Photoinduced Charge Transfer and Trapping on Single Gold Metal Nanoparticles on TiO2

We present a study of the effect of gold nanoparticles (Au NPs) on TiO2 on charge generation and trapping during illumination with photons of energy larger than the substrate band gap. We used a novel characterization technique, photoassisted Kelvin probe force microscopy, to study the process at the single Au NP level. We found that the photoinduced electron transfer from TiO2 to the Au NP increases logarithmically with light intensity due to the combined contribution of electron–hole pair generation in the space charge region in the TiO2–air interface and in the metal–semiconductor junction. Our measurements on single particles provide direct evidence for electron trapping that hinders electron–hole recombination, a key factor in the enhancement of photo(electro)catalytic activity.

KPFM is sensitive to local variations in the work function of materials. The work function depends on the specific material, adsorption layers (e.g., water), oxide layer thickness, dopant concentration, electrostatic charge, surface dipole moments and temperature. 1 The operation principle is described in Figure S1. between tip and surface. Under the KPFM operation (c), the electric field is nullified by applying and external voltage (Vext dc) to the tip. In this case: WTiO2  Wtip, therefore the tip acquires a positive voltage. With the values of the Vext obtained at each point of the surface sample, the surface voltage is mapped.

Surface Photovoltage (SPV) under illumination exposure in Kelvin Probe Force Microscopy
The increase in SPV under illumination exposure can be explained by taking into account the upwards band bending in the semiconductor surface space charge region (Su-SCR) and as a consequence, the promotion of holes to the surface.
The depletion region depth 2 Figure S2 shows the energy band diagrams for tip and sample in darkness (thick black) and under illumination (thin purple). The metallic tip work function is not altered by light exposure. However, with irradiation, at the surface, all three bands lower their energy value by e.SPV: The flattening of the partial band bending upon illumination implies a decrease in the metal oxide work function (a). When tip and sample are electrically disconnected (a) their Fermi levels are not aligned. When connected (b), the alignment is achieved by the flow of electrons from the TiO2 to the tip, creating an electrical field. The VCPD is larger under illumination. Therefore, the larger the band flattening, the higher the VCPD (positive) increase and, thus, the higher (positive) SPV. When operating in KPFM, an external potential is applied to the tip equal to the VCPD, and thus removing the electrical field (E) ( Figure S2).  Figure S2. Band diagrams for tip (PtIr5) and sample (TiO2, n-type) in the dark (black) and under UV light (purple) when the tip and sample are electrically disconnected (a) and connected (b). The light exposure causes the bands to partially flatten. At the surface: ECB-EF (dark)  ECB+EF (light). Accordingly, the VCPD is larger under illumination and therefore the SPV value will be larger. SPV = VCDP (light)-VCDP (dark). Pure gold nanoparticles (NPs) have been generated using the gas-phase approach 3 . In this work a so-called Multiple Ion Cluster Source (MICS) has been used. This method allows the fabrication of ligand-free NPs that can be soft-landed on surface in well-controlled atmospheres. The set-up has three independent magnetrons (one-inch diameter each) placed in an aggregation zone. [4][5][6] The pure gold target (99.95%) is magnetron sputtered in a well-controlled atmosphere (Ultra High Vacuum, UHV, base pressure in the low 10 -9 mbar range) guarantying the purity of the extracted atoms and ions. Subsequently the atoms recombine producing the NPs that are extracted from the aggregation zone in the form of a beam thanks to differential pumping. 7 The NPs beam passes through an exit slit located at the end of the aggregation zone and is projected into a second UHV deposition chamber where the substrates are placed. The NPs soft-land on the substrates surfaces that are placed at normal incidence to the beam without deformation (i.e.: height equal to diameter). 8 The main advantages of the MICS are the production of ligand-free nanoparticles that can be deposited on any surface provided that it is vacuum compatible together with a narrow size distribution. Both the fabrication rate and size of the nanoparticles depend on the fabrication parameters; in our case we have used the following parameters: argon flux at gold magnetron = 30 sccm (standard cubic centimeters per minute), total argon flux = 100 sccm, 9 Figure S4. a) AFM image of Au NPs on TiO2 and b) its size distribution. The particle height data were fit to a log-normal distribution resulting in an average nanoparticle diameter of 2.9 and a standard deviation of 0.5 nm (analysis of 115 nanoparticles).  It should be noted that the spatial resolution of the VCPD images in the text is roughly equivalent to the tip diameter, typically around 40 nm in our experiments.

