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Spatiotemporal imaging of charge transfer in photocatalyst particles


The water-splitting reaction using photocatalyst particles is a promising route for solar fuel production1,2,3,4. Photo-induced charge transfer from a photocatalyst to catalytic surface sites is key in ensuring photocatalytic efficiency5; however, it is challenging to understand this process, which spans a wide spatiotemporal range from nanometres to micrometres and from femtoseconds to seconds6,7,8. Although the steady-state charge distribution on single photocatalyst particles has been mapped by microscopic techniques9,10,11, and the charge transfer dynamics in photocatalyst aggregations have been revealed by time-resolved spectroscopy12,13, spatiotemporally evolving charge transfer processes in single photocatalyst particles cannot be tracked, and their exact mechanism is unknown. Here we perform spatiotemporally resolved surface photovoltage measurements on cuprous oxide photocatalyst particles to map holistic charge transfer processes on the femtosecond to second timescale at the single-particle level. We find that photogenerated electrons are transferred to the catalytic surface quasi-ballistically through inter-facet hot electron transfer on a subpicosecond timescale, whereas photogenerated holes are transferred to a spatially separated surface and stabilized through selective trapping on a microsecond timescale. We demonstrate that these ultrafast-hot-electron-transfer and anisotropic-trapping regimes, which challenge the classical perception of a drift–diffusion model, contribute to the efficient charge separation in photocatalysis and improve photocatalytic performance. We anticipate that our findings will be used to illustrate the universality of other photoelectronic devices and facilitate the rational design of photocatalysts.

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Fig. 1: Relating anisotropic structures to surface charge distribution.
Fig. 2: Time-resolved photoemission electron microscopy of E-Cu2O particles.
Fig. 3: Transient SPV spectra of EH-Cu2O.
Fig. 4: Selective cocatalyst loading and photocatalytic performance.

Data availability

The data that support the findings of this study are available at or from the corresponding authors upon request.


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This work was conducted by the Fundamental Research Center of Artificial Photosynthesis (FReCAP) and financially supported by the National Natural Science Foundation of China (22088102, 22102173, 22073097), CAS Projects for Young Scientists in Basic Research (YSBR-004), National Program on Key Basic Research Project (2021YFA1500600, 2018YFA0208700), and Dalian Institute of Chemical Physics Innovation Foundation (DICPSZ201801).

Author information

Authors and Affiliations



R.C., F.F. and C.L. conceived the research. R.C. carried out the experiments, analysed the experimental data and wrote the manuscript. Z.R., Y. Liang, and G.Z. collected the TR-PEEM and XPEEM data. T.D. performed transient SPV spectroscopy measurements. R.L., Y. Liu and S.P. performed DFT calculations and simulations. P.Z. and K.H. supervised the DFT calculations. Y.Z. assisted in photocatalytic activity measurements. H.A. assisted in Raman microscopy measurements. C.N. assisted in data analysis. C.L. proposed the project. F.F. and C.L. supervised the project. Z.R., T.D., F.F. and C.L. discussed the data and revised the manuscript.

Corresponding authors

Correspondence to Fengtao Fan or Can Li.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Anisotropic facet engineering of Cu2O particles.

ae, SEM images obtained at low (a) and high (b) magnifications, AFM images (c), KPFM images (d), and SPVM images (e) of Cu2O particles with morphologies varying from a cube to an octahedron. Scale bars, (a) 20 μm and (be) 2 μm. Proportions (P) are defined as P = S{111} / (S{001} + S{111}), where S{111} and S{001} represent areas of the {111} and {001} facets, respectively. The KPFM images show that the surface potential signals increase with P, indicating a gradually decreasing p-type doping level from facet {001} to {111}. The higher surface potential of the {001} facet than that of the {111} facet on a truncated octahedral particle suggests a higher p-type doping level near the {001} facet because the two facets have the same Fermi energy. The SPVM images exhibit negative signals due to the electron transfer to the surface and indicate a larger number of electrons are distributed on the {001} facet. f, Surface potential distributions across the {001} and {111} facets indicated as lines in d. g, Histograms of the SPV signals extracted from the {001} and {111} facets of polyhedral Cu2O particles with various morphologies. Gaussian fits are used to determine the average signals. h, Correlation between the CPD and SPV signals based on the differences between the {001} and {111} facets of polyhedral Cu2O particles with various morphologies. The data are extracted from f, g.

