Deconvoluting the influences of 3D structure on the performance of photoelectrodes for solar-driven water splitting

Abstract

Three-dimensionally (3D) structured photoelectrodes offer a number of potential benefits for solar fuel production compared to conventional planar photoelectrodes, including decreased optical losses, higher surface area for catalysis, easier removal of product species, and enhanced carrier collection efficiency. However, 3D structures can also present challenges, such as lower photovoltage and larger surface recombination. Quantifying and understanding the advantages and disadvantages of 3D structuring can maximize benefits, but this goal is not trivial because the factors that affect photoelectrode performance are intertwined. In this article, we provide an overview of the benefits and challenges of using 3D photoelectrode structures and present a systematic approach for deconvoluting the most common effects of 3D structure on photoelectrode performance. As a basis for this study, metal–insulator–semiconductor (MIS) photoelectrodes consisting of p-Si micro-pillar arrays with well-defined diameter, pitch, and height were fabricated by reactive ion etching (RIE). A general framework for modeling the influences of 3D structure on photoelectrode current–potential performance is presented, and a comparison of the loss mechanisms in 3D and planar photoelectrodes is illustrated using loss analysis diagrams. We expect that most of the measurements and analyses that we demonstrate for MIS photoelectrodes can be applied with equal success to liquid-junction and p–n junction 3D structured photoelectrodes.

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I. Introduction

Solar-driven water splitting with photoelectrochemical (PEC) cells is a promising means to produce storable hydrogen (H₂) fuel from renewable solar energy without any CO₂ emissions. For these reasons, the development of photoelectrode materials for PEC-based solar fuel production has been a subject of intensive research ever since PEC-driven water splitting was first reported in 1972.^1–3 Despite these intense efforts, researchers have yet to demonstrate a photoelectrode that is stable, efficient, and made from only earth-abundant materials. In the search for the “ideal” photoelectrode, thousands of material compositions have been explored,^4–6 and high-throughput screening for new materials remains an active and important topic of research.^7,8 The material composition and bulk properties of the semiconducting light absorber are not the only factors that determine photoelectrode performance. The nano-, micro-, and macro-structure of the photoelectrode, along with the complex interactions between components (catalysts, semiconductor, insulating layers, electrolyte), are also of great importance.

A wide variety of three-dimensional (3D) photoelectrode architectures have been explored as a means for improving photoelectrode performance.^9–20 The possible influences of 3D structuring on photoelectrode performance are numerous, with some of the most common influences listed in Table 1. Most of these effects generally have a positive impact on performance, resulting in improved operating potential and/or photocurrent of the 3D photoelectrodes compared to their planar counterparts. Enhanced performance can be achieved through decreased kinetic overpotential losses, increased light absorption, enhanced product removal, and improved carrier collection. Improved carrier collection through 3D structuring can be particularly effective for materials with inherently poor charge transport properties, such as transition metal oxides. Not all aspects of 3D structuring are beneficial for solar water splitting, however. For example, increases in junction area decrease photovoltage, and the high surface area-to-volume ratio in 3D-structured electrodes can lead to high surface recombination losses.

Table 1 Photoelectrode properties commonly influenced by 3D structuring. The most commonly observed effects on performance are listed along with experimental techniques for quantifying and deconvoluting individual influences from the net photoelectrode behavior

	Properties influenced by 3D structure	Measurement technique(s) used for quantification
1	Optical	UV-Vis spectroscopy, ellipsometry
2	Carrier collection	External quantum efficiency (EQE), scanning photocurrent microscopy (SPCM), electron-beam induced current (EBIC), transient absorption spectroscopy (TAS)
3	Photovoltage	Linear sweep voltammetry (LSV), intensity-dependent open circuit voltage, Mott–Schottky analysis
4	Surface recombination	Current–voltage curves, EBIC, SPCM, TAS
5	Catalytic	LSV (Tafel analysis), cyclic voltammetry (CV) stripping experiments, scanning electrochemical microscopy (SECM)
6	Mass transport/bubble dynamics	LSV, chronoamperometry, use of surfactant, electrochemical impendence spectroscopy (EIS), video analysis

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Due to the numerous and often coupled influences of 3D structuring on photoelectrode performance, evaluating the maximum achievable performance becomes a non-trivial, but important task. Improved performance for 3D structured photoelectrodes is often reported, but a quantitative understanding of the underlying structure/property relationships responsible for this improvement is often lacking. Deeper knowledge is required to answer the following questions: what is the maximum theoretical improvement in photoelectrode performance that can be achieved by a given 3D structure? How does this maximum improvement vary with material composition, material quality, and the specific geometries of various 3D architectures? If the measured performance of a 3D photoelectrode lags behind predicted performance, how can one diagnose the source of those inefficiencies and make modifications to close the performance gap? How does one deconvolute the various influences listed in Table 1 and use that knowledge to maximize the benefits and minimize the disadvantages of 3D structuring?

Answering these questions is essential for realizing the full potential of a given photoelectrode material, and developing conceptual and experimental platforms for answering them is a major motivation of this article. Herein, we apply an approach that combines a variety of experimental techniques with modeling of photoelectrode performance to deconvolute the complex and interrelated influences listed in Table 1. In doing so, the achievable limits of performance of 3D photoelectrode architectures can be established; a further consequence is the identification of structure–property relationships with valuable predictive power for optimization of these 3D architectures. We demonstrate this approach on well-defined p-Si micro-pillar array photocathodes used to drive the hydrogen evolution reaction, but most of the methodologies are equally applicable to other photoelectrode types (e.g. liquid or p–n junction cells) and PEC chemistries (e.g. CO₂ reduction or oxygen evolution). These 3D structured p-Si photoelectrodes have a metal–insulator–semiconductor (MIS) architecture, which has shown great promise for achieving both high efficiency and good stability.^12,21–24

The remainder of this article is organized as follows: after describing the core methodologies used in this work, the synthesis and physical characterization of the 3D p-Si MIS photocathodes are presented. Next, each of the major influences of 3D structure in these samples is systematically analyzed by a combination of experimental measurements and/or modeling. Finally, knowledge gained from the separate measurements is combined to construct comprehensive loss-analysis figures, highlighting the differences in losses between the planar and 3D structured electrodes.

II. Results and discussion

2.1 Methodologies

Four key methodologies are used in this study to deconvolute the influences of 3D structure on photoelectrode properties and performance:

2.1.1 Uniform samples. 3D photoelectrodes are fabricated that have well-defined and uniform geometries over the entire sample surface. Such uniformity is important for establishing structure–property relationships from experiments that characterize photoelectrode properties over large areas.

2.1.2 Combined modeling and experiment. Modeling the optical, physical, and electrochemical properties of 3D photoelectrode structures is of great value for verifying experimentally observed structure–property relationships, deconvoluting different loss mechanisms, and guiding the design of more efficient photoelectrodes.

2.1.3 Micro- and macro-scale analysis. Conventional techniques that evaluate the average properties of photoelectrodes over macroscopic areas are complemented by local analysis techniques that provide information about the performance or properties of individual 3D structures at length scales that are less than or equal to the size of the 3D features.

2.1.4 “Wet” and “dry” analysis. Samples are evaluated in both PEC mode (“wet”, in the presence of an electrolyte), and in photovoltaic (PV) mode (“dry”, in the absence of an electrolyte) in order to deconvolute solid-state and electrochemical properties.

In this work, we investigated p-Si-based MIS photocathodes as a case study to illustrate these methodologies and describe the associated measurement techniques. The Si MIS structure is an excellent model system for this study because its solid-state junction enables optoelectronic measurements in the dry environment and the large effective minority carrier diffusion lengths of Si enable one to measure carrier collection behavior at the microscale rather than nanoscale.

2.2 Characterization of 3D MIS photocathodes

The p-Si MIS photocathodes consist of uniform arrays of micro-pillars made by reactive ion etching (RIE) of p-Si(100) wafers followed by cleaning, oxidation, and metal deposition steps. Within the MIS architecture, the catalytic metal layer is separated from the light-absorbing semiconductor by an ultrathin insulating layer, commonly an oxide. The major advantage of the MIS design is that it offers a means of decoupling photoelectrode stability from efficiency, a trade-off that has been one of the largest obstacles to progress in PEC research.^1,25,26 As illustrated in Fig. 1a, this trade-off is overcome in MIS photoelectrodes through the use of the thin but stable insulating layer, which protects the underlying narrow band gap semiconductor from the potentially corrosive electrolyte. Importantly, this insulating layer is thin enough to enable tunneling of photogenerated charge carriers from the narrow-band gap semiconductor to the metallic layer. In this work, the insulating layer is comprised of SiO₂, formed by rapid thermal oxidation (RTO) at 950 °C. The SiO₂ layer separates the Si absorber layer from the thin, semi-transparent metallic layer, which consists of Pt nanoparticles that were electrodeposited onto e-beam deposited Ti. As previously described in detail,²⁷ the bilayer structure of the metal layer is chosen to decouple the metal layer's role as active catalyst (Pt) from its role in determining the built-in voltage across the MIS junction (Ti). The reader is referred to the following literature for more detailed descriptions of the physics and design principles of MIS photoelectrodes^{24,26,28–32} and MIS PV cells.^33,34

Fig. 1 (a) Schematic side-view of a 3D metal–insulator–semiconductor (MIS) photocathode on which the hydrogen evolution reaction (HER) is taking place. (b–f) SEM images of a series of p-Si, MIS photocathodes consisting of arrays of micro-pillars fabricated by reactive ion etching (RIE). The pillar arrays in (c–f) consist of pillars with radii of 3 μm and varied pitch of (c) 11 μm, (d) 16 μm, (e) 23 μm, and (f) 38 μm. (g and h) SEM images of planar RIE photoelectrode lacking pillars. All scale bars shown in SEM images apply to the x dimension only.

The RIE process produces uniform arrays of micro-pillars arranged in a close packed pattern, as seen in SEM images (Fig. 1c–f). Achieving a high degree of uniformity is important because it ensures that micro-scale measurements performed at one location of the sample are representative of the entire sample surface, allowing for comparison of locally-measured performance to macro-scale measurements. The critical geometric parameters of the Si micro-pillars are the diameter, pitch, and height (Fig. 1b). Fig. 1 shows SEM images for a series of samples that formed the basis of this study and consisted of pillars with top diameter of 6 μm, height of 27 μm, and pitch between 11 μm and 38 μm. For almost all samples, pillars did not have perfectly vertical sidewalls, but were slightly tapered with an angle between ≈3° and 8° with respect to the surface normal that decreased with increasing pillar density. Next, contamination was removed and surface roughness decreased by wet chemical treatment as described in Section IV. Following chemical treatment, a thin SiO₂ insulating layer was grown by RTO at 950 °C in an N₂/O₂ environment. The low work function Ti layer was then deposited by e-beam evaporation, followed by electrodeposition of Pt catalyst particles. Although variation in particle size existed, electrodeposition produced a high density of nanoparticles on the pillar tops, side-walls, and basal areas (Fig. S4†). Typical Pt particle diameters ranged between 28 nm and 55 nm, and TEM images (Fig. S2†) showed that the particles exhibited a porous structure similar to that observed previously for electrodeposited Pt.³⁵

Although the SEM images in Fig. 1 show good pillar to pillar uniformity, the RIE process causes etch damage that varies on surfaces of the pillar tops, pillar side walls, and basal regions between the pillars. As seen in TEM images (Fig. S2†), the surfaces of the pillar tops did not exhibit etch damage because they were protected by photoresist, but the surfaces of the pillar side-walls (Fig. S6†) and basal regions possessed a higher degree of nanoscale roughness. A second difference between the MIS junctions on the top, basal, and side-wall surfaces was the thickness of the Ti layer deposited by e-beam deposition. This Ti layer, which is partially oxidized to TiO_x after exposure to air,²⁷ is significantly thinner on portions of the side-wall surfaces due to parallax effects including self-shadowing from adjacent pillars. Despite planetary rotation of the samples during e-beam deposition, cross-sectional SEM measurements indicated that the thickness of the Ti layer is about 65% less on the pillar side-walls compared to the pillar tops (Fig. S3†). A third difference between pillar top, side-wall, and basal surfaces was the nature of the electrodeposited Pt particles. A relatively high density of Pt particles was obtained across much of the sample surface, although some variation in particle density and size exists on the pillar tops, side walls, and basal regions (Fig. S4†).