6.
Length of the Schottky junction depleted region for finite and small

Au nanoparticle
A theoretical analysis of charge transfer in metal catalysts supported on a doped TiO2 carrier has been performed by Ioannides et al. 13 The development of the theoretical model is based on the metal-semiconductor contact theory and was used to calculate the amount of charge transferred to supported metal crystallites, as a function of the electronic structure of the semiconducting support and the metal crystallite size

Theoretical calculation of the electrostatic interaction forces between tip and surface
The experiments discussed in the present work have been performed using AFM imaging in non-contact dynamic force microscopy, and using the gradient/frequency shift of electrostatic interaction to implement Kelvin Force Microscopy. As discussed previously 14 , for these experimental conditions a realistic model of the tip can be described by two parameters, the radius R of the tip apex, simulated as a paraboloid, and an opening angle  of cone representing the tip shaft, as shown in the inset of figure S7. Assuming a smooth transition (first derivative is continuous) at the point where the tip shape changes from parabolic to conical, this uniquely defines the overall tip shape. Figure S7. Tip profile (gray) and electric field distribution E 2 (, z) using the experimental parameters obtained from the TEM image of figure S5: Rtip = 17.5 nm, tip cone angel tip = 35°. The field distribution curves (red lines) were calculated for a set of tip-sample distances d from 6 to 10 nm. The thick red line corresponds to the field E 2 (, z) for d = 8 nm, using arbitrary units in the ordinate. The abscise  is the distance of the tip apex from the origin in the polar coordinate system. Inset: tip geometry used for modelling the electric field on the surface assuming a parabolic shape for the apex transitioning to a mesoscopic cone shaft.
With the model for electrostatic forces described by Colchero et al. 14 , the electrostatic field on a metallic surface is calculated for this tip-sample system and shown in figure S7 using the parameters obtained from Figure S5: Rtip = 17.5 nm, tip = 35° and a tip-sample distance of about 8 nm. The thick red line corresponds to d=8 nm, and the thinner lines correspond to field distributions for d ranging between 6-10 nm, in steps of 0.5. The electrostatic field intensity can be interpreted as the tension (units of pressure, N/m 2 ) generated by the field lines connecting (opposite) charges on tip and sample.

Electrostatic lateral resolution
As discussed in more detail elsewhere, 14 the (total) surface integral over this field intensity on the sample surface gives the total electrostatic force gradient: Therefore, the electrostatic field intensity can be interpreted as the aperture function for electrostatic measurements, which essentially defines resolution in KPFM mode, in good agreement with our experiments.
As can be observed from the Figure S7, at a distance of 10 nm from the symmetry axis (X), the field intensity E 2 (, z), decays to about 50% of its maximum. We can also observe that although the maximum of the field intensity varies significantly with distance (as does the total electrostatic force), the width of these curves -of the order of the tip radius-stays essentially the same, implying that the lateral resolution is similar for the range of tip-sample distances (z) shown. We attribute this to the fact that for all the field distributions shown in Figure S5 tip-sample distance is (significantly) smaller than the tip radius. For z > R however, the field distributions become wider, leading to a reduced electrostatic resolution, as expected and as discussed previously 14 .
5.2 Surface potential difference between two conductors with different size: bulk and Nanosize.
The interaction force gradient induced by the lever and the cone´s tip is strongly reduced in the range of distances relevant in the AFM experiments. Only the apex of the tip contributes to the total force. 14 For distances smaller than the radius of the tip (z < Rtip): By using the force gradient as signal source for the interaction in KPFM, local contact potential differences can be obtained. 14 Since the primes indicating derivatives, we obtain for the second derivative of the capacitance: The total potential V between tip and sample includes the contact potential difference between tip and sample (VCPD) and the external potential applied (Vbias(x,y)+Vac sin et); the force gradient signal that is used for the KPFM detection (1e component of the electrostatically induced tipsample interaction) is then: Where sin is the ac component of the bias potential externally applied to the tip. In    between the TiO2 surface and the area above the Au NP (V) will be smaller than in the previous geometry since the tip feels the effect of the small Au NP and also the larger TiO2 surface area around the Au NP. Note that the force (and force gradient) induced by electrostatic interaction is due to the field between tip and sample given by E 2 (,z), as shown in Figure S7. To calculate the Z+2R NP Z experimental surface potential difference V expected for the case of the small Au NP, the two contributions: tip-Au NP (at a distance of Z), and tip-TiO2 surface below the Au NP (at a distance of of Z+2RNP), should be included. This can be interpreted as two capacitances in parallel. The AFM tip then "feels" a weighted effective potential difference VCPD_NP, where these two contributions add to VCPD_NP, weighted by the corresponding capacitance second derivative: By applying equation S4: and substituting S7 and S8 in S6, with the experimental values: Z = 10 nm, Rtip = 18.5 nm and RNP = 1.5 nm, V =VCPD_TiO2 -VCPD_NP equals 120 mV. Therefore, a significant reduction in surface potential difference between TiO2 and Au ( Figure S8b) of 87% is expected with respect to the difference in the bulk case ( Figure S8a). However, the experiment shows an even lower value for this difference (12 mV, Figure 4a). The depletion region around the Au NP could be playing a role in further decreasing the difference. In addition, the presence of image charges also reduces the electrostatic interaction force, as explained in the next section.

