# Operando Photoemission Imaging of the Energy Landscape from a 2D Material-Based Field-Effect Transistor

Dario Mastrippolito, Mariarosa Cavallo, Davy Borowski, Erwan Bossavit, Clement Gureghian, Albin Colle, Tommaso Gemo, Adrien Khalili, Huichen Zhang, Ankita Ram, et al.

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To cite this version:

Dario Mastrippolito, Mariarosa Cavallo, Davy Borowski, Erwan Bossavit, Clement Gureghian, et al. Operating Photoemission Imaging of the Energy Landscape from a 2D Material-Based Field-Effect Transistor. ACS Nano, 2025, 19 (9), pp.9241-9249. 10.1021/acsnano.5c00256. http://onlinelibrary.wiley.com/doi/abs/10.1021/acsnano.5c00256

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Distributed under a Creative Commons Attribution 4.0 International License
Operando Photoemission Imaging of the Energy Landscape from a
2D Material-based Field Effect Transistor

Dario Mastrippolito¹, Mariarosa Cavallo¹, Davy Borowski², Erwan Bossavit¹,³, Clement Gureghian¹,
Albin Colle¹, Tommaso Gemo¹, Adrien Khalili¹, Huichen Zhang¹, Ankita Ram², Erwan Dandeu¹,
Sandrine Ithurria⁴, Johan Biscaras⁵, Pavel Dudin³, Jean-François Dayen², José Avila³, Emmanuel
Lhuillier¹, Debora Pierucci¹*

¹ Sorbonne Université, CNRS, Institut des NanoSciences de Paris, 4 place Jussieu, 75005 Paris,
France.

² Université de Strasbourg, IPCMS-CNRS UMR 7504, 23 Rue du Loess, 67034 Strasbourg,
France.

³ Synchrotron SOLEIL, L'Orme des Merisiers, Départementale 128, 91190 Saint-Aubin, France.

⁴ Laboratoire de Physique et d'Etude des Matériaux, ESPCI, PSL Research University, Sorbonne Université, CNRS, 10 rue Vauquelin, 75005 Paris, France.

⁵ Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, 75005 Paris, France.

**Abstract:** As the integration of transition metal dichalcogenides (TMDC) becomes more advanced for optoelectronics, it is increasingly relevant to develop tools that can correlate the structural properties of the materials to their electrical output. To do so, the determination of the electronic structure must go beyond the hypothesis that the properties of the pristine material remain unaffected after device integration, which generates changes in the dielectric environment, including electric fields that are likely to renormalize the electronic spectrum. Here, we demonstrate that nanobeam photoemission spectroscopy is a well-suited tool to unveil the device energy landscape under operando conditions. Both the gate-induced vertical field and the drain in-plane vectorial electric field can be determined with a sub µm resolution. We conduct a correlative description of a field effect transistor, to connect its bias-modified energy landscape with transistor electrical output. The method appears highly suited to unveil how the actual geometry of the flake (thickness, edge effect, presence of structural defects...) is driving the current flow within the device. Lastly, the method appears fully compatible with traditional fabrication for devices, therefore making it relevant for systematic rational optimization of TMDC-based electronic devices.

**Keywords:** 2D materials, photoemission, operando, field-effect transistor, electric field.

*To whom correspondence should be sent: pierucci@insp.upmc.fr
# INTRODUCTION

Transition metal dichalcogenides (TMDCs) are a special class of quantum-confined materials in which the size reduction down to the monolayer (ML) regime brings strong renormalization of the electronic structure.¹ This enables the emergence of quantum confinement that makes TMDC opto-electronically active, with the most striking evidence being the observation of increased photoluminescence emission.² Compared to III-V semiconductor-based quantum wells, excitonic effects in TMDCs are strongly reinforced thanks to an enhanced dielectric contrast. This not only affects the material band gap but also its electronic feature, as later discussed in the paper.

Equally important has been the demonstration of charge conduction through TMDCs, paving the way for driving their optical features with an electrical knob. In this quest, the design of TMDC-based field-effect transistors (FETs) has been an important step toward the integration of two-dimensional semiconductors into electronic devices.³,⁴ Compared with silicon-based technology, TMDCs offer the benefit of a direct band gap that is highly relevant in the context of phototransistors for which performances are driven by the magnitude of the light-matter interaction.

The FET offers a high degree of flexibility with quasi-independent tuning of the carrier velocity and carrier density. FET design has opened up the interaction of TMDC with large electric fields,⁵,⁶ which, beyond the dielectric gate, can also be obtained from electrolytes⁷ or the interaction with ferroelectric layers.⁸ A very large electric field can induce a massive distortion of the electronic structure, lifting the valley degeneracy⁹,¹⁰ or inducing large doping. These effects have led to the emergence of new electronic phases such as superconductivity.¹¹,¹²

X-ray photoemission¹³ appears as a particularly suited tool to probe the electronic structure modifications.¹⁴⁻¹⁸ Nevertheless, X-ray photoemission usually lacks the spatial resolution necessary to unveil edge and interface-related effects. Microscopy techniques based on near-field methods (scanning tunneling microscopy in particular) or electron microscopy¹⁹⁻²¹ can be used to assess local effects (i.e., at the atomic scale), but their high spatial resolution often makes them miss the mesoscale range relevant to the device operation. As TMDC integration gets more advanced, it becomes relevant to develop tools to assess the electronic structure of the device under operando conditions, moving beyond the traditional assumption that the properties of the material remain mostly unchanged once integrated into the device. Therefore, changes in the dielectric environment and the influence of applied electric fields are also considered.

In this paper, we investigate operando the use of nanobeam X-ray photoemission²²⁻²⁶ as a tool to probe the energy landscape of planar back-gated TMDC-based FETs. The method enables a direct measurement of the FET lever arm: the gate-induced energy shift of the energy profile in eV·V⁻¹. We use this method as a way to assess the gate effect as a function of the flake thickness and device geometry (i.e., flake on top or bottom of source-drain contacts). In the last part of the paper, we exploit the high spatial resolution of the setup to unveil the vectorial distribution of the electric field resulting from drain-source bias application. In particular, we can correlate the presence of structural defects and morphology in the flake with the localization of bias drops.

