Unexpected Electron Transport Suppression in a Heterostructured Graphene-MoS2 Multiple Field-Effect Transistor Architecture.

We demonstrate a graphene-MoS2 architecture integrating multiple field-effect transistors (FETs), and we independently probe and correlate the conducting properties of van der Waals coupled graphene-MoS2 contacts with those of the MoS2 channels. Devices are fabricated starting from high-quality single-crystal monolayers grown by chemical vapor deposition. The heterojunction was investigated by scanning Raman and photoluminescence spectroscopies. Moreover, transconductance curves of MoS2 are compared with the current-voltage characteristics of graphene contact stripes, revealing a significant suppression of transport on the n-side of the transconductance curve. On the basis of ab initio modeling, the effect is understood in terms of trapping by sulfur vacancies, which counterintuitively depends on the field effect, even though the graphene contact layer is positioned between the backgate and the MoS2 channel.

Formed when two or more atomically thin crystals are bonded by van der Waals (vdW) interaction,[1] vdW heterostructures are intriguing architectures, enabled by the discovery of two-dimensional (2D) materials, such as graphene, hexagonal boron nitride, and transition metal dichalcogenides (TMDs). Within this family, peculiar junctions can be obtained when graphene is used as a contact material for a TMD monolayer. While the interface between a TMD and a conventional, bulk metallic electrode tends to display Schottky behavior due to intrinsic and extrinsic Fermi pinning phenomena,[2−4] vdW graphene–TMD junctions yield well-behaved linear transport characteristics.[5] This contacting approach has been successful in improving TMD-based devices,[6] and together with the side-contacting approach,[7−9] it is commonly used for the realization of most devices based on 2D materials. Graphene–TMDs heterostructures were employed for many other applications, e.g., in flexible photodetectors.[10] Nevertheless, the exact physics behind graphene–TMD vdW junctions is still debated[11−13] and difficult to probe in a direct way. In particular, devices typically include only two contacts, which makes the effects on the transport characteristics due to the interface not easy to distinguish from those due to the resistivity of the 2D materials, since typically only the global conductance of the device can be measured. Charge transfer phenomena,[14] strain,[15] and charge trapping in defects[16−18] might also play an important role. Furthermore, in the case of field-effect devices, the low density of states in the vicinity of the Dirac point leads to weak screening properties despite the metallic nature of graphene.[19] This implies that a nontrivial response to field effect can be observed and exploited in device concepts.[20,21] Gating on graphene–MoS2 heterostructures has been widely investigated from a numerical[22] and experimental[5,23−25] point of view and in different stacking configurations. Indeed, the reciprocal electrostatic screening of the junction materials can affect the contact resistance, and it was shown theoretically that MoS2 can screen the field effect on graphene, or not, depending on the order of the specific stacking sequence.[22] Nevertheless, to the best of our knowledge, direct experimental evidence of how the formation of vdW interfaces leads to changes in the transport properties of the individual materials involved in field-effect transistor (FET) devices is still missing.

Results and Discussion

The progress of large-scale chemical vapor deposition (CVD) techniques gives us the opportunity to investigate vdW interfaces from a different angle. High-quality and large-scale monocrystalline flakes of graphene[26,27] and TMDs[28,29] can be reproducibly grown. When this technique is associated with a patterning of the seed points, predictable flake arrays of chosen sizes can be achieved,[30] enabling the fabrication of multiple parallel devices combining different 2D materials. Here, we take advantage of this opportunity to demonstrate a graphene–dichalcogenide architecture where a monocrystalline MoS2 channel is contacted by a large number of monocrystalline graphene stripes, each of them crossing the whole MoS2 channel as schematized in Figure . Each stripe can thus act as ohmic contact for a MoS2 backgated FET (see cross section AB in Figure ) and be simultaneously contacted at its terminations to implement an additional MoS2-covered graphene FET (cross section CD in Figure ). This structure can so act as a MoS2 FET and as a set of graphene FETs at the same time, which will be referred to as a multi-FET in the following.

