Charge separation via asymmetric illumination in

Articles https://doi.org/10.1038/s41560-018-0194-0

Charge separation via asymmetric illumination in photocatalytic Cu2O particles Ruotian Chen1,2, Shan Pang1, Hongyu An1,2, Jian Zhu1, Sheng Ye1, Yuying Gao1,2, Fengtao Fan1* and Can Li1* Solar-driven photocatalytic reactions provide a potential route to sustainable fuels. These processes rely on the effective separation of photogenerated charges, and therefore understanding and exploring the driving force for charge separation is key to improving the photocatalytic performance. Here, using surface photovoltage microscopy, we demonstrate that the photogenerated charges can be separated effectively in a high-symmetry Cu2O photocatalyst particle by asymmetric light irradiation. The holes and electrons are transferred to the illuminated and shadow regions, respectively, of a single photocatalytic particle. Quantitative results show that the intrinsic difference between electron and hole mobilities enables a diffusion-controlled charge separation process, which is stronger than that caused by conventional built-in electric fields (40 mV versus 10 mV). Based on the findings, we assemble spatially separated redox co-catalysts on a single photocatalytic particle and, in doing so, enhance the performance for a model photocatalytic reaction by 300%. These findings highlight the driving force caused by charge mobility differences and the use of asymmetric light illumination for charge separation in photocatalysis.

P

hotocatalysis using semiconductor particles is a promising technology for converting solar energy into clean chemical fuels1,2. The effective spatial separation and migration of photogenerated charges to surface reaction sites are key to improving photocatalytic solar fuel production3,4. The aligned built-in electric fields usually formed at the surface or buried interface in photocatalytic systems are generally considered as the main driving force for charge separation that drives the targeted surface reaction5,6. Accordingly, several surface/interface engineering strategies have been developed to create strong built-in electric fields, which include co-catalyst loading7,8, phase junctions9,10, heterojunctions11,12 and crystal facet architecture13,14. As a result, the electrons and holes are separated and transferred to two spatially separated surface locations, where they are utilized for chemical reactions. This research emphasizes the importance of a built-in electric field in driving electrons and holes to different surface reaction sites, which improves photocatalytic performance. Though the aligned built-in electric field has made an important contribution to charge separation (drifted charge separation), charge separation via the diffusion of charge carriers (diffused charge separation), another charge separation pathway in semiconductors, should also be conceivable15,16, but is poorly understood and has seldom been investigated in actual photocatalytic systems17,18. Herein, as a proof-of-concept study, we imaged the diffused charge separation process initiated by asymmetric light illumination on a high-symmetry Cu2O photocatalyst particle. A driving force for charge separation in these photocatalysts, caused by the charge mobility difference and asymmetric light illumination, was clearly produced. With this strong driving force, the photogenerated charges can be effectively used to assemble spatially separated redox co-catalysts on a single photocatalyst particle, which leads to a significantly improved performance of the photocatalytic degradation of methylene blue.

Charge separation under asymmetric illumination

Cubic Cu2O single crystals (Supplementary Fig. 1) were prepared as a model photocatalytic system due to their highly desirable properties towards solar energy conversion19–22 and highly symmetrical structure (cubic phase (Supplementary Fig. 2)), which rules out the influence of the intrinsic asymmetric built-in electric field on charge separation23–25. Figure 1a shows the experimental design of this study for diffused charge separation. Two light sources with a tunable light intensity and opposite irradiation direction were employed to perform asymmetric photoexcitation on the Cu2O crystals. Kelvin probe force microscopy (KPFM)26,27 was combined with the aforementioned light system to map the nanometre-resolution surface photovoltage (SPV)28–30, which can directly indicate the charge separation31,32. Here this method is called surface photovoltage microscopy (SPVM). A light source with a tunable wavelength from a xenon lamp was equipped with a chopper to perform spatially resolved surface photovoltage spectroscopy (SRSPS) (Methods gives the details)33. Localized SPV measurements were performed on cubic Cu2O particles grown along the (111) orientation on asymmetric photoexcitation (turning off the laser light source), as shown in Fig. 1b. A shadow facet on the back side and illuminated facet on the front side can be formed by xenon lamp irradiation with the light direction nearly parallel to the fluorine-doped tin oxide (FTO) substrate (inset in Fig. 1b), which resulted in a photogenerated carrier concentration gradient between the illuminated facet and shadow facet (Fig. 1b). Interestingly, the two facets showed opposite photoinduced surface potential changes (Fig. 1c,d). On illumination, the surface potential of the illuminated facet increased by 30 mV, whereas the surface potential of the shadow facet decreased by 10 mV (Fig. 1e). These results indicated that the types of photogenerated charge on the two facets differed from each other under asymmetric illumination. To investigate further the relationship between the two types of charge carrier, surface potential signals tuned with 5 Hz modulated light