# DISCUSSION AND RESULTS

## WSe₂-based Field-effect Transistor

We start by fabricating a planar back-gated FET where the TMDC-based flake comes as the top layer, see **Figure 1a** for a side view of the device. This strategy has the benefit of minimizing the
exposure of the flake to fabrication steps that may contaminate it. Such contamination could hide
the signal later acquired through X-ray photoemission under a dominant contribution from organics.
Details of the procedure are provided in the methods section. Briefly, a silicon substrate with an
oxidized surface is used as a mechanical wafer and functionalized with a gate through optical
lithography. The entire substrate is then coated with 40 nm of alumina (deposited by atomic layer
deposition) which serves as the gate dielectric. Such thickness enables a large sheet capacitance
and a large resulting current modulation, while keeping the leakage current below the channel flow.²⁷
It is worth noting that we use a rather conventional fabrication procedure here, rather than h-BN
flake-based gating, so that the method is suited for a potential wafer-scale fabrication. Using a
second step of optical lithography we fabricate the drain-source electrodes. The channel is 20 µm
long and the underlying gate completely covers this area, later ensuring the presence of a
homogenous plane to define the electrostatic potential and limit sample photo-charging. Note also
that the contact pad location is chosen to minimize the impact on the photoelectron path (i.e., avoid
any possible deflection of photoelectrons by current-induced magnetic fields and stray electric
fields). Finally, a WSe₂ flake is exfoliated from a bulk crystal and carefully transferred over the FET
channel, see **Figure 1b** for a top view of the device. In such FET, the application of a drain bias is
used to accelerate the electrons/holes, while the gate bias tunes the carrier density, which gives two
independent knobs to control the current density flowing within the channel.

Raman spectroscopy is then used to assess the quality of the deposited material and determine its thickness. Six Raman modes are observed in the 200-400 cm⁻¹ range, matching the fingerprint of WSe₂, see **Figure 1c**. We then collect a Raman spectrum map over the FET channel area and then depict the ratio of the E₂g in-plane mode intensity over the A₁g out-of-plane mode intensity (a minor contribution from a 2LA mode overlaps the latter), see **Figure 1d**. A higher value for the ratio indicates that the flake thickness gets close to its few-layer regime.²⁸,²⁹ This is further confirmed by atomic force microscopy (AFM, see Figure S1) which measures a thickness of 3.6 nm (roughly 5 layers) over most of the flake surface. From an electrical point of view, the material behaves as a p-type material³ (**Figure 1e**), with a rise of the sample conductance only under negative gate bias. The current modulation reaches 2.5 orders of magnitude while the gate bias is tuned from -5 to 5 V. Lastly, the material is found to be photo-responsive upon illumination at 405 nm which corresponds to an energy larger than the material band gap, see **Figure 1f**.

<figure><img src="image_3.png" /><figcaption>a</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>c</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>e</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>d</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>f</figcaption></figure>

<figure><img src="image_9.png" /></figure>
**Figure 1** Top-WSe₂ flake-based field effect transistor. a. Schematic of the device. b. Optical microscopy image of the device. Scale bar is 20 µm wide. c. Raman spectrum from the WSe₂ flake in the area of the channel (purple point location in part d). d. Raman map, showing the ratio of the E₂g in-plane mode over the A₁g out-of-plane mode intensity (which is overlapped to a minor contribution of 2LA mode), over the channel area. Scale bar is 5 µm wide. e. Transfer curve (drain and gate current as a function of gate voltage under constant -3 V drain-source bias). Curve is measured at 250 K. f. IV curve for the top flake device in the dark and under illumination by a blue (405 nm) laser diode, in which operating power is tuned. Measurements were acquired while the gate was floating.

Now that we have assessed the quality of the FET and its functional operability, we aim to probe its electronic structure thanks to nano-beam photoemission spectroscopy conducted at the ANTARES beamline³⁰ of Synchrotron SOLEIL. The synchrotron beam is first monochromatized to produce a photon flux at 95 eV. This low-energy soft X-ray beam is favorable to maximize both the signal coming from the sample surface and the output flux which results from beam focusing via a Fresnel zone plate. This generates an X-ray spot of 700 nm at the sample level, as shown in **Figure 2a**. The sample stage is then moved to enable point-by-point imaging, where for each point the electron analyzer collects a photoemission spectrum. In the energy range of interest (below 95 eV), the WSe₂ flake exhibits two main core levels: W 4f and Se 3d, as shown in **Figure 2b**. The latter (**Figure 2c**), being the one with the highest cross section at 95 eV, will be the one we will later track to generate a binding energy map.
<figure><img src="image_10.png" /><figcaption>**Figure 2** X-ray Photoemission microscopy. a. Schematic of the soft X-ray photoemission microscopy setup acquiring data on the top-WSe₂ flake-based FET shown in Fig. 1. ZP stands for Fresnel zone plate and OSA for order sorting aperture. b. Survey spectrum acquired at 95 eV, highlighting the presence of the two main core levels (W 4f and Se 3d) at low binding energy. c. High-resolution core level spectrum relative to the Se 3d state acquired at 95 eV. d. ARPES signal relative to the valence band for the top WSe₂ flake-based FET acquired along the Γ-K direction.</figcaption></figure>

