# Electric Field Distribution within a Van der Waals Heterostructure

Dario Mastrippolito, Mariarosa Cavallo, Erwan Bossavit, Clement Gureghian, Albin Colle, Tommaso Gemo, Giorgia Strobbia, Dries de Pesseroey, Marco Paye, Adrien Khalili, et al.

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To cite this version:

Dario Mastrippolito, Mariarosa Cavallo, Erwan Bossavit, Clement Gureghian, Albin Colle, et al. Electric Field Distribution within a Van der Waals Heterostructure. Nano Letters, 2025, 10.1021/acs.nanolett.5c02475. [https://doi.org/10.1021/acs.nanolett.5c02475](https://doi.org/10.1021/acs.nanolett.5c02475). [arXiv:2207.09765](https://arxiv.org/abs/2207.09765).

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Distributed under a Creative Commons Attribution 4.0 International License
Electric Field Distribution within a Van der Waals Heterostructure

Dario Mastrippolito¹,², Mariarosa Cavallo¹, Erwan Bossavit¹,², Clement Gureghian¹, Albin Colle¹, Tommaso Gemo¹, Giorgia Strobbia¹, Dries De Pesseroey¹, Marco Paye¹, Adrien Khalili¹, Huichen Zhang¹, Johan Biscaras³, James K. Utterback¹, Pavel Dudin², José Avila², Emmanuel Lhuillier¹, Debora Pierucci¹*

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

²Synchrotron SOLEIL, L'Orme des Merisiers, Départementale 128, 91190 Saint-Aubin, France.

³ Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, 75005 Paris, France.

**Abstract:** Van der Waals heterostructures offer a playground for optoelectronics with the promise of coupling a broad range of materials while lifting the constraints of epitaxy. Optimization of such devices also requires careful control of the spatial localization of the in-plane and out-of-plane electric field.-Therefore, *operando* tools giving direct access to the local energy and electric field landscape are necessary. Here, we demonstrate that nanobeam X-ray photoemission imaging is an effective method to map the electric field in a 2D flake-based multielectrode transistor and a WS₂/MoSe₂ heterostructure while the electrical biases are applied.-We discuss how the shape and geometry of the flake, the electrical contacts, and the overlapping of the flakes impact the field distribution. In the region where flakes overlap, the in-plane electric field distribution aligns in the two materials, whereas the out-of-plane field distribution resulting from the gating charge injection deviates from a homogeneous distribution.

**Keywords:** 2D materials, van der Waals heterostructure, photoemission, operando, field-effect transistor, electric field.

*To whom correspondence should be sent: pierucci@insp.upmc.fr
Van der Waals (vdW) heterostructures offer the possibility to combine different materials with various properties while avoiding epitaxial fabrication, raising great hopes to engineer hybrid materials in a Lego-like manner.¹ This strategy proved to be effective in controlling the excitonic response and bandgap modulation of two-dimensional (2D) semiconductors fabricated with a type II band alignment to achieve a redder band gap than that of the two involved semiconductors.² Beyond the spectral shaping, this allows for modulation of the radiative lifetime.³

While progress has been made on the optical side via vdW stacking, driving such devices electrically (i.e., through a bias application) seems a more efficient strategy in the long term and allows different operation in the same device. Since the first report of the field-effect transistor (FET),⁴,⁵ the application of an electric field over a 2D material enables shaping the electronic band structure. For example, the band gap magnitude can be reversibly tuned, and other electronic phases (i.e., superconductivity⁶⁻⁹) can even be induced under very large fields (>V.nm⁻¹).

Because the electric field is a relevant knob for the control of material properties, its application within the heterostructure and, in particular, its spatial localization, appears critical to investigate. For instance, achieving electroluminescence requires localizing a bias drop of the order of the band gap, specifically over the optically active area. Therefore, spectroscopic methods sensitive to local electric fields have to be developed and have to be compatible with *operando* operations.