1 State Key Laboratory of Catalysis, Dalian National Laboratory for Clean Energy, The Collaborative Innovation Centre of Chemistry for Energy Materials (iChEM), Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China. 2University of Chinese Academy of Sciences, Beijing, China. *e-mail: [email protected]; [email protected]

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Fig. 1 | Charge separation between the illuminated facet and shadow facet under asymmetric illumination. a, Experimental set-up for SPV imaging of the Cu2O photocatalyst. Two light sources with a tunable light intensity and opposite irradiation direction were employed to perform the asymmetric photoexcitation. b, Illustration of asymmetric-irradiation-induced illuminated and shadow regions on a typical cubic Cu2O particle grown along the (111) orientation. c,d, Corresponding surface potential images in the dark state (c) and under illumination (d) (λ = 450 nm). e, Surface potential values extracted across the dashed lines in c and d. The dashed black line corresponds to the position of the edge between the illuminated facet and the shadow facet. f, Transient surface potential signals on the illuminated facet (blue) and shadow facet (red) collected with 5 Hz modulated light. g, SPVM image of the particle obtained by subtracting the surface potential in the dark from the surface potential under illumination. h,i, Phase (h) and amplitude (i) of SPS acquired at the centre of the illuminated facet (blue) and shadow facet (red). j, SPV signals of illuminated (blue) and shadow (red) facets plotted as a function of light intensity. The light intensity is shown as percentages of the total light intensity of 4 mW cm–2. d.c., direct current.



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Fig. 2 | Impact of illumination symmetry on the charge separation. a, AFM image of a Cu2O particle. The particle was simultaneously irradiated by a xenon lamp (λ = 450 nm) and a laser (λ = 450 nm) with the irradiation direction as shown. The lamp intensity was 4 mW cm–2. The laser intensity varied from 0% to 100% of the lamp intensity. b–f, The corresponding SPVM images of the same particle under dual light irradiation. The laser intensity is tuned to 0% (b), 10% (c), 20% (d), 40% (e) and 100% (f) of the lamp intensity. g, The mean of the SPV signals collected at the centre regions of the illuminated facet (blue) and shadow facet (red) under the illumination conditions in b–f. The error bars of 5 mV were obtained from the electronic noise (random errors) of the external lock-in amplifier.