2.3 Current–potential performance of Si-based 3D MIS photoelectrodes

The performance of each photoelectrode was measured by linear sweep voltammetry (LSV) in deaerated 0.5 mol L⁻¹ H₂SO₄ under simulated AM 1.5G illumination (Fig. 2). The LSV curve for a planar RIE control sample is also included. This planar sample underwent the identical processing steps as the other 3D samples except that it was not covered with patterned photoresist during the RIE process, resulting in a pillar-free surface having the same texture as the basal regions of the 3D-structured samples. Qualitatively, two major trends are evident in Fig. 2: (i) LSV curves shift to negative potentials as the pillar density increases and (ii) limiting current densities increase as the pillar density increases. In the remainder of this paper we use the methodologies described above to quantitatively evaluate the structure–property relationships that lead to the differences in performance seen in Fig. 2.

Fig. 2 LSV curves of p-Si MIS photocathodes shown in Fig. 1 and measured in deaerated 0.5 mol L⁻¹ H₂SO₄ under simulated AM 1.5G illumination at 100 mV s⁻¹.

2.4 Modeling current–potential curves of 3D structured photoelectrodes

A model that can accurately describe the photocurrent versus electrochemical potential (E) behavior of a photoelectrode can serve as a useful framework for deconvoluting the various influences of 3D structure. For a well-behaved, illuminated junction, the starting point for this model is the diode equation,³⁶ which describes the relationship between the current (I) passing through the junction and the voltage (V) across it:where j_o is the dark saturation current density, A_j is the junction area, q is the elementary charge, n is the diode ideality factor, k is the Boltzmann constant, T is the temperature, j_L(V) is the photo-generated current density, and A_hv is the projected 2D area of illumination. For solid-state junctions, A_j is the interfacial area between the two materials that form the junction. For absorber materials such as the prime Si wafers used in this work, the long effective minority carrier diffusion lengths (L_e) ensures that j_L is relatively independent of voltage over the range of potentials of interest.³⁷ The analysis provided herein therefore treats j_L as being voltage-independent, but there are many absorber materials for which this assumption is not valid, and the voltage dependent behavior of j_L should be also modeled for those materials.

The diode equation accounts for carrier generation and collection, but it does not account for voltage losses associated with electrochemical charge transfer resistance, ohmic resistances, and more. In order to account for these losses, it is convenient to work with a model that treats current implicitly.³⁸ This model describes the voltage difference between E, the potential applied to the Fermi level of the bulk semiconductor, and , the standard reduction potential of the half reaction taking place at the surface of the photoelectrode. For the hydrogen-evolving photocathodes being studied in this work, is given by:³⁸

where η_cat is the kinetic overpotential loss associated with electrocatalytic charge transfer, η_mt is the overpotential due to mass transport, R_Ω is the sum of the ohmic series resistances in the cell, and ϕ(I) represents other possible voltage drops. Solving eqn (1) for the junction voltage, V, and substituting that expression for V(I) into eqn (2) results in the following expression for the current–potential (I–E) behavior of a hydrogen-evolving photocathode:

This current–potential (I–E) model will be used throughout the remainder of this paper as a framework for understanding the influence of 3D structure on photoelectrode properties and performance.

2.5 Effects of 3D structure on photoelectrode performance

2.5.1 Optical absorption and reflection. 3D structure can strongly affect the photo-generated current density, j_L, of a photoelectrode by altering the fraction of incident light that is reflected from (R) and/or transmitted through (T) a photoelectrode. The relationship between j_L, R, and T can be seen in eqn (4):where λ is the wavelength of incident light, q is the elementary charge, h is Planck's constant, c is the speed of light, P_hv is the spectral irradiance of the incident light, and IQE is the internal quantum efficiency, defined as the percentage of absorbed photons converted into current. Besides reflection and transmittance, a third possible source of optical loss in photoelectrodes is the parasitic absorption of light by catalysts, overlayers, and/or electrolyte. These absorption losses are collectively accounted for in eqn (4) by A_L(λ), the fraction of incident light absorbed by materials located between the light source and semiconductor layer(s) of the photoelectrode. The integral in eqn (4) is typically evaluated from UV wavelengths up to the wavelength corresponding to the band gap energy of the semiconductor of interest.

Because the silicon photoelectrodes used in this study are optically thick, T is close to zero across visible wavelengths, and the primary sources of optical losses are reflectance from the front surface of the photoelectrode and absorption of light by the Ti overlayer. When analyzing reflection losses, it is important to recall that optical reflectance may be specular or diffuse. When the angle of incidence (θ_i) is equal to the angle of reflection (θ_r), the reflection is characterized as specular, or “mirror-like” reflection. By contrast, diffusely reflected light is that for which θ_i does not equal θ_r, a situation that is often caused by scattering from front, back, or internal surfaces or internal scattering centers. Both types of reflection can be highly dependent on the wavelength-dependent indices of refraction of the constituent materials. However, it is well known that geometric factors, such as roughness, thickness, and shape, can also strongly influence optical properties.³⁹ The size of 3D features is particularly important when the feature size becomes equal to or less than the wavelength of incident light because optical properties can be significantly altered at these length scales.^40–42 For a perfectly flat single crystal electrode, almost all of the reflection is specular (Fig. 3a). However, light incident on a 3D-structured photoelectrode (Fig. 3b) may interact with the nano- or micro-structures on the surface, resulting in diffusely-reflected light.

Fig. 3 Optical properties of micropillar arrays. Schematic side-views of (a) planar and (b) 3D-structured photoelectrodes. (c) Photograph taken at an angle of ≈45° of four micropillar array samples from Fig. 2. Image (d) UV-Vis total reflectance (R_T) spectra of planar and 3D-structured MIS samples from (c). (e) Average values of total reflectance (R_T) and diffuse reflectance (R_D) of samples in (c) between 400 nm to 700 nm. (f) Predicted change in limiting current due to 3D structuring based on UV-Vis data compared to the actual change in limiting current densities in the LSV curves in Fig. 2.

In order to quantify the influence of 3D structuring on the optical reflectance, the reflectance properties of the photoelectrodes were measured by ultraviolet-visible (UV-Vis) spectroscopy. The total reflectance (R_T) spectra of the 3D photoelectrodes, measured with an integrating sphere, are provided in Fig. 3d. These spectra show that the planar MIS electrode exhibits substantially higher reflectance across the entire range of wavelengths compared to the 3D structured samples. By measuring the specular reflectance (R_S), the diffuse reflectance (R_D) was also calculated. In Fig. 3e, the average values of R_T and R_D between 400 nm and 700 nm in Fig. 3d are plotted as a function of pillar density. R_D is observed to initially increase with pillar density due to the increased light scattering off of the 3D structures. However, R_D decreases for the sample with the largest pillar density because a high percentage of the photons that are diffusely reflected from the surface of the photoelectrode are absorbed by the closely-packed neighboring pillars. From Fig. 3e, the planar control sample has an average R_T of 42% for normal incidence light, but this value drops to 24% for the sample with the highest pillar density. The difference in reflection is evident upon visual inspection of the samples at an angle of ≈45° (Fig. 3c), and becomes even more pronounced when the angle of incidence deviates from the surface normal (Fig. S7†). While the decrease in R_T is significant for these micro-structured photoelectrodes, it should be noted that nano- or micro-structuring has been shown to reduce R_T of photoelectrode¹³ and PV^22,43 cell surfaces below 3%.

For all samples at normal incident illumination, the reflection losses predicated from UV-Vis reflectance measurements constitute a major source of photocurrent loss. However, the data shown in Fig. 3 overestimates the reflection losses that are incurred during photoelectrode operation, in which reflection occurs off of the electrolyte/photoelectrode interface instead of the air/photoelectrode surface. This difference in reflection results from differences in the indices of refraction, n_r, of air and the aqueous electrolyte. As described by the Fresnel equations,⁴⁴ reflectance at an interface is highly dependent on the difference in index of refraction values of the two materials forming that interface. While Si and the thin TiO_x coating contain large indices of refraction, air has a very low index of refraction. Because the index of refraction of the aqueous electrolyte (n_r ≈ 1.33)⁴⁵ is larger than that of air (n_r ≈ 1.00), reflection losses are lower during photoelectrode operation than the values provided in Fig. 3. Assuming that the Ti overlayer on the MIS photocathodes in this study have an index of refraction equal to that of anatase TiO₂ (n_r ≈ 2.52),⁴⁶ the Fresnel equations predict that reflectance of normal incident light from a planar surface immersed in an aqueous electrolyte should be ≈49% lower than when the reflectance is measured in air.

Optical losses due to parasitic absorption can also impact photoelectrode performance. In the MIS photocathodes of this study, parasitic absorption losses may result from light absorption by the partially oxidized Ti overlayer, Pt nanoparticles, and the electrolyte. It has previously been shown that the absorption of light by aqueous electrolyte, especially at IR wavelengths, can be significant for photoelectrodes containing narrow band gap semiconductors.⁴⁷ The p-Si photocathodes studied in this work only exhibit significant photoconversion at wavelengths from ≈300 nm to 900 nm (Fig. 6), a range in which the absorption of light by water is negligible at electrolyte thicknesses < 5 cm.⁴⁷ In order to approximate the optical losses originating from the Pt co-catalysts, a control sample was fabricated in which Pt nanoparticles were electrodeposited onto a transparent glass substrate coated with a thin, conductive layer of indium tin oxide (ITO). As determined from SEM images of this sample (Fig. 3f inset), the 2D coverage of Pt nanoparticles on this sample (θ_Pt ≈ 13%) was very similar to the coverage of Pt nanoparticles employed on the p-Si photoelectrodes used in this study. This sample thus offers a means of characterizing the optical losses that can be attributed to light blocking by the Pt nanoparticles. In Fig. 3f, the UV-Vis transmittance spectra for the Pt/ITO/glass sample is compared to that of a bare ITO/glass substrate, showing that the presence of the electrodeposited Pt nanoparticles decreased transmittance by an average of 5.5% (absolute) over the wavelength range between 400 nm and 700 nm. This value represents an upper limit on the amount of light blocked by the Pt nanoparticles, since some light scattered by the particles is not collected by the UV-Vis spectrometer in transmittance mode.

