Understanding Photovoltage in Insulator-Protected Water Oxidation Half-Cells

A common practice when studying water splitting half-reactions is to use a degenerately doped reference semiconductor working electrode that is capable of providing the same chemical and solid-state matrix as a photoelectrode, but in which a high surface carrier concentration is achieved by doping rather than light absorption. Among the most important attributes of the reference working electrode, compared to the corresponding photoabsorber substrate for insulator-protected cells are 1 – similar surface chemical bonding of the overlying insulator and/or of catalyst layers and 2 – similar electrochemical potential of the hole (for water oxidation) or electron (for water reduction) so that the electrode exhibits similar conduction of these carriers to the surface. A perfect reference anode would reproduce all phenomenon of the photoanode except for the effect of photovoltage produced in the latter, thus allowing for precise determination of any recombination processes and other losses. Figure 1 below shows the band diagram of a p⁺Si/SiO₂/TiO₂/Metal/Electrolyte half-cell and an overlaid equivalent circuit diagram to illustrate the conduction in this common reference for silicon photoanodes.

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Majority holes may encounter some series resistance internal to the semiconductor as well as external resistances (back side contact, wires, instrument resistance, etc.) denoted here as R_S. In the insulator-stack, two pathways are depicted, namely a shunt pathway R_sh for the possibility of filamentary or pinhole-mediated conduction and a general impedance Z_I,h+, which will depend on the insulator's properties. In this particular system, research has shown that the conduction mechanism through the SiO₂ is a tunneling process^5,9 and through TiO₂ films greater than ∼2 nm thickness is bulk, trap-mediated conduction.^6,7 In principle, for n number of distinct insulator layers in the stack and k parallel conduction pathways, there are n^k permutations of conduction mechanisms. With two pathways and a bilayer insulator (e.g. SiO₂/TiO₂), there are four permutations: both insulator layers shunted, neither shunted, one, or the other shunted. Physically, shunting through both insulators in this bilayer or through the TiO₂ layer only are the most probable outcomes for shunt conduction. Therefore we will consider a possible shunt (for instance due to metal filaments) across the entire insulator stack. A similar simplification cannot be made for the impedance Z_I,h+ which we believe⁶ to be trap-mediated leakage conduction in parallel with a layer capacitance across the TiO₂ layer and tunneling conduction in parallel with a layer capacitance across the SiO₂ layer in Figure 1. Recent work has indicated that the two insulators interact in such a way that limited bulk conduction in the TiO₂ may decrease the injection efficiency across the SiO₂ into the TiO₂.¹⁰ Equivalently, a thinner SiO₂ may increase the efficiency of tunneling into traps beyond the interface with TiO₂.

Figure 2 shows typical cyclic voltammetry results with a p⁺Si/SiO₂/TiO₂/Metal/Electrolyte half-cell measured using the reversible ferri/ferrocyanide redox couple in 1 M KCl(aq). An increase in insulator impedance is observed as an increase of the peak-to-peak splitting of the cyclic voltammograms. This system provides a valuable case study to investigate the different circuit components and their ultimate effects on photovoltage.

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From the equivalent circuit diagram, we can express Ohm's law for the redox reaction of Figure 2 with a p+Si anode as:

where the voltage is referenced to the reversible redox potential E⁰ for the ferri/ferrocyanide couple (FFC) and experiences potential losses due to series resistance R_S, shunt resistance R_sh, the insulator impedance Z_I,h+, the charge transfer resistance at the electrolyte interface R_ct and the electrolyte impedance Z_E respectively. Ultimately, all of these elements must be understood and optimized. When focusing on the anode half-cell, a reference electrode is typically placed close to the working electrode (W.E.) to remove voltage drops elsewhere in the cell including all contributions of the counter electrode and the electrolyte impedance between the reference and counter. The electrolyte resistance remaining between the reference and the working electrode (a component of Z_E), is known as the uncompensated series resistance (R_u) and, while minimal in many cells, can be quite significant in others, particularly if low conductivity solutions are required. As needed, electrochemical impedance spectroscopy (EIS) can be used to determine the uncompensated resistance and subtract its effects. An EIS correction can also remove any additional series resistance from the electrode structure, assuming the various layers are non-interacting. Such corrections allow for a great simplification of Equation 1. Assuming negligible shunting of current, leaves only the insulator impedance and the depletion impedance of the solution due to diffusion limitations which results in a voltage offset, E_diff, which is responsible for the peak shape:

Two quantities are commonly extracted from reversible redox cyclic voltammograms such as those in Figure 2: the E_1/2 (the average of the peak positions, a good approximation of the zero-current potential) and the peak-to-peak splitting (from which the DC resistance in can be determined). From the solar cell perspective, it is the zero-current potential, or open-circuit photovoltage, and the DC resistance that are of interest while, from the electrochemical perspective, the E_1/2 and peak to peak splitting are common metrics. Important differences can arise, however, between the values of these parameters from either solar cell or electrochemical measurements of the same anode structure, depending on the symmetry or asymmetry of the reduction and oxidation conduction pathways. For the p⁺Si case, conduction is essentially symmetric, representing majority holes from the semiconductor combining with electrons from the Ir or holes being created in the semiconductor as electrons are injected into the Ir. Figure 2 reflects this symmetry at positive and negative potential about the zero-current point. The potentials of the peak currents, E_pa and E_pc, can be obtained from Equation 2. The peaks are displaced from E⁰_FFC by plus a diffusional splitting from the depletion offset potential,E_diff, which has a value of ∼29 mV for the one-electron ferri/ferrocyanide couple at room temperature.¹¹ The peak to peak splitting (P2P) and half peak potential are given in Equations 3 and 4:

In this case, the E_1/2 is approximately equal to the reversible redox potential and zero-current potential. The DC device resistance can also be exactly measured either by modelling the peak-to-peak behavior with electrochemical simulation software or by vigorously stirring the solution and making short, rapid potential sweeps to obtain non-diffusion limited current measurements. In the limit of perfect mixing, the slope at the zero-current potential also provides a measure of Z_I,h+. In the case of a complex and significant impedance inconsistent with a linear series resistance, a more sophisticated computational model is needed to quantify the impedances. The best performing devices, however, often have low overall resistance, making the simple linear model generally applicable. The simple relationships of Equations 3 and 4 are useful to help clarify the more complicated relationships inherent in the minority-carrier photoanode devices.

The simplest possible photoanode structure consists of a single semiconductor layer capable of forming an electrochemical junction with the electrolyte, remaining stable itself, and even catalyzing the reaction. These Type 0 structures have been studied extensively in the literature in part because of the attractiveness of a simple architecture. Unfortunately, the underlying physical properties that control corrosion stability and photovoltaic efficiency of semiconductors are linked, such that Type 0 structures do not generally achieve stable and efficient solar-driven electrolysis.^5,7 The protection layers discussed herein and reported in the literature have permitted the use of highly efficient photovoltaic materials with enhanced stability that allow for the advancement of solar fuel and solar chemical technology. The simplest thin insulator-protected structure that achieves high efficiencies and stabilities as a photoanode is the nSi/SiO₂/TiO₂/Metal device utilizing TiO₂ for protection and the surface metal layer as both an OER catalyst and a contact for the resulting Schottky junction. The Schottky junction with nSi splits photogenerated electron-hole pairs, providing the holes needed for water oxidation. Figure 3 shows the band diagram and equivalent circuit diagram for the Type 1 nSi photoanode similar to Figure 1 for the reference p⁺Si anode.