To highlight the good quality of our FET fabrication, an angle-resolved photoemission spectroscopy (ARPES) map has been acquired inside the channel, see **Figure 2d**. Here, we clearly observe the band dispersion on a sample made with conventional lithography process and deposited on a surface that presents some roughness (as opposed to preparation requiring the use of hexagonal boron nitride as a flat surface³¹). In particular, gold electrodes deposited via thermal evaporation often exhibit a texture with features that can be as large as several nm. However, the small spot of the X-ray beam plays a crucial role in preventing a signal averaging over a large area, still enabling the observation of the dispersive band. The ARPES data of **Figure 2d** shows the dispersive valence band along the Γ-K direction, where the prominent sharp feature at Γ corresponds to the top of the valence band in multilayer WSe₂. The electronic structure of the top-lying valence bands in WSe₂ is
derived primarily from the W 5d orbital and the Se 4p orbitals (at Γ mostly the out-of-plane ones, $d_z^2$ and $p_z$).⁵,³² At a photon energy of 95 eV used in our measurements, the photoionization cross-section of the W 5d orbitals is significantly larger than that of the Se 4p orbitals,³³ which enhances the contributions of tungsten-derived states to the ARPES spectra. The top of the valence band for multilayer WSe₂ presents a larger band curvature with respect to the monolayer³⁴, resulting in a reduced effective mass for the hole, which may contribute to an enhancement in carrier mobility. The upper band fit leads to a 0.26 $m_0$ hole effective mass, with $m_0$ being the free electron mass. This is consistent with the expected mass along the Γ-K direction for a multilayer WSe₂ flake,³⁵ as revealed from AFM measurement (Figure S1).

## Impact of edge effect and thickness

In the next step, we use the nanobeam to track the energy of the Se 3d state while the device is under operation (i.e., with drain and gate biases applied). The rigid shift of the X-ray photoemission spectrum makes the tracking of the Se 3d states equivalent to the tracking of the valence band, while the peaked aspect of the state and its higher intensity with respect to the valence band ease the later fitting procedure. The detailed procedure to process the data is described in Figure S2. The general procedure relies on the fit of the Se 3d state with a doublet Gaussian line shape (to account for both Se 3d$_{5/2}$ and Se 3d$_{3/2}$ contributions with a 0.82 eV spin-orbit splitting) which enables the generation of a Se 3d binding energy map. From the latter, we then subtract, point by point, the same map acquired while all the electrodes are grounded. This procedure removes any residual effect that may result from sample charging. The obtained energy shift map then provides enhanced contrast of the effect induced by the bias application.

Typical obtained energy shift maps are presented in **Figure 3a** and b for two different gate biases (+3 and +7 V), with the source and drain electrodes grounded. The maps display a clear change of the potential in the area corresponding to the channel and the magnitude of the change appears tunable with gate bias. To better quantify the change with gate bias, we then plot the horizontal profile of the energy shift along the channel length, see **Figure 3c**. Over the electrodes, the energy shift is zero, as expected, since the electrodes set the potential. In the channel, a clear modulation that can reach 0.32 eV around the middle of the channel is observed. Notably, mapping reveals that the energy shift is not completely homogeneous within the channel. This behavior clearly mimics variations in the adhesion of the flake on the dielectric and the possible presence of edge effects that concentrate field lines, as better evidenced by the in-plane field discussed later.

We can also correlate the magnitude of the shift with the flake thickness. The top right corner of the flake, which appears twice as thick (as depicted from AFM in Fig. S1), clearly presents a reduced gate effect, as further discussed in detail. In the thin part of the flake, we can then quantify the gate lever arm from a linear fit of the energy shift magnitude as a function of the applied gate bias, see **Figure 3d**. A linear fit of the gate-induced shift vs applied voltage leads to $\alpha_{top}=40$ meV.V$^{-1}$.
<figure><img src="image_11.png" /><figcaption>**Figure 3** Gate effect and field effect lever arm. a. (resp b.) Energy shift map for the Se 3d state when +3 V (resp +7 V) is applied over the gate while drain and source are grounded. c. Energy shift profile over the channel for three different gate biases applied. d. Maximum energy shift observed within the channel as a function of the applied gate bias and its linear fit, leading to a 40 meV·V⁻¹ slope. All measurements are acquired at 250 K.</figcaption></figure>

We then study the effect of the FET geometry by switching to a sample where the flake is in direct contact with the dielectric while depositing the drain-source electrodes on top of the flake. This configuration has the advantage of improving the interface with the gate by avoiding the formation of an air gap, while the drain-source electrodes interface with the flake is also expected to be similarly improved. This hypothesis is confirmed by the stronger on-off ratio determined from the transfer curve (Figure S3) that now reaches 4.5 orders of magnitude, which is a factor 100 larger than the value obtained from the top flake FET (Figure 1e).

Conversely, the bottom flake geometry presents the drawback of exposing the flake directly to a step of lithography, which could potentially contaminate its surface. However, in practice, monitoring the ARPES signal (Figure S3) and the evolution of the Se 3d core level remains feasible.⁵,⁶ The obtained device is imaged in Figure 4a and schematized in Figure S3. To further address the impact of thickness on the gate-induced energy shift we have chosen to use a flake of varying thickness: a thin area at the bottom (≈3 nm) and a thicker (≈10 nm) one at the top, as measured by AFM imaging, see Figure S4. For such a flake, the energy shift map unveils a gate-induced shift limited only to the thin area, see Figure 4b and c, consistently with the screening length estimated ≈7 nm.³⁶,³⁷ In upper TMDCs, there is a strong screening of the gate effect with increasing thickness,⁵,⁶ also responsible for the large excitonic effect in this material family. This situation contrasts quite drastically with the case of colloidal nanocrystal films³⁸⁻⁴⁰ for which the decay length of the gate effect has been estimated to be at around 75 nm,⁴¹ thus enabling the use of much thicker films for applications such
as phototransistors, which require combining both light absorption and gate induced carrier density tunability.

In this geometry, the range of the gate-induced energy shift can be as large as 0.7 eV, twice the value obtained for the top flake geometry while thicknesses are similar at around 3 nm. As a consequence, the current modulation obtained in this configuration is enhanced by a factor of 100. Nevertheless, the operation is not trivial since the shift with gate bias appears nonlinear, see **Figure 4d**. We interpret this effect as follows: in the low gate bias regime, the generated charges are primarily used to passivate the surface of the dielectric, thereby having minimal impact on the flake itself. Conversely, under large gate bias, the dielectric becomes fully passivated, and the additional charges primarily affect the flake.