Raman spectroscopy has been extensively used in the context of 2D materials, in particular as a tool to determine the material thickness and fast-identified fingerprints of the 2D phase. Raman mode frequencies appear sensitive to electric fields,¹⁰⁻¹² but also to strain.¹³⁻¹⁵ For this reason, the observed induced shifts are often mixed with strain, and the method is not really suited to unambiguously map the electric fields. Kelvin probe force microscopy (KPFM) is a valid alternative offering the high spatial resolution of near-field microscopy down to tens of nm, and can be used to probe the electrostatic landscape. Nevertheless, KPFM measurements are also influenced by long-range coupling to electrodes and are hence more sensitive to electrode geometry.

Here, we explore the determination and visualization of the electric field distribution thanks to scanning photoemission microscopy (SPEM).¹⁶ A sub-µm soft X-ray beam is used to locally probe the system, while the sample is scanned and a photoemission spectrum is acquired at each point. This results in a hyperspectral map of the device energy landscape. In particular, the method has been successfully applied under *operando* conditions to determine the energy landscape of the nanocrystals-based device,¹⁷⁻²¹ and was recently extended to the case of a single flake of 2D materials,²² in a simple geometry (i.e., one flake bridging two electrodes). In this paper, we aim to use the high spatial resolution of the SPEM method to determine how the electric field is distributed within a single flake in a complex environment with different electrode terminals and within a WS₂/MoSe₂ heterostructure under *operando* conditions. Both the effect of drain (i.e., in-plane) and gate (i.e., out-of-plane) electric fields are addressed, with particular emphasis on behaviors that deviate from the simple electrostatic model.

To introduce the method of photoemission microscopy and its ability to map a device energy landscape, we start by applying it to a multi-electrode field effect transistor (FET) whose channel is made of a WSe₂ flake. A schematic of the device is shown in **Figure 1a** and S3a for a top-view image. A backside gold gate electrode is first deposited on a Si/SiO₂ substrate and coated with Al₂O₃ (40 nm) that acts as dielectric. The presence of gold underneath the transition metal dichalcogenides (TMDC) flake is critical to limit charging effects during the photoemission experiments. Then, a WSe₂ flake is dry transferred on top of the gate area. Finally, through a conventional optical lithography process, three electrodes are deposited to possibly generate a complex (i.e., beyond dipole distribution) pathway for the electrons to reach the electrodes.
The sample is mapped using X-ray photoemission imaging conducted at ANTARES beamline of the Synchrotron SOLEIL. The soft X-ray beam (hν= 95 eV) is first focused using a Fresnel lens to form a small spot of around 700 nm at the sample level. The sample is scanned, and a photoemission spectrum is acquired for each step. In practice, we track a core level such as W 4f (Figure 1b and S6b for Se 3d), and observe how its binding energy will be affected by the application of gate and drain biases. In a rigid shift scenario of the band structure, the shift of the core level follows that of the valence band, so the shift map presented later corresponds to the shift observed for the conduction and valence bands. The detailed procedure to process data is described in Figures S1-S2. The procedure relies on the decomposition of the core-level spectrum that allows the generation of a binding energy map. Then the map acquired under bias is then subtracted from the corresponding map collected in the grounded configuration, enabling the creation of an energy shift map (ΔBE). This procedure also has the benefit of removing any residual photocharging effect, ensuring that only the shifts induced by the application of electric fields get displayed.

Thanks to the high spatial resolution of SPEM (<μm), not only can the scalar energy shift map be obtained but also its gradient, which gives direct access to the vectorial electric field. The in-plane electric field can be obtained from $\vec{F} = -\vec{\nabla}V$, where V is the electric potential. Since ΔBE, the binding energy shift induced by the applied bias, is directly related to the experimental data, this relationship can be expressed through $\vec{F} = -\vec{\nabla}\Delta BE = - (\frac{\partial \Delta BE}{\partial x} \hat{x} + \frac{\partial \Delta BE}{\partial y} \hat{y})$.