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In this case, there are two different impedances Z_I,e- for electrons that can move via the TiO₂ conduction band and Z_I,h+ for holes that traverse the TiO₂ via states in the bandgap. Possible shunt current paths will have a much greater impact on holes under reverse bias than on electrons under forward bias in this structure. This is a typical Schottky structure, so the junction is rectifying in the dark, blocking electrons from moving from the metal into the semiconductor. A shunt through the insulator layers would presumably not affect this pathway unless it also formed an Ohmic contact to the semiconductor, eliminating the band bending of the Schottky junction locally.

Figure 4 shows ferri/ferrocyanide cyclic voltammetry data from Type 1 nSi devices where increasing impedance increases the peak-to-peak splitting, but the effect is asymmetric. The anodic hole current experiences a greater penalty than the reductive electron current. Comparison to the data collected from p⁺Si anodes in the dark (Fig. 2) indicates that this behavior is consistent with a TiO₂-thickness dependent photovoltage loss, as we describe in great detail in another report.⁷

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To describe this effect, the hole impedance is expressed as two terms, IR_I,h+ to describe the linear series resistance loss that is also encountered in the p⁺Si reference sample with majority holes, and E_{extraction-loss}, a charge extraction loss that describes increased recombination in the junction of the nSi Schottky device as a result of insulator-impedance and is not seen in the p⁺Si reference sample. With these two terms as variables and considering the open-circuit photovoltage E_OC as a constant, Equation 2 becomes:

The peak anodic current E_pa will include the diffusion splitting described above, the charge extraction loss E_{extraction-loss}, and the IR loss from the hole pathway depicted in Figure 3. The peak cathodic current E_pc will now differ, not including any charge extraction loss, and including an IR loss from the electron pathway of Figure 3 instead. Considering these factors, the equations for peak-to-peak splitting and half peak potential are now:

The charge extraction photovoltage loss has been described in detail in other work.⁷ The loss can be understood via Gauss' Law as the need to sustain a certain charge density on the semiconductor-insulator interface in order to set the field at the surface of the semiconductor, which in turn determines the fields in the insulators, and, from that, the current density sustained across the insulator. The E_{extraction-loss} term scales linearly with the thickness of the insulator and can be related to the dielectric constants of the protective layers such that low-k SiO₂ incurs a much higher loss than higher-k materials such as Al₂O₃ and TiO₂. Importantly for this work, E_{extraction-loss} is a function of the current density (greater hole accumulation at the semiconductor surface is required to achieve higher current across a leaky capacitor), meaning that the photovoltage will no longer be equal to the open-circuit photovoltage at any arbitrary current density but will instead be a decreasing function of current density as referenced to the p⁺Si device. By extension, the E_1/2 measured by reversible redox chemistry does not correspond to the E_OC nor does the E_P2P directly correspond to the hole impedance. Equation 6 and 7 differentiate the effects of the oxidative and reductive current for reversible redox and can be used to understand the photovoltage in those systems and in water oxidation half-cells.

Recent work has shown that a buried p⁺n junction can decrease or even eliminate the charge extraction loss for more resistive oxides by sustaining a high hole concentration at the semiconductor/oxide interface.^7,10 In this case, the only difference between the p⁺nSi photoanode and the p⁺Si anode reference will be the difference between hole and electron transport pathways affecting the reductive forward bias, as shown in Figure 5. For anodic operation, the two are now essentially identical.

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Considering these factors, the equations for peak-to-peak splitting and half-peak potential are identical to those for the nSi case, but without the charge extraction loss:

Figure 6 shows example cyclic voltammograms of the Type 2 device measured in the reversible redox couple ferri/ferrocyanide. As seen in Figure 6, the asymmetry of Figure 4 is completely removed and the curves trend almost identically to the p⁺Si reference case. This indicates that there are no significant differences in the forward and reverse bias current on the device. In terms of the equivalent circuit diagram, it suggests that the two impedances can actually be combined and treated as a simple resistor in series with the diode. The peak to peak splitting is therefore the same as the p⁺Si case and the E_1/2 = E⁰_FFC – E_OC, which is the same as the p⁺Si case as well, shifted only by the constant open-circuit photovoltage. This simplification should hold true as long as the conduction across the insulator layers is fully decoupled from charge extraction from the junction. In the limits of either a very thin degenerately doped surface region or a very thick and resistive insulator, this assumption breaks down and the charge extraction penalty will still be significant. Another recent report has shown that, with ALD-Al₂O₃, a similar p⁺n buried junction greatly reduces the charge extraction penalty but does not remove it completely. This is likely attributable to the high resistance of the thicker Al₂O₃ films.¹⁰