were collected on the illuminated facet and shadow facet (Fig. 1f). Both signals showed periodic changes of 5 Hz, but with opposite trends when the light was on and off, which suggests that photogenerated holes and electrons were separated and transferred to the illuminated facet and shadow facet, respectively. SPVM showed a clear spatial correlation between the photogenerated charge distribution and illumination distribution (Fig. 1g). Photogenerated holes (positive SPV, purple region) were imaged in the illuminated region, whereas photogenerated electrons (negative SPV, red region) were imaged in the shadow region. This result reasonably demonstrates that the carrier concentration gradient arising from asymmetric illumination drives charge separation between the illuminated facet and the shadow facet. SRSPS was then used to explore this phenomenon further. The phase degrees of SPV on the two facets were shifted by 180° with respect to each other (Fig. 1h), which directly evidenced charge separation between the two facets. The SPV spectra of the two facets with opposite signs showed that charge separation between them only occurred at superband excitation with the onset at about 642 nm (Supplementary Fig. 3a–c) and became remarkable at a high photon energy (Fig. 1i (Supplementary Fig. 3b,d). This charge separation process was also strongly dependent on the light intensity (Fig. 1j). A light intensity below 0.8 mW cm–2 cannot drive the photogenerated electrons to the shadow facet, which indicates the importance of a high light intensity in the observation of diffused charge separation (Supplementary Fig. 3e). To rule out the intrinsic differences between the illuminated facet and shadow facet that may cause charge separation, SPVM images of single particles were collected using different rotating angles, but with a fixed illumination direction (Supplementary Fig. 4). The illuminated regions were always observed to show hole accumulation, whereas the shadow regions always showed electron accumulation. The SPV values of the illuminated facet and shadow facet are consistent, independent of the rotating angles. The results not only demonstrate the homogeneity of the facets, but also indicate that the tip–sample geometry has little effect on the observed charge separation behaviour because the tip–sample geometry changes with rotating angles. Furthermore, the SPV spectra of all the facets showed similar SPV signals and SPVM images under symmetric illumination, which indicates a homogeneous hole distribution over the whole particle (Supplementary Fig. 5). Furthermore, randomly selected particles also showed similar surface potentials and SPV responses (Supplementary Fig. 6a–f). These results demonstrated

that there were no intrinsic differences between the facets of the Cu2O particles, both in the dark and under illumination. Charge separation between the illuminated facet and shadow facet only arose under asymmetric illumination. Other factors that may affect this asymmetric charge separation behaviour were also investigated. It was found that the interface between the FTO substrate and Cu2O would not affect this charge separation behaviour due to the small interfacial band bending (~5–10 mV) and the narrow width of the space charge region (SCR) at this interface (Supplementary Fig. 6g). To exclude the possible influence of Faradaic processes, such as water and oxygen reduction reactions, on the charge separation behaviour34, we performed the same experiment under nitrogen protection (Supplementary Fig. 7). The SPV values showed a very minor change (intrinsic carrier) eliminates the effect of the intrinsic carrier and is important for the observation of the photo-Dember effect.

Asymmetric co-catalyst assembly

To verify whether these spatially separated photogenerated carriers were available for surface reactions, two typical photodeposition reactions based on reduction (with photogenerated electrons) and oxidation (with photogenerated holes) were carried out under asymmetric illumination using the reactions13: AuCl −4 + 3 e − → Au ↓ + 4 Cl− Mn2 + + x H 2O + (2x−2)h+ → MnOx ↓ + 2x H +

where x = 1.5–2. Figure 5a shows the photoreductive deposition of Au on a typical Cu2O-3 particle. Au particles were observed to be mainly deposited on the shadow facet, whereas the illuminated facet became rough due to photocorrosion. Also, the photodeposition of Au and MnOx with electrons and holes is shown in Fig. 5b. As expected, Au particles were deposited on the shadow facets via photoreduction, whereas MnOx agglomerates were deposited on the illuminated facets via photooxidation. Similar results were observed in atomic force microscopy (AFM) images (Supplementary Fig. 11) and could also be achieved using Cu2O-4 particles (Supplementary Fig. 12). The selective depositions of MnOx and Au on the two faces further confirmed that holes were transferred to the illuminated facet and electrons to the shadow facet under asymmetric illumination. These particles were further examined by SPVM to investigate the charge separation behaviour, as shown in Fig. 5c,d. Increased SPV signals were observed on both the illuminated facet (from 30 to 44 mV) and shadow facet (from –10 to –19 mV) with opposite directions after the selective photodeposition of Au on the shadow facet. Dual depositions of Au and MnOx on specific sites with spatial separation were found to increase further the SPV signal on the illuminated and shadow facets by 20 and 11 mV, respectively (Fig. 5e). We attributed the improvement in charge separation to the modified built-in electric field due to the change in surface potential after the deposition of Au and MnOx (Supplementary Figs. 13 and 14). The deposition of MnOx decreased the surface potential, which promoted holes to the surface, whereas the deposition of Au increased the surface potential, which promoted electrons to the surface (Supplementary Fig. 13). Furthermore, a potential difference of about 80 mV was formed between the shadow facet (high potential) and illuminated facet (low potential) after the selective depositions of Au and MnOx, respectively (Supplementary Fig. 14a–c).