Extended Data Fig. 2 LEEM observations and DFT calculations.

ac, LEEM image of EH-Cu2O particles recorded at 10 eV (a) and LEED patterns recorded at 30 eV for the {001} (b) and {111} (c) facets of EH-Cu2O particles circled in a. The LEED patterns and the ratio of the reciprocal lattice a* and b* (\(\frac{\surd 3}{\surd 2}\)) determine the (1×1) surface structures for {001} and {111} facets (see detailed analyses in Methods). di, Optimized geometries of the {001} (df) and {111} (gi) surfaces of Cu2O without (d, g) and with VCu (e, h) or (H-VCu) (f, i) defects. The red, pink, and white spheres represent O, Cu, and H atoms, respectively. j, Calculated formation energies of the (H-VCu) defects on the {001} and {111} facets at the HSE06 level based on the 2×2 periodic Cu2O slab structures depicted in di (see details in Methods). These results indicate that the formation of (H-VCu) defects is much more favourable at {111} facets compared to {001} facets. k, Charge density difference obtained for the Cu2O {111} surface structure (i) with a (H-VCu) defect. The red, blue, and white spheres represent O, Cu, and H atoms, respectively. The yellow and cyan colours denote the increase and decrease in electron density, respectively. The obtained results demonstrate that the formation of (H-VCu) defects increases the electron density at Cu atoms. We also performed a Bader charge analysis and found that the averaged charge on Cu atom decreased from 0.514 to 0.495 after the formation of (H-VCu) defects. Therefore, the presence of (H-VCu) lowers the valences of the surrounding Cu atoms.

Extended Data Fig. 3 Anisotropic defect engineering for truncated octahedral Cu2O particles.

ac, Ensemble-averaged Cu 2p3/2 XPS (a), Cu LMM Auger (b), and deconvoluted Auger (c) spectra for E-Cu2O, EH-Cu2O, and H-Cu2O particles. The Cu 2p3/2 peaks were fitted with the two components centred at approximately 932.4 and 933.6 eV, which correspond to Cu2O and VCu species, respectively53. The Cu LMM Auger peaks were fitted with two main peaks located at 570.0 eV (Cu2O) and in the range of 568.2–568.8 eV (an overlap of the Cu0 and Cu2+peaks), and three peaks at 573.1, 567.1, and 565.2 eV indicating different transitions states. The component in the the range of 568.2–568.8 eV was further fitted with two peaks corresponding to Cu0 (568.2 eV) and Cu2+ (568.8 eV). The contributions of Cu0 and Cu2+ increase and decrease after switching from E-Cu2O to H-Cu2O, respectively, indicating increased (H-VCu) defects and decreased VCu defects from E-Cu2O to H-Cu2O. d, Confocal Raman spectra of {001} and {111} facets of EH-Cu2O particles with Raman peaks assigned based on previous reports54. Inset, optical image of EH-Cu2O particles. The Raman peak intensity was normalized to that of 2Eu phonon mode at Raman shift of 217 cm-1. The 2Eu phonon mode is intrinsic to Cu2O crystals owing to the strong coupling to yellow excitation and hence can be used as a ref. 55. The T1u (TO) phonon mode at Raman shift of 124 cm-1 is Raman inactive for the perfect Cu2O crystal but can be observed in the presence of VCu defects, and therefore the T1u (TO) phonon mode is related to the presence of VCu defects54. e, Normalized Raman spectra of {001} and {111} facets of E-Cu2O, EH-Cu2O, and