<figure><img src="image_3.png" /><figcaption>**Figure 1** Operando probing of electric field with a 2D material. a. Schematic of a multiterminal device whose channel is made of a 2D WSe₂ flake and probed spatially using nanobeam photoemission. FZP and OSA stand for Fresnel zone plate and optical sorting aperture, respectively. b. XPS spectrum relative to the W 4f core level from the WSe₂ flake. c. Binding energy shift map for $V_{D1}=-0.5$ V, $V_{D2}=+0.5$ V, and $V_{D3}=+0$ V. d. Binding energy map for $V_{D1}=+1$ V, $V_{D2}=+1$ V, and $V_{D3}=+0$ V. Black arrows overlaid on the energy shift maps in b. and c. indicate the orientation and the magnitude of the electric field. e. In-plane electric field map for $V_{D1}=-0.5$ V, $V_{D2}=+0.5$ V, and $V_{D3}=+0$ V. f. In-plane electric field map, for $V_{D1}=+1$ V, $V_{D2}=+1$ V, and $V_{D3}=+0$ V.</figcaption></figure>

**Figure 1c-d** display the energy shift map for two configurations of applied bias. In Figure 1c, the top electrode is grounded and the potential of the two other electrodes is chosen in a symmetric way ($V_{D1}=-0.5$ V, $V_{D2}=+0.5$ V); so that the top electrode feels an effective zero potential. The energy shift map displays a continuous evolution of the potential. This is confirmed by the field intensity map
(Figure 1e), which is rather homogeneous in the channel area of interest between the three electrodes, meaning that the potential is dropping continuously. The field concentration seen at the bottom of the electrodes can be explained by the device geometry as shown in Fig. S3 and is not evidence of a Schottky barrier.

The electric field lines (arrows in Figure 1c) are close to the one expected for a dipolar distribution, with however a visible asymmetry between the top and bottom of the $V_1$ and $V_2$ electrodes, which also manifests itself as a concentration of the electric field near the bottom of these electrodes (Figure 1e). This behavior comes from a thicker part of the $WSe_2$ flake located below the sample (see the extended picture in Figure S3a), which has a higher conductivity than the thin part connected to the electrodes, as confirmed by our simulations. Indeed, we have simulated the thin and thick parts of the flake and the electrodes as a grid of local resistors with adjustable resistance values for the two areas of the flake, and we find that a homogeneously conductive flake would produce a symmetric voltage map (Figure S3c), however a more conductive thicker area (about 20 times more conductive) reproduce closely the experimental behavior (see Figure S3d-e). This suggests that the thicker part of the flake plays the role of homogenizing the potential distribution and can significantly impact the energy landscape even if located away from the electrodes.

In the second configuration ($V_{D1}=+1$ V, $V_{D2}=+1$ V, and $V_{D3}=+0$ V, Figure 1d-f), the potential becomes nearly uniform across the bottom region of the flake, effectively setting the entire potential of the flake. The electric field lines are now directed toward the top electrode, which is grounded. In this region, the field intensity is clearly above its average value, and almost the entire voltage drop is located near the top electrode (Figure 1f). We attribute this field concentration to the tip-shaped geometry of the flake near the top electrode, which funnels all field lines toward the tip, which is also well captured by our resistor network simulation (Figure S3f). This example illustrates how the finite size and geometry of the TMDC flake can generate modification of the electric field distribution compared to bulk materials, and the edge/shape effect can become central.

Now that we have established the method and demonstrated its relevance in the context of TMDCs, we apply it to a vdW heterostructure, which further raises questions about the field distribution. In a simple vdW heterostructure made of two flakes partially overlapping, we can anticipate two extreme cases. If one of the flakes has a quasi-metallic behavior (as it would be for graphene), the flake acquires the potential of the electrode to which it is connected, and most of the bias drop will occur on the semiconducting flake. Reasonably, in this case, the potential in the overlapping area will mostly depend on the quality of the interfacial contact. The other extreme limit corresponds to the case where the two flakes are semiconducting with a similar conductivity; in this case, the bias drop is expected to occur continuously, following a bulk-like model. The reality might certainly be intermediate with effects relative to the flake geometry, as pointed out in Figure 1d-f, and the quality of the interface. In the next section, we will concentrate on the second case to reveal how the potential distribution is actually affected.

