Alkali antimonide photocathodes have wide applications in free-electron lasers and electron cooling. The short lifetime of alkali antimonide photocathodes necessitates frequent replacement of the photocathodes during a beam operation. Furthermore, exposure to mediocre vacuum causes loss of photocathode quantum efficiency due to the chemical reaction with residual gas molecules. Theoretical analyses have shown that covering an alkali antimonide photocathode with a monolayer graphene or hexagonal boron nitride protects it in a coarse vacuum environment due to the inhibition of chemical reactions with residual gas molecules. Alkali antimonide photocathodes require an ultra-high vacuum environment, and depositing a monolayer 2D material on it poses a serious challenge. In the present work, we have incorporated a novel method known as intercalation, in which alkali atoms pass through the defects of a graphene thin film to create a photocathode material underneath. Initially, Sb was deposited on a Si substrate, and a monolayer graphene was transferred on top of the Sb film. Heat cleaning around 550–600 °C effectively removed the Sb oxides, leaving metallic Sb underneath the graphene layer. Depositing Cs on top of a monolayer graphene enabled the intercalation process. Atomic force microscopy, Raman spectroscopy, x-ray photoelectron spectroscopy, low energy electron microscopy, and x-ray diffraction measurements were performed to evaluate photocathode formation underneath the monolayer graphene. Our analysis shows that Cs penetrated the graphene and reacted with Sb and formed Cs3Sb.

Alkali antimonide photocathodes are of keen interest around the world in the application of high-brightness photoinjectors, due to their high quantum efficiency (QE) with visible light, low emittance, and relatively easy and reproducible growth recipe.1–4 As a result, improving the performance of alkali antimonide materials as electron sources has remained a sustained focus of the photocathode community.5–9 The mechanisms that contribute to the degradation of the QE of alkali antimonide photocathodes are reactions with gas molecules present in the ambient vacuum,10,11 ion back bombardment during beam operation,12 and material losses from the heat dissipation by incident laser.13 Besides, beam halo could also cause desorption of gas molecules from the beam pipe, which affects the vacuum near the cathode area, and causes loss of QE.2 The gas molecules such as O2, CO2, CO, and H2O from the vacuum environment can participate in the irreversible chemical reactions with the cathode materials, which, in turn, causes loss of QE and, thus, a reduction in the lifetime of the photocathode.

To increase the robustness and lifetime of the alkali antimonide photocathodes, a thin layer of dielectric coating materials such as NaI, CsI, CsF, SiO, and MgO2 has been explored.14,15 However, further employment of this coating has not been implemented due to limited protection and attenuated spectral response.15 Theoretical estimations have shown that a thin layer coating of two-dimensional (2D) materials such as graphene or hexagonal boron nitride (hBN) could possibly act as a protection layer that inhibits the photocathode material’s reaction with the residual gas molecules present in the vacuum environment.16 

The deposition of a thin 2D material onto an activated photocathode is challenging. First of all, alkali antimonide photocathodes are grown in an ultra-high vacuum (UHV) environment, and the commonly used wet transfer methods17,18 are not feasible in a clean UHV environment. Besides, these cathodes are sensitive to temperature increase. A temperature higher than 70 °C could initiate loss of cesium from the cathode.13 Hence, a direct fabrication of a 2D material into an activated photocathode is also not viable as the process requires a high substrate temperature (750° or higher19,20). Liu et al. showed alkali antimonide photocathode’s growth onto a thin layer of graphene, supported with a TEM grid.21 The concept is novel; however, the presence of the nanostructured TEM grid makes it impractical to use in high voltage photoinjectors.

In this article, we present the results of Cs intercalation through graphene to create cesium antimonide photocathode covered with a monolayer graphene on top. We first deposited a thin layer of Sb on a Si substrate, and a monolayer graphene was transferred on top of the Sb thin film covered Si substrate (denoted as Sb/Si) using a wet transfer method. Raman spectroscopy, atomic force microscopy (AFM), and x-ray photoelectron spectroscopy (XPS) measurements were performed to evaluate the quality of the transferred graphene and the Sb layer underneath. Heat cleaning was performed up to a temperature of 600 °C, and XPS was used to evaluate the heat cleaning temperature required for successful removal of Sb oxides underneath the graphene without loss of metallic Sb. Cesium intercalation was achieved by depositing sufficient amount of Cs on top of graphene. Low energy electron microscopy (LEEM), x-ray diffraction (XRD), and XPS measurements were performed to characterize alkali antimonide formation underneath the graphene.