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To give a clear and quantitative summary of the improvement in charge separation after Au and MnOx deposition, the drift SPV values were calculated and isolated from the diffusion SPV values to describe quantitatively the modification of built-in electric fields (Supplementary Fig. 14d). Figure 5f shows the impact of an asymmetric co-catalyst assembly on the built-in electric field. The upward band bending of 10 mV increased to 24 mV on the illuminated facet and decreased to 1 mV on the shadow facet after the selective deposition of Au on the shadow facet. Furthermore, the spatially separated dual deposition of MnOx and Au led to an increase in the upward band bending to 40 mV on the illuminated facet and inverted the upward band bending to the downward band bending of 10 mV. As a result, an aligned built-in electric field directed from the shadow facet to the illuminated facet was formed throughout the particle, which dramatically promoted the charge separation between the illuminated and shadow facets. Based on this, a preliminary study on the photocatalytic degradation of methylene blue showed that the assembly of spatially separated dual co-catalysts with the photo-Dember effect significantly improved the photocatalytic activity to tenfold and threefold that of the Cu2O crystals for bare and randomly deposited co-catalysts, respectively (Supplementary Fig. 15). The results indicated the significance of the photo-Dember effect in assembling spatially separated cocatalysts for a highly efficient charge separation and, consequently, an improved photocatalytic performance.

Finally, taking a cubic Cu2O-3 single crystal as a prototype, we summarized the significant role played by diffused charge separation in an actual photocatalyst with high symmetry (Supplementary Fig. 16). The cubic Cu2O photocatalyst possessed two opposing built-in electric fields with a 10 mV drifted SPV on both facets, which produced no net driving force for charge separation between the facets. On asymmetric illumination, the photoDember effect provided strong parallel driving forces of 20 mV on both facets, which resulted in SPVs of 30 mV on the illuminated facet and –10 mV on the shadow facet due to the different vector directions of the built-in electric fields in the SCRs. The resulting aligned diffusion SPV driving force of 40 mV drove the charge separation between the illuminated facet and shadow facet to afford spatially separated photooxidation and reduction on the two facets, which led to the deposition of the dual co-catalysts, MnOx and Au, on the illuminated and shadow facets, respectively. The asymmetric co-catalyst assembly can form an additional driving force, which was proved to be an aligned built-in electric field, and resulted in a driving force of 90 mV throughout the particle, which significantly improved the photocatalytic performance.

Conclusions

Photocatalytic technology offers the potential to provide renewable hydrogen by solar-driven water splitting or to produce hydrocarbons directly from sunlight, water and CO2. However, the low Nature Energy | www.nature.com/natureenergy


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Nature Energy charge-separation efficiency due to the lack of directional driving forces strongly limits the solar-to-hydrogen efficiency or, more generally, the solar-to-fuel efficiency. Here, our results show a general driving force of directional charge separation in photocatalysis caused by the charge mobility difference and asymmetric light illumination (photo-Dember effect). The driving force is competitive or even stronger than conventional built-in electric fields and enables the photogenerated holes and electrons to be efficiently spatially separated for solar-driven chemical reactions. Moreover, the controllable charge separation via external light manipulation can be used to initiate a spatially controlled asymmetric co-catalyst assembly and produce a stronger additional directional driving force. These directional driving forces can improve the charge separation efficiency of photocatalysts and, in the future, may be applied in the context of solar water splitting or CO2 reduction to increase the efficiency of solar fuel production.