Figure 1

Multi-FET device architecture. (a) Monocrystalline contact stripes obtained by patterning a periodic array of graphene CVD flakes (scale bar is 100 μm). (b) Monocrystalline CVD MoS2 flakes before transfer onto the SiO2/Si substrate (scale bar is 50 μm). (c) Optical picture of one of the studied devices implementing a multiple FET structure, as visible in the cross section sketches: graphene multicontact MoS2 FET (AB section) and MoS2-covered graphene FET (CD section).

Such an arrangement allows us to study the conducting properties for the different components of graphene–MoS2 systems, highlighting the suppression of the electron-side transconductance in MoS2-covered graphene, in coincidence with the conducting threshold of free MoS2 in the main device channel. This behavior is apparently at odds with recent predictions for defect-free MoS2;[22] nonetheless, it can be understood in terms of a gate-driven trapping by sulfur vacancies which further highlights the nontrivial weak screening properties of graphene.

Both the patterning procedures and the formation of vdW interfaces can significantly perturb the properties of the 2D materials. For this reason, photoluminescence (PL) and Raman spectroscopy were employed to characterize the 2D crystals at relevant device processing steps. In Figure a–c, we report Raman spectra of a typical transferred MoS2 flake and analyze the influence of the graphene contact stripes. We analyze a MoS2 flake with a small bilayer island both in regions with and without graphene. The Raman spectra of bilayer MoS2–graphene heterostructure and bare MoS2 bilayer are reported in the Supporting Information. The characteristic A1g and E2g modes visible in Figure a exhibit a strong dependence on thickness,[33] and their separation of Δω ≃ 19 cm–1 is in good agreement with the expected monolayer nature of the MoS2 flake. The shift of the A1 mode in Figure b,c can be interpreted as caused by the interlayer interaction between MoS2 and graphene, as reported in ref (34). Nevertheless, a recent work[35] proposes an alternative interpretation in terms of doping and strain, extending the scope of a method which is typically used for bare graphene[32] and bare MoS2.[31] The following discussion is based on this last interpretation. Starting from the strain and doping reference lines reported in ref (31), we consider the correlation plot in Figure b, where the position of the A1g peak is plotted against the one of E2g.[31] The mean Raman shifts of the E2g and A1g peaks in graphene-free regions are 384.5 ± 0.3 and 403.3 ± 0.4 cm–1, respectively. These values are quite close to the neutrality point, located at the intersection between the zero strain and zero doping lines (E2g = 384.6 ± 0.2 cm–1 and A1g = 402.7 ± 0.2 cm–1) .[31] Interestingly, Raman shifts from regions where MoS2 overlaps graphene (E2g = 383.4 ± 0.5 cm–1 and A1g = 404.3 ± 0.3 cm–1) indicate a variation in both tensile strain distribution of ≈0.10–0.35% and a sizable electron reduction of (3.0 ± 1.8) × 1012 cm–2. Thanks to the sensitivity of the A1g peak on doping,[36] the spatial doping modulation of MoS2 due to graphene can be directly appreciated in the map of the A1g position in Figure c. The map is shown in overlay to an optical picture of the flake, to highlight the good correlation between the map patterns and the position of the graphene stripes. Consistent evidence is obtained from the graphene Raman data shown in Figure d–f. In Figure d, the graphene spectra in the presence/absence of MoS2 are compared. Both curves show a single sharp Lorentzian-shaped 2D peak, which is a typical signature of monolayer graphene,[37] and no D peak, which indicates a negligible density of defects.[38] The absence of defects was confirmed for all the fabrication steps (see the Supporting Information). We also note that when graphene is covered in MoS2 (orange curve), a strong baseline appears below the Raman peaks due to the MoS2 PL signal. As in the case of MoS2, the strain and doping profiles can be derived from the Raman data,[32] based on the correlation plot of the 2D and G modes reported in Figure e, where the strain and doping reference lines are taken from ref (32) (see Supporting Information for additional correlation plots). The positions of the G and 2D peaks in regions free from MoS2 are 1582.7 ± 0.9 and 2676.2 ± 2.2 cm–1, respectively, corresponding to a p-type doping. In contrast, Raman data collected in MoS2-covered regions (1585.4 ± 1.5 and 2685.8 ± 3.7 cm–1 for the G and 2D peaks, respectively) fall on the strain line, thus indicating a neutralization of graphene. The variation of mean peaks position corresponds to an electron increase of (2.3 ± 1.5) × 1012 cm–2 and to a variation of strain nature from tensile to compressive. The spatial modulation of the doping can be seen from the 2D peak position map in Figure f, showing a good correlation with the position of the MoS2 flake. A modified strain is also observed, turning from slightly tensile to compressive, ≈ 0.10–0.30%. We note that the doping and strain trends observed where MoS2 and graphene overlap are opposite and are thus consistent. We further highlight that while the discussed analysis of the Raman data indicates an electron transfer from MoS2 to graphene[35] the absolute equilibrium carrier densities are not obvious to quantify. This is due to the presence of photoexcited carriers during the Raman measurements, and to the unknown exact calibration of the zero-strain and zero-doping points (standard values from refs (31) and (32) were used). The formation of the heterojunction can be further investigated based on the PL spectra of MoS2, which are reported in Figure a. Three main peaks are highlighted by Gaussian deconvolution. These peaks are attributed to the A exciton (1.81 eV), the B exciton (1.94 eV), and the trion (1.71 eV).[39,40] We observe that the presence of graphene modifies the MoS2 response and that the signal of the A exciton is quenched when MoS2 is coupled to graphene (orange curve) with respect to stand-alone MoS2 (blue curve): indeed, a lowering of the A intensity by ∼30% and a line shape broadening from ∼66 meV to ∼96 meV is retrieved. The spatial modulation of the effect can be directly appreciated from the maps of the intensity and width of the A exciton in Figure b,c, respectively. Additional spectroscopic data are reported in the Supporting Information.