The parasitic absorption loss associated with light transmittance through the Ti overlayers was not directly measured in this study, but is also expected to contribute to the total optical losses. Because the precise composition of the partially oxidized Ti layer was not known, absorption losses could not be calculated using the Beer–Lambert law. Nonetheless, it is reasonable to assume that the absorption losses associated with the Ti overlayer are not greatly affected by 3D structure under normal incident illumination, since light must pass through Ti layers of similar thickness (≈15 nm) for both planar and 3D structured samples.

2.5.2 Carrier collection. A frequently cited advantage of 3D structured photoelectrodes is the ability to achieve larger photocurrents than planar photoelectrodes due to orthogonalization of light absorption and collection of minority charge carriers.^10,11 As illustrated in Fig. 4a, this advantage arises from the fact that minority carriers must be generated, on average, within a distance that is less than the sum of the effective minority diffusion length (L_e) and the depletion width of the junction (W). For planar photoelectrodes, the amount of harvested photocurrent will be very small if the optical absorption depth is significantly greater than the carrier collection length, (L_e + W). However, 3D-structured photoelectrodes are not subject to this constraint because carriers generated greater than (L_e + W) from the illuminated front surface may travel orthogonal to the direction of light absorption. In the case of the 3D pillar structures investigated in this work, minority electrons generated deep within a pillar may be collected at the pillar sidewall instead of the top of the pillar. This enhanced carrier collection results in a higher IQE, and thus higher j_L.

Fig. 4 Modeled enhancement of carrier collection for AM 1.5G illumination. (a) Schematic side-view of micro-pillar illustrating enhanced charge carrier collection efficiency due to orthogonalization of light absorption and carrier collection in 3D structured photoelectrode. (b) Modeled enhancement of photocurrent in a c-Si micro-pillar under AM 1.5G illumination compared to a planar region (I_pillar/I_planar) as a function of pillar height and carrier collection length (L_e + W) assuming that r < (L_e + W). (c) Modeled enhancement in photocurrent for c-Si micropillar as a function of dimensionless radius (r/(L_e + W)) and carrier collection length for a constant pillar height of 25 μm.

The increase in j_L in 3D-structured photoelectrodes due to enhanced carrier collection is strongly dependent on the photoelectrode geometry, the wavelength of incident light, and the absorber layer properties such as absorption coefficient, α(λ), dopant density, and L_e. Values of L_e, defined as the average distance a minority carrier can travel before recombination takes place, can vary by orders of magnitude depending on the absorber material. L_e can approach several mm for high-purity silicon wafers with low- to moderate doping levels,⁴⁸ but L_e values for oxide semiconductors are more commonly less than 50 nm due to charge localization and high intrinsic defect concentrations.⁴⁹ In order to illustrate the influence of 3D structure and (L_e + W) on enhanced carrier collection, the maximum expected photocurrent enhancement for cylindrical Si micropillars under normal incidence AM 1.5G irradiation was calculated numerically. For this analysis, photon absorption was modeled using the Beer–Lambert law and optical absorption coefficient data for c-Si.⁵⁰ The IQE(λ) was set to 100% for photons absorbed within (L_e + W) of the 3D junction and having energy greater than the bandgap of Si (E_g = 1.12 eV), and set to zero for all photons absorbed further than (L_e + W) from the closest junction. Modeling IQE as a step function introduces some error in the predicted photocurrent, but still provides a useful basis for understanding trends in how enhanced carrier collection depends on 3D structure.

The ratio of photocurrent generated by light absorbed in a pillar structure relative to that for an identical planar surface illuminated with AM 1.5G light was modeled as a function of pillar height (Fig. 4b), as well as the dimensionless pillar radius, (r/(L_e + W)) (Fig. 4c). In Fig. 4b, the photocurrent ratio, I_pillar/I_planar, increases logarithmically with pillar height as an increasingly larger fraction of the carriers generated from long wavelength photons are collected at pillar side-walls. I_pillar/I_planar is furthermore seen to be a strong function of (L_e + W), especially for (L_e + W) < 10 μm. This observation is consistent with a well-known generality in the solar PV and photoelectrochemistry fields: increase in photocurrent due to enhanced carrier collection in 3D structured solar cells and photoelectrodes is most significant for contaminated⁴⁸ or low-quality materials having low L_e.² In Fig. 4c, the photocurrent enhancement is a constant for pillar radii r ≤ (L_e + W), reflecting the fact that excessive micro- or nano-structuring of photoelectrode materials is not beneficial for carrier collection. However, radii that are significantly greater than (L_e + W) result in decreased carrier collection because carriers generated at the center of the pillar are not able to reach the pillar top or sidewall.

From Fig. 4b and c, it is evident that L_e is a critical design parameter in the fabrication of efficient 3D photoelectrodes because it determines the range of optimal pillar radii for enhanced carrier collection and the pillar height needed to achieve meaningful carrier collection at pillar sidewalls. Knowing the value of L_e is thus of great utility in the successful design of efficient 3D photoelectrodes. In this work, scanning photocurrent microscopy (SPCM) based on focused 532 nm and 790 nm laser beams was used to determine L_e for a planar RIE control sample. Values of L_e = (12.1 ± 1.0) μm and (12.2 ± 0.9) μm were measured using the 532 nm and 790 nm lasers, respectively (Fig. S8†). Confidence intervals for L_e values were calculated based on two-sided 95% confidence intervals. Based on a value of L_e = 12.0 μm and pillar height of 27 μm, Fig. 4b predicts a local photocurrent enhancement of 19% for photons that are incident on the pillar tops. However, the basal regions in between the pillars do not benefit from enhanced carrier collection efficiencies. For the 3D photoelectrode with the highest density pillars investigated in this study, pillars cover 48% of the 2D surface, meaning that the benefit of enhanced carrier collection is predicted to increase the light-limiting photocurrent, j_L, by ≈9% compared to the planar control sample.

Experimental determination of the extent of carrier collection enhancement was achieved with both macro- and micro-scale measurements. At the micro-scale, the carrier collection enhancement of individual Si micro-pillars at normal incident angle was measured with in situ SPCM using laser excitation at 532 nm and 790 nm. In these measurements, the focused laser beam locally produces photocurrent, which was measured as a function of laser beam position with respect to pillar features (Fig. 5a). Within a given sample, the basal regions between pillars are representative of a planar control because carriers generated from laser light incident on these areas travel parallel to the direction of illumination to be collected. SPCM was performed with two different lasers because the enhanced carrier collection due to 3D structuring is highly dependent on incident wavelength. The expected (modeled) wavelength dependence of the photocurrent enhancement (I_pillar/I_base) is shown in Fig. 5b for c-Si micropillars (L_e = 10 μm). Significant improvement in carrier collection is only expected for wavelengths greater than 700 nm, for which the absorption depth in c-Si begins to become comparable to L_e. Thus, Fig. 5b predicts that there should be negligible photocurrent enhancement for the 532 nm laser when it is positioned over the pillar, but significant enhancement for longer wavelength light such as that from a 790 nm laser beam.

Fig. 5 Enhanced carrier collection measured by in situ SPCM. (a) Schematic of in situ SPCM measurement. (b) Ratio of modeled photocurrent for monochromatic light sources of different wavelengths absorbed through the top of the pillar (I_pillar) to that absorbed through the base (I_base) as a function of c-Si pillar height. It is assumed that the pillar radius r < 2(L_e + W). PEC SPCM images taken with (c) 790 nm and (d) 532 nm lasers (P_o ≈ 4 μW). The color bar applies to both (c) and (d). PEC SPCM line scans using 790 nm and 532 nm laser beams over p-Si MIS micropillars having diameters of (e) 6 μm and (f) 28 μm at the tops of the pillars. All SPCM line scans were done with an applied potential of −50 mV vs. RHE in 0.5 mol L⁻¹ H₂SO₄.

SPCM photocurrent maps of a single 6 μm diameter micropillar, taken with 790 nm (Fig. 5c) and 532 nm (Fig. 5d) laser beams, clearly reveal wavelength-dependent photocurrent enhancement. As expected from Fig. 5b, almost no improvement in photocurrent is observed for local illumination of the pillar top with the 532 nm laser, for which the c-Si absorption depth at 532 nm ≈ 1 μm is much less than the carrier collection length, (L_e + W). By contrast, pronounced improvement in photocurrent is observed for the SPCM map produced with the 790 nm laser beam, for which absorption depth at 790 nm ≈ 10 μm is similar to (L_e + W), resulting in significant carrier collection through the pillar sidewalls, and thus an increase in the local photocurrent. This behavior is also observed in SPCM line scans taken across the same pillar (Fig. 5c). The slight increase in photocurrent at the edges of the pillar is due to light scattering off of the tapered pillar side walls and absorbed by adjacent pillars and base. Importantly, excellent quantitative agreement is seen between the measured photocurrent enhancement (I_pillar/I_base) and that predicted in Fig. 5b, further confirming that the differences in photocurrent maps for 532 nm and 790 nm lasers reflect differences in carrier collection due to 3D structuring. Good agreement of SPCM results with modeling (Fig. 4c) was also observed when SPCM measurements were performed on larger pillar sizes to view the effect of pillar radius on the enhanced carrier collection behavior. As seen in the SPCM line scans over a 28 μm diameter pillar (Fig. 5f), a significant decrease in photocurrent is observed when the 790 nm laser beam is positioned at the center of the pillar where the distance from the sidewalls is greatest. This effect becomes more pronounced for even larger pillars, where the local photocurrent at the center of the pillar becomes similar to that generated off the pillar (Fig. S9†).

A more common, but less direct, means of viewing photocurrent changes due to enhanced carrier collection is to perform macroscopic external quantum efficiency (EQE) measurements on 3D structured and planar samples. In Fig. 6, EQE spectra measured at an applied potential of 0.0 V vs. RHE are shown for planar and 3D structured photoelectrodes. These curves reveal higher relative photocurrent for the 3D micropillar sample at longer wavelengths compared to the planar control sample, consistent with the SPCM results for 532 nm and 790 nm lasers in Fig. 5. In Fig. 6b, the increase in EQE(λ) for the 3D photoelectrode relative to the planar photoelectrode is shown as a function of wavelength. While negligible difference in EQE is observed for 532 nm light, the EQE increased by 35% for the 3D photoelectrode under 790 nm illumination. This relative increase in EQE at 790 nm for these macroscale measurements is less than the relative improvement in local photocurrent observed in the microscale SPCM measurements with the 790 nm laser (≈45% improvement), which can be attributed to the fact that the pillars only cover ≈48% of the 3D structured surface.

Fig. 6 (a) EQE spectra for planar and 3D micropillar array electrodes in deaerated 0.5 mol L⁻¹ H₂SO₄ under an applied potential of 0.0 V vs. RHE. (b) Percent increase in EQE(λ) for the 3D structured photoelectrode compared to the planar photoelectrode.

An additional useful feature of the macroscopic EQE curves is that this data can be fit to the Gartner model to obtain an estimate of the effective minority carrier diffusion length.⁵¹ Performing this analysis on the EQE curves in Fig. 6 gives effective diffusion lengths of 11 μm and 22 μm for the planar and 3D structured samples, respectively. The value obtained for the planar photoelectrode is in good agreement with the value of L_e obtained by SPCM line scans, but the value of L_e for the 3D structured sample is significantly higher. This is because the fit to the macroscopic EQE curve gives an effective diffusion length that assumes a planar geometry for the sample. Stated otherwise, the 3D-structured sample is able to collect carriers as if it were a planar sample possessing an effective minority carrier diffusion length of 22 μm. However, the next section shows that the local minority carrier diffusion lengths in an individual micropillar are significantly less than this value.