H-Cu2O particles. The normalized T1u (TO) Raman peak intensity of each facet was extracted to denote the facet-dependent VCu density and was correlated to the facet-dependent SPV signals in Fig. 1g. f, Correlations between normalized T1u (TO) Raman peak intensity and defect density determined by X-ray spectroscopy. The blue and red data points were obtained from cubic Cu2O particles with surface defects varying from VCu to (H-VCu) based on data from the Ref. 18. The green data points were collected from the {001} and {111} facets of EH-Cu2O particles with Raman peak intensity shown in d and VCu density determined by micro-area XPS. The VCu density (square points) was calculated by the ratio of the peak areas of VCu and total Cu 2p3/2 peak areas of the in XPS spectra. The net defect density (circle points) was calculated by the ratio of the difference between the areas of the Auger Cu LMM peaks related to (H-VCu) and VCu and the area of the total Auger Cu LMM peak. The blue line is the linear fit of the blue points. The good linear relation, which is also consistent for the data of EH-Cu2O, indicates the reliability of using VCu-related Raman peak intensity to denote VCu density. The red points indicate that the decrease of VCu density corresponds to the increase of (H-VCu) density and their densities are roughly the same at VCu-related Raman peak intensity of ~0.7. g, XPEEM image of a single EH-Cu2O particle with photoelectron signals collected and integrated in the Cu 2p3/2 range. Inset, PEEM image of the same particle. h, i, Facet-dependent Cu 2p3/2 (h) and O 1s (i) XPS profiles recorded from the {001} and {111} facets of the EH-Cu2O particle in g. The fitting procedure for Cu 2p3/2 is similar with that in a. The ratios between the peak areas of VCu and total peak areas obtained for the {001} and {111} facets are 6.7% and 1.7%, respectively, confirming a higher VCu density on the {001} facet. The peaks of O 1s were freely fitted with three components that included the main peak at 530.6 eV corresponding to O in Cu2O, a higher binding energy peak at 531.4 eV corresponding to O–H bond56, and a lower binding energy peak at 529.8 eV corresponding to unsaturated O57. These results confirm selective incorporation of H atoms into the {111} facet to form O–H bonds. j, XPEEM image of EH-Cu2O particles collected in the Cu LMM Auger spectral range. k, Facet-dependent Cu LMM Auger spectra recorded from the EH-Cu2O particles in j. Constrained fitting was performed for the three peaks at 916.5 eV (Cu2O), 918.4 eV (Cu0), and 917.8 eV (VCu), and three other peaks at 913.4, 919.4, and 921.3 eV that indicate different transitions. The spectra demonstrate that apparent Cu0 species, assigned to (H-VCu) defects, were selectively formed at {111} facets. l, X-ray absorption microscopy image of EH-Cu2O particles. The X-ray absorption signals were obtained for the Cu L2,3 edges. m, Facet-dependent Cu L2,3 edge X-ray absorption spectra recorded for the {001} and {111} facets of the EH-Cu2O particles in m. The spectra are normalized to the same intensity at 963.0 eV. The white line intensity (933.5 eV) of the {001} facets is larger than that of the {111} facets, confirming the higher oxidation state of Cu on the {001} facets58.