A thin film of Sb with a thickness of around 10 nm was deposited onto an epi-ready Si (100) wafer using RF sputtering at the Center for Nanoscale Materials (CNM) at Argonne National Laboratory (ANL). The purity of Sb sputtering target was 99.999%. Based on a tapping mode AFM measurement, the freshly grown sputtered Sb thin-films have a nominal average roughness of around 0.3 nm. The sputtered Sb thin films have extremely fine grains with 8–10 nm lateral grain dimension. The results of the characterization of the Sb coated Si wafers are shown in the supplementary material (Fig. S1).

A monolayer graphene was transferred onto the Sb layer using a well known wet transfer method.17,18 Details of the workflow are shown in Fig. 1. Here, we have used the terminology Gr/Sb/Si to refer to a Sb coated Si substrate covered with a monolayer of graphene. The overall topography and the roughness of the transferred graphene monolayer were measured using peak force tapping mode AFM. Figure 2(a) shows an AFM image of the Gr/Sb/Si sample with a scale bar of 1 µm. Figure 2(b) shows the zoom-in image of the same sample with a scale bar of 400 nm. The AFM scans were acquired at CNM using a Bruker FastScan system in peak force tapping mode. Figure 2(c) shows the Raman spectrum of the Gr/Sb/Si sample. Raman spectroscopy was carried out at CNM using a confocal Raman Microscope (Renishaw inVia). The Raman excitation was achieved with a 632 nm diode laser. The spectra were averaged over three accumulations using the WiRE software from Renishaw.22 The G and 2D peaks of the monolayer graphene on Sb/Si are positioned at ∼1588 and ∼2677 cm−1, respectively. The ratio of I2D/IG is equal to 2.7, which is well in the range of the characteristics of monolayer graphene.23 The average roughness is 0.7 nm, and the naturally formed wrinkles in the thin-film are the main contributors to the roughness. The monolayer regions away from the wrinkles appear to be very smooth with an average roughness of around 0.2 nm. The wrinkles and defects in the graphene film are found to act as intercalation sites for alkali atoms, which is crucial for the intercalation process regulated by the van der Waals interaction.24 

FIG. 1.

General workflow of this study. Sb was deposited on a Si substrate, and a monolayer graphene was transferred on top of the Sb using a wet transfer method. Exposure to air in the transfer process caused oxidation of the Sb. UHV annealing at 550–600 °C desorbed the oxides, and the metallic Sb remained underneath the graphene layer. Intercalation was achieved by depositing Cs, and cesium antimonide was formed underneath the graphene layer.

FIG. 1.

General workflow of this study. Sb was deposited on a Si substrate, and a monolayer graphene was transferred on top of the Sb using a wet transfer method. Exposure to air in the transfer process caused oxidation of the Sb. UHV annealing at 550–600 °C desorbed the oxides, and the metallic Sb remained underneath the graphene layer. Intercalation was achieved by depositing Cs, and cesium antimonide was formed underneath the graphene layer.

Close modal
FIG. 2.

(a) AFM measurement of the Sb sample covered with a monolayer graphene (Gr/Sb/Si) with a scale bar of 1 µm, (b) Zoom-in AFM image of the sample with a scale bar of 400 nm, (c) Raman measurement of the Gr/Sb/Si sample using an 632 nm laser excitation.

FIG. 2.

(a) AFM measurement of the Sb sample covered with a monolayer graphene (Gr/Sb/Si) with a scale bar of 1 µm, (b) Zoom-in AFM image of the sample with a scale bar of 400 nm, (c) Raman measurement of the Gr/Sb/Si sample using an 632 nm laser excitation.