2.5.3 Surface recombination. Surface recombination can be highly detrimental to photoelectrode performance for samples with highly defective surfaces or interfaces, especially when surface recombination rates are significantly higher than bulk recombination rates. Usually, high surface recombination rates result in a decrease in the effective minority carrier diffusion length (L_e) and an increase in the dark saturation current density. These adverse effects of surface recombination become more pronounced in 3D structured photoelectrodes or photovoltaic cells due to their increased surface area to volume ratio compared to planar cells.⁵²

In this work, the influence of surface recombination on 3D MIS photoelectrodes was investigated using electron beam induced current (EBIC) measurements in an ultra-high vacuum (UHV) environment. Fig. 7a contains a schematic side-view of the EBIC set-up used in this study, whereby the electron beam is injected into the top of the pillar and the electrical current measured between a probe contacting the pillar top and the back contact of the sample. Using this arrangement, current is measured as a function of the energy of the incident electron beam, which determines the absorption depth of the beam and thus the location of electron/hole pair generation with respect to the pillar top. Importantly, electrical characterization between the pillar tops and the basal regions immediately adjacent to the pillar revealed open-circuit behavior, indicating that the thin metal layer of the MIS structure is not continuous between the pillar tops, sidewalls, and the basal regions surround the pillars. A consequence of the discontinuous metal layer is that minority carriers generated far from the pillar top are not able to reach the current-collecting probe through conduction along the metal layer on the side-wall, but must travel up the pillar itself and cross the MIS junction at the pillar top. This carrier transport behavior is in contrast to a working device, in which the sidewalls are themselves current collectors through which minority carriers can be collected and directly transferred to oxidant species (H⁺) in the electrolyte through an electrochemical reaction.

Fig. 7 Analyzing surface recombination in micropillars with EBIC. (a) Schematic side-view of an EBIC measurement being performed on a micropillar. (b) Dependency of the collection probability, function ϕ(z), on beam position with respect to distance from the top of the pillar (z = 0). It is assumed that ϕ(z) = 0 in the interval [0, z_d] (this is a thin, electrically inactive “dead” layer”), ϕ(z) = 1 in the interval [z_d, W] (over the depletion width), and decays exponentially with length scale L_e for z > W. Also shown are the generation rate profiles G(z) for two values of beam energy, as described in the text. We take G(z) = 0.6 + 6.21(z/z₀) − 12.4(z/z₀)² + 5.69(z/z₀)³,⁸⁹ where the length scale z₀ varies with electron beam energy as described in the text. (c) Collected EBIC current versus beam energy for a pillar with 15 μm diameter, compared with the data fit. Fit parameters are z_d = 25 nm, W = 1 μm, and L_e = (4.3 ± 0.4) μm. (d) Variation of the effective diffusion length with pillar diameter, both measured and obtained from fitting to eqn (5).

The observed open circuit behavior in the UHV environment is useful for EBIC measurements because it enables one to determine the surface recombination velocity, S, of carriers at the sidewalls. In a working device where the sidewalls collect current, the surface recombination has little effect on j_L. This is because the electric field associated with the Schottky contact is maximized near the sidewall, so that charges there are separated before they recombine. However, surface recombination is detrimental to open circuit voltage (V_oc) because it increases dark current at forward bias. In the limit where the surface recombination velocity is much greater than both (W/τ_bulk) and the bulk diffusion velocity (, where D is the minority carrier diffusivity), j_o is proportional to S.⁵³

The relative influence of bulk and surface recombination on the photovoltage varies with pillar diameter due to the changing ratio of the pillar surface area to the pillar volume. The effective carrier lifetime τ_eff is determined by solving the diffusion equation in a radial geometry as a function of radial position ρ, with the boundary condition that the radial diffusion current j_ρ at pillar radius r satisfies j_ρ(r) = S × n(r), where S is the surface recombination velocity, and n(r) is the electron concentration at ρ = r (see ESI for details†). This leads to:

where D is the minority carrier diffusivity (assumed to be the bulk value), and β₀ = 2.481 is the first root of the order 0 Bessel function. The above expression applies in the limit S ≫ D/r; the more general expression is given in the ESI.† The effective minority carrier diffusion length is given by .

Values of L_e can be obtained from EBIC measurements using a least-squared fitting procedure based on the curves shown in Fig. 7b. This figure illustrates the spatial distribution of the generated excited electron–hole pairs, G(z), and the collection probability of an electron–hole pair as a function of the distance, z, that the exciton is generated from the collection probe. The total collected current is given by the product of these two functions. The electron–hole pair excitation profile is assumed to be known a priori (see caption of Fig. 7), and depends primarily on the electron beam energy: larger electron beam energies result in a spatial distribution of excited electron–hole pairs which penetrates deeper into the bulk. The relationship between the length scale of the excitation, z₀, and the beam energy, E_beam, is given by: z₀ = 0.043 × C₀/(ρ/ρ₀) × (E_beam/E₀)^1.75, where ρ is the mass density, ρ₀ = 1 g cm⁻³, C₀ = 1 μm is a constant, and E₀ = 1 keV.⁵⁴ The precise form of the generation profile is given in the caption of Fig. 7. By systematically varying the beam energy and measuring the current, the parameters describing the collection probability, such as L_e, may be obtained through a least-squares fitting procedure. An example of one such fit is shown in Fig. 7c for a pillar with radius of 15 μm. The primary experimental uncertainty arises from variation in the collected current at the top of the pillar, which generally varies between 1% to 9%. There is also uncertainty in the modeling from the use of the empirical formula describing the generation profile of electron hole pairs. By comparing this empirical distribution to more accurate Monte Carlo models of electron beam induced electron–hole pair generation, we find that introducing a 5% uncertainty in the length scale of the excitation is appropriate. The ensuing uncertainty in L_e is determined by performing fits using excitation length scales of z₀ + 0.05z₀ and z₀ − 0.5z₀.

This procedure was repeated for a series of pillars with varying radius, and the fitted values of L_e are shown in Fig. 7d as a function of pillar radius. The uncertainties associated with the reported L_e values arise from the uncertainty in the generation profile, as described above. Fig. 7d shows that the effective diffusion length decreases with decreasing radius, due to the enhanced influence of surface recombination as the surface area/bulk ratio increases. Performing a least-squares fitting procedure of eqn (5) to the data gives a surface recombination velocity of S = (8.5 ± 2.0) × 10⁴ cm s⁻¹. For reference, values of S between 50 cm s⁻¹ and 500 cm s⁻¹ have been commonly achieved for lightly doped p-Si wafers passivated by thermal SiO₂, while values of S less than 10 cm s⁻¹ have been achieved for more resistive Si wafers (>100 Ω cm) with thermally-grown SiO₂ overlayers.⁵⁵ The large value of S for the RIE-fabricated Si micropillars studied in this work underscores the importance of passivating the surfaces of the semiconductor in 3D structured photoelectrodes. In addition to rapid thermal annealing, two other common approaches to decreasing surface recombination velocities in Si solar cells include passivation by chemical vapor deposition of silicon nitride (SiN_x) and the introduction of fixed charges near the Si interface to induce an inversion layer that repels majority carriers from that interface.⁵⁵

2.5.4 Photovoltage. This section discusses the influence of 3D structuring on the photovoltage that is generated by the illuminated photoelectrode. Closely tied to photovoltage is the open circuit potential (E_oc), defined as the electrochemical potential at which no net photocurrent is observed. E_oc for a photoelectrode based on a solid-state MIS junction is primarily determined by two factors: (i) potential drops across interfacial layers, χ, and (ii) the V_oc of the junction, which is a function of the dark saturation current density (j_o) and illumination intensity (P_hv). Together, χ and V_oc determine E_oc with respect to the standard reduction potential of the redox reaction of interest:

Within eqn (6), the sign in front of V_oc is negative for photoanodes, and positive for photocathodes, while the sign of χ depends on the charge polarization associated with a given interface. Interfacial potential drops in photoelectrodes can originate from several different sources, including the electrochemical double layer,⁵⁶ insulating dielectric or passivation layers,^57,58 and surface dipoles associated with strongly bound adsorbates.⁵⁹ Most often, χ does not intrinsically depend on 3D structuring or junction area, although processing involved with fabricating 3D-structured photoelectrodes can alter χ compared to a planar photoelectrode of the same material. By contrast, the total dark saturation current of a junction, j_o,t = (j_o × A_j), and thus its V_oc, is highly dependent on the 3D area of the junction.² This relationship between junction area (A_j) and V_oc is observed by taking the diode equation (eqn (1)) at open circuit (I = 0 A) and solving for V = V_oc:

When [(j_L × A_hv)/(j_o × A_j)] ≫ 1, eqn (7) simplifies to:

If χ = 0, then E_oc = V_oc when referenced versus the reversible redox potential. For constant n and j_o, eqn (8) predicts a linear relationship between V_oc and ln(A_j/A_hv). Because (A_j/A_hv) is usually greater than one for 3D structured photoelectrodes, the photovoltage of a 3D structured photoelectrode will almost always be less than that which can be obtained for an otherwise identical planar sample for which (A_j/A_hv) = 1. This decrease in photovoltage due to 3D structuring is an inherent disadvantage of 3D structured photoelectrodes. Fig. 8a contains the experimentally measured E_oc values for our series of samples under 100 mW cm⁻² intensity, along with modeled curves of V_ocversus ln(A_j/A_hv) calculated from eqn (8) for n = 1.35 and j_o = 1 × 10⁻⁸ A cm⁻². For the experimental data, A_j was taken to be equal to the physical 3D area of the photoelectrode, A_3D, which is calculated from the micropillar dimensions and the pillar packing densities. From Fig. 8a, good linearity is observed for the first four samples of the series, but the E_oc data point for the sample with the highest pillar density deviates substantially from this trend. This indicates that the effective n and/or j_o of the highest pillar density sample are substantially different from the other samples. In order to verify this hypothesis, it follows from eqn (8) that n and j_o for an individual sample can be estimated by plotting the measured E_ocversus ln(j_L), where j_L is varied by adjusting the illumination intensity and E_oc is measured separately at the same intensity under open circuit conditions. From this plot (Fig. 8b), the values of n and j_o for a given sample can be estimated from the slope and intercept, respectively. These values are plotted in Fig. 8c, revealing that both the n and j_o values of the sample with the highest pillar density are indeed significantly higher than those of the planar and low-density pillar samples.

Fig. 8 Variation in photovoltage with increased level of 3D structuring. (a) Experimental (solid diamonds) and calculated (dashed lines) values of open circuit potential (E_oc) as a function of the area ratio (A_j/A_hv). Calculated values of E_oc are based on eqn (6) for n = 1.35, j_L = 22 mA cm⁻², and j_o = 1 × 10⁻⁸ A cm⁻², where n and j_o are taken from figure (c) for the planar sample. (b) Experimentally-measured E_oc values for a series of p-Si MIS photocathodes with varying A_j/A_hv at different illumination intensities. (c) Values of n and j_o obtained from linear fits to the data in (b) based on eqn (6). j_o in (c) is the dark saturation current density normalized by the net junction area of the electrode, A_j, which is assumed to be equal to the physical 3D surface area as estimated from SEM images.