<figure><img src="image_12.png" /></figure>

**Figure 4** Bottom-WSe₂ flake-based field effect transistor. a. Optical image of the bottom flake FET. Scale bar is 10 µm. Difference of contrast unveils a difference in thickness, see also AFM image in Figure S4. b. Energy shift map for the Se 3d state when +10 V is applied over the gate while drain and source are grounded. c. Energy shift profile along x=160 µm in the map from part b. The graph stresses a direct connection between gate-induced energy shift and flake thickness. d. Energy shift in the area where the flake is the thinnest as a function of the applied gate bias.

In-plane vectorial electric field distribution and its correlation to defect
In the final part of the paper, we take advantage of the high spatial resolution of the method to access the vectorial distribution of the electric field$^{42,43}$ and conduct correlative microscopy between the device structure and the field distribution. Whereas the first part of the paper focuses on vertical fields, here we are interested in the in-plane electric field resulting from drain-source bias application. The in-plane electric field can be obtained from $\vec{F} = -\vec{\nabla}V$, where $V$ is the electric potential. Since $\Delta BE$, the binding energy shift induced by the applied bias (obtained after subtracting the grounded map from the biased ones), directly represents the voltage drop, this relationship relates to the experimental data through $\vec{F} = -\vec{\nabla}\Delta BE = -\left(\frac{\partial\Delta BE}{\partial x}\hat{x} + \frac{\partial\Delta BE}{\partial y}\hat{y}\right)$. **Figure 5a** displays an arrow plot, where both the direction and magnitude of the arrows are determined by the electric field. This map is superimposed on the binding energy shift map.

The field magnitude appears strongly connected to the flake geometry. For the sake of illustration, the field magnitude is weak in the top tip (area for y values >190 µm in **Figure 5a**). This part of the flake is poorly connected to the two electrodes and the weak magnitude of the field will prevent this part of the device from taking part in photocurrent generation. In this sense, photoemission microscopy appears as a relevant tool to determine what is the effective opto-electronically active area of a TMDC-based device. Conversely, the thickness of the flake seems to have little effect, as opposed to what was observed for the gate bias. Here, the in-plane field distribution does not display any major discontinuity in the bottom part of the flake (area for y<170 µm in **Figure 5a**).

Regarding the directionality of the field, the homogeneous part of the flake displays the expected behavior of a field perpendicular to the edge of the electrodes that set the potential in the FET geometry. Two main deviations are observed: one at the edges of the flake, where the field tends to funnel toward the part of the flake connected to the electrode, and the second at structural defects, which appear to drive both the direction and localization of the bias drop. **Figure 5a** shows a clear wrinkle with a ≈45° angle with respect to the electrode edges. AFM reveals that the latter is clearly associated with a height discontinuity. Its presence was not affecting the gate-induced energy shift, see **Figure 5b**, possibly because in this area, the effect was fully screened. However, the in-plane field has a clearly enhanced magnitude (x2.5) along this line, see **Figure 5b**. The accumulation of bias drop along such lines reduces the remaining bias drop over the structure compared to its spatially average value which can clearly induce some deviations between the measured properties and those expected when assuming a homogeneous field over the flake.
<figure><img src="image_13.png" /><figcaption>**Figure 5** Electric field distribution in the bottom-WSe₂ flake-based FET. a. Energy shift profile while -1 V drain-source bias is applied. A vector plot is superimposed which depicts the orientation and magnitude of the electric field. b. Scalar map of the magnitude of the electric field.</figcaption></figure>

## CONCLUSION

High-resolution soft X-ray photoemission spectroscopy appears to be a well-suited tool for unveiling the energy landscape of TMDC-based devices. The method appears robust enough to be compatible with a regular device fabrication process. In particular, there is no need for h-BN encapsulation, either as a dielectric gate or to flatten the flake, which could have been seen as a clear limitation from the perspective of scaling up the production and legitimate the wafer-scale integration. The method is particularly insightful when used to correlate the FET electrical output with structural information. We used it to determine the FET lever arm and how the geometry is affecting it. We bring direct evidence of a strong screening of the gate effect for thickness above a few nm. The *operando* mapping capability of the device is particularly relevant to unveil deviation of behavior from basic electrostatic law such as spatial inhomogeneity or accumulation of bias drop along line defects. As illustrated here in the case of line defects, we anticipate that such direct insight into the role of defects will contribute to a better understanding of the local and non-local transport properties of large-scale van der Waals materials where domain boundaries play a key role in the charge carriers diffusion processes,⁴⁴ including for non-local transport.⁴⁵ The method being atom selective it will be now highly appealing to expand the concept to van der Waals heterostructures and other two-dimensional semiconductors beyond the TMDC group.

## Methods

**Electrodes fabrication:** The substrate (Si/SiO₂ wafer, 300 nm oxide layer) is cleaned by sonication in acetone bath, then rinsed with acetone and IPA and dried with N₂. Final cleaning is obtained by O₂ plasma. First, the gates are patterned by photolithography. An adhesion primer (TI PRIME) is spin-coated and then baked at 110°C for 1 min. Then, the photoresist (AZ5214E) is spin-coated and baked at 110°C for 1 min before a UV exposure of 1.5 s through the lithography mask. The sample
is then baked at 110 °C for 2 min for resist inversion, and flood exposed to UV light for 40 s. Development is carried out for 20 s in AZ726MIF, followed by rinsing in de-ionized water. The surface is plasma cleaned before thermal evaporation of the metal for the electrodes (5 nm Ti/40 nm Au). Lift-off is carried out in acetone bath for 30 min. After fabrication of the gate electrodes, 40 nm of Al₂O₃ are deposited by atomic layer deposition (ALD, 450 cycles) to form the gate dielectric. Finally, a second photolithographic process is performed to pattern the source and drain electrodes, with an evaporation of 5 nm Ti/40 nm Au (in the case of the bottom flake, this last step is carried out after the flake deposition).