Close modal

The Gr/Sb/Si sample was initially characterized using XPS to find the chemical states and study the decomposition of Sb oxides through the graphene monolayer under elevated temperatures. The decomposition study of Sb oxides was performed in the multi-probe surface analysis system located at the Center for Functional Nanomaterials (CFN) at Brookhaven National Laboratory (BNL). XPS measurements were carried out in an ultrahigh vacuum (UHV) system with a base pressure of 2 × 10−9 Torr equipped with a hemispherical electron energy analyzer (SPECS Phoibos 100MCD analyzer) and twin anode x-ray source (SPECS, XR50). Al-Kα (1486.6 eV) radiation was used at 10 kV and 30 mA. The angle between the analyzer and the x-ray source is 45°, and photoelectrons were collected along the sample surface normal.

The first intercalation experiment was carried out at the x-ray photoemission electron microscopy (XPEEM) end-station of the Electron Spectro-Microscopy beamline (ESM, 21-ID) of the NSLS-II, BNL. The end-station offers low energy electron microscopy (LEEM), low energy electron diffraction (LEED), XPEEM imaging, and synchrotron XPS at photon energies ranging from 20 eV up to 1500 eV. The base pressures in the growth chamber and the LEED/LEEM characterization chamber were around 1 × 10−10 and 3 × 10−10 Torr, respectively. This is a full-field microscope with a field of view from a few to 100 µm and a spatial resolution from a few to few tens of nm, depending on the mode of operation. Under the LEEM mode, it operates with an internal electron source, where the electrons with energies ranging from zero to a few hundred eV impinge on the sample surface. These electrons interact with the surface and are elastically backscattered or diffracted back into the electron optics and form an image. LEEM provides spatially resolved information about local surface potential, sample morphology, and crystalline domain distribution, among others. The LEEM images and synchrotron XPS spectra were taken after the heat treatment and after the Cs deposition.

We performed the second intercalation experiment in the UHV cathode synthesis and x-ray analysis chamber at BNL.25 The x-ray measurements were performed at the integrated in situ and resonant hard x-ray studies (ISR) beamline located at NSLS-II, BNL. The photon energy of the incident x-ray beam was 11.48 keV (λ = 1.08 Å) with a nominal beam diameter of 50 µm focused at the sample position. The x-ray diffraction pattern was collected via two Dectris Eiger R 1M x-ray cameras mounted on-axis (75 cm away from the sample) and 30° off-axis (27 cm away from the sample) with the sample plane, respectively. The x-ray fluorescence signal was collected through a vortex multi-cathode x-ray detector mounted 45° with respect to the sample surface normal and 30 cm away from the sample. The detector was provided by NSLS-II detector and research equipment pool. The XRD was measured with 2θ ranging from 5° to 30°. The base pressure in the growth chamber was 1.5×1010 Torr with the partial pressure of water and oxygen 10 times lower than the base pressure.

During the wet transfer of graphene onto Sb film, Sb was first exposed to deionized (DI) water and then air, which caused the formation of oxides. It is essential to remove the oxide layer before intercalation for the successful growth of the cesium antimonide. Hence, we performed decomposition studies at elevated temperatures to identify the temperature required for Sb oxide removal. In the decomposition study, we used two samples: one with ∼10 nm Sb deposited on a Si substrate with no graphene layer (Sb/Si) and the other with ∼10 nm Sb on Si, but covered with a monolayer graphene (Gr/Sb/Si).

In the decomposition study of Sb/Si, we heat cleaned the sample at 200, 300, and 400 °C and performed XPS measurements at each temperature. During heat treatment, the temperature was ramped up at a rate of less than 15 °C per min until the desired heat cleaning temperature was reached. Heat cleaning was performed for 10 min at a certain temperature. The desorption study of the Sb/Si sample works as a reference for the Gr/Sb/Si sample, which is covered with a monolayer graphene. Figure 3(a) shows the Sb 3d3/2 and Sb 3d5/2 peaks at different substrate temperatures. During XPS data acquisition, all the individual spectra were taken at 50 eV pass energy and 0.05 eV energy steps, and all the spectra were charge corrected by setting the C–C component of the C 1s binding energy to 285 eV. At room temperature (RT), the Sb/Si sample consists of both metallic and oxide forms of Sb. In our case, the Sb oxides were mostly Sb2O3. Heat cleaning around 200 °C did not make any difference in terms of Sb oxide reduction. Heat cleaning around 300 °C resulted in an almost total loss of Sb oxides. Heat cleaning around 400 °C caused a total loss of Sb from the surface. After the 400 °C heat cleaning, only the SiO2 peak was visible in the XPS spectra. During heat treatment, the chamber pressure went up to 2 × 10−8 Torr.