The variation in the n and j_o values in Fig. 8c can most likely be attributed to (i) differences in local junction properties of pillar tops, pillar side walls, and basal areas and (ii) the fact that the relative surface areas of these junction types, A_ji, vary significantly for the series of samples used in this study. For example, the sample with the highest pillar density also has the highest percentage of its total junction area located on pillar side walls. From high resolution SEM images, it is evident that pillar side-walls contain significantly higher roughness at the nanoscale, making it likely that the junction quality at the pillar side walls is significantly worse than the comparably smoother pillar tops and basal surfaces. Thus, it is not surprising that the analysis presented in Fig. 8 indicates that the high pillar density sample has the highest effective j_o and n values, and that the E_oc of this sample is lower than one would predict from eqn (8) based solely on of its A_j/A_hv ratio.

2.5.5 Electrocatalysis. In addition to decreasing reflection losses and enhancing carrier collection, another potential advantage of 3D-structured photoelectrodes is the ability to decrease kinetic overpotential losses, η_cat, through an increase in the electrocatalytically active surface area (A_cat) relative to the 2D illuminated area, A_hv. For photoelectrodes utilizing a metallic co-catalyst, a 3D structured photoelectrode can support a larger loading of co-catalyst particles than a planar sample without the co-catalyst preventing a large fraction of incident light from reaching the underlying semiconductor. This is particularly true for instances where the catalyst is deposited on surfaces that are perpendicular to the incident light, such as the sidewalls of the micropillar studied in this work.

In general, the influence of increased A_cat on kinetic losses can be modeled with the Butler–Volmer equation, which describes the kinetically-limited current–potential (I–E) relationship for electrochemical charge transfer across an electrode surface. For electrochemical reactions in which the rate determining step involves the transfer of a single electron, the Butler–Volmer equation is:⁶⁰

where i_o is the exchange current density, A_cat is the area of the catalytically active sites, α is the transfer coefficient, R is the gas constant, and F is the Faraday constant. i_o and α strongly depend on the intrinsic catalytic properties of the catalytically active sites on the photoelectrode surface. α can have a value between 0.0 and 1.0, while the value of i_o can vary by many orders of magnitude for hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) catalysts.^61,62 When modeling the kinetic overpotential losses at larger overpotentials and in the absence of mass transport constraints, one of the exponential terms in eqn (9) drops out, giving the Tafel equation,where β = −(2.3RT/αF) is the Tafel slope. This expression for η_cat can then be used in eqn (3) to model the I–E curve behavior of the photoelectrode. If ϕ(I), the rate of the back reaction, solution IR losses, and mass transport losses are negligible, eqn (3) simplifies to:

Eqn (11) is a useful framework for highlighting some effects of 3D structure on photoelectrode current–potential (I–E) performance in well-controlled cases, but does have limitations. Notably, it does not account for mass transfer overpotentials, which are listed explicitly in eqn (3) but in practice are often difficult to deconvolute from kinetic overpotentials for fast reactions such as the hydrogen evolution reaction.⁶³ For photoelectrodes operating under conditions where mass transport overpotential losses are likely to be significant, such as low reactant concentrations and/or ultra-low loadings of catalyst, the reader is referred to recent publications that discuss this topic in detail.^64,65

The influence of catalytic properties on the current–potential (I–E) behavior of a photoelectrode is modeled in Fig. 9a, in which eqn (11) was used to model the LSV curves of a photocathode for four different values of (A_cat/A_hv) and assuming that the surface contains a highly active catalyst with β = −40 mV per decade of current and i_o = 1 × 10⁻³ A cm⁻². Values of (A_cat/A_hv) less than one have been included to account for instances where the catalytically active sites do not cover the entire photoelectrode surface. With decreasing (A_cat/A_hv), the LSV curve shifts to more negative potentials, reflecting the need for a larger kinetic overpotential in order to sustain a given photocurrent through a smaller catalytically active surface area. Conversely, increased (A_cat/A_hv) shifts the LSV curve to positive potentials because the net photocurrent is distributed across more active sites such that a lower kinetic overpotential is required. For large loadings of highly active catalysts such as the blue curve in Fig. 9a, eqn (11) predicts an apparent increase in the photocurrent onset potential. However, such an observation is unlikely to be seen experimentally due to the occurrence of the back reaction, which was omitted from this analysis.

Fig. 9 Evaluating kinetic overpotential losses. (a) Modeled LSV curves based on eqn (11) for a photocathode with varied catalyst loading as described by the ratio (A_cat/A_hv). The black line gives the solid-state IV curve characteristics based on the diode equation and using the following parameters: A_j = A_hv, j_o = 1 × 10⁻¹⁰ A cm⁻², n = 1.1, χ = 0, and j_L = 25 mA cm⁻². Kinetic overpotential losses were modeled based on Tafel kinetics using values of i_o = 1 × 10⁻³ A cm⁻² and β = −40 mV per decade of current that are typical of a highly active HER catalyst such as Pt. The HOR back reaction has been ignored in this analysis, and the current has been normalized to the photoactive surface area, A_hv. (b) Modeled HER kinetic overpotential losses calculated as a function of (A_cat/A_hv) using eqn (10) at constant (I/A_hv) = 10 mA cm⁻². Curves are shown for the high activity catalyst from (a) and a lower activity HER catalyst characterized by i_o = 6 × 10⁻⁵ A cm⁻² and β = −80 mV per decade of current. (c) Experimental IR-corrected LSV curves recorded in deaerated 0.5 mol L⁻¹ H₂SO₄ for control samples consisting of varied loadings of Pt particles electrodeposited onto metallic p⁺Si substrates coated with 15 nm Ti. Inset shows the overpotential at 10 mA cm⁻² as a function of catalyst surface area (A_cat) normalized to the geometric electrode area (A_geo).

While Fig. 9a illustrates the effect of the catalyst loading on η_cat, Fig. 9b illustrates the influence of the intrinsic activity of the catalyst that is deposited on the photoelectrode surface. In Fig. 9b, the kinetic overpotential losses at I = 10 mA cm⁻² were modeled as a function of (A_cat/A_hv) for electrode surfaces coated with highly active co-catalyst like Pt or less active HER co-catalyst such as Ni. There is a strong dependence of η_cat on A_cat for both catalysts, but this dependence is greatest for the less active catalyst due to its larger Tafel slope. As noted by previous studies,^2,66Fig. 9b illustrates how 3D structuring can be especially beneficial for decreasing kinetic losses of less active catalysts by supporting higher catalyst loadings without incurring unacceptable levels of optical losses associated with those catalysts.

In order to independently estimate the kinetic overpotential losses associated with the samples used in this study, control samples were fabricated by electrodepositing different loadings of Pt nanoparticle catalysts onto conductive, degeneratively-doped p⁺Si substrates that were first coated with a 15 nm Ti overlayer to mimic the surface of photoelectrodes. Because the substrate is degenerate, it is not photo-active, and serves as a conductive metallic substrate for which the IR-corrected LSV curve can be used to directly measure the kinetic overpotential losses at the electrode surface.^21,67Fig. 9c contains the LSV curve for control samples with three different Pt loadings (A_cat/A_geo), where the values of A_cat were taken to be the electrochemically active surface area (ECSA) of the Pt catalysts as determined by analysis of the integrated hydrogen under potential deposition (H_upd) current from cyclic voltammetry (CV) curves. As expected from the Tafel equation and as seen in the inset of Fig. 9c, the kinetic overpotential at (I/A_geo) = 10 mA cm⁻² decreases linearly with log(A_cat/A_geo), although the dependence is fairly weak due to the relatively small absolute value of β for Pt HER catalysts.

Importantly, the high catalytic activity of Pt ensures that the Pt loading necessary to maintain low kinetic overpotential losses is well below levels that would block a significant fraction of incident light.^64,68 Consistent with these prior studies, we found that 2D Pt particle coverage of only ≈9.4% was sufficient to maintain kinetic losses of ≈100 mV at 10 mA cm⁻² on a p⁺Si electrode coated with 2 nm SiO₂ and 15 nm Ti. For this reason, and because this topic has been evaluated in detail elsewhere,⁶⁶ we did not compare the influence of catalyst loading on planar versus 3D structured photoelectrodes. Instead, the deposition time used to electrodeposit Pt catalyst was kept the same for all photoelectrode samples investigated in this study.

2.5.6 Mass transport (bubble dynamics). Another important effect of 3D structure on the performance of a photoelectrode being used for water splitting is its influence on the nucleation, growth, coalescence, and detachment of gas-phase H₂ or O₂ bubbles that form on the photoelectrode surface. Herein, the collective behavior of gas bubbles is referred to as “bubble dynamics”, which can strongly affect photoelectrode conversion efficiency.^12,13,69,70 In general, the presence of bubbles on the photoelectrode surface is detrimental to performance, resulting in higher optical reflection, increased solution IR losses, decreased carrier collection, and higher kinetic overpotentials due to decreased catalytic surface area, A_cat. The magnitude of undesirable effects of bubble dynamics on electrode performance can vary greatly, and is often heavily dependent on the wettability and/or morphology of the electrode surface. Additionally, experimental conditions such as current density, electrode orientation, ionic concentration, temperature, pressure, applied potential, and hydrodynamics can influence the bubble dynamics on gas-evolving electrodes.^71–73 Previous studies have reported the tendency of 3D structured photoelectrodes to promote bubble detachment at smaller size and lower coverage on the photoelectrode surface, leading to improved performance.^12,13 Similar qualitative observations were made for the photoelectrodes studied in this work, as seen in the optical images in the insets of Fig. 10 comparing the size and coverage of bubbles on planar and 3D structured photoelectrodes.

Fig. 10 Measuring bubble-induced photocurrent losses. (a and b) LSV curves measured at different scan rates in the presence and absence of surfactant for (a) planar and (b) 3D-structured Si photocathodes. Red curve: 20 mV s⁻¹ in 0.5 mol L⁻¹ H₂SO₄, black curve: 100 mV s⁻¹ in 0.5 mol L⁻¹ H₂SO₄, blue curve: 20 mV s⁻¹ in 0.5 mol L⁻¹ H₂SO₄ + surfactant. Arrows show the direction of the LSV scan. The 20 mV s⁻¹ scans were scanned from negative to positive to ensure that a significant amount of bubbles were present at lower current densities. Insets show photographs of photoelectrode surfaces after LSV measurements (no surfactant), with the width of both exposed photoelectrodes being ≈1 cm. (c and d) Chronoamperometry measurements in the absence (open markers) and presence (solid markers) of surfactant.