Methods

Sample preparation. Cubic Cu2O single crystals were prepared on a FTO conducting substrate using an electrodeposition method similar to that previously reported51. Isolated cubic Cu2O crystals were deposited galvanostatically with a current density of 0.3 mA cm–2 from a 0.02 M Cu(NO3)2 (AR (Sinopharm Chemical)) aqueous solution. Different sizes of cubic Cu2O single crystals were prepared with the deposition time of 50 s, 300 s, 600 s and 1,800 s. The Cu2O crystals are denoted as Cu2O-1, Cu2O-2, Cu2O-3 and Cu2O-4 according to their increasing size of 0.9, 1.8, 2.6 and 5.2 μm, respectively, according to their scanning electron microscopy (SEM) images (Supplementary Fig. 1). For all the depositions, the pH of the solution was adjusted to 4.7 prior to deposition using 0.2 M NaOH. The deposition was carried out at 60 °C. The method ensured a firm contact between the sample and conducting substrate, which is important for KPFM measurements27. The cubic shape was controlled using Cu(NO3)2 as the precursor52. The n-type surface depletion layer was produced under acidic conditions37,38, and the surface depletion layer can be adjusted by tuning the deposition current53. These particles were well-defined cubes with uniform shapes and sharp edges in a highly isolated manner that can minimize light scattering from other particles. Photodeposition of Au and MnOx. The photodeposition of Au was carried out using HAuCl4 as a precursor and water as a hole scavenger. A mixed solution of 100 μM HAuCl4 and 100 μM MnSO4 was used as the precursor for the dual deposition of Au and MnOx. Before deposition, the precursor solutions were dropped onto the Cu2O samples with a thin solution layer. For asymmetric photodeposition, the samples were surrounded by blackout materials. A 450 nm laser with a light intensity of 4 mW cm–2 was focused onto the samples. The light incident direction was tuned to be parallel to the FTO substrate. For random photodeposition, the laser beam was extended and the samples were surrounded by reflectors to achieve irradiation from all directions. Supplementary Fig. 13a illustrates the photodeposition. During deposition, a thin solution layer was added if the solution was exhausted. The accumulated deposition time was 1 h. SPV measurement. The surface potential (contact potential difference (CPD)) images of the samples were measured using KPFM (Bruker) under an ambient atmosphere in an amplitude-modulated (AM)-KPFM mode. AM-KPFM was used due to its high energy resolution (5 mV) at a low alternating current (a.c.) voltage (Supplementary Fig. 17). The a.c. voltage was set to 0.5 V to avoid a high bias-induce band bending54. The lift mode was adopted with a lift height of 100 nm for the SPVM images. To obtain the quantitative SPV values, the tip was fixed on the centre of a facet with a lift height of –20 nm, which thus avoided the possible cross-talk effect by the compensation of the tip and cantilever42–44. In the lift mode, the topography and surface potential signals were sequentially recorded. The Pt/ Ir-coated Si tip was used as a Kelvin tip with a spring constant of 1–5 N m–1 and resonant frequency of 60–100 kHz. The SPV was the difference in the surface potential (CPD) before and after illumination, defined as SPV = CPDlight – CPDdark (ref. 31). The SPV was directly related to the photogenerated charge separation, whose amplitude and sign denoted the ability of the charge separation and the direction of charge transport, respectively32,55. To acquire a spatially resolved SPV, a combined KPFM system with an illumination system was set up as shown in Fig. 1a. To investigate the impact of asymmetric illumination, two light sources were used. One light source possessed a tunable wavelength from a xenon lamp and could be used to measure surface photovoltage spectra (SPS). Monochromatic light was obtained from the light of a 300 W xenon arc lamp (PLS-SXE300 (Beijing Perfectlight Co. Ltd)) using a Zolix Omni-λ500 monochromator and was focused on the sample using a lens with a 4° grazing angle. The direction of illumination was perpendicular to the tip-cantilever direction (as shown in Fig. 1a) to avoid the shadowing effect by the tip and cantilever (Supplementary Fig. 18)42. The light intensity of the 450 nm monochromatic light was 4 mW cm–2, measured