**Flake deposition (on top)** Using the scotch tape exfoliation technique, thin layers of van der Waals materials have been exfoliated from their bulk 3D crystals and transferred onto a PDMS polymer attached to a glass slide. After exfoliation, a careful optical microscope inspection was done to identify and isolate the flakes with the desired thickness and quality. A custom micro-positioning transfer station was used for precise alignment and transfer of the flakes onto the pre-patterned electrodes on the substrate. This process involved heating the substrate to 45°C, allowing for controlled expansion of the PDMS stamp upon contact. The stamp was then gradually brought into contact with the substrate, with the temperature incrementally raised by 10°C to ensure optimal adhesion of the 2D flakes onto the substrate. The PDMS retraction was carefully executed using mechanical and temperature control to avoid any damage or misalignment.

**Flake deposition (bottom):** WSe₂ thin flakes are mechanically exfoliated from a bulk WSe₂ single crystal (hq Graphene) using blue tape (Nitto) and transferred to a sticky polydimethylsiloxane (PDMS) sheet, which is attached to a glass slide and acts as a viscoelastic stamp. The selected thin WSe₂ flake on PDMS is deterministically transferred to the Al₂O₃ gate electrode area using a micromanipulator stage. Deposition is carried out by bringing the PDMS sheet into contact with the substrate and then slowly detaching the PDMS sheet. Al₂O₃ substrate was pre-cleaned with O₂ plasma. After deposition, the flake was cleaned in an acetone bath, rinsed with IPA, and dried with N₂ gun. To enhance the adhesion of the flake on the Al₂O₃ substrate, the flake is annealed at 110 °C for 60 min in a glove box.

**AFM imaging:** AFM images were acquired in non-contact mode using an NX20 setup (Park Systems) and an n-type doped Si cantilever RTESPA-300 (Bruker).

**Raman spectroscopy and imaging:** Measurements were performed at room temperature using a Horiba Labram Soleil confocal Raman microscope with a 100x objective and a 532 nm laser excitation, resulting in a laser spot having a diameter of ≈ 1 µm. The spectrometer calibration was set using the 520.7 cm⁻¹ first-order peak of a Si (100) single crystal. The spectra were recorded between 200-450 cm⁻¹ with a 1800 lines/mm grating resulting in an effective resolution of 1.2 cm⁻¹. The laser power at the exit of the objective was carefully reduced with a neutral density filter to avoid any damage to the flake set at 0.8 % of the total laser power, which corresponds to about 0.75 mW. The Raman maps were acquired with a laser exposure of 10 sec with two accumulations for each point spectrum.

**Electrical characterization:** The samples are mounted on the cold finger of a closed cycle He cryostat, whose temperature is controlled and assessed by a Lakeshore 325. The devices are connected to a Keithley 2634B source meter to apply gate and drain biases and measure the resulting currents. The measurements were conducted under a secondary vacuum. The measurements under illumination are collected while the channel device area is illuminated by a 405 nm laser diode (Coherent Corp.).
**Photoemission microscopy:** Photoemission experiments are conducted at the ANTARES beamline of Synchrotron SOLEIL. The synchrotron beam, which is ≈2.5-3 mm wide, is focused using a zone plate (i.e., Fresnel lens), see **Figure 2a**. The latter is made to operate at low energy (below 100 eV), to obtain optimal focusing. In this case, the beam width at the sample position can be down to around 700 nm. The sample is then scanned and the photoelectrons are collected using an MBS A-1 hemispherical electron analyzer.46 The sample holder is moved with steps ranging from 500 to 2000 nm, and a series of photoemission spectra is collected for each point. These spectra are acquired with a 200 eV pass energy, providing a 15.8 eV window with a 17 meV energy step, and are then averaged. Here, we focus on the Se 3d state, see **Figure 2c**. Data acquisition lasts from a few minutes to an hour, depending on the targeted map size. For acquisitions with bias applied, we systematically subtract the grounded map during data during the analysis to remove possible charging effect, see Figure S2 for more detail on the data analysis. We use linearly horizontal polarized photons with a photon energy of 95 eV and all measurements were conducted at 250 K. For all the core level maps, the angular dispersion of the analyzer (±15°) is neglected by integrating the spectra over all angles. The sample was mounted on the operando sample holder equipped with electrical contacts. These electrical contacts, on the side of the sample holder, were bonded with gold wires that were connected to the sample pads via silver paste. The sample was connected to two Keithley 2450 to apply drain and gate biases. ARPES data were collected with the same experimental condition, without neglecting the angular dispersion of the analyzer. The ARPES images are acquired over the channel area of the devices after precise alignment along the ГК direction of the Brillouin zone. Before the photoemission experiments, samples were loaded in the ultra-high vacuum (UHV) system and annealed gently for 24 hours at 150 °C to remove any surface adsorbates from air exposure. Photoemission data are calibrated to the experimental Fermi level of the gold, taken as reference.

## DATA AVAILABILITY

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

## ACKNOWLEDGMENTS

We thank Stephane Lorczy for his help in sample preparation and Herve Cruguel for his help with AFM. We thank the chemistry laboratory of Synchrotron SOLEIL for access to the Raman spectrometer and Stephanie Blanchandin and Karine Chaouchi for their supervision of the instrument. The project is supported by ERC grant AQDtive (grant n°101086358) and from French National Research Agency (ANR) through the grants Bright (ANR-21-CE24-0012-02), MixDferro (ANR-21-CE09-0029), Quicktera (ANR-22-CE09-0018), Operatwist (ANR-22-CE09-0037-01), E-map (ANR-23-CE50-0025), DIRAC (ANR-24-ASM1-0001), camIR (ANR-24-CE42-2757), Piquant (ANR-24-CE09-0786), and Labex NanoSaclay, (ANR-10-LABX-0035). We acknowledge the use of clean-room facilities from the "Centrale de Proximité Paris-Centre" and support from Renatech+ for micro and nanofabrication. This project has also received financial support from the CNRS through the MITI interdisciplinary programs (project WITHIN) and Region Ile de France through Sesame project INSIDE. JFD also thanks the Region Grand-Est (Project Phoenix), IdEx Unistra (ANR 10 IDEX 0002), SFRI STRAT'US project (ANR 20 SFRI 0012), and EUR (QMat-ANR-18-EUR-0016) under the framework of the French Investments for the Future Program.
## COMPETING INTEREST

The authors declare no competing interests.