There are at least two mechanisms by which 3D-structuring can influence the coverage of bubbles on an electrode surface. The first relates to the wettability, or hydrophobic character, of the electrode surface. When the electrode surface is hydrophilic, the low solid–liquid surface tension results in a large bubble contact angle, defined as the angle between the solid–gas and liquid/gas interfaces with an apex at the triple-phase contact point. This large contact angle corresponds to a lower adhesion force to the electrode surface, and consequently leads to a lower average bubble departure diameter and average bubble coverage.⁷⁴ 3D structuring, or surface roughness, can influence the wettability of a surface and lead to significant deviation in the observed contact angles compared to the Young contact angle for a smooth surface.⁷⁵ The relationship between 3D-structuring, or roughness, and wettability has been most commonly described by the Wenzel and Cassie–Baxter models. According to both models, surface roughness tends to make a hydrophobic surface more hydrophobic, and a hydrophilic surface more hydrophilic.^76,77 These models and the general phenomena they describe are most commonly applied to the behavior of liquid droplets on a 3D structured surface, but many of the basic principles can also be extended to the inverse case of a gas bubble immersed in liquid solution and attached to a solid surface. In the Cassie–Baxter model, the interstitial spaces between 3D features on a surface are occupied by the same phase as the bulk fluid (i.e. liquid electrolyte in this study), and Wenzel behavior is characterized by instances when the droplet or bubble attached to the 3D structured surface extends down into the interstitial spaces.⁷⁵

The physical constraints on bubble growth imposed by the geometry of the micro-pillar environment may also be an important factor for bubbles that nucleate in the basal regions. For example, the maximum achievable diameter of a spherical gas bubble that nucleates on the basal surface between pillars is limited by the pitch and diameter of adjacent pillars. Above this diameter, bubble detachment should be favored over continued growth whereby the bubble would have to contort itself into energetically-unfavorable shapes with high surface area to volume ratios. Bubble growth on pillar tops is also expected to experience geometric constraints that lead to enhanced detachment. For bubble nucleation on the top of a pillar, the maximum diameter of the base of the bubble, where it is attached to the electrode, is limited to the diameter of the pillar. As a bubble continues to grow, this constraint on the triple phase contact diameter necessitates a larger contact angle. According to the Young–Duprè equation, which describes the relationship between the liquid surface tension, contact angle and adhesion force of a bubble or droplet on a surface,⁷⁸ this increase in contact angle should decrease the adhesion force, and therefore lead to bubble detachment at a smaller diameter than would be expected on an otherwise identical planar electrode. Coalescence of bubbles from the tops of neighboring pillars may also decrease bubble detachment diameters, as similarly observed for studies of disc electrodes of varied pitch.⁷⁹ Overall, the combined effects of 3D surface morphology on bubble dynamics are expected to facilitate detachment of bubbles from the electrode surface, leading to lower bubble coverage on the surface and a smaller influence on photoelectrode performance.

In this study, the net influence of gaseous bubbles on the total photocurrent generated by a photoelectrode was measured by two commonly-used electroanalytical techniques: LSV and chronoamperometry (CA). When measured by LSV, the influence of bubbles can be viewed by changing the scan rate of the LSV curve or by adding a surfactant to the electrolyte. Scan rate, ν, influences bubble dynamics by affecting the total charge passed during the LSV measurement, and thus the total amount of gaseous H₂ or O₂ evolved. In Fig. 10a and b, LSV curves were recorded for planar and 3D photoelectrodes at two different scan rates. At the faster scan rate of 100 mV s⁻¹, the short scan time limits the amount of H₂ bubbles evolved, thereby minimizing their negative influence on the measured photocurrent. However, significantly more H₂ bubbles are generated during the longer LSV measurements conducted at the slower scan rate of 20 mV s⁻¹. For the planar sample (Fig. 10a), this lower scan rate results in significant decrease in reduction current density at all potentials due to the more substantial build-up of bubbles on the surface. By contrast, the scan rate has negligible influence on LSVs performed on the 3D structured sample (Fig. 10b), indicating that the H₂ bubbles evolved from that surface under the slow scan rate had little influence on photoelectrode performance. For both samples, it should be noted that the oxidation peak observed at positive potentials in the LSV curves that were scanned from negative to positive potential is due to the hydrogen oxidation reaction.

Another means of altering the gas bubble dynamics on the electrode surface is by adding a surfactant to the electrolyte to decrease the surface tension at the liquid/vapor interface (γ_LV) and/or to alter nucleation rates.^13,80,81 Referring again to the Young–Duprè equation, a decrease in γ_LV lowers the work of adhesion holding the bubble to the surface, consequently decreasing the average bubble size at which that adhesion force is exceeded by the buoyancy and/or hydrodynamic forces that lead to bubble detachment from the surface. In turn, the smaller bubble departure diameter results in a lower surface coverage of bubbles and therefore minimization of their adverse effects. Fig. 10a and b also contain LSV curves measured in the presence of a surfactant. During these measurements, a constant stream of small bubbles, barely visible to the naked eye, evolved from the photoelectrode surface with very low bubble coverage. For both the planar and 3D structured MIS photoelectrodes, the LSVs conducted at 20 mV s⁻¹ in the presence of surfactant are very similar to the 100 mV s⁻¹ scans carried out in the surfactant-free solution. The similarity of these two LSV curves for the planar electrode indicates that the scan rate of 100 mV s⁻¹ was fast enough to avoid significant bubble-induced losses in the surfactant-free solution, verifying its use as a “bubble-free” control measurement in this study.

The effect of bubbles on photoelectrode surface can also be viewed during constant potential CA measurements performed with and without surfactant (Fig. 10c and d). Consistent with the LSV measurements in Fig. 10b, the CA curves performed at two different applied potentials for the 3D photoelectrode are nearly independent of the presence of surfactant, again highlighting the ability of the 3D structure to facilitate efficient transport of H_2(g) away from the photoelectrode surface. Unlike the 3D structured photoelectrode, the photocurrents in the CA curves measured for the planar photoelectrode exhibit a strong dependence on the presence of the surfactant (Fig. 10c). With the surfactant present, H₂ bubbles were observed to detach from the electrode surface almost immediately. Without surfactant, large H₂ bubbles slowly grew on the photoelectrode, blocking an increasingly higher percentage of the electrode surface as the recorded photocurrent gradually decreased. Every 20 s to 30 s, the growing bubbles eventually coalesce, leading to their detachment from the electrode surface and resulting in a sharp increase in photocurrent as a portion of the photoelectrode is temporarily freed of bubbles. Although 3D structuring is not the only way to mitigate the detrimental effects of bubbles on a photoelectrode surface, these measurements clearly highlight an advantage of 3D structured electrodes and illustrate how gas bubbles can strongly influence the steady state performance of photoelectrodes.

2.6 Overall current–voltage loss analysis

By combining experimentally measured parameters with the modeling framework described in this paper, it is possible to estimate the losses associated with various factors (optical, bulk recombination, bubbles, kinetics) and compare these losses between photoelectrodes. These losses can be visualized using loss analysis diagrams, which display the voltage and current losses of the photoelectrode as a function of applied electrochemical potential. Similar loss-analysis diagrams, often referred to as polarization curve figures, are routinely used in the fuel cell field to illustrate the dependency of ohmic, kinetic, and mass transport losses on operating current.^82–84 Such diagrams can be of great utility for comparing the magnitudes and types of efficiency losses between various electrodes.

Fig. 11 contains loss analysis diagrams for the planar control sample (Fig. 11a) and the sample with the highest pillar density (Fig. 11), the two samples that exhibit the greatest differences in their LSV curves in Fig. 2. The current–voltage curves of the photoelectrodes were modeled based on eqn (3), and each of the loss “wedges” were calculated as described in Section XI of the ESI.† Parameters needed to model individual wedges, such as n and i_o for modeling the solid-state behavior, were obtained from experiments specifically designed to determine those parameters. Since the LSV curves in Fig. 2 were performed at relatively high scan rate so as to minimize the influence of gas bubbles, the bubble-induced current and overpotential losses have been omitted from this analysis. Further details of construction of the loss analysis figures are provided in Section XI of the ESI.†

Fig. 11 Loss analysis diagrams comparing losses in (a) the planar control photoelectrode and (b) the 3D structured photoelectrode with the highest pillar density. The solid red line represents the modeled LSV curve. j_L is the photo-limiting current density, and j_max,Si is the maximum theoretical current density that can be achieved under AM 1.5G illumination. Solid-state losses refer to losses associated with bulk and surface recombination losses in the Si semiconductor and at the Si/SiO₂ interface, respectively.

Fig. 11 highlights several of the advantages and disadvantages of 3D structuring, and serves as a useful summary of many of the key findings regarding the p-Si photocathodes studied in this work:

(i) The light-limiting photocurrent density (j_L) of the 3D structured photoelectrode increases by about 35% compared to the planar sample. As shown in Section 2.5.1, the main reason for this improvement in j_L is an increase in optical absorption by the 3D structured photoelectrode due to decreased optical reflection losses. Enhanced carrier collection for minority carriers generated by long-wavelength photons in the 3D-structured photoelectrode also contributes to the increase in j_L, but the analysis in Section 2.5.2 showed that the relative increase due to this influence should only be ≈9% (equivalent to 2 mA cm⁻²) for the high density pillar sample compared to the planar control. Nonetheless, it must be noted that the benefit of 3D structure on enhanced carrier collection will be much larger for photoelectrodes with low quality semiconductors that are characterized by smaller effective minority carrier diffusion lengths.

(ii) The higher junction area and lower junction quality of the 3D structured photoelectrode decreases its photocurrent onset potential by ≈250 mV compared to the planar sample due to the significant increase in the dark saturation current. This photovoltage loss is the single largest disadvantage of 3D structuring in this study, and the photovoltages recorded for all samples are significantly lower than the record photovoltage of 0.63 V that was recently demonstrated using n-Si MIS photoanodes.³¹ For reference, the world record V_oc for a c-Si solar cell operated under AM 1.5 illumination is 0.706 V,⁸⁵ very close to the theoretical maximum V_oc ≈ 0.713 V that is calculated based on the bandgap of Si (E_g = 1.1 eV).⁸⁶

(iii) Both samples suffered from significant ohmic losses. About 85–90% of the series resistance is attributed to the contact resistance associated with the indium solder back contact, with the remainder associated with the uncompensated solution resistance. The back contact resistance could be significantly reduced with low-resistance back contacts made by alloy formation or work function matching between the semiconductor and metallic back contact.

(iv) Good agreement between the experimental and modeled LSV curves is obtained for both the planar and 3D structured photoelectrodes, although some deviation exists at positive potentials for the latter. This disagreement may result from modeling the photoelectrode surface as a single homogeneous junction over its entire surface, whereas the local junction properties are likely to vary substantially between pillar tops, side-walls, and basal regions. For more complex 3D-structured photoelectrodes with disparate interfacial properties associated with different surfaces on the 3D features, it will likely be necessary to use numerical modeling and/or separate sets of equations for each region to explicitly account for these differences.

Collectively, the advantageous influences of 3D structure on photoelectrode performance were outweighed by its detrimental effects in this work. This outcome is exemplified by the fact that the IR-corrected photoelectrode conversion efficiency of the planar RIE sample was 5.8%, while that for the 3D structured photoelectrode was only 2.6% (see ESI Section X describing the calculation of photoelectrode efficiency†). This result underscores the important message that 3D structuring is not always beneficial, especially for semiconducting materials possessing effective minority carrier diffusion lengths that are similar to or greater than the optical absorption depth over most of the wavelength range of interest.

III. Conclusions

This study has demonstrated a systematic approach to deconvoluting the various influences of micro-scale 3D structure on the performance of p-Si MIS photocathodes. This approach was made possible by (i) synthesizing a series of samples with well-defined micropillar geometries, (ii) employing a suite of experimental measurements designed to isolate specific influences of 3D structure, and (iii) combining experiment with modeling to establish structure–property–performance relationships. Through this knowledge, a comprehensive current–potential model of photoelectrode performance was developed that can help to explain and predict the performance of 3D structured photoelectrodes compared to their planar counterparts. This model can be used to construct loss analysis diagrams for comparing loss mechanisms between samples and identifying opportunities for improved performance. Many of the tools and methods demonstrated in this paper can be extended to other photoelectrode materials and 3D electrode architectures, helping to accelerate the development and optimization of PEC technology.