Theoretical model for calculating electric charge inside the nanoparticle
By simplifying the modeling of the elements that play a role in the electrostatic interaction between tip and surface, an analytic expression for the electrostatic forces and charges can be obtained. The following approximations have been implemented ( Figure S9a): 1. A spherical conductive tip with a radius Rtip and a charge Q.
3. An infinite plane with a charge density  added on the sample surface in order to simulate the surface contact potential.
D is the tip-sample scanning distance. A DC as well as an AC voltage are externally applied to the tip during KPFM operation: The potential applied to the tip in addition to the contact electric field generated by the surface charge density induce an electrostatic force between tip and sample. The force has been simulated with the Generalized Image Charge Method (GICM), 15 which uses image charges to model the charge that appears in all surfaces and cancels the electric field inside the metallic elements.
When the tip scans over the bare sample (with no NP on it, Figure S9a), the tip initially is electrostatically equivalent to that of a charge Q inside which is related to the electrostatic potential applied to it. By assuming a sphere as the shape of the tip, the value of Q can be calculated: Q = 40 Rtip (Vdc+Vac sin(t)) (S10) A second contribution to the tip charge is the image charge -q which originates from the constant electric field generated by the surface charge density Both tip charges (Q and -q ) induce image charges inside the conducting sample (q and -Q).
Where Ne is the number of charge elements on the conducting sample. If only the first image charge obtained from the GICM is taken into account, then N = 3 (corresponding to , -Q and q inside the sample). Combining equations 2 and 3, we obtain three contributions to the electrostatic force: one that is independent of , a second one that is proportional to sin(t) and a third one proportional to sin(2t). In KPFM, we focus on the signal proportional to sin(t) since the bias voltage applied to the tip (Vdc) is the value that cancels this force contribution.
To model the electrostatic force on the tip when the tip scans above a metal nanoparticle placed on the sample surface ( Figure S9b), an additional term must be included. The extra contribution originates from the charge trapped in the nanoparticle (qN), as shown in Figure S9b. In the simplest scenario there will be 3 charged contributions inside the tip and 5 charged elements on the surface.
The interaction force, in this case, will be: It is worth noting that in order to nullify this force component, the voltage Vdc' applied to the tip must be different from the previous case (Vdc), since now more contributions to the force are present. As can be observed in Figure S9b, there are two contributions to the force: qN (the charge on the nanoparticle) and -qN (its image charge inside the conducting sample) that are very close to each other because the nanoparticle radius (RN) is very small compared to Rtip. Since these two contributions are proportional to qN with opposite sign and very close to each other, in a standard KPFM setup, the electrostatic interaction force that these two charges will exert on the tip will be up to 5 times smaller than the force theoretically felt by the tip when assuming only the original qN.
Assuming an additional simplification to the model, where we consider Rtip>>RN and Rtip>>D, we can obtain qN from the following expression: For the values of the experiment (Rtip=18.5 nm, RN= 1.5 nm, D= 10 nm), the charge inside the nanoparticle obtained with our model is 5.25 10 -20 C when we do not apply any additional illumination (V'dc-Vdc=8mV) and 1.64. 10 -19 C when the sample is illuminated (V'dc-Vdc=25mV).