To address this question, we focus on a $WS_2/MoSe_2$ vdW heterostructure. This specific combination is selected because it has the benefit that each material has a core level below 95 eV (W 4f for $WS_2$ and Se 3d for $MoSe_2$), allowing them to be tracked with the SPEM setup. In addition, this choice of materials is further motivated by their (i) reasonable stability and (ii) capacity to exfoliate flakes much larger than the experimental spatial resolution (700 nm). An optical image of this device is presented in Figure 2a, which is a backgated FET whose channel is composed of two flakes, $WS_2$ and $MoSe_2$, stacked with an overlapping region that defines the vdW heterostructure zone. The $WS_2$ flake lies
on top of the MoSe₂ flake, and both are connected to two top electrodes acting as drain-source terminals. The gate consists of a 40 nm-thick Al₂O₃ dielectric layer with a bottom gold electrode to prevent photocharging, just as for the multielectrode FET discussed in **Figure 2**. In this case, the drain-source electrodes are chosen wide, covering the entire flake area to rule out finite size effects due to the electrode shape that will affect the electric fields, as demonstrated in the multielectrode FET. Thus, with this configuration, we can directly observe the field distribution within the channel composed of the flakes. Atomic force microscopy (Figure S4) is used to determine the thickness of each flake, which was found to be around 2.3 nm for WS₂ and 2.4 nm for MoSe₂, corresponding to trilayers for both of them.

We used Raman mapping to unambiguously determine the presence of both flakes. This enables a complete determination of their shape, including the region underneath the covering WS₂ flake in the heterostructure zone, see **Figure 2b-c** and S5, by tracking a Raman mode specific to each material (i.e., 2LA(M) for WS₂ and the A₁g(Γ) for the MoSe₂). The benefit of Raman spectroscopy is that it relies on the detection of scattered photons, which can penetrate and return from the entire heterostructure, including overlapping regions. This allows mapping of both flakes, even in the stacked area. The resulting Raman maps show homogeneous and well-defined signals for each flake, confirming the uniformity of the flakes across the probed regions. In contrast, photoemission imaging, as shown later, detects photoelectrons, which can only escape from the topmost layer, thus preventing any signal from the underlying flake in the overlapped region.

We then investigated the device using the X-ray photoemission imaging to determine the local band alignment, see **Figure 2d**. A core-level map was first acquired to precisely locate the measurement regions, followed by the acquisition of the angle-integrated photoemission spectra around the Γ point of the Brillouin zone for each area (i.e., WS₂, MoSe₂, and the heterostructure) (see Figure S6). This allows us to determine the energy of the valence band maximum relative to the Fermi level in each region. Considering the flake thickness, we estimate their respective quasi-particle band gap to be 1.58 eV²³ for WS₂ and 1.35 eV²⁴ for MoSe₂, respectively. In both cases, we found the Fermi level to be in the upper part of the band gap, indicating an n-type character for both flakes. However, the energy separation between the Fermi level and the conduction band minimum is smaller in the case of WS₂, indicating a higher electron density (at least thermally activated). In addition, WS₂ exhibits a larger band gap compared to MoSe₂ (i.e., smaller hole density), therefore, we anticipate the heterostructure WS₂/MoSe₂ to form a n⁺-n junction, in agreement with previous reports where similar flake thicknesses (3 monolayers for each) have been used.²⁵⁻²⁸