FIG. 3.

XPS spectra of the Sb 3d peak at different temperatures. Measurements were performed with an Al-Kα x-ray source with a photon energy of 1486.6 eV. (a) A bare Sb/Si sample. (b) An encapsulated Gr/Sb/Si sample.

FIG. 3.

XPS spectra of the Sb 3d peak at different temperatures. Measurements were performed with an Al-Kα x-ray source with a photon energy of 1486.6 eV. (a) A bare Sb/Si sample. (b) An encapsulated Gr/Sb/Si sample.

Close modal

After that, we performed the desorption study of the Gr/Sb/Si sample. We heat cleaned the sample at 200, 300, 400, 500, and 600 °C and measured the XPS spectra at each temperature. Heat cleaning was performed for 10 min at a certain temperature. During heat treatment, the chamber pressure went up to 6 × 10−8 Torr. We observed that it takes ∼600 °C to remove the Sb oxides from underneath the graphene monolayer. Figure 3(b) shows Sb 3d3/2 and Sb 3d5/2 peaks at different temperatures of the Gr/Sb/Si sample. The presence of a strong peak of metallic Sb after heating at elevated temperatures is a solid indication that the graphene monolayer protected the Sb from leaving the surface even when the heat treatment was performed at 600 °C.

We performed the first intercalation experiment at the XPEEM end station of the electron spectro-microscopy beamline (ESM, 21-ID) of the NSLS-II, BNL. LEEM images were taken after the 600 °C heat cleaning and after the Cs deposition, respectively. Figure 4(a) shows a LEEM image acquired just after the 600 °C heat treatment for 10 min. The red encircled area denotes an example of a Sb droplet under the graphene layer, which was formed at this high heat treatment temperature. In all intercalation experiments that follow, the heat cleaning temperature was limited to 550 °C and Sb droplet formation was not observed. The thick dark lines were wrinkles on the graphene monolayer. We observed similar features using AFM on Gr/Sb/Si sample, shown in Fig. 2(b). Figure 4(b) shows the LEEM image after the Cs deposition. The Cs source was commercial Alkali Metal Dispensers (AMD) from SAES Getters.26 During Cs deposition, the temperature of the sample was around 80 °C. Figure 4(b) shows the disappearance of the Sb droplets previously visible on the heat treated sample. The wrinkles are visible and appear brighter due to the Cs accumulation, which reduced the work function. The vanishing of Sb droplets and the change in contrast indicate reactions between Sb and Cs.

FIG. 4.

LEEM images with 30 µm field-of-view. (a) The 600 °C heat treated graphene covered Sb sample (Gr/Sb/Si) and (b) the same sample after the Cs deposition.

FIG. 4.

LEEM images with 30 µm field-of-view. (a) The 600 °C heat treated graphene covered Sb sample (Gr/Sb/Si) and (b) the same sample after the Cs deposition.

Close modal

We performed XPS measurements in the same system, both after the heat treatment and after the Cs deposition. The synchrotron x ray used in this measurement was 800 eV, which makes the measurement very surface sensitive. We obtained the XPS spectra of C 1 s, Sb 3d3/2, Sb 3d5/2, Cs 3d3/2, and Cs 3d5/2. In the XPS spectra, the most important ones are the Sb peak and the Cs peak. Figure 5(a) shows the Sb 3d5/2 peak after the heat treatment and after the Cs deposition. The Shirley background was subtracted from the spectra, and peak fitting was performed using CasaXPS27 with Lorentzian asymmetric line shape convoluted with a Gaussian. The binding energy of all the spectra was referenced to the C–C component of the C 1s peak at 285 eV. Both Sb and Cs have a 3d doublet peak, 3d3/2 and 3d5/2; however, 3d3/2 has a much lower intensity compared to 3d5/2 peak and is not shown here. Since the measurement was surface sensitive due to the use of low photon energy compared to a lab source or hard x ray, a minuscule amount of Sb oxide left on the surface was visible in the XPS spectrum of the heat treated sample.