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Photovoltage in a half-cell is always defined relative to some reference. In some cases, that reference can be a constant, for example the reversible redox potential of an electrolyte species, E⁰, or the thermodynamic water oxidation or reduction potential. In other cases, reference samples or devices have also been used such as the p⁺Si dark anode described above in this paper or the noble metal catalyst or ideal fuel cell reported in the work of Heller.² Measurement of the photovoltage at zero current, or the open-circuit voltage, can be directly carried out in a redox solution with a well-defined potential by simply measuring the voltage across the device at zero current. Most potentiostats can perform these measurements automatically and they can also be done with an independent voltmeter contacting the working and reference electrodes. In this section, the photovoltage will be explored relative to the p⁺Si dark anode. This allows for determination of photovoltage in a solution without a well-defined redox potential. Furthermore, it provides a well quantified system to explore the device performance as a function of current density identifying any successive losses, such as the E_{extraction-loss} mentioned above. By contrast in the discussion section, leading results reported from different groups will be compared using the voltage of the photoelectrode relative to a constant, thermodynamic reference because this is most effective for comparing results across different device types and experimentally incorporates the catalyst overpotential, which is an important loss for practical water-splitting devices.

Referring once again to cyclic voltammetry, the photovoltage shift for a reversible-redox couple can, in principle, be taken as the zero-current point of the photoanode measurement relative to the zero-current point of the p⁺Si dark anode, which is also the E_1/2 for p⁺Si, the reversible redox potential described in the prior section. This approach is ideal for measuring open-circuit photovoltage. In relatively conductive cells, this measurement can be done without difficulty; however, in cells with a higher impedance, the current-voltage relationship is generally non-linear and the current remains near zero over an extended range of voltage. Considering Figure 4, it can be seen that the zero-current point seems to move to the right with increasing TiO₂ thickness, while the difference in voltage from curve to curve at higher current densities changes more rapidly. The same effect can also be observed in the water oxidation measurements for this particular kind of loss and is characteristic of a charge extraction barrier. By subtracting Equation 4 from Equation 7, we obtain a different, and more easily measured photovoltage. This difference between the E_1/2 values for the Type 1 nSi photoanode and reference p⁺Si systems is:

Equation 10 indicates that the half-peak potential shift equals the open circuit photovoltage modified by a term comparing the relative impedances of the hole and electron pathway through the structure and half of the charge extraction loss. This equation represents an averaging of forward and backward electrochemical reactions at the anode. With the terms delineated in this way, it can be directly compared to the shift of the water oxidation reaction. In this case, the overpotential shift between the Type 1 nSi photoanode and a reference p⁺Si anode for the water oxidation reaction at given current densities (potentials E_I) can be written as:

Equation 12 shows that the water oxidation overpotential is a function of the thermodynamic water oxidation potential E⁰_O2/H2O, a Nernstian term dependent on O₂ partial pressure and pH, the activation overpotential which is a function of the catalyst-reaction relation, and an impedance loss from hole conduction through the structure. The photoanode is only different from the reference anode in the photogenerated minority holes which gives the photovoltage. Because no averaging of forward and backward reactions is being done, the result is the open-circuit photovoltage and the full charge extraction loss remains, unlike in the reversible redox case.