IV. Methods and materials

4.1 Fabrication

4.1.1 Photolithography. A thin layer of hexamethyldisilazane (HMDS) was coated on Si wafer in a HMDS prime oven at 150 °C for 5 min, followed by spin-coating photoresist at a speed of 4000 revolutions per minute for 1 min, then soft-baked at 115 °C for 1 min. The resulting wafer was placed into a contact mask aligner together with our custom-designed mask, then was illuminated with a broadband source with an energy dose of 125 mJ cm⁻² in vacuum contact mode. The wafer was treated with a developer for 1 min and then thoroughly rinsed with deionized H₂O.

4.1.2 Reactive ion etching. The patterned wafer was placed in a vacuum oven at 90 °C for 30 min to remove the remaining solvent and resist. After 1 min of O₂ plasma treatment with reactive ion etching (RIE) to ensure the removal of the residual resist, the wafer was placed under O₂ (10.1 μmol s⁻¹) and SF₆ (69.9 μmol s⁻¹) plasma for etching Si. The height of the Si pillars was controlled by varying the etching time while maintaining the other conditions the same. After the sample was removed from the RIE chamber, the remaining resist was removed by ultrasonication of the wafer in an acetone bath for 15 min, followed by placing in a bath of post-etch residue remover for 20 min at 90 °C.

4.1.3 Rapid thermal annealing (RTA). The resulting sample underwent three cycles of surface oxide formation and removal steps as an extra impurity removal process. The samples were placed in an RTA furnace and were annealed at 1000 °C for 6 min under 807 μmol s⁻¹ of O₂, followed by immersion in a hydrofluoric acid (HF) solution with mass fraction of 0.02 for 5 min. This process was repeated two more times. The samples were then annealed to 950 °C for 10 s in an O₂/N₂ mixture with an O₂ mole fraction of 0.08, cooled to 250 °C in pure N₂, and annealed in forming gas (H₂/N₂ mixture) with H₂ mole fraction of 0.10 at 1000 °C for 60 s. Ellipsometry performed on a planar RIE control sample lacking any pillars indicated that the thickness of the thermally-grown oxide was 1.9 nm, consistent with previous work.³⁴

4.1.4 Metal deposition. 15 nm of Ti (99.99%) was then deposited by electron beam evaporation on all microarray samples using an evaporator system with a base pressure of 1.3 × 10⁻⁵ Pa. For some control samples, 2 nm of Pt (99.99%) was deposited immediately after the Ti deposition without breaking vacuum. Both depositions were performed without substrate heating and under planetary rotation so that the evaporated metal was deposited on the pillar side-walls in addition to the pillar tops and basal regions. Film thicknesses were monitored with quartz crystal thickness monitors and measured with transmission electron microscopy (TEM). For micropillar samples, Pt nanoparticles were deposited by electrodeposition from a stirred deposition bath consisting of 3 mmol L⁻¹ K₂PtCl₄ and 0.5 mol L⁻¹ NaCl. LSV curves conducted in the deposition bath in the dark and under illumination are provided in the ESI, Section I.† Electrodeposition was performed under simulated air mass (AM) 1.5G illumination while applying a potential of −0.1 V versus Ag/AgCl for 120 s.

4.2 Characterization

4.2.1 Photoelectrode characterization and preparation. Optical reflectance spectra of photoelectrode samples were measured with a UV-Vis spectrophotometer. The instrument was equipped with an integrating sphere to measure total and diffuse reflectance. Scanning electron microscope images were taken with an accelerating voltage of 2 kV. Samples were assembled into photoelectrodes for electrochemical measurements by applying In solder back contacts and Cu wire leads, followed by sealing in 2 to 3 layers of vinyl electroplating tape containing a well-defined 0.43 cm² circular opening on the front of the sample that was made by a cork bore. The exposed area was 1.02 cm² for some experiments analyzing the influence of gas bubbles on photoelectrode performance in order to minimize the influence of bubbles that adhere to the edge of the opening.

4.2.2 Electrochemical measurements. All photoelectrochemical measurements were carried out in deaerated 0.5 mol L⁻¹ H₂SO₄ prepared from 18 MΩ cm deionized water and H₂SO₄ that conforms to specifications defined by the Committee on Analytical Reagents of the American Chemical Society. Macroscopic photoelectrochemical measurements were performed in a glass/quartz PEC test cell similar to that described in a previous publication.⁸⁷ The cell contained two compartments, allowing for the Pt wire counterelectrode to be separated from the main compartment by a porous glass frit. A Ag/AgCl reference electrode (+0.22 V versus reversible hydrogen electrode (RHE) in 0.5 mol L⁻¹ H₂SO₄) was used as the reference electrode in most experiments. The head space of the main compartment was continuously purged with N₂ during measurements. Illumination was provided by a 300 W Xe arc lamp fitted with a collimating lens and AM 1.5G filter. For most experiments, the lamp was calibrated to AM 1.5G intensity of 100 mW cm⁻² with a Si reference solar cell. For open circuit photovoltage measurements, the light intensity was adjusted to values between 6 mW cm⁻² and 166 mW cm⁻² by adjusting the focus of the in-line collimating lens. Angular photocurrent dependency was measured by rotating the photoelectrode position within the PEC test cell (see ESI†). The influence of bubbles on photoelectrode performance was quantified using linear sweep voltammetry (LSV) and chronoamperometry measurements in the presence and absence of 4-(1,1,3,3-tetramethylbutyl)phenyl-polyethylene glycol surfactant. The concentration of surfactant was approximately 50 μmol L⁻¹ based on the use of two drops of surfactant that were added to the electrolysis solution using the supplier-provided dispenser.

4.2.3 External quantum efficiency (EQE). EQE measurements were performed over the range 300 nm to 1100 nm, with measurements taken in 10 nm increments for a dwell time of 2.0 s and using chopped (43 Hz), low power (40 μW to 900 μW) monochromatic light beam focused to ≈2 mm. No additional external bias light was used in order to avoid excessive bubble formation. Bias voltage was applied through a current-preamplifier such that the operating potential of the photoelectrode was in the limiting current regime of its LSV curve over the entire range of light intensity. EQE(λ) was computed at each wavelength based on the measured photocurrent and irradiance at each wavelength. Additional details can be found in the ESI Section VII.†

4.2.4 Scanning photocurrent microscopy (SPCM). SPCM measurements were performed on a commercial Raman microscope system with an XY positioning stage (10 cm × 8 cm scan range, 100 nm minimum step size), and an optical microscope coupled to a frequency-doubled Nd:YAG 532 nm laser and 785 nm diode laser. Low-profile electrochemical test cells were machined out of polytetrafluoroethylene. Three-electrode measurements utilized a Pt wire counter electrode and a miniature Ag/AgCl reference electrode. Deaerated 0.5 mol L⁻¹ H₂SO₄ was injected with a syringe and the cell was sealed with a glass window and electroplating tape, but the cell was not air tight. Incident laser power, used to convert photocurrent to external quantum efficiency, was measured with a commercial optical meter. Most SPCM measurements were performed with an incident laser intensity of ≈4 μW, and mapping and linescans were usually carried out with dwell time of 1 s. Electrochemical measurements were performed with a potentiostat. Photocurrent was calculated by subtracting the dark background current (measured before and after the SPCM map or linescan) from the total current. SPCM image processing was performed using a high-performance language for technical computing.

4.2.5 Electron beam induced current (EBIC). Electron beam induced current was measured in a scanning electron microscope (SEM) equipped with a micro-manipulator having a tungsten probe (500 nm tip radius). The electrical probe was placed on top of the Pt/Ti Schottky contact on Si pillars. The ohmic contact of the Si substrate was grounded. An electron beam was irradiated through the thin Pt layer at different acceleration beam voltages (3 keV to 30 keV), generating electron–hole pairs within a corresponding generation volume.⁸⁸ EBIC signals were measured using a low-noise current amplifier under computer control.

Acknowledgements

The majority of this research was performed while D. V. E. and Y. L. held National Research Council Research Associateship Award positions at the National Institute of Standards and Technology. Y. L. also acknowledges support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology Center for Nanoscale Science and Technology, award 70NANB10H193, through the University of Maryland. The authors acknowledge the assistance and support of the staff at the NIST Center for Nanoscale Science and Technology (CNST) NanoFab facility. A. A. T. acknowledges partial support by Science of Precision Multifunctional Nanostructures for Electrical Energy Storage (NEES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under award DESC0001160. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC0494AL85000. The authors acknowledge Sandra Claggett and Igor Levin at NIST for assistance with TEM sample preparation and measurements, respectively.

