene. An analogue potentiostat (Whistonbrook Technologies Ltd.) is used to synchronise SHG data acquisition and electrochemical measurements using a TTL trigger pulse and a custom LabView program. More details on data processing, including discussion of smoothing algorithms for the first derivative calculations can be found accompanying Figure S13.  wide aperture for rectangular glass window that allows 800 nm light to reach the sample and reflected 400 nm SHG light to leave the cell. Three openings are included in the top of the cell to allow access for working and counter electrodes as well as a contact for the working electrode. The hematite working electrode is mounted to a plastic "lid" (not shown here for clarity) which holds the electrode in place and is fixed to the cell body with epoxy.
A potential concern in the SHG experiment is that the steady-state carrier population is significantly changed by either the 800 nm incident light (through multiphoton absorption or via the population of sub-band gap states) or as a result of band gap excitation by the 400 nm photons from SHG. As noted in the main text the current-voltage response of the -Fe2O3 electrode was measured whilst being excited by the 800 nm laser using identical conditions to those in the SHG experiment and no photocurrent was detected (see Figure S8 below). This is in line with expectations based on the absorption coefficients of the -Fe2O3 electrode and the known photoactivity (incident photon to current efficiency, IPCE) behaviour of this type of electrode. At 800 nm the absorption coefficient is ca. 1 x 10 3 cm -1 , 2 so photon absorption can occur via the presence of defect states however we are unaware of any reports where 800 nm excitation has led to the generation of long-lived charges and a detectable photocurrent (for example see references 1,3,4 which are typical for the field and show zero photocurrent at excitation wavelengths greater than 600 nm). 400 nm photons can lead to band gap excitation of -Fe2O3 but it is possible to estimate the steady-state carrier concentration as a result of SHG and we find this to be several orders of magnitude lower than Nd (~10 19 cm -3 , see table S1 below). We arrive at this conclusion as: 800 nm incident power = 25 mW = 1 x 10 17 photons s -1 The efficiency of SHG will be dependent on multiple factors including amongst others the electrolyte and the concentration used, the nature of the FTO/Fe2O3 interface and the applied potential. We are unaware of reported values for SHG efficiencies for a -Fe2O3 aqueous interface but a review of the literature indicates that quantum efficiencies on the order of 10 -6 are considered a reasonable upper estimate here. 5 This gives rise to a maximum rate of 400 nm generation of 1 x 10 11 photons s -1 From the beam diameter (500 m) and sample thickness (ca. 150 nm, see Figure S5) and assuming complete absorption of the 400 nm SHG (which we recognise is an over-estimate/worst case scenario) we arrive at an estimated maximum carrier generation rate of 3.4 x 10 18 s -1 cm -3 . Fast transient absorption spectroscopy has shown that following band gap excitation with fs pulses there is significant carrier-recombination on the ps-ns timescale even at low excitation intensities even when the -Fe2O3 sample is positively biased. 6 The majority of the carriers are found to have decayed within 100 s. This observed fast recombination is in-line with the maximum IPCE reported for the -Fe2O3 sample used here which is ca. 10-12% at 400 nm 1 and we would anticipate that the steady-state change in carrier density is on the order of 10 17 cm -3 , approximately two orders of magnitude below Nd in the dark.

UV-Vis absorption spectroscopy:
All UV-Vis spectra were recorded on a Shimadzu UV-2600 spectrophotometer, used in transmission mode with the internal detector. Note that the high annealing temperature had caused the underlying glass structure of the hematite electrode to lose some transparency across the spectrum due to scattering.
The data in Figure 2 (main text) is shown as a % transmission relative to air as no suitable background sample (e.g. bare FTO or annealed bare FTO) could be used due to this scattering. The in-situ surface hole concentration measurements (Figure 3, main text) were also carried out on the same spectrometer, this time in kinetics mode (at 625 nm) during a linear sweep measurement. The hematite electrode is mounted in a quartz cuvette with a Pt wire counter electrode and Ag wire pseudo-reference electrode.
Steady-state surface hole concentration measurements ( Figure 5, main text) were carried out on a custom-built photo-induced absorption spectrometer, see Figure S15 for more details. Figure S3: SEM images of the electrodeposited hematite films used throughout this study. Scale bars correspond to 10 µm (left) and 1 µm (right).