FIG. 5.

(a) XPS measurement after the heat treatment at 550 °C for around 10 min and after the Cs deposition. There is a binding energy shift of around 0.45 eV of metallic Sb 3d5/2 toward the lower binding energy after the Cs deposition. (b) The Cs 3d5/2 peak after the Cs deposition; the same sample after the 500 °C heat treatment for 10 min. The synchrotron photon energy in the measurement was 800 eV, and the spectra are shown with Shirley background subtracted.

FIG. 5.

(a) XPS measurement after the heat treatment at 550 °C for around 10 min and after the Cs deposition. There is a binding energy shift of around 0.45 eV of metallic Sb 3d5/2 toward the lower binding energy after the Cs deposition. (b) The Cs 3d5/2 peak after the Cs deposition; the same sample after the 500 °C heat treatment for 10 min. The synchrotron photon energy in the measurement was 800 eV, and the spectra are shown with Shirley background subtracted.

Close modal

The binding energy of metallic Sb 3d5/2 after the heat treatment was 528.7 eV, which is in close agreement with the published data.28,29 After the Cs deposition, we observed a chemical shift of 0.45 eV of the Sb 3d5/2 metallic peak toward the lower binding energy. The shift in the binding energy suggests the formation of a Cs–Sb compound. Previously, a binding energy shift of 2–3 eV toward the lower binding energy after the Cs3Sb cathode formation was reported.30,31 The low chemical shift of the Sb 3d5/2 is associated with the fact that we intentionally deposited a limited amount of Cs due to the sensitivity of the LEEM system. Flooding the system with Cs could cause system failure while operating LEEM.

Cesium also reacted with Sb and leftover oxygen, which created another prominent peak at 531.6 eV. This is a Sb5+ peak, which is assigned to CsSbO3.32,33 The binding energy of O 1 s peak in Cs2O appears at around 527.5 eV.32,34 From Fig. 5(a), we can rule out the possibility of forming any Cs2O. Cs11O3 appears at 531.7 eV,31 which is very close to the assigned peak of CsSbO3. We excluded the possibility of formation of Cs11O3, since metallic Sb peaks drop after the Cs deposition and two significant peaks appear. Besides, Cs11O3 forms due to oxidation when there is external exposure of oxygen on the sample.31 

Figure 5(b) shows the Cs 3d5/2 peak just after the Cs deposition and the same sample after the 500 °C heat treatment. We did not observe any plasmon peaks, which are associated with energy loss of electron from the metal surface. We observed a noticeable Cs peak even after the 500 °C heat cleaning. The duration of heat cleaning was ∼10 min. Previously, Petrović et al. reported that at about 500 °C, desorption of Cs starts from the intercalated phase through the cracks in graphene associated with wrinkles.24 Retention of enough Cs after the 500 °C heat treatment indicates that enough Cs penetrated the graphene layer that could not come out in the annealing process.

To further verify the intercalation and formation of photocathode underneath the graphene layer, we performed in situ x-ray measurements at beamline 4ID at NSLS-II, BNL. We followed the similar heat treatment method; however, the Cs source in this case was an effusion cell, which can produce a much higher Cs flux than the previously used Getter Cs sources. The details of the Cs effusion cell are mentioned elsewhere.25 The Cs deposition rate was ∼0.22 Å/s, and the duration of Cs deposition was around 40 min. A total of ∼52 nm of Cs was deposited onto the sample. Stoichiometry estimated from real time XRF is included in the supplementary material. Figure 6(a) shows the XRD spectra of the Gr/Sb/Si sample at three stages: as-loaded, 550 °C heat-treated, and after the Cs deposition. On the as-loaded sample, the three prominent peaks are Sb[006], Sb[003], and Sb2O3[220]. The low Sb crystallinity could be associated with the wet transfer of the graphene monolayer, which required the use of acetone, water, and heat treatment to properly transfer the graphene on a Sb/Si substrate. After the 550 °C heat treatment for ∼10 min, Sb2O3 disappeared from underneath the graphene layer, which matches with our previous XPS measurement. After the Cs deposition, the Sb crystalline phase disappeared completely and was converted to new alkali antimonide crystalline phases, which are identified as CsSbO3[113] and Cs3Sb[220]. The XRD peak identification matches with the known database.35 X-ray fluorescence results (supplementary material) yield the final sample stoichiometry to be Cs:Sb = 3:1, indicating that although not well crystallized, Sb was fully converted to Cs3Sb in the reaction. Similar behaviors in the evolution of the diffraction pattern were also observed for sequentially grown Cs2Te.25 

FIG. 6.

(a) The XRD spectrum of the Gr/Sb/Si sample at three stages: as-loaded, 550 °C heat-treated for ∼10 min, and after the Cs intercalation. (b) Spectral response of the Gr/Sb/Si sample after the Cs intercalation.

FIG. 6.

(a) The XRD spectrum of the Gr/Sb/Si sample at three stages: as-loaded, 550 °C heat-treated for ∼10 min, and after the Cs intercalation. (b) Spectral response of the Gr/Sb/Si sample after the Cs intercalation.

Close modal

We measured the spectral response of the intercalated sample in the same system after the XRD measurement. The QE was measured using an incident light with a wavelength ranging from 200 to 600 nm using an optical system consisting of a laser driven light source and a Cornerstone monochromator. The cathode was biased at 80 V at the pickup anode, which was ∼10 mm away from the cathode, and the photoelectron current was measured with a Keithley 6517B electrometer. In Fig. 6(b), it is plotted with respect to the photon energy of the incident laser. The peak QE observed was 0.8% at around 5 eV photon energy. We ignored the optical transmission loss of the monolayer graphene, which is about 2.3% for white light.36 The optical transmission loss of the glass window over different wavelengths is measured and taken into account in the QE calculation. By extrapolating the QE1/2 vs photon energy, the work function of the sample appears to be ∼2.20 eV, which is lower than the previous density functional theory (DFT) estimate of the Cs3Sb covered with a monolayer graphene.16 The most probable cause is the excess Cs on the surface, which could not make it through the graphene layer. The DFT analysis showed that in the presence of Cs adatoms, the work function of graphene could be reduced to as low as ∼2.05 eV.37 However, it has a negligible contribution to photon absorption and the spectral response curve represents the compound underneath the graphene. The spectral response we obtained from a fully converted cesium antimonide film covered with a monolayer graphene matches the spectrum reported by Liu et al.21 

In conclusion, we have successfully grown an alkali antimonide photocathode with a monolayer graphene protective layer on top using the Cs intercalation of graphene. XRD measurements have confirmed the formation of Cs3Sb cathodes. Photoemission was measured through the monolayer graphene with photon energies ranging from 2.0 to 5.0 eV. The maximum QE observed was 0.8% at around 5 eV photon energy. Further improvement of QE could be made possible by optimizing the graphene transfer, optimizing Sb and Cs deposition, and possibly using other 2D materials such as hBN as a protective layer. This work serves as an initial step in the use of a 2D material as a protective layer that could result in the fabrication of photocathodes that achieve a high QE, a long lifetime, and stability in a moderate to high vacuum environment.

See the supplementary material for the characterization of the Sb/Si sample, XPS spectra of carbon peak of the Gr/Sb/Si sample, and XRF spectra of the Cs3Sb photocathode with a monolayer graphene on top.

This research used resources of the Center for Functional Nanomaterials and the National Synchrotron Light Source II, both of which are U.S. Department of Energy (DOE) Office of Science User Facilities operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704. This work was funded by the U.S. Department of Energy, under SBIR Grant No. DE-SC0021511. The work performed at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, was supported by the U.S. DOE, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.

The authors have no conflicts to disclose.

Jyoti Biswas: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Mengjia Gaowei: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Ao Liu: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Writing – review & editing (equal). Shashi Poddar: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Liliana Stan: Investigation (equal); Writing – review & editing (supporting). John Smedley: Investigation (equal); Writing – review & editing (supporting). Jerzy T. Sadowski: Conceptualization (equal); Investigation (equal); Writing – review & editing (supporting). Xiao Tong: Investigation (equal); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material