9.
Au NP on TiO2 CPD image of large areas.  Frequency. The value of the resonance frequency in the images is close to the value of the free cantilever resonance frequency and thus the contrast in the images is weak. Thus it can be concluded that the scanning of the images was performed out of contact. If tip-sample contacts happen during the imaging process, when operating the AFM in air, liquid necks could form, even at low relative humidity values. The formation and rupture of liquid necks induces a delay in the oscillation frequency of the cantilever which is reflected in the resonance frequency image. 11. Evaluation of carbonaceous molecular species on TiO2 (110) by means of sum frequency generation spectroscopy.
In order to evaluate the self-cleaning efficiency of 365 nm wavelength irradiation on TiO2 (110) we have performed sum frequency generation (SFG) spectroscopy experiments. SFG is a powerful method of studying molecules at surfaces. It is a surface-specific technique which intensity is enhanced when the frequency of the infrared beam is in resonance with an SF-active molecular vibrational mode.
We used a picosecond laser system to generate a 1064 nm near-infrared light with repetition rate of 20 Hz. A Laser Vision optical parametric generator and amplifier system converts the 1064 nm to a visible 532 nm beam and a mid-infrared beam ranging between 2200 cm -1 to 4000 cm -1 .
Sum frequency generation is achieved when the visible and infrared beams overlap spatially and temporally on the sample. We collected the sum frequency signal reflected from the sample's surface (reflectance mode). The beam orientations in all the SFVS experiments were: 45˚ for the 532 nm beam, and 56˚ for the mid-infrared beam, with respect to the perpendicular plane (reference plane). The polarization combination used in this work was SSP (S-polarized light for the SF output and for the input visible beam, and P-polarized light for the input infrared beam).) The measurements were performed in air. The temperature was 296 K and the relative humidity 40%.  Figure S13a) shows 6 SF spectra taken before irradiation (t= 0) and during irradiation with 365 nm wavelength light, at increasing exposure times. After 1 hour of UV illumination, the carbonaceous species are removed from the surface. After keeping the sample 1-2 hours in the dark, the presence of carbonaceous components can be observed again (Fig. S13b).
Since the sample was exposed to 365 nm wavelength light irradiation before the KPFM experiments and the whole experiment did not last for more than 45 minutes, we do not expect carbonaceous species from ambient contamination to play an important role in the present work results.
Figure S13 a) SFG spectra before illumination (0 min) and after 365 nm of wavelength light illumination (0.5 mW/cm 2 ) at increasing time exposure. Carbonaceous species are removed from the surface after 1 hour of illumination. b) Spectra taken in darkness after the experiment shown in a). After 1-2 hours with the light off, peaks corresponding to CH species start being observed again.
SFG spectra were also performed in order to probe the presence of a water layer on the sample surface. Figure S14 shows a SFG spectrum of TiO2 in the region where the OH vibrational modes of water are expected to be found: a well-defined, narrow peak at 3700 cm -1 , conventionally assigned to the free OH mode of the adsorbed water molecule, and two broad peaks centered around 3150 and 3400 cm -1 , commonly assigned to hydrogen-bonded OH. It is well-known that there is adsorbed water on an oxide surface, but because there is no peak in the hydrogen-bonded OH stretching vibration region, it can be concluded that no liquid water layer but isolated water molecules exist on the surface in the present case. Thus, a low quantity of water molecules could be adsorbed on the TiO2 surface, but without forming a liquid layer. Figure S14. SFG spectra before irradiation in the region of the OH vibrational modes of water.