Characterisation data of the -Fe2O3 electrodes
We note that some areas close to the edge of the electrodeposited films exhibit fissures, as shown in the image in Figure S4. SEM EDX mapping shows Fe inside the fissures, suggesting that the hematite layer is present across the entirety of the exposed surface.     We find that the intercept is frequency dependent (-0.4 to -0.6 V between 89 and 4.76 kHz). The limitations of a Mott Schottky (MS) analysis of -Fe2O3 have been discussed in detail elsewhere. 8 In particular it is important to recognise that the measured capacitance has contributions from both the Helmholtz layer and space charge layer capacitance (CSC and CH respectively, Eq S1).
Eq. S1 Typically, it is assumed that CSC << CH but as we show in the main text the presence of surface states leads to an applied potential dependence of the distribution across the interface and this gives rise to the non-linearity (and frequency dependence) of the plots of 1 2 vs. applied potential seen in Figure   S9. Therefore, from this data alone it is not possible to determine how ∆ vs. ∆ is varying and the measured intercepts only give an estimate of the flat band potential. Following recent guidelines 8 we have therefore carried out a 2 nd measurement of the flat band potential by assessment of the chopped photocurrent ( Figure S10). This shows a transition between anodic and cathodic photocurrent spikes at ca. -0.46 V. Referencing the Ag/Ag + pseudo reference electrode to a Ag/AgCl we measure a potential difference of +0.1 V but as we note in the main text the exact measured potential versus Ag/Ag + is found to be sensitive to the cell geometry used. Using the chopped photocurrent measurements to approximate the flat band potential (Vfb), the slopes of the Mott-Schottky plots at the three different frequencies are used to approximate the dopant density (ND) using the Mott-Schottky equation: And by extension the space charge layer width (WSC): Where C is the differential capacitance, ε0 is the permittivity of free space, holds for when the potential drop is changing primarily across the space-charge layer with negligible change in the potential drop across the double layer (∆ ). If the potential is also dropping across the double layer then we can approximate that will be Eq. S5 In Equation S5 we have approximated the field to be constant over the electrical double layer, giving a linear relationship in-line with several past studies. 10,11 This is reasonable as in this work we have carried out experiments only at high electrolyte concentrations (0.1 M NaOH) and potential drop within the electrolyte is primarily across the Helmholtz layer.
Expansion of equation S5, and considering that the change in ISHG is proportional to the square of PSHG gives rise to Where the exponential terms account for the phase differences between the interfacial χ (2)  Therefore, we conclude that a large (relative to the potential indepdendent SHG response) linear change in ISHG with applied potential at potentials positive of flat-band is indicative of ∆ϕ SC >> ∆ϕ DL . This is in agreement with past SHG studies on related materials (TiO2) that reached the same conclusion. 12,13 The conclusion that the linear change in ISHG between 0.2 and 0.6 V is due to ∆ϕ SC >> ∆ϕ DL is further supported by the photocurrent response recorded in the main text (figure 2) which rises steeply in this potential region before plateauing at ~0.5 V (vs. Ag/AgCl, ca. 0.6 V Ag/Ag + ). It is widely accepted that the increase in photocurrent with applied potential is due to the increased charge separation efficiency which occurs as a result of the electric field across the space charge layer. This requires ∆ϕ SC ≠ 0 and the only other scenario we can identify which may give rise to a linear response in ISHG requires ∆ϕ SC << ∆ϕ DL which does not appear compatible with the photocurrent response. 14

SHG response of FTO vs Fe2O3 interface:
As the potential is initially made more positive in both panels in Figure S11, ISHG increases at a roughly constant rate, in line with their being a continuous increase in EDC. For an ideally behaving n-type semiconductor surface in an aqueous electrolyte it is well understood that as the potential of the electrode is made more positive the majority of the potential drop occurs across the space charge region and hence ESC will increase and this is reflected in the strong linear potential dependence of the SHG response between -0.2 and +0.4 V in Figure S11a. Conversely, both the initial magnitude (peak area of ~ 900 for FTO vs. 3000 for α-Fe2O3) and relative change (~10% increase for FTO vs. 230% for α-Fe2O3) of the FTO response over the same potential range are smaller ( Figure S11b). The high conductivity of FTO under dark conditions would prevent the formation of a space charge layer, leading to a system dominated by the interfacial response (χ (2) >> χ (3) ), which could explain this lower signal as there is minimal enhancement from the static electric field.