Extended Data Fig. 4 Anisotropic charge transfer in EH-Cu2O particles.

a, Reproducibility of SPVM images for EH-Cu2O particles. b, AFM images of EH-Cu2O particles used for modulation measurements. Scale bars, 2 μm. c, SPV signals obtained for the {111} and {001} facets of EH-Cu2O particles in b under 6-Hz chopped light illumination. d, I–V curves obtained by C-AFM for the {111} and {001} facets of EH-Cu2O particles in b in the dark (grey line) and under the 450-nm light illumination (blue and red lines). e, SPV values obtained at different light powers for the {111} and {001} facets of EH-Cu2O particles in b. The error bars are based on the electronic noise of the modulated SPV signals via an external lock-in amplifier.

Extended Data Fig. 5 TR-PEEM studies of EH-Cu2O particles.

a, b, Schematic illustration of the energy path of electrons with negative (a) and positive (b) pump–probe delay times. VAC, CB, CBM, VCusplit, VCu, VBM, and VB denote the vacuum energy level (VAC), conduction band (CB), conduction band minimum (CBM), energy level of split copper vacancy (VCusplit), energy level of a simple copper vacancy (VCu), valence band maximum (VBM), and valence band (VB), respectively. The vacuum energy level is set to 0 eV. The CBM energy level is determined from Ref. 59. The energy levels of VCu and VCusplit located at 0.2–0.3 eV and 0.4–0.5 eV above VBM, respectively, and no donor levels exist near CBM in Cu2O60. c, Band structure of Cu2O calculated by the HSE06 hybrid functional, which indicates that photogenerated carriers can only be excited into the Γ-valley and that the energy of photogenerated carriers in the Γ-valley is lower than other valleys by ~1 eV; therefore, intervalley scattering cannot occur. The curvity of CBM is approximately six times larger than that of VBM at the Γ point, indicating that the excitation energy of 2.4 eV mostly generates hot electrons while hot holes can be neglected. d, PEEM image of a EH–Cu2O particle with different regions marked along the light irradiation direction. Inset, PEEM image of the same particle with a different intensity scale bar featuring a bright ring at the particle–substrate interface (region 1) due to electric field distortion effect and a dark tail on the right side of the particle due to shadowing effect. e, Energy-integrated TR-PEEM signals for different regions marked in d. f, PEEM image of other EH–Cu2O particles. g, Energy-integrated TR-PEEM signals for different regions marked in d and f. The photoelectron intensities in e and g were obtained by subtracting the intensities at negative delay times and were divided by the collected area for quantitative comparison. Comparing TR-PEEM signals collected from different regions of {111} facets, we found that electric field distortion affected TR-PEEM signals at regions in the vicinity of substrate and shadowing effect affected TR-PEEM signals at shadow facets. These effects had a small impact on TR-PEEM signals at lateral facets and had a negligible impact for top facets. Therefore, we conducted TR-PEEM study on {001} and {111} facets parallel to the substrate. No field enhancement effects were observed at the inter-facet edge region (region 4). h, i, Dynamics of the normalized energy-integrated photoelectron signals at 1 ns (h) and within the initial 2 ps (i) with different excitation carrier densities. j, Fitting of decay dynamics at different excitation carrier densities via the single-component exponential decay function. k, Log/log plots of the decay time constant versus the excitation carrier density. At the initial times, the dynamics is independent on the carrier density, excluding the recombination and Auger processes on this timescale. At longer times, the dependence of the decay dynamics on the excitation carrier density is of the order (n) of ~0.8, indicating the simultaneous occurrence of the radiation recombination (n = 1) and trapping (n = 0) processes. The Auger process (n = 2) is negligible owing to the relatively low carrier density (1017 cm−3).

Extended Data Fig. 6 Inter-facet charge transfer mechanism for EH-Cu2O particles.

a, Potential distribution across the interface between {001} and {111} facets. The KPFM image is mapped at a tip lift height of 10 nm to minimize cross-talk effects. b, Fitting of the potential distribution and strength of the inter-facet built-in electric field. The fitting process (see details in Methods) resulted in doping density (Nd) on the order of ~1014 cm−3, electric field strength of 1.7 kV/cm, and width of 680 nm. c, Band diagram for the interface between the {001} and {111} facets based on the data in b. d, Schematic showing the photo-induced inter-facet charge transfer in the drift regime. e,f, Evolution of SPV signals with time studied using the conventional drift–diffusion model at different electron temperatures (e) and at different mobilities (f) (see Methods for details). g, h, Model of the inter-facet electron transfer in the quasi-ballistic regime (see Methods for details). i, Group velocity of electrons (blue points) in the conduction band (Inset) along the Г→R direction determined by DFT calculations using the HSE functional (see Methods).

Extended Data Fig. 7 Energy-resolved TR-PEEM measurements of hot electron relaxation.