Photoelectrochemical characterization
For the H2 evolution experiments, current density (at dark and under illumination) and voltage dependence were measured with a potentiostat-galvanostat PGSTAT204. A gas chromatography coupled to the photoelectrochemical cell was used to quantify the photogenerated hydrogen.
Photovoltage in electrochemical experiments also follows also a logarithmic behavior vs. irradiance ( Figure S15 Figure S16 shows a Nyquist plot obtained at 0.4V vs Ag/AgCl under dark and illumination conditions. Charge transfer resistance decreases on both types of samples when exposed to illumination or when a potential is applied. The samples with Au NPs present lower resistance than those without NPs, both in the dark and under illumination. Therefore, the presence of Au NPs improves the conductivity of electrons through the TiO2. Energy band edges of a semiconductor can be experimentally estimated from the determination of the flat band potential (VFB). This value can be determined by Electrochemical Impedance Spectroscopy (EIS) and using the Mott-Schottky equation. 16 The flat band potential serves to set the Fermi level of a semiconductor. 17 In order to determine the space charge layer capacitance, AC modulated cyclic voltage scans from 0V to -1.2V (vs Ag/AgCl), at 400 kHz, were performed, at dark conditions. The capacitance of the space charge layer is calculated by assuming: where w is angular frequency and is the imaginary part of complex impedance. The dependence of CSC on bias potential is described by the Mott-Schottky equation: where CSC is the measured differential capacitance per area unit, 0 is the elementary charge, εSC is the dielectric constant, ε0 is the electrical permittivity of vacuum, ND/A is carrier density.
Therefore, from the 1/ 2 vs. plot, VFB can be easily obtained by the interception with the xaxis. The term kBT/e0 usually can be neglected because of its low value.

AFM modification for light implementation and light calibration
A fiber-coupled LED (M365FP1, Thorlabs Inc.) was used for illuminating the sample (wave length 365 nm). Small modifications were needed in order to introduce the light beam in the vertical optical path of the Cypher ES (Asylum Research, Oxford Instruments) AFM head: 1. The view module has to be lifted 5 cm to allow for space underneath for a small positioning stage and the beamsplitter attached to it. The fiber is placed at the center of the stage. By means of the stage micrometer screws, the position of the spot on the sample can be relocated. The UV beam reaches the beamsplitter from the side and deflects it 90 degrees down towards the cantilever and sample.
2. After the 90 degrees beam splitter deflection, the beam goes through the AFM head dichroic hot mirror and from there to the objective lens. Since the objective was designed for fluorescence operation, a good optical performance is achieved at 365 nm of wavelength.
3. After the beam reaches the cantilever and sample, it gets reflected back up towards the view module. The camera at the view module is not sensitive to UV, therefore, in order to be able to inspect the placement of the UV spot on the surface and its diameter, a piece of the UV/VIS Detector Card VRC1 (Thorlabs) was placed instead of the sample. UV incident light generates visible light emission. Figure S20 shows an image of the beam spot at the surface of the detector card obtained with the View Module, when focusing on the sample (a) and when focusing on the cantilever (b).
(a) (b) Figure S20. Images from the View Module when the camera is focused on the sample surface: a piece of UV detector card (VRC1, UV/VIS Detector Card: 250 to 540 nm, Thorlabs) (a), and when focused on the cantilever. The tip of the cantilever protrudes at the end of the cantilever (ATEC-EFM, Nanosensors), so neither the cantilever, nor the tip shadows the surface from the UV light.
The size of the spot is around 300-500 microns in diameter. Since the tip of the cantilever extends out from the edge of the cantilever (ATEC-EFM cantilevers, Nanosensors), the surface underneth the tip is not shadowed from the UV light.
We have experimentally measured the SPV of the metal cantilever. We performed KPFM on samples which do not adsorb UV light (i.e., graphite), while turning on and off the UV light. Since the CPD measures the difference in electric contact potential between the tip and the sample, if the light had any effect on the tip surface, it would be noticed on the CPD image. Results show that the CPD value is the same in the dark and under light exposure in all the cantilevers used here, confirming that the metal coating of the tip is intact. TEM images of the metal tips also show an unbroken metal layer ( Figure S5).
To calibrate the light intensity ( Figure S21), we replaced the sample by the sensor S120VC, from Thorlabs. For each value of the UV LED current we recorded a light power measurement.
The irradiance value was obtained by dividing the light power by the area of the UV spot on the sample.  Adj. R-Square 1 Figure S21. UV light power calibration We took care to remove the chip from the cantilever holder when performing the calibration. The cantilever partially shadows the UV spot area, underestimating the number of photons arriving to the sample.