To confirm this electronic structure, we characterized the electrical transport of the FET device, see **Figure 2e-f**. The FET transfer curve (**Figure 2f**) displays an electron-only conducting behavior, with a rise of conductance upon positive gate bias, consistent with the band alignment determined from photoemission. The minimum of conductance of the drain current occurs under negative gate bias, which is also consistent with a native n-type character of the device. The IV curve (**Figure 2e**) appears rectifying with roughly one order of magnitude of excess current in the forward bias mode. Forward bias operation is obtained for negative drain bias corresponding to the negative electrode connected to WS₂, which also confirms the stronger n-type doping for WS₂ compared to MoSe₂. At this point, it is worth understanding by *operando* SPEM how this excess doping will impact the relative conductivity within the two flakes and, therefore, how the bias drop will localize over the two flakes.
<figure><img src="image_4.png" /><figcaption>**Figure 2** WS₂/MoSe₂ heterostructure. a. Optical microscopy image of the WS₂/MoSe₂ heterostructure in the channel area of the FET. b. Peak position map of the 2LA(M) Raman mode of WS₂ (353.5 cm⁻¹). c. Peak position map of the A₁g(Γ) Raman mode of MoSe₂ (241 cm⁻¹). Scale bars in parts a-c are 5 µm long. d. Band alignment for the WS₂/MoSe₂ heterostructure. e. IV curve acquired as the gate is grounded. f. Transfer curve of the FET (drain and gate currents as a function of the gate bias under constant drain-source bias of -0.5 V), while the channel is the WS₂/MoSe₂ heterostructure.</figcaption></figure>

In the next step, we use X-ray photoemission imaging to map the bias drop over the heterostructure for various applied drain-source biases, see **Figure 3a-c** and Figure S7 for the associated profiles. At low bias and in forward polarization, the energy drop appears very continuous (**Figure 3a**) and the electric field very homogeneous over all the channel area (**Figure 3d**). In particular, there is no field concentration at the contacts or at the flake edges. This suggests the formation of an ohmic contact and that the bias drop in the heterostructure area is the same for both flakes; otherwise, discontinuities would have been observed. In other words, the higher doping of the WS₂ flake remains too weak to make it act as a metal, and the semiconductor behavior is maintained for both of them. At low field and under reverse polarization (V<sub>DS</sub>=+1V, see **Figure 3b** and e), the field distribution deviates from the one under forward polarization with some field concentration near the electrode. This concentration of the field becomes even clearer under stronger reverse polarization (V<sub>DS</sub>=+2 V, see **Figure 3c** and f, and Figure S7 for associated profiles). This translates into a strong concentration near the electrodes and more clearly near the drain, where nearly 1 V of potential drop accumulates over a few µm. Conversely, there is still no discontinuity at the flake interface. This localization of the field suggests a high-quality interface between the two flakes, and that charge injection at the electrode is the actual bottleneck for transport in this device.<sup>29,30</sup> Such a result is not completely surprising since the high work function of gold (5.1 eV)<sup>31</sup> is not well suited to inject electrons into an n-type semiconductor. Replacing it with a lower work function electrode will reduce the Schottky barrier but may come at the price of a higher tendency for oxidation.
<figure><img src="image_5.png" /><figcaption>**Figure 3** In-plane electric field within the WS₂/MoSe₂ heterostructure. a. Energy shift map while V<sub>DS</sub>=-1 V (forward bias). b. Energy shift map while V<sub>DS</sub>=+1 V (reverse bias). c. Energy shift map while V<sub>DS</sub>=+2 V (reverse bias). d. In-plane electric field map while V<sub>DS</sub>=-1 V. e. In-plane electric field map while V<sub>DS</sub>=+1 V. f. In-plane electric field map while V<sub>DS</sub>=+2 V.</figcaption></figure>

In the last part of the paper, we focus on how the gate bias impacts the energy landscape of the WS₂/MoSe₂ heterostructure, see **Figure 4**. Immediately, we can notice that the electrostatic doping of the flake is uneven (**Figure 4a**). In the WS₂ flake, electrostatic doping is clearly stronger in the center of the flake and reduced not only at the interface with the electrode that sets the potential at zero voltage (drain and source electrodes are grounded), but also along all the edges.

It is also worth stressing that electrostatic doping in the area where the two flakes overlap is not prevented for the top flake, whereas the underneath MoSe₂ flake may have screened the gating.<sup>32,33</sup> In this sense, the charge injection is reasonably occurring through the part of the flake in direct contact with the dielectric, and then the charges get spread all over the flake, including the heterostructure area.