In many of the studies reported recently, the insulator impedance has been systematically varied by changing the thickness of one or more insulator layers in oxide-protected photoelectrodes. Impedance can also be varied in other ways, for example by doping, post-deposition treatments, microstructure changes, or by controlling the shunt path density. For all such studies, it is useful to know the relationship between Equation 10 and 13 above, the reversible redox couple E_1/2 shift and a half-cell water oxidation shift. This can be accomplished by taking partial derivatives with respect to the factor that is systematically varied to control impedance. In recent studies, this factor has been the insulator thickness. In this section, it is assumed that the open-circuit voltage is independent of the hole conduction impedance Z_I,h+, and that the E_{extraction-loss} term, which only affects holes in photoanode operation, can represent all photovoltage loss with respect to changes in Z_I,h+. Previous work on MIS solar cells has shown that the E_OC does in fact decrease linearly with the thickness of the insulator layer,¹² but that effect, measured with ultrathin oxides explicitly, was much smaller than the current-dependent E_{extraction-loss} seen here with thicker oxides. With this assumption of constant E_OC, the partial derivatives of the E_1/2 shift and half reaction overpotential shifts with respect to insulator thickness t_i are:

If the two values on the left hand sides of Equations 14 and 15 are measured at the same current density, the E_{extraction-loss} is identical, producing a relation between the two shifts:

Equation 16 indicates that the E_1/2 shift is half of the water oxidation overpotential shift measured in the half-cell adjusted for half the impact of any difference in hole and electron conductivity in the structure. To gain some quantitative insight into this analytical model, Table I lists values of the E_1/2 trend with TiO₂ thickness (peak currents 1–2 mA/cm²) and half of the water oxidation overpotential shift (at 1 mA/cm²) for varying TiO₂ thickness in three sets of anodes with SiO₂/TiO₂/Metal over the indicated substrate type where the metal used is iridium as before. All sets show bulk-limited conduction in which a constant field is required across the TiO₂ to drive a constant current; however, the absolute magnitude of the required field is different by about a factor of three between the 'more' and 'less' conductive set. Such changes in insulator conductivity at the same nominal thickness indicate variations in the TiO₂ trap and/or shunt path density. A comparison between the two shifts and any residual difference between the values in reference to Equation 16 shows a similar relationship for both Type 1 sets at presumably different TiO₂ resistivities.

Table I. E_1/2 and ½ OP shift comparisons for two TiO₂ protected sets with different TiO₂ resistivity.

Photoanode			Residual
sets	(mV/nm)	(mV/nm)	(mV/nm)
Type 1 nSi (more conductive)	−20.7	−24.3	+3.6
Type 1 nSi (less conductive)	−54.0	−49.7	−4.3
Type 2 p+nSi (less conductive)	∼0	∼0	∼0

The residual is the difference between the E_1/2 shift and half of the water oxidation overpotential shift. According to Equation 16 this should be equal to half of the difference in resistance scaling between the electron and hole pathway through the device. The two values from the Type 1 nSi devices, +3.6 mV/nm and −4.3 mV/nm suggest a very small difference in contributed resistance for the two carrier pathways. Further evidence comes from the Type 2 p⁺nSi devices with less conductive TiO₂. The residual is approximately zero (0.3 mV/nm) in the situation where the charge extraction loss should be completely removed and the photovoltage is approximately constant with respect to insulator thickness. In the previous section it was assumed that only a charge extraction loss affects the anodic current in comparing ferri-ferrocyanide redox data and water oxidation overpotential data from identical anode structures. The data in Table I are consistent with Equation 16, supporting the conclusion that the charge extraction loss occurs when the insulator is placed inside the junction across which photogenerated electrons and holes are separated (i.e. Type 1 anodes).