Figure 2

Raman measurements of the MoS2–graphene structures. (a) MoS2 Raman spectra after transfer on top of the graphene stripes: both spectra from MoS2 on top of graphene (orange) and graphene-free MoS2 (blue) are reported. (b) Correlation plot of the position of A1g as a function of the position of E2g. Zero-strain and zero-doping lines are taken from ref (31) (514.5 nm laser excitation). (c) Map of the position of A1g. (d) Raman spectra of graphene after the MoS2 transfer: both spectra in the presence (orange) and absence (green) of the MoS2 overlayer are reported. (e) Correlation plot of the position of 2D peak as a function of the position of G peak. Zero-strain and zero-doping lines are taken from ref (32) (514.5 nm laser excitation). (f) Map of the position of the 2D peak. Correlation plots in panels b and e were obtained from Raman spectra collected as far as possible from the flakes boundaries to avoid spillover effects from neighboring regions and do not derive from the data sets used in panels c and f.

Figure 3

Photoluminescence measurements of the MoS2–graphene structures. (a) PL spectra of MoS2 both in a region where it overlaps graphene (orange) and in a graphene-free region (blue). Gaussian fits of A and B excitons are shown in dashed and dotted lines, respectively. (b) Map of the position-dependent quenching of the A exciton signal. (c) Map of the position-dependent A exciton broadening. All maps are shown in overlay to an optical image of the analyzed flake; scale bars in the panels correspond to 10 μm.