References

1. M. Gratzel, Nature, 2001, 414, 338–344.
2. M. G. Walter, E. L. Warren, J. R. McKone, S. W. Boettcher, Q. X. Mi, E. A. Santori and N. S. Lewis, Chem. Rev., 2010, 110, 6446–6473.
3. Y. Tachibana, L. Vayssieres and J. R. Durrant, Nat. Photonics, 2012, 6, 511–518.
4. H. Ye, J. Lee, J. S. Jang and A. J. Bard, J. Phys. Chem. C, 2010, 114, 13322–13328.
5. J. W. Lee, H. C. Ye, S. L. Pan and A. J. Bard, Anal. Chem., 2008, 80, 7445–7450.
6. J. M. Gregoire, C. Xiang, S. Mitrovic, X. Liu, M. Marcin, E. W. Conrnell, J. Fan and J. Jin, J. Electrochem. Soc., 2013, 160, F337–F342.
7. N. Lewis, Electrochem. Soc. Interface, 2013, 43–49.
8. K. Sliozberg, D. Schaefer, T. Erichsen, R. Meyer, C. Khare, A. Ludwig and W. Schuhmann, ChemSusChem, 2015, 8, 1270–1278.
9. E. L. Warren, S. W. Boettcher, M. G. Walter, H. A. Atwater and N. S. Lewis, J. Phys. Chem. C, 2011, 115, 594–598.
10. S. W. Boettcher, J. M. Spurgeon, M. C. Putnam, E. L. Warren, D. B. Turner-Evans, M. D. Kelzenberg, J. R. Maiolo, H. A. Atwater and N. S. Lewis, Science, 2010, 327, 185–187.
11. J. M. Spurgeon, H. A. Atwater and N. S. Lewis, J. Phys. Chem. C, 2008, 112, 6186–6193.
12. M. H. Lee, K. Takei, J. J. Zhang, R. Kapadia, M. Zheng, Y. Z. Chen, J. Nah, T. S. Matthews, Y. L. Chueh, J. W. Ager and A. Javey, Angew. Chem., Int. Ed., 2012, 51, 10760–10764.
13. J. H. Oh, T. G. Deutsch, H. C. Yuan and H. M. Branz, Energy Environ. Sci., 2011, 4, 1690–1694.
14. C. Liu, N. P. Dasgupta and P. Yang, Chem. Mater., 2014, 26, 415–422.
15. C. Cheng, H. Zhang, W. Ren, W. Dong and Y. Sun, Nano Energy, 2013, 2, 779–786.
16. S. Y. Noh, K. Sun, C. Choi, M. Niu, M. Yang, K. Xu, S. Jin and D. Wang, Nano Energy, 2013, 2, 351–360.
17. C.-Y. Lee, L. Wang, Y. Kado, R. Kirchgeorg and P. Schmuki, Electrochem. Commun., 2013, 34, 308–311.
18. X. B. Chen, S. H. Shen, L. J. Guo and S. S. Mao, Chem. Rev., 2010, 110, 6503–6570.
19. K. Sivula, F. Le Formal and M. Graetzel, ChemSusChem, 2011, 4, 432–449.
20. B. Liu, C.-H. Wu, J. Miao and P. Yang, ACS Nano, 2014, 8, 11739–11744.
21. Y. W. Chen, J. D. Prange, S. Duhnen, Y. Park, M. Gunji, C. E. D. Chidsey and P. C. McIntyre, Nat. Mater., 2011, 10, 539–544.
22. J. Liu, B. W. Liu, S. Liu, Z. N. Shen, C. B. Li and Y. Xia, Surf. Coat. Technol., 2013, 229, 165–167.
23. M. J. Kenney, M. Gong, Y. Li, J. Z. Wu, J. Feng, M. Lanza and H. Dai, Science, 2013, 342, 836–839.
24. J. C. Hill, A. T. Landers and J. A. Switzer, Nat. Mater., 2015, 14, 1150–1155.
25. A. J. Nozik and R. Memming, J. Phys. Chem., 1996, 100, 13061–13078.
26. T. Zhu and M. N. Chong, Nano Energy, 2015, 12, 347–373.
27. D. V. Esposito, I. Levin, T. P. Moffat and A. A. Talin, Nat. Mater., 2013, 12, 562–568.
28. A. G. Munoz and H. J. Lewerenz, ChemPhysChem, 2010, 11, 1603–1615.
29. H. J. Lewerenz, K. Skorupska, A. G. Munoz, T. Stempel, N. Nusse, M. Lublow, T. Vo-Dinh and P. Kulesza, Electrochim. Acta, 2011, 56, 10726–10736.
30. A. G. Scheuermann, K. W. Kemp, K. Tang, D. Q. Lu, P. F. Satterthwaite, T. Ito, C. E. D. Chidsey and P. C. McIntyre, Energy Environ. Sci., 2016, 9, 504–516.
31. A. G. Scheuermann, J. P. Lawrence, K. W. Kemp, T. Ito, A. Walsh, C. E. D. Chidsey, P. K. Hurley and P. C. McIntyre, Nat. Mater., 2016, 15, 99–105.
32. N. Y. Labrador, X. Li, Y. Liu, J. T. Koberstein, R. Wang, H. Tan, T. P. Moffat and D. V. Esposito, Nano Lett., 2016, 16, 6452–6459.
33. R. Singh, M. A. Green and K. Rajkanan, Sol. Cells, 1981, 3, 95–148.
34. R. B. Godfrey and M. A. Green, Appl. Phys. Lett., 1978, 33, 637–639.
35. J. Ustarroz, T. Altantzis, J. A. Hammons, A. Hubin, S. Bals and H. Terryn, Chem. Mater., 2014, 26, 2396–2406.
36. M. X. Tan, P. E. Laibinis, S. T. Nguyen, J. M. Kesselman, C. E. Stanton and N. S. Lewis, Prog. Inorg. Chem., 1994, 41, 21–144.
37. X. X. Liu and J. R. Sites, J. Appl. Phys., 1994, 75, 577–581.
38. R. H. Coridan, A. C. Nielander, S. A. Francis, M. T. McDowell, V. Dix, S. M. Chatman and N. Lewis, Energy Environ. Sci., 2015, 8, 2886–2901.
39. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis and H. A. Atwater, Nat. Mater., 2010, 9, 368–368.
40. L. Y. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens and M. L. Brongersma, Nat. Mater., 2009, 8, 643–647.
41. S. J. Kim, I. Thomann, J. Park, J.-H. Kang, A. P. Vasudev and M. L. Brongersma, Nano Lett., 2014, 14, 1446–1452.
42. S. Hu, C.-Y. Chi, K. T. Fountaine, M. Yao, H. A. Atwater, P. D. Dapkus, N. S. Lewis and C. Zhou, Energy Environ. Sci., 2013, 6, 1879–1890.
43. J. Oh, H. C. Yuan and H. M. Branz, Nat. Nanotechnol., 2012, 7, 743–748.
44. J. M. Bennett, in Handbook of Optics, ed. M. Bass and V. N. Mahajan, McGraw Hill, 3rd edn, 2010, vol. 1, ch. 12, p. 31.
45. Index of refraction of inorganic liquids, in CRC Handbook of Chemistry and Physics, ed. W. M. Haynes, D. R. Lide and T. J. Bruno, CRC Press, Taylor and Francis Group, LLC, 97th edn, 2016, ch. section 4, p. 132.
46. Physical and optical properties of minerals, in CRC Handbook of Chemistry and Physics, ed. W. M. Haynes, D. R. Lide and T. J. Bruno, CRC Press, Taylor and Francis Group, LLC, 97th edn, 2016, ch. section 4, pp. 133–138.
47. H. Doscher, J. F. Geisz, T. G. Deutsch and J. A. Turner, Energy Environ. Sci., 2014, 7, 2951–2956.
48. A. Boukai, P. Haney, A. Katzenmeyer, G. M. Gallatin, A. A. Talin and P. Yang, Chem. Phys. Lett., 2011, 501, 153–158.
49. S. Lany, J. Phys.: Condens. Matter, 2015, 27, 283203.
50. M. A. Green and M. J. Keevers, Prog. Photovoltaics, 1995, 3, 189–192.
51. J. R. McKone, A. P. Pieterick, H. B. Gray and N. S. Lewis, J. Am. Chem. Soc., 2013, 135, 223–231.
52. B. M. Kayes, H. A. Atwater and N. S. Lewis, J. Appl. Phys., 2005, 97, 114302.
53. S. J. Fonash, J. Appl. Phys., 1980, 51, 2115–2118.
54. A. E. Grün, Zeitschrift für Naturforschung A, 1957, 12, 89.
55. A. G. Aberle, Prog. Photovoltaics, 2000, 8, 473–487.
56. R. Memming, Semiconductor Electrochemistry, Wiley, 2001.
57. A. G. Scheuermann, J. D. Prange, M. Gunji, C. E. D. Chidsey and P. C. McIntyre, Energy Environ. Sci., 2013, 6, 2487–2496.
58. B. Seger, S. D. Tilley, T. Pedersen, P. C. K. Vesborg, O. Hansen, M. Graetzel and I. Chorkendorff, J. Mater. Chem. A, 2013, 1, 15089–15094.
59. W. A. Smith, I. D. Sharp, N. Strandwitz and J. Bisquert, Energy Environ. Sci., 2015, 8, 2851–2862.
60. A. J. Bard and L. R. Faulkner, in Electrochemical Methods, John Wiley & Sons, Inc., 2nd edn, 2001, ch. 3, pp. 87–136.
61. C. C. L. McCrory, S. Jung, J. C. Peters and T. F. Jaramillo, J. Am. Chem. Soc., 2013, 135, 16977–16987.
62. C. C. L. McCrory, S. Jung, I. M. Ferrer, S. M. Chatman, J. C. Peters and T. F. Jaramillo, J. Am. Chem. Soc., 2015, 137, 4347–4357.
63. W. C. Sheng, H. A. Gasteiger and Y. Shao-Horn, J. Electrochem. Soc., 2010, 157, B1529–B1536.
64. Y. Chen, K. Sun, H. Audesirk, C. Xiang and N. S. Lewis, Energy Environ. Sci., 2015, 8, 1736–1747.
65. E. Kemppainen, A. Bodin, B. Sebok, T. Pedersen, B. Seger, B. Mei, D. Bae, P. C. K. Vesborg, J. Halme, O. Hansen, P. D. Lund and I. Chorkendorff, Energy Environ. Sci., 2015, 8, 2991–2999.
66. C. W. Roske, E. J. Popczun, B. Seger, C. G. Read, T. Pedersen, O. Hansen, P. C. K. Vesborg, B. S. Brunschwig, R. E. Schaak, I. Chorkendorff, H. B. Gray and N. S. Lewis, J. Phys. Chem. Lett., 2015, 6, 1679–1683.
67. S. Hu, M. R. Shaner, J. A. Beardslee, M. Lichterman, B. S. Brunschwig and N. S. Lewis, Science, 2014, 344, 1005–1009.
68. L. Ji, M. D. McDaniel, S. Wang, A. B. Posadas, X. Li, H. Huang, J. C. Lee, A. A. Demkov, A. J. Bard, J. G. Ekerdt and E. T. Yu, Nat. Nanotechnol., 2015, 10, 84–90.
69. A. Berger and J. Newman, J. Electrochem. Soc., 2014, 161, E3328–E3340.
70. S. Hernandez, G. Barbero, G. Saracco and A. L. Alexe-Ionescu, J. Phys. Chem. C, 2015, 119, 9916–9925.
71. C. Sillen, E. Barendrecht, L. J. J. Janssen and S. J. D. Vanstralen, Int. J. Hydrogen Energy, 1982, 7, 577–587.
72. D. Fernandez, P. Maurer, M. Martine, J. M. D. Coey and M. E. Moebius, Langmuir, 2014, 30, 13065–13074.
73. H. Vogt, Electrochim. Acta, 1989, 34, 1429–1432.
74. K. Zeng and D. Zhang, Prog. Energy Combust. Sci., 2010, 36, 307–326.
75. A. Marmur, Soft Matter, 2006, 2, 12–17.
76. R. N. Wenzel, Ind. Eng. Chem., 1936, 28, 988–994.
77. A. B. D. Cassie and S. Baxter, Trans. Faraday Soc., 1944, 40, 0546–0550.
78. M. E. Schrader, Langmuir, 1995, 11, 3585–3589.
79. C. Brussieux, P. Viers, H. Roustan and M. Rakib, Electrochim. Acta, 2011, 56, 7194–7201.
80. Q. Chen, L. Luo, H. Faraji, S. W. Feldberg and H. S. White, J. Phys. Chem. Lett., 2014, 5, 3539–3544.
81. L. King and S. S. Sadhal, Heat Mass Transfer, 2014, 50, 373–382.
82. S. Park, Y. Shao, R. Kou, V. V. Viswanathan, S. A. Towne, P. C. Rieke, J. Liu, Y. Lin and Y. Wang, J. Electrochem. Soc., 2011, 158, B297–B302.
83. P. P. Mukherjee, Q. Kang and C.-Y. Wang, Energy Environ. Sci., 2011, 4, 346–369.
84. M. K. Debe, Nature, 2012, 486, 43–51.
85. M. A. Green, Prog. Photovoltaics, 2009, 17, 183–189.
86. M. A. Green, in Solar Cells, ed. J. Nick Holonyak, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1982, pp. 85–102.
87. D. V. Esposito, O. Y. Goue, K. D. Dobson, B. E. McCandless, J. G. G. Chen and R. W. Birkmire, Rev. Sci. Instrum., 2009, 80, 125107.
88. H. J. Leamy, J. Appl. Phys., 1982, 53, R51–R80.
89. T. E. Everhart and P. H. Hoff, J. Appl. Phys., 1971, 42, 5837–5846.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6se00073h

‡ These authors contributed equally to this work.

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