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.


Graphene
Raman spectroscopy allows to monitor the evolution of graphene properties throughout the fabrication process described in the sketches in Fig. S1 a. Fig. S1 b shows graphene Raman spectra at different steps of fabrication. In these spectra D peak is not measurable. The intensity of the D peak is always faint and barely measurable above noise (less than 6 counts) even on the edge of the graphene stripes, as shown in panel e. Therefore, the higher ratio I D /I G at the edge of the mapped graphene stripes in panel b, is related, as expected, to the high concentration of defects at the graphene stripes edges. In Fig. S3, we reported all the maps for the G and 2D peaks parameters. Clearly, data show that the presence of the MoS 2 has a strong influence on the 2D peak, while the G peak is only slightly affected.

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Such a behavior is confirmed by considering the histograms of Fig. S4, and in particular the panel (c) where we report the ratio between the intensity of the 2D peak and the intensity of the G peak: here two different groups of datasets can be clearly identified. One with a higher ratio, corresponding to the graphene outside of the MoS 2 flake, and another one with a lower value corresponding to the graphene under the flake.     areas, probably due to a residual trapping of gas between the two monolayers. S1 Table S1 reports the relevant parameters of the topography.
S-9 The IVs of all our graphene stripes are found to be highly linear even when graphene is covered by MoS 2 , demonstrating that our graphene stripes operate in the linear response regime. Fig. S9 shows a representative measurement obtained at zero gate voltage, for the stripe with 69% MoS 2 coverage.
S-10 In order to support our conclusions and compare them with existing