Effect of ionic strength:
For data presented in the main text we used 0.1 M NaOH as the electrolyte in order to operate at the relevant (active) pH values used for hematite, and to avoid substantial local pH changes which could occur during water oxidation if a lower pH were to be used. Experiments at the same pH (0.1 M NaOH) but a higher ionic strength (by adding NaClO4 as a supporting electrolyte to reach 2 M ionic strength) were carried out and are overlaid below ( Figure S12a). In the raw data there does not seem to be an appreciable difference between the two different ionic strengths. The inconsistent dropouts in the 2 M data due to bubbles stuck to the surface limited further analysis (such as calculating d[SHG]/dV) without manually removing the dropouts which may introduce an unnecessary level of human bias. At 0.1 M NaOH the Debye length is approximately 1 nm ( Figure S12b) and it is typically assumed that for the potential to drop across the space charge layer, the width of this layer would need to be similar to or less than the Debye length. In table S1 we estimate the width of the space charge layer to be > 8.5 nm , therefore further increasing the electrolyte concentration, which will further decrease the Debye length to < 1 nm, is not be predicted to change the distribution of the potential drop across the interface, inline with our data in Figure S12b.

SHG data processing:
This section describes the treatment of the SHG data from the output of the spectrometer to the analysis of the first derivatives. Each voltage sweep experiment results in a set of spectra over time containing a single peak at 400 nm, corresponding to the SHG signal. The integrated peak areas can be plotted against the corresponding potential values during the voltage sweep, as shown in Figure 3, since the start of both electrochemical and spectroscopic experiments are synchronised with a TTL trigger pulse.
As detailed in the main text and in the discussion above, the gradient of the potential-dependent SHG response can provide insight into the relative contributions of the second and third order susceptibilities to the observed SHG signal. Thus, analysis of these gradients by taking the first derivative of the SHG response with respect to applied potential is a useful procedure to aid our understanding of the system.
Conventionally this kind of analysis requires pre-smoothing of experimental data to reduce noise in the resulting first derivative data. The default option for this smoothing in OriginLab (and many other code libraries) is the Savitzky-Golay algorithm, which has been shown to produce excessively noisy data and has issues with boundary artifacts. 15 An alternative smoothing algorithm was proposed by Schmid et al.
(denoted as Modified Sinc) which improves on these deficiencies. 15 Both algorithms were applied to the data from Figure 3 in the main article and comparisons between the two smoothing methods is shown in Figure S13 below. The data smoothed using the Modified Sinc method appears to better match the experimental data (black lines in Figure S13a Figure S17: VIA (left) and PIA (right) responses of the electrode obtained from the raw data above.
These steady-state absorption and photocurrent measurements are then used to estimate the reaction order (α) and relative rate constant for water oxidation (kwo) using the kinetic analysis described by Le Formal et al. 16 The change in absorbance at 625 nm is directly proportional to the surface hole concentration, while the simultaneous current density directly reports on the rate of charge consumption (i.e. the flux of holes to the surface, Jh+). Under steady-state conditions when the PIA amplitude reaches a plateau the surface hole concentration does not experience any net change: [ℎ + ] = 0 Eq. S7 The water oxidation current also reaches a plateau in this region, indicating the flux of holes to the surface is equal to the rate of water oxidation by surface holes: Eq. S10 Which indicates the gradient of a log-log plot of PIA amplitude versus current density is proportional to α. Calculation of kwo from Equation S9 using α = 1 and α = 3 shows that the relative rate constant for water oxidation is constant within the 1 st and 3 rd order regimes. We also plot the highest current density data for α = 8 which again shows that the relative rate constant for water oxidation is roughly constant with hole density but we caution that there are significant errors in the fitting of the VIA data under these conditions. to the left of the dashed line kwo is constant for  = 1. In the middle kwo is constant for  = 3 on the righthand side using  = 8 we also see that the kwo is not strongly dependent on hole density.  proportional to surface hole concentration) from the VIA measurements.