## Supporting Information

Supporting Information includes (i) Structural characterization of the top flake FET, (ii) Procedure to analyze data from X-ray photoemission microscopy, (iii) Structural and electrical characterization of the bottom flake FET.

## REFERENCES

(1) Ugeda, M. M.; Bradley, A. J.; Shi, S. F.; Da Jornada, F. H.; Zhang, Y.; Qiu, D. Y.; Ruan, W.; Mo, S. K.; Hussain, Z.; Shen, Z. X.; Wang, F.; Louie, S. G.; Crommie, M. F. Giant Bandgap Renormalization and Excitonic Effects in a Monolayer Transition Metal Dichalcogenide Semiconductor. *Nat Mater* **2014**, *13* (12), 1091–1095.

(2) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS₂: A New Direct-Gap Semiconductor. *Phys Rev Lett* **2010**, *105* (13), 136805.

(3) Kim, I.; Higashitarumizu, N.; Rahman, I. K. M. R.; Wang, S.; Kim, H. M.; Geng, J.; Prabhakar, R. R.; Ager, J. W.; Javey, A. Low Contact Resistance WSe₂ P-Type Transistors with Highly Stable, CMOS-Compatible Dopants. *Nano Lett* **2024**, *24* (43), 13528–13533.

(4) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS₂ Transistors. *Nat Nanotechnol* **2011**, *6* (3), 147–150.

(5) Brumme, T.; Calandra, M.; Mauri, F. First-Principles Theory of Field-Effect Doping in Transition-Metal Dichalcogenides: Structural Properties, Electronic Structure, Hall Coefficient, and Electrical Conductivity. *Phys Rev B* **2015**, *91* (15), 155436.

(6) Brumme, T.; Calandra, M.; Mauri, F. Electrochemical Doping of Few-Layer ZrNCl from First Principles: Electronic and Structural Properties in Field-Effect Configuration. *Phys Rev B* **2014**, *89* (24), 245406.

(7) Zhang, Y.; Ye, J.; Matsuhashi, Y.; Iwasa, Y. Ambipolar MoS₂ Thin Flake Transistors. *Nano Lett* **2012**, *12* (3), 1136–1140.

(8) Salazar, R.; Varotto, S.; Vergnaud, C.; Garcia, V.; Fusil, S.; Chaste, J.; Maroutian, T.; Marty, A.; Bonell, F.; Pierucci, D.; Ouerghi, A.; Bertran, F.; Le Fèvre, P.; Jamet, M.; Bibes, M.; Rault, J. Visualizing Giant Ferroelectric Gating Effects in Large-Scale WSe₂/BiFeO₃ Heterostructures. *Nano Lett* **2022**, *22* (23), 9260–9267.

(9) Gong, K.; Zhang, L.; Liu, D.; Liu, L.; Zhu, Y.; Zhao, Y.; Guo, H. Electric Control of Spin in Monolayer WSe₂ Field Effect Transistors. *Nanotechnology* **2014**, *25* (43), 435201.

(10) Yao, Q. F.; Cai, J.; Tong, W. Y.; Gong, S. J.; Wang, J. Q.; Wan, X.; Duan, C. G.; Chu, J. H. Manipulation of the Large Rashba Spin Splitting in Polar Two-Dimensional Transition-Metal Dichalcogenides. *Phys Rev B* **2017**, *95* (16), 165401.
(11) Saito, Y.; Itahashi, Y. M.; Nojima, T.; Iwasa, Y. Dynamical Vortex Phase Diagram of Two-Dimensional Superconductivity in Gated MoS<sub>2</sub>. *Phys Rev Mater* **2020**, *4* (7), 074003.

(12) Saito, Y.; Nakamura, Y.; Bahramy, M. S.; Kohama, Y.; Ye, J.; Kasahara, Y.; Nakagawa, Y.; Onga, M.; Tokunaga, M.; Nojima, T.; Yanase, Y.; Iwasa, Y. Superconductivity Protected by Spin-Valley Locking in Ion-Gated MoS<sub>2</sub>. *Nature Physics* **2015** *12:2* **2015**, *12* (2), 144–149.

(13) Wilson, N. R.; Nguyen, P. V.; Seyler, K.; Rivera, P.; Marsden, A. J.; Laker, Z. P. L.; Constantinescu, G. C.; Kandyba, V.; Barinov, A.; Hine, N. D. M.; Xu, X.; Cobden, D. H. Determination of Band Offsets, Hybridization, and Exciton Binding in 2D Semiconductor Heterostructures. *Sci Adv* **2017**, *3* (2), e1601832.

(14) Henck, H.; Ben Aziza, Z.; Pierucci, D.; Laourine, F.; Reale, F.; Palczynski, P.; Chaste, J.; Silly, M. G.; Bertran, F.; Le Fèvre, P.; Lhuillier, E.; Wakamura, T.; Mattevi, C.; Rault, J. E.; Calandra, M.; Ouerghi, A. Electronic Band Structure of Two-Dimensional WS<sub>2</sub>/Graphene van Der Waals Heterostructures. *Phys Rev B* **2018**, *97* (15), 155421.

(15) Nguyen, P. V.; Teutsch, N. C.; Wilson, N. P.; Kahn, J.; Xia, X.; Graham, A. J.; Kandyba, V.; Giampietri, A.; Barinov, A.; Constantinescu, G. C.; Yeung, N.; Hine, N. D. M.; Xu, X.; Cobden, D. H.; Wilson, N. R. Visualizing Electrostatic Gating Effects in Two-Dimensional Heterostructures. *Nature* **2019**, *572* (7768), 220–223.