The graphene stripes form ohmic contacts to the MoS2 channel and lead, at room temperature and in vacuum conditions (P < 10–5 mbar), to highly linear two-wire I–V curves over the ±2 V range. In Figure a, we report the ISD versus VSD characteristics of a representative MoS2 FET, measured as a function of the gate voltage (VG) in the 0–80 V range. The transfer characteristic in Figure b indicates a positive threshold voltage, with a sizable clockwise hysteresis, as frequently reported in the literature for FETs based on 2D materials and nanowires,[41−45] as well as in Kelvin probe microscopy experiments.[46] The effect is generally ascribed to the slow dynamics of trap states leading to a time-dependent screening of the field effect of the gate. Trap states may have several origins, including defects at the SiO2 substrate interface,[45] adsorbates,[44] or MoS2 point defects.[43] In our devices, possible sources of traps include interfaces between MoS2, graphene, and SiO2 (see the AFM data in the Supporting Information), as well as S vacancies in MoS2, which are known to occur in quite large densities (typically few 1013 cm–2) in CVD flakes.[47,48] The field-effect mobility of the MoS2 carrier can be estimated from the transfer characteristic according towhere CG is the capacitance and the MoS2 trapezoid channel sketched in the inset of Figure b is approximated as a rectangle with a length L = 5.5 ± 0.3 μm and width W = 19.5 ± 0.5 μm. Considering both curves in the hysteresis loop, we extract two mobility values, and similar analysis on different FETs yielded field-effect mobilities in the range of 5.3–6.6 cm2/(V s). Given that gate hysteresis generally indicates that part of the gate-induced carriers end in charge traps, field-effect measurements are known to overestimate the carrier density induced in the channel and to underestimate mobility.[42,49] Both the mobility values above should thus be considered as a lower bound to the true room-temperature electron mobility in the specific MoS2 flake. The method also neglects the effect of contact resistances, which may lead to a mobility underestimation but are not expected to have a significant effect in the explored transport regime, based on preliminary four-wire measurement data.

Figure 4

Transport characteristics of MoS2. (a) Room-temperature I–V characteristics of the MoS2 channel as a function of the gate voltage VG in the 0–80 V range. (b) Transfer characteristics show a strong hysteresis, with red arrows indicating the sweep direction. Red dashed lines are the linear fits used to estimate the field-effect mobility for each of the two curves. Inset: an optical image of the measured device, with a sketch of the channel geometry and contacts highlighted by black dots.

Our multi-FET devices were specifically designed for comparing the MoS2 transport characteristics with the electron configuration in the graphene stripes, which play here the dual role of the contact in the MoS2 FET and of the channel in MoS2-covered graphene FETs. The I–V curves of all our graphene stripes are found to be highly linear (a representative measurement is reported in the Supporting Information), and in Figure we report the transfer characteristic of various graphene FETs as a function of the VG, from which we obtain a mobility. These measurements are carried out at a fixed VSD (0.2 V), as a function of VG. In the plot sequence of Figure c–g, we compare the conductivity of stripes characterized by a different MoS2 coverage: Conductivity is calculated from the total resistance using the geometrical form factor of the stripe, and contact resistances are estimated by comparing the p-side of the gate sweeps. MoS2 coverage is quantified from the ratio between the area of the MoS2–graphene and the graphene regions; see the optical pictures in Figure a,b. Coverage goes from 0% (MoS2-free graphene in Figure c) to 79% (Figure g). A clear trend is observed in the transfer characteristics: curves go from a conventional ambipolar behavior in Figure c to a limit of strongly quenched n-type conduction for the largest coverage in Figure g. The observation of a quenching of the field effect in graphene–TMD heterostructures has been reported in the literature, for instance in both WS2 and MoS2–graphene heterostructures and in graphene functionalized with different materials, such as TiO2 or organic molecules.[10,17,18,50−52] The important role of MoS2 on electron transport suppression is clear as no deep suppression is observed in bare graphene stripes on SiO2 devices.[53] However, the observed behavior is somewhat puzzling since, ideally, MoS2 should not affect carrier density in graphene when positioned on top of back-gated graphene due to the reciprocal screening in the vdW heterostructure.[22]