a,b, Pseudocolour images of the energy-resolved and time-resolved photoelectron signals obtained for {001} (a) and {111} (b) facets. The signals in high-energy and low-energy regions were integrated to show the dynamics of hot electrons and electrons near the CBM. c, d, Fitting the energy-resolved photoelectron signals with a hot Fermi–Dirac distribution and density of states in the conduction band for the {001} (c) and {111} (d) facets at different decay times as labelled (see Methods for fitting details). The grey points denote the experimental data, and the solid lines are the fitting curves. e, Decays of the electron temperature observed for the {001} and {111} facets. The electron temperatures are extracted from the fitting parameters of the plots in c and d. Error bars represent the standard deviation from the fits in c and d. The decays were fitted with a one-phase exponential association equation with plateau before exponential begins. The fitting results show that the decays begin at 0.05 ps with a time constant of 0.17 ps for the {001} facets and begin at 0.02 ps with a time constant of 0.1 ps for the {111} facets. The faster decay for the {111} facets is owing to hot electron transfer from the {111} to {001} facets, which occurs at delay time of ~0.05 ps. During the inter-facet electron transfer, the electron temperature displays no decay for the {001} facets, indicating that the transferred electrons are non-thermal in the energy space. f, Electron temperature decay observed at longer times with a bi-exponential fit for the {001} facets. The temperature decay follows the bi-exponential model with time constants of 0.20 and 2.96 ps. g,h, Decays of the high-energy electrons obtained at different excitation carrier densities for the {001} (g) and {111} (h) facets. The decay traces were fitted with Equations (4) and (5) in Methods for the {111} and {001} facets, respectively. All photoelectron intensities were normalized to the intensity at 0 ps. The initial growth of photoelectron intensity for the {001} facets was affected by the excitation carrier density, which displayed a larger increment at a lower excitation density. This effect can be attributed to the slight energy relaxation induced by electron–electron scattering at high excitation density. The excitation carrier density produced little effect on the decay dynamics for the two facets. The decay time constant varied slightly in the range of 0.15–0.18 ps for the {001} facets and in the range of 0.05–0.06 ps for the {111} facets. i, Physical picture of electron relaxation process that includes electron–electron interactions leading to the formation of a hot electron ensemble before 0.1 ps, electron–optical phonon scattering at 0.2 ps, and electron–acoustic phonon scattering at 2.96 ps. The electron–phonon scattering follows a two-temperature model and leads to energy relaxation23. j, k, Energy distribution spectra of the photoemitted electrons obtained for the {001} (j) and {111} facets (k) of EH-Cu2O particles at different delay times. The delay times span from −47 ps to approximately 1700 ps from bottom to top. The characteristic time delays are labelled. The peak positions of the photoelectron spectra at delay times from −47 to −1 ps are averaged; subsequently, the averaged peak position is set as the benchmark to evaluate the photo-induced shifts of peak position, which are extracted as SPV signals.

Extended Data Fig. 8 Effects of the bulk-to-surface charge transfer and measurement conditions.

a, PEEM image of cubic Cu2O particles. b, TR-PEEM signals of the {001} facets of cubic Cu2O and EH-Cu2O. c, Pseudocolour image of the energy-resolved and time-resolved photoelectron signals obtained for the {001} facets of the cubic Cu2O particles in a. d, Transient SPV signals of the {001} facets of cubic Cu2O and EH-Cu2O particles. The SPV signals of cubic Cu2O were extracted from the peak shifts of the time-resolved photoelectron spectra in c. The delay time in the x axis was shifted by 1 ps to show the SPV evolution on the logarithmic timescale. The SPV signals of cubic Cu2O solely originaate from the bulk-to-surface electron transfer owing to the existence of a p-type surface SCR, while the SPV signals of EH-Cu2O result from a combination of the bulk-to-surface electron transfer and inter-facet electron transfer. Therefore, a comparison of SPV signals obtained for cubic Cu2O and EH-Cu2O can help decouple bulk-to-surface and inter-facet electron transfer processes. The bulk-to-surface electron transfer yields a maximum SPV at ~10 ps, and the contribution to SPV signals on the subpicosecond scale is very small. The decoupled data are presented in Fig. 2e. e, XPEEM image of EH-Cu2O particles. fi, XPS profiles obtained for the {001} (f,g) and {111} (h,i) facets of the EH-Cu2O (marked in e) under the dark and 2.4-eV excitation conditions. Single peak fits were performed to quantify the photo-induced peak shifts extracted as SPV signals in ultrahigh vacuum (UHV). j, Comparison of the steady-state SPV signals of EH-Cu2O particles obtained in UHV (~10−8 Pa) and air from the photo-assisted XPS and SPVM data, respectively. It shows that measurement conditions affect the SPV signals very little, which indicates that these SPV signals are induced by the charge transfer within Cu2O particles and the effects of absorbed molecular on the particle surface can be eliminated. k, SPV spectra of EH-Cu2O particles recorded in different environments using the fixed-capacitor approach. The atmospheric control is enabled by using a home-made chamber with a vacuum background of 10−3–10−4 Pa. Above data indicate that different measurement conditions produce little effects on SPV, allowing the combination of different approaches to obtain holistic SPV signals.