(16) Graham, A. J.; Nguyen, P. V.; Park, H.; Nunn, J.; Kandyba, V.; Cattelan, M.; Giampietri, A.; Barinov, A.; Xu, X.; Cobden, D. H.; Wilson, N. R. Band Alignments, Conduction Band Edges and Intralayer Bandgap Renormalisation in MoSe<sub>2</sub>/WSe<sub>2</sub> Heterobilayers. *2D Mater* **2024**, *11* (4), 045021.

(17) Agnoli, S.; Ambrosetti, A.; Menteş, T. O.; Sala, A.; Locatelli, A.; Silvestrelli, P. L.; Cattelan, M.; Eichfeld, S.; Deng, D. D.; Robinson, J. A.; Avila, J.; Chen, C.; Asensio, M. C. Unraveling the Structural and Electronic Properties at the WSe<sub>2</sub>-Graphene Interface for a Rational Design of van Der Waals Heterostructures. *ACS Appl Nano Mater* **2018**, *1* (3), 1131–1140.

(18) Lim, C. young; Kim, S.; Jung, S. W.; Hwang, J.; Kim, Y. Recent Technical Advancements in ARPES: Unveiling Quantum Materials. *Current Applied Physics* **2024**, *60*, 43–56.

(19) Hachtel, J. A.; Idrobo, J. C.; Chi, M. Sub-Ångstrom Electric Field Measurements on a Universal Detector in a Scanning Transmission Electron Microscope. *Adv Struct Chem Imaging* **2018**, *4* (1), 10.

(20) Ishikawa, R.; Findlay, S. D.; Seki, T.; Sánchez-Santolino, G.; Kohno, Y.; Ikuhara, Y.; Shibata, N. Direct Electric Field Imaging of Graphene Defects. *Nat Commun* **2018**, *9* (1), 3878.

(21) Murthy, A. A.; Ribet, S. M.; Stanev, T. K.; Liu, P.; Watanabe, K.; Taniguchi, T.; Stern, N. P.; Reis, R. Dos; Dravid, V. P. Spatial Mapping of Electrostatic Fields in 2D Heterostructures. *Nano Lett* **2021**, *21* (17), 7131–7137.

(22) Joucken, F.; Avila, J.; Ge, Z.; Quezada-Lopez, E. A.; Yi, H.; Le Goff, R.; Baudin, E.; Davenport, J. L.; Watanabe, K.; Taniguchi, T.; Asensio, M. C.; Velasco, J. Visualizing the Effect of an Electrostatic Gate with Angle-Resolved Photoemission Spectroscopy. *Nano Lett* **2019**, *19* (4), 2682–2687.
(23) Dale, N.; Mori, R.; Utama, M. I. B.; Denlinger, J. D.; Stansbury, C.; Fatuzzo, C. G.; Zhao, S.; Lee, K.; Taniguchi, T.; Watanabe, K.; Jozwiak, C.; Bostwick, A.; Rotenberg, E.; Koch, R. J.; Wang, F.; Lanzara, A. Correlation-Driven Electron-Hole Asymmetry in Graphene Field Effect Devices. *NPJ Quantum Mater* **2022**, *7* (1), 9.

(24) Hofmann, P. Accessing the Spectral Function of in Operando Devices by Angle-Resolved Photoemission Spectroscopy. *AVS Quantum Science* **2021**, *3* (2), 021101.

(25) Nguyen, P. V.; Teutsch, N. C.; Wilson, N. P.; Kahn, J.; Xia, X.; Graham, A. J.; Kandyba, V.; Barinov, A.; Xu, X.; Cobden, D. H.; Wilson, N. R. Field-Dependent Band Structure Measurements in Two-Dimensional Heterostructures. *Nano Lett* **2021**, *21* (24), 10532-10537.

(26) Dunfield, S. P.; Bojar, A.; Cacovich, S.; Frégnaux, M.; Klein, T.; Bramante, R.; Zhang, F.; Regaldo, D.; Dufoulon, V.; Puel, J. B.; Teeter, G.; Luther, J. M.; Bouttemy, M.; Nordlund, D.; Zhu, K.; Moore, D. T.; van Hest, M. F. A. M.; Kleider, J. P.; Berry, J. J.; Schulz, P. Carrier Gradients and the Role of Charge Selective Contacts in Lateral Heterojunction All Back Contact Perovskite Solar Cells. *Cell Rep Phys Sci* **2021**, *2* (8), 100520.

(27) Sinha, S. K.; Chaudhury, S. Impact of Oxide Thickness on Gate Capacitance - A Comprehensive Analysis on MOSFET, Nanowire FET, and CNTFET Devices. *IEEE Trans Nanotechnol* **2013**, *12* (6), 958-964.

(28) Zeng, H.; Liu, G. Bin; Dai, J.; Yan, Y.; Zhu, B.; He, R.; Xie, L.; Xu, S.; Chen, X.; Yao, W.; Cui, X. Optical Signature of Symmetry Variations and Spin-Valley Coupling in Atomically Thin Tungsten Dichalcogenides. *Sci Rep* **2013**, *3* (1), 1608.

(29) Zhao, W.; Ghorannevis, Z.; Amara, K. K.; Pang, J. R.; Toh, M.; Zhang, X.; Kloc, C.; Tan, P. H.; Eda, G. Lattice Dynamics in Mono- and Few-Layer Sheets of WS₂ and WSe₂. *Nanoscale* **2013**, *5* (20), 9677-9683.

(30) Avila, J.; Asensio, M. C. First NanoARPES User Facility Available at SOLEIL: An Innovative and Powerful Tool for Studying Advanced Materials. *Synchrotron Radiat News* **2014**, *27* (2), 24-30.