using a power meter. The light intensity was adjusted using a series of attenuation slices. A chopper was seated between the monochromator and a focused lens with a frequency of 5 Hz to obtain transient SPV signals. To acquire the SRSPS and quantitative SPV signals, the tip was scanned in a very small region (usually approximately 10 nm) to average the surface potential signal while maintaining spatial resolution. Meanwhile, the 5 Hz light-modulated CPD signals were exported from the front panel of the Nanoscope V controller using a BNC (Bayonet Neill–Concelman) connector fed into the SR830 DSP Lock-In Amplifier and synchronized with the chopped signal. The obtained amplifying SPV signals and phase signals, together with the wavelength of the incident light, constituted the SPS and SPV phase spectra, respectively. Using the modulated SPV measurements, the random errors of the SPV signals due to electronic noise can be reduced to 5 mV (Supplementary Fig. 8 gives the statistics data), in contrast to the signals errors of about 10–20 mV obtained directly from the KPFM potential channel (Supplementary Fig. 19 gives the statistics data). The amplitude of the SPV was calibrated using the actual CPD changes under chopped illumination. The other light source was a 450 nm laser equipped with a neutral density filter. The light intensity could be adjusted from 0 to 100 mW cm–2, which ensured saturation of the measured SPV. The light was almost parallel to the substrate and provided a symmetric light excitation in combination with the aforementioned light source. SPVM was measured by continuously mapping the surface potential images in dark and light conditions in the same locations. The difference in the surface potential images in the light and dark was extracted as an SPV image. All SPV images in the article were acquired using 450 nm light with a light intensity of 4 mW cm–2. To investigate the possible effect of cross-talks on our measurement (which may affect surface potential values in AM-KPFM measurements)43,44, we investigated the effect of lift height (Supplementary Fig. 8), a.c. bias (Supplementary Fig. 19) and tip geometry (Supplementary Fig. 20) on the measured results. These results all showed that the SPV values on both the illuminated facet and the shadow facet are affected only a little by these factors and the effect of cross-talk on the AM-KPFM measurements are not the cause of the observed charge separation between the illuminated facet and shadow facet, which further confirms the credibility of our results and conclusions. SEM. Sample morphologies were examined by SEM taken with a Quanta 200 FEG scanning electron microscope. The operation voltage was 30 kV. Raman spectroscopy. White-light optical images and Raman spectra were collected using a Renishaw InVia confocal Raman microscope and an Olympus ×100 objective. A 532 nm laser was used as the excitation light. To prevent the sample from laser-induced damage, the laser power at the sample was set to 0.2 mW. Theoretical calculation. Theoretical calculations of the Dember SPV were based on Poisson and continuity equations. The simulation and fitting program was written in Matlab scripts using Matlab software. To describe the charge separation and transport in Cu2O, we used the continuity equation given by56: ∂Δp(x , t ) ∂ 2Δp(x , t ) ∂Δp(x , t ) ∂E Δp(x , t ) −μp E = Dp −μp Δp(x , t ) − ∂t ∂x ∂x τp ∂x 2

(2)

where ∆p(x,t) is the excess hole density, Dp is the hole diffusion coefficient and E is the extra electric field. E that corresponds to the x coordinate is a finite difference, and E can be regarded as a constant in each of the differential units. For the diffused process, equation (1) can be reduced to a one-dimensional diffusion equation57: ∂ 2Δp (x , t ) Δp (x , t ) ∂Δp (x , t ) = Dp − ∂t τp ∂x 2

(3)

To calculate the SPV induced by diffusion, the Poisson equation was employed: ∂E p ∂x

=−

e (p − n ) εε0

(4)

where Ep is the electric field induced by separated holes and electrons, e is the absolute value of the electron charge, ε is the relative dielectric constant and ε0 is the vacuum dielectric constant. The solution of equation (2), substitution of the excess hole and electron densities, p(x) and n(x), into the Poisson equation (3), and integration of the electric field Ep over the separated distance of electrons and holes can produce an equation for photovoltage SPV(t): SPV(t ) =

∫0

d

Ep (x , t )dx

(5)

For reasonable values, the doping density N = 1014 cm–3 (ref. 50), dielectric constant ϵ = 7.2 (ref. 58) and the hole mobility = 50 cm2 V–1 s–1) (ref. 59). Dp/Dn = μp/μn according to the Einstein relationship, set as 10, 102 and 103, respectively.