Extended Data Fig. 9 Facet-dependent absorption and schematic illustration of the charge transfer in EH–Cu2O particles.

a, Diffuse reflectance spectra of cubic Cu2O, EH-Cu2O, and octahedral Cu2O. b, c, Tauc plots obtained for cubic and octahedral Cu2O particles in the direct transition (b) and indirect transition (c) regimes. They show that the absorption of {001} facets reflects indirect transitions with a bandgap (Eg) of 1.91 eV and that the absorption of {111} facets reflects direct transitions with Eg of 2.05 eV. d, Facet-dependent SPV spectra for EH-Cu2O and spectral-dependent absorption length of Cu2O (reported by Malerba et al.37). As positive SPV signals are related to (H-VCu)-induced trapping, they can reflect the depth distribution of (H–VCu) defects. The SPV signals obtained for the {111} facet reach a maximum at an excitation wavelength below 480 nm corresponding to an absorption length of 60 nm. These results indicate that (H-VCu) defects are primarily distributed within 60 nm in the near-surface regions on the {111} facet. e, Tauc plot of direct transitions for EHCu2O. The onset of the Tauc plots is in good agreement with the SPV spectrum of {111} facet; hence, the absorption edge of the {111} facet of EH-Cu2O is equal to 2.04 eV. f, Tauc plots of indirect transitions for EH-Cu2O. The onset of the Tauc plots agrees well with the SPV spectrum of {001} facet; hence, the absorption edge of the {001} facet of EH-Cu2O is equal to 1.91 eV. g, Schematic illustration of the charge separation on the {001} and {111} facets of EH-Cu2O with the sub-bandgap excitation. h, Schematic illustration of the holistic charge transfer processes occurring in EH-Cu2O.

Extended Data Fig. 10 Cocatalyst deposition and photocatalytic performance.

ac, SEM (a), AFM (b), and KPFM (c) images for EH-Cu2O particles with photodeposition of Au (EH-Cu2O/Au). Scale bars, 2 μm. d, CPD distribution along the line in c. The data show the local increase in the surface potential at Au sites, demonstrating an enhancement of the built-in electric field. e, f, SEM images for E-Cu2O (e) and H-Cu2O (f) particles photodeposited with Au. They are denoted as E-Cu2O/Au and H-Cu2O/Au, respectively. g, SPVM image of an H-Cu2O/Au particle. Inset, the corresponding AFM image. h, SPV distributions across the {111} and {001} facets obtained before and after the Au deposition on H-Cu2O particles. i, Determination of the driving force of the anisotropic charge transfer in Cu2O photocatalytic particles by calculating the differences of SPV signals between different facets. j, Time course of photocatalytic H2 evolution for different Cu2O photocatalyst particles. The lines represent linear fits for determining the rates of H2 generation. The association between anisotropic SPV signals and photocatalytic activities can be understood as follows. A photocatalytic process requires photogenerated electrons and holes at surface to drive photooxidation and photoreduction reactions simultaneously. Therefore, effective charge separation refers to creating photogenerated electrons and holes that are localized on the spatially separated surface of the photocatalyst. For cubic Cu2O, the SPV vectors of different facets are cancelled out due to symmetry considerations and the SPV difference equals to 0, which means no driving force for effective charge separation. In this case, photogenerated electrons are distributed at surface whereas holes are confined in the bulk by the symmetric surface built-in electric field, rendering the photocatalytic reaction inactive. Facet engineering yields an inter-facet built-in electric field for effective electronhole separation between different facets, resulting in the observed anisotropic SPV signals and a detectable photocatalytic reaction rate (E-Cu2O). However, the SPV vectors of different facets are partially offset, only resulting in a small driving force. Nevertheless, the conjoint facet engineering and defect engineering enable effective accumulations of electrons and holes at different facets via a synergistic effect of inter-facet built-in electric field and anisotropic trapping. Consequently, the SPV vectors are aligned, leading to significant enhancements of anisotropic SPV signals and photocatalytic activity for EH–Cu2O. A further selective cocatalyst assembly enhances both the positive SPV signals of {111} facets and negative SPV signals of {001} facets by ~50%, and therefore facilitates both photogenerated electrons and holes accumulations at surfaces, further improving the photocatalytic activity by 50% for EH-Cu2O/Au.

Supplementary information

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Supplementary Video 1

Animated video created by TR-PEEM images of a single EH-Cu2O photocatalyst particle. The image intensity represents accumulation (red) and depletion (blue) of photoexcited electrons.

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Chen, R., Ren, Z., Liang, Y. et al. Spatiotemporal imaging of charge transfer in photocatalyst particles. Nature 610, 296–301 (2022).

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