In the MoSe₂ flake, the edge effects are less striking due to the quasi-rectangular shape of the flake, its large size, and its orientation parallel to the electrode. Indeed, we mostly observe a gradient of electrostatic doping from the right electrode, which is grounded, to the center of the channel. As visible from **Figure 4b**, the horizontal profile of energy shift also shows a clear discontinuity of the potential at the interface between the two flakes. In this sense, the electrostatic doping of the two flakes seems mostly related to the way they are connected to the dielectric and their shape. This behavior contrasts with the effect observed for the in-plane electric field, for which the difference in flake conductivity is mostly washed out, and the two flakes acquire similar potentials.

As a function of gate bias, the electrostatic doping appears clearly non-linear, see **Figure 4c**. Such nonlinearity is generally attributed to the effect of dielectric passivation. The first charges injected are used to passivate the surface of the Al₂O₃. Then, only at values of gate bias greater than 2 V, the effective charge injection comes into play, inducing the electrostatic doping on the semiconductive flake and displacing its energy level. This behavior can be connected to the transport data, where in the transfer curve, we clearly observe an increase in the conductance at around V<sub>GS</sub>=+3 V, which corresponds to the efficient bending of the conduction band by the gate.
The shift in the two materials seems to or less follow each other (possibly because coupling enables a charge transfer), which is why we choose not to interpret the two steps electrostatic doping of the transfer curve as the successive doping of the flake.

<figure><img src="image_6.png" /><figcaption>**Figure 4** Gate-induced energy variation within the WS₂/MoSe₂ heterostructure. a. Energy shift map as VGS=+5 V is applied (VDS=0 V). b. Gate-induced energy shift profile for VGS=+5 V, along y=17 µm horizontal direction, (dashed line in part a). c. Average energy shift over the area of the heterostructure corresponding to WS₂ flake area, MoSe₂ flake area, and the heterostructure as a function of the applied gate bias.</figcaption></figure>

To summarize, we have demonstrated that photoemission imaging is a suited method to locally unveil the energy and electric field landscape generated by in-plane and out-of-plane electric fields within a 2D vdW heterostructure. In particular, the method brings evidence for deviations of the energy landscape from the bulk model. Though a more systematic study including more materials and geometries will be required in the future, we can already draw some general rules regarding the effect of such electric fields and how geometrical factors may influence them:

* In the area where two flakes overlap, both flakes acquire a similar in-plane potential. However, the gate-induced energy shift can be strongly different, though the bottom flake is not preventing the electrostatic doping of the top flake.

* Contacts can be a clear bottleneck for transport and accumulate a significant portion of the drain-source bias, requiring a rationalized choice of the metal electrode. It is critical to control the thickness homogeneity, as variations in flake thickness impact the field distribution.

* The shape and finite size of the flakes have a clear effect. The presence of tips in the flake shape, which are very common in exfoliated and CVD-grown flakes, funnels the electric field lines. Conversely, the gate-induced electrostatic doping occurs mostly in the center of the flake. This also implies that for the design of a field-effect transistor, the contact electrodes should not be fabricated in the middle of the flake, since it will reduce the gate-induced shift.

Such design rules appear very helpful for the design of optimized 2D materials-based devices and will be useful for a variety of applications beyond field-effect transistors, such as photodetectors, modulators, or planar light-emitting devices.

## DATA AVAILABILITY

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

We thank Stephane Lorcy for his help in sample preparation at the ANTARES beamline. The AFM data were acquired at the Advanced AFM experimental platform of INSP of Sorbonne University. We also thank Hervé Cruguel for his support with AFM data acquisition. 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.

## COMPETING INTEREST

The authors declare no competing interests.

## Supporting Information

Supporting Information includes the following. (i) Methods. (ii) Procedure for X-ray photoemission imaging data processing. (iii) Electrostatic modelling of the multielectrode transistor. (iv-vi) Structural, Raman, and X-ray photoemission spectroscopy data relative to the WS₂/MoSe₂ heterostructure.

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