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Determination of diffusion SPV. The total SPV consists of built-in electric fieldinduced drifted SPV and diffusion-induced SPV. The drift SPV was the same for both illuminated and shadow facets due to the high symmetry of the built-in electric field (Supplementary Fig. 5). The diffusion SPV of the two facets possessed opposite signs and equal magnitudes. The SPV of the illuminated facet is given by: SPVilluminated = SPVdrift + SPVdiffusion

(6)

whereas the SPV of the shadow facet is given by: SPVshadow = SPVdrift−SPVdiffusion

(7)

According to the expressions for SPVilluminated and SPVshadow, we can obtain the magnitude of diffusion SPV using: SPVdiffusion =

1 (SPVilluminated−SPVshadow) 2

(8)

and the drift SPV using: 1 SPVdrift = (SPVilluminated + SPVshadow) 2

(9)

Therefore, we can measure the diffusion SPV and drift SPV according to equations (7) and (8) by measuring the SPV values of the illuminated and shadow facets. The SPV signals were recorded according to the average SPV values at the centre region (20 nm × 20 nm) of the facet. This method was reliable based on our experimental data, as follows: for the Cu2O-3 sample, the SPV of the illuminated facet was measured as 30 mV and that of the shadow facet was measured as –10 mV (Fig. 1f,i). We also measured the drift SPV as about 10 mV (Fig. 3d) and directly derived a diffusion SPV of 20 mV according to equation (5). This measured result corresponded well with the values derived from equations (7) and (8). Based on equations (7) and (8), we derived a drift SPV of 10 mV and diffusion SPV of 20 mV, according only to the SPV of the illuminated facet and shadow facet, without the need to measure the drift SPV using the method shown in Fig. 3. The diffusion SPV expression was derived according to the electric field induced by the Dember effect, given by31: E (x ) =

(Dp−Dn)

(

dδn (x) dx

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σ0 + e(μn + μp )δn(x )

(10)

where σ0 = e(μn nb + μp pb ) is the dark conductivity of the sample , nb is the intrinsic electron density, pb is the intrinsic hole density and n(x) is the charge density. Then, the diffusion SPV can be calculated by integrating equation (9). Using the boundary condition (particle size) and the Einstein relations gives: SPVDember =

kT μn −μp  1 + A  ln   e μn + μp  1 + Ae−αd 

(11)

e(un + up )βI0

where A = is the ratio of light conductivity and dark conductivity, σ0 I0 is the light intensity, β is a proportionality factor that is dependent on the conversion of photon flux to carrier flux, A is calculated as 10 by conductive AFM (Supplementary Fig. 10), α is the absorption coefficient and d is the charge separation distance, dependent on the particle size. k = 1.38 × 10–23 J K–1, T = 298 K and e = 1.6 × 10–19 C. Photocatalytic reaction. The prepared Cu2O-3 samples with or without the cocatalyst deposition were used in the model photocatalytic reaction. The samples with FTO substrate (2 × 2 cm2) were placed in 4 ml of 10 μM methylene blue solution. Prior to irradiation, the samples were set to the desorption–adsorption equilibrium in the dark condition for 1 h. A 300 W xenon lamp with an optical cutoff filter (λ ≥ 420 nm (L-42 (Kenko))) was used as the light source. After different irradiation times, 2 ml of solution was used for the ultraviolet–visible (UV–vis) characterization. The UV−vis spectrum was recorded on a UV–vis spectrophotometer (JASCO V-550). Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Received: 20 October 2017; Accepted: 1 June 2018; Published: xx xx xxxx

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant no. 21633015, 21773228), the National Key Basic Research Program of China (973 Program, grant no. 2014CB239403) and the Strategic Priority Research Program and Equipment Development Project of the Chinese Academy of Sciences, grant no. XDB17000000, YJKYYQ20170002.

Author contributions

R.C. conceived and conducted most of experiments, and analysed data; S.P. conducted the theoretical simulation; H.A. analysed the SPV data and conducted Raman measurements; J.Z. helped in the SPVM measurements; S.Y. helped in the activity measurements; Y.G. analysed KPFM data; F.F. conceived most of the experiments and analysed data. The manuscript was written by R.C. and F.F.; C.L. proposed the project, analysed data and revised the manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/ s41560-018-0194-0. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to F.F. or C.L. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