The previous sections defined the photovoltage in insulator-protected photoanodes referenced to p⁺Si reference anodes. Those sections also examined common electrochemical metrics, the peak-to-peak splitting and half-peak potential in cyclic voltammetry using standard redox couples and how they are related to the photovoltage. In this final discussion, notable results from water-splitting photocathodes and photoanodes will be investigated and directly compared by presenting a power metric relative to the thermodynamic potential of water reduction or oxidation respectively. This analysis assumes that a useful water-splitting cell will be composed of both a photoanode and a photocathode in order to generate a large enough photovoltage to drive water-splitting. The voltage needed to drive a device-relevant current density, such as 10 mA/cm², across the whole water splitting cell will include the thermodynamic potential of water-splitting 1.229 V as well as activation overpotentials for each half reaction, series resistance losses to reach the required current density, solution losses, product separation losses and more. Literature results are typically carried out with a three electrode setup and some also subtract the uncompensated series resistance. So the voltage required to reach 10 mA/cm² does not yet account for many of the losses. The solution resistance, for example, would easily contribute ten or more ohms requiring another 100 mV or more at 10 mA/cm². Highly acidic solutions tend to be the most conductive, so results in acid will likely require less additional potential to overcome the solution loss.

Tables II and III present a selection of recent results for water reduction cathodes and water oxidation anodes, specifically listing those that involve some form of semiconductor corrosion protection layer, either using insulators or metals (catalysts). Most reports describe multiple electrode structures, so effort was taken to select the best results from each type, but also to add notes about the context for that result. Power producing half-cells are listed as having a positive photovoltage relative to the reversible potential, whereas power losing half-cells are listed as having a negative photovoltage relative to the reversible potential. All values are given relative to the hydrogen evolution thermodynamic potential (for cathodes) and oxygen evolution potential (for anodes). The next column lists the photovoltage needed from the other half-cell to provide the minimum 1.229 V needed. There are several advantages and disadvantages to listing the data in this way. The catalyst choice, loading, surface area, and other catalyst parameters play a large role in both HER and OER activity and it is possible certain approaches are quite promising in stability and/or open-circuit voltage, while being poor in catalysis, for example the 2015 result from Mei that used Pt as a demonstration of a non-nickel high work function metal.¹³ More importantly as a disadvantage, these two tables do not include all the losses mentioned above meaning they represent underestimations of the voltage needed. Chief among the advantages of such a listing is the comparison of the power at a possible operating point i.e. for the voltage needed at 10 mA/cm² operating current density. Looking at the photovoltage needed from the other half-cell indicates where today's research efforts are with respect to realizing an unassisted, stable, and efficient water splitting device.

To illustrate, consider a tandem cell with semiconductors having bandgaps of 1.1 eV and 1.8 eV respectively.¹⁴ In this scenario, the 1.1 eV material (for example silicon) must likely provide over 600 mV of potential to combine with 1.1 V or more supplied by the larger bandgap semiconductor. The best pSi Schottky junction cathode results from Esposito¹⁵ and Feng¹⁶ achieve up to 500 mV photovoltages, while n⁺pSi junctions have achieved nearly 600 mV.¹⁷ For photoanodes, the most recent results⁷ achieve photovoltages as high as 630 mV with p⁺nSi and up to 550 mV with nSi, with somewhat resistive TiO₂ protection layers. Reports in which the TiO₂ resistance is greatly reduced have achieved photovoltages of 400 mV or less in many cases with nSi and 400 mV–520 mV with p⁺nSi.⁸ Several reported photoelectrodes were not included in the tables because their performance was either notably poorer than those listed or the results did not reach the required current density of 10 mA/cm²_. For instance, hematite is a widely-studied photoanode material with a bandgap near 2.2 eV, but has yet to produce 10 mA/cm² of photocurrent even when highly active iridium OER catalysts are used.¹⁸ MnO_x is listed in this table as a passivation layer, but a recent report concludes that it is not well suited for such purposes.¹⁹ Work continues in developing it as an OER catalyst, but the best illuminated results reported imply negative potentials (power losing cells) of several hundred millivolts after accounting for the photovoltage. Protection layers including graphene or other carbon films have also been explored^20–22 as has Ta₂O₅ as a protection layer for nZnO absorbers,²³ but, in general produce worse results than those listed. Additional structures are also listed in a recent comprehensive review.⁴