Figure 5

Effect of the MoS2 overlayer on electron transport in the graphene contact stripes. (a, b) Optical images of the two devices used to estimate the effect of different MoS2 coverage levels on conduction in the graphene stripes. Used contacts are highlighted by colored dots. (c–g) Transfer characteristics of the graphene stripes for different MoS2 coverages ranging from 0 to 79%. The curve colors match the ones used to highlight the contacts in panels (a) and (b): red, 48%; blue, 55%; yellow, 69%; and purple, 79%; the black curve corresponds to a reference MoS2-free graphene stripe (device image not shown).

We ascribe the origin of this apparent discrepancy as due to vacancies in TMDs.[47,48] This is a reasonable assumption, since we mentioned above that another possible source of trap states could be the SiO2 substrate. Nevertheless, the effect of the SiO2 substrate is secondary. In fact, the not-covered graphene stripe reported in Figure c has a standard symmetric behavior despite the presence of the SiO2 substrate. Moreover, the major contribution to the electron transport suppression from the sulfur vacancies can be deduced from the behavior reported in Figure c–g where a clear trend can be observed: The suppression increases as the MoS2 coverage increases. Furthermore, it is worth noting that the electrical transport of exfoliated graphene covered by exfoliated MoS2 usually does not present this suppression of the electron transport.[54] In order to corroborate our hypothesis, and highlight the effect of sulfur vacancies, we perform density functional theory (DFT) calculations.

Using DFT,[55] we made an ab initio analysis of the electronic states of graphene–MoS2[56] in the presence of sulfur vacancies: These have an energy that falls in the gap[57] of MoS2 and are located at a distance of few Angstroms from graphene, so their effect is hard to evaluate without a first-principles approach (see the “Methods” section and the Supporting Information for further details). Numerical calculations were performed using a density of S-vacancies of ρv ≈ 1.8 × 1013 cm–2. In Figure a, we report the electronic band structure and projected density of states (DOS) of the graphene–MoS2 heterostructure for VG = 0: As visible in the plot, the Fermi energy of the system lays in the proximity of the MoS2 midgap states generated by the S-vacancies. This suggests that such states may influence the mobile carrier density induced in the graphene layer by the gate when VG ≠ 0. This is confirmed by calculations performed at different values of VG. As shown in Figure b, even if MoS2 is placed on top of graphene, it affects the carrier density induced by the gate in the graphene layer. In particular, the n-side of the field-effect response is reduced by ∼50%; this, combined with the likely increased scattering[48,58,59] caused by the large DOS close to the Fermi energy, clearly reproduces the behavior reported in Figure . The sulfur vacancies work as charge traps only for positive gate voltages and thus only for electron carriers. The sulfur vacancies generate a midgap state above the neutrality point, and scattering due to midgap states reduces the conductivity as described by the formulawhere neff is the effective density of the charge carrier in the graphene sheet (∼50% of the induced doping charge), kF is the Fermi momentum due to the effective density of the charge carrier neff, ρv is the density of S-vacancies, and R = 3 Å is the average radius of the vacancy.[48] In Figure , the quantitative estimation of the conductivity is shown. We used a range of ρv similar to the one used in the ab initio calculations. We plot the data only for positive gate voltages because the midgap states affect the transport properties only in that sector. In Figure c,d, the atomistic structure and the model of the typical setup for a field-effect measurement are shown. The charge density isosurfaces, together with the planar averaged carrier charge density, give a pictorial view of the different behavior with negative and positive backgate voltages. We point out that our results do not contradict, but rather complement, the conclusion drawn in recent literature:[22] Calculations also show that no charge transfer is obtained in the case of defect-free MoS2 since in that limit the TMD cannot support any electron state in the relevant energy range (see the Supporting Information). Nonetheless, it is interesting to highlight that in the presence of vacancies a TMD overlayer can indeed have an impact on the backgate response of these vdW heterostructures and of devices based on them, extending the range of nontrivial consequences of the weak screening properties of graphene.

Figure 6

Field-effect response in the presence of S-vacancies. The impact of sulfur vacancies was simulated by removing one S atom from a MoS2 supercell (density of S-vacancies of ρv ≈ 1.8 × 1013 cm–2). (a) Supercell band structure and projected density of states (DOS) of the graphene–MoS2 interface (VG ≈ 23 V corresponding to a charge induced by field effect n ≈ −6 × 1012cm–2). The red dashed line indicates the Fermi energy EF. In the DOS plot, pristine graphene is indicated with a continuous line, and the S-vacancy appears as a peak close to the Dirac point. (b) Field-effect-induced charge distribution as a function of gate voltage VG, evaluated as the difference between the gated (VG ≠ 0) and ungated case (VG = 0). The solid (dashed) red line indicates the excess holes on the graphene (MoS2) monolayer, while the solid (dashed) blue line indicates the excess electrons. (c, d) Side view of the gated graphene–MoS2 interface. In the two panels, the charge isosurface for VG < 0 (left) and VG > 0 (right) is evaluated as the difference between the charge densities for the gated and ungated limit. The location of the S-vacancy in the supercell is marked by the green ball.

Figure 7

Quantitative estimate of the conductivity of graphene. Midgap states associated with sulfur vacancies can suppress mobility in graphene by increasing electron scattering. Conductivity suppression was calculated for three different densities of sulfur vacancies ρv, using the carrier densities reported in Figure .

Conclusions

We have demonstrated a graphene–MoS2 architecture integrating multiple graphene-contacted MoS2 FETs and MoS2-covered graphene FETs and used it to correlate the field-effect characteristics of a MoS2 monolayer with the conducting properties of graphene used to contact it. Such a study cannot be performed in a conventional FET structure since the individual resistive contributes cannot be discriminated in any obvious and direct way. Our results show that MoS2 can affect the field-effect conduction of a back-gated graphene monolayer, even when placed on top of the vdW stack, and the suppression of conduction in the graphene stripes is observed over a gate voltage range which is consistent with the conduction threshold of the MoS2 channel. This behavior is explained in terms of a filling of sulfur vacancies in the MoS2, as supported by ab initio calculations. The suppression of the electron transport can be exploited for the development of engineered optoelectronic devices based on van der Waals heterostructures,[10] taking advantage of the low contact resistance of graphene in our multi-FET heterostructure.

Methods

Nanofabrication

The multi-FET fabrication starts from a square array of ∼150 μm wide single-crystal monolayer graphene flakes, with a spacing of 200 μm. Arrays are grown on Cu foil via CVD[30] and then transferred on a p++ Si substrate covered by 300 nm thermal SiO2 using a delamination procedure and a semidry method based on a PMMA vector.[26] Before the MoS2 transfer, the samples were cleaned from PMMA using an overnight immersion in acetone, followed by 2 min rinse in isopropanol, 3 min in AR 600–71 remover, and finally in deionized water. The next fabrication step was the patterning of graphene into a set of 5 μm wide and 5 μm spaced stripes. To this aim, we spun PMMA AR-P679.04 and baked the samples at 120 °C for 5 min. The stripe patterns were defined via electron-beam litography (EBL) using a SEM Zeiss Ultraplus with a Raith lithographic module, an energy of 20 keV and a dose of 300 μC/cm2. The samples were then developed in AR 600–56 for 2 min and a half. Then, graphene was etched by means of reactive ion etching (RIE) using Ar and O2 (5:80 sccm). Finally, the samples were again cleaned from PMMA with an overnight immersion in acetone and isopropanol rinsing. Single-crystal MoS2 monolayer flakes with an average size of 50 μm were grown via CVD following refs (60) and (61). Single-crystal monolayer MoS2 flakes were then transferred on the graphene stripes, using a semidry method.[60,61] The transfer process employed for MoS2 is very similar to the one for graphene except for the delamination step, which was obtained by immersing the sample in a 1 M solution of NaOH rather than by an electrochemical method.[60] Given the chosen spacing between the stripes, the process typically yields various devices with 4–5 contacts and, since the flakes are triangular, with an uneven coverage of the graphene stripes. A final post-transfer patterning was performed to remove excess material, using a laser writer Micro Writer ML3 and a S1818 photoresist mask with a 300 nm PMMA interlayer to protect the 2D materials form contamination by the photoresist. We then cleaned the samples with warm acetone (20 min) and chloroform for 1.5 h. To complete the devices, we defined a set of Cr/Au (10/50 nm) metallic electrodes, via EBL, evaporation, and lift-off. Using this method, 10 devices were fabricated in two batches and three multi-FETs were measured.

Experimental Section

The properties of graphene and MoS2 were monitored by Raman and photoluminescence spectroscopy, using a Renishaw InVia spectrometer equipped with a 532 nm laser and a 100× objective lens (N.A. 0.85). Laser power was ∼1mW and the typical acquisition time was 4 s.[62] Transport measurements were performed in a vacuum chamber using source-measure units K4200 and K2614B and a Femto DDPCA-300 current preamplifier.

Numerics

We carried out DFT calculations by using QUANTUM ESPRESSO (QE),[63−67] which uses a plane wave basis set. The pseudopotentials were taken from the standard solid-state pseudopotential (SSSP) accuracy library[68−72] with increased cutoffs of 50 and 400 Ry for the wave functions and the density. The exchange-correlation potential was treated in the GGA, as parametrized by the Perdew–Burke–Ernzerhof (PBE) formula,[73] with vdW-D2 correction as proposed by Grimme.[74] For the BZ integrations, we employed a Marzari–Vanderbilt smearing[75] of 10–3 Ry with a Monkhorst–Pack (MP)[76]-point grid with 18 × 18 × 1 (24 × 24 × 1) points for self-consistent calculations of the charge density (density of states). The heterostructure of monolayer MoS2 on top of monolayer graphene is shown in Figure c,d, where an 8 × 8 MoS2 supercell is placed on a 10 × 10 supercell of graphene. The considered heterostructure model contains 391 (392) atoms in the unit cell for the simulation with (without) S-vacancy, corresponding to a density of S-vacancies of ρv ≈ 1.8 × 1013 cm–2. We keep the lattice constant of graphene unchanged at a0 = 2.46 Å[55,77] and compressed the lattice constant of MoS2 by roughly ∼2.4%: from 3.15 Å[78] to 3.075 Å. We considered a supercell with about 18 Å of vacuum along the c-direction between periodic images. We optimize the geometrical structures by relaxing only the atomic positions until the components of all the forces on the ions are less than 10–3 Ry/Bohr, while we keep fixed the lattice parameters.

In Figure c,d, a model of the typical setup for a field-effect measurement is shown. The graphene–MoS2 is placed in front of a metal gate. The layers are then charged with the same amount of opposite charge, leading to a finite electric field in the region between the heterostructure and the gate. In order to avoid spurious and artificial electric field between the different slabs of the repeated unit cell, an electric field generated by a dipole plate of opposite charge has been included next to the gate. Furthermore, to avoid the direct interaction between the charge-density of the system and the gate, a potential barrier has been included.[66,67] In order to mimic the experimental values, in Figure b, we rescaled the values of VG considering that in the real experiment there is a 300 nm thick layer of SiO2 between the metal gate and the graphene–MoS2 interface. We use the VESTA[79] code to visualize the geometrical structure and the isosurfaces and to produce the plots in Figure . To obtain information on the charge transfer between the two moieties (graphene–MoS2), we performed a topological analysis of the electron density by means of the Bader procedure[80−83] as implemented in CRITIC2.[84,85]