(31) Ulstrup, S.; Koch, R. J.; Schwarz, D.; McCreary, K. M.; Jonker, B. T.; Singh, S.; Bostwick, A.; Rotenberg, E.; Jozwiak, C.; Katoch, J. Imaging Microscopic Electronic Contrasts at the Interface of Single-Layer WS₂ with Oxide and Boron Nitride Substrates. *Appl Phys Lett* **2019**, *114* (15), 151601.

(32) Yeh, P. C.; Jin, W.; Zaki, N.; Zhang, D.; Liou, J. T.; Sadowski, J. T.; Al-Mahboob, A.; Dadap, J. I.; Herman, I. P.; Sutter, P.; Osgood, R. M. Layer-Dependent Electronic Structure of an Atomically Heavy Two-Dimensional Dichalcogenide. *Phys Rev B* **2015**, *91* (4), 041407.

(33) Yeh, J. J.; Lindau, I. Atomic Subshell Photoionization Cross Sections and Asymmetry Parameters: $1 \le Z \le 103$. *At Data Nucl Data Tables* **1985**, *32* (1), 1-155.

(34) Liu, E.; van Baren, J.; Lu, Z.; Taniguchi, T.; Watanabe, K.; Smirnov, D.; Chang, Y. C.; Lui, C. H. Exciton-Polaron Rydberg States in Monolayer MoSe₂ and WSe₂. *Nature Communications* **2021**, *12* (1), 6131.
(35) Choudhary, T.; Peter, J.; Biswas, R. K. Exploring Anisotropic Carrier Transport in WSe₂-WTe₂ Superlattices: A Computational Study. *Langmuir* **2024**, *40* (26), 13476–13485.

(36) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Theory of Neutral and Charged Excitons in Monolayer Transition Metal Dichalcogenides. *Phys Rev B* **2013**, *88* (4), 045318.

(37) Das, S.; Appenzeller, J. Where Does the Current Flow in Two-Dimensional Layered Systems? *Nano Lett* **2013**, *13* (7), 3396–3402.

(38) Cavallo, M.; Bossavit, E.; Matzen, S.; Maroutian, T.; Alchaar, R.; Dang, T. H.; Khalili, A.; Dabard, C.; Zhang, H.; Prado, Y.; Abadie, C.; Utterback, J. K.; Dayen, J. F.; Silly, M. G.; Dudin, P.; Avila, J.; Lhuillier, E.; Pierucci, D. Coupling Ferroelectric to Colloidal Nanocrystals as a Generic Strategy to Engineer the Carrier Density Landscape. *Adv Funct Mater* **2023**, *33* (34), 2300846.

(39) Cavallo, M.; Alchaar, R.; Bossavit, E.; Zhang, H.; Dang, T. H.; Khalili, A.; Prado, Y.; Silly, M. G.; Utterback, J. K.; Ithurria, S.; Dudin, P.; Avila, J.; Pierucci, D.; Lhuillier, E. Inside a Nanocrystal-Based Photodiode Using Photoemission Microscopy. *Nanoscale* **2023**, *15* (21), 9440–9448.

(40) Cavallo, M.; Ram, A.; Pandey, S.; Maroutian, T.; Bossavit, E.; Ledos, N.; Khalili, A.; Zhang, H.; Prado, Y.; Nguyen, D. L.; Dang, T. H.; Majjad, H.; Biscaras, J.; Avila, J.; Dayen, J. F.; Lhuillier, E.; Pierucci, D. Using Wafer Scale Ferroelectric Domains of LiNbO₃ to Form Permanent Planar P-n Junction in Narrow Band Gap Nanocrystals. *Appl Phys Lett* **2023**, *123* (25), 253505.

(41) Cavallo, M.; Bossavit, E.; Zhang, H.; Dabard, C.; Dang, T. H.; Khalili, A.; Abadie, C.; Alchaar, R.; Mastrippolito, D.; Prado, Y.; Becerra, L.; Rosticher, M.; Silly, M. G.; Utterback, J. K.; Ithurria, S.; Avila, J.; Pierucci, D.; Lhuillier, E. Mapping the Energy Landscape from a Nanocrystal-Based Field Effect Transistor under Operation Using Nanobeam Photoemission Spectroscopy. *Nano Lett* **2023**, *23* (4), 1363–1370.

(42) Khalili, A.; Cavallo, M.; Bossavit, E.; Alchaar, R.; Dang, T. H.; Dabard, C.; Zhang, H.; Ledos, N.; Parahyba, V.; Potet, P.; Utterback, J. K.; Prado, Y.; Silly, M. G.; Dudin, P.; Avila, J.; Pierucci, D.; Lhuillier, E. In Situ Mapping of the Vectorial Electric Field within a Nanocrystal-Based Focal Plane Array Using Photoemission Microscopy. *ACS Appl Electron Mater* **2023**, *5* (8), 4377–4384.

(43) Cavallo, M.; Mastrippolito, D.; Bossavit, E.; Curti, L.; Khalili, A.; Zhang, H.; Ledos, N.; Prado, Y.; Dandeu, E.; Rosticher, M.; Ithurria, S.; Dudin, P.; Avila, J.; Pierucci, D.; Lhuillier, E. Operando Investigation of Nanocrystal-Based Device Energy Landscape: Seeing the Current Pathway. *Nano Res* **2024**, *17* (12), 10376–10385.

(44) Krasavin, S. E.; Osipov, V. A. Electrical Resistivity of Polycrystalline Graphene: Effect of Grain-Boundary-Induced Strain Fields. *Sci Rep* **2022**, *12* (1), 14553.

(45) Phillips, M.; Mele, E. J. Charge and Spin Transport on Graphene Grain Boundaries in a Quantizing Magnetic Field. *Phys Rev B* **2017**, *96* (4), 041403.

(46) Avila, J.; Lorcy, S.; Dudin, P. ANTARES: Space-Resolved Electronic Structure. *J Electron Spectros Relat Phenomena* **2023**, *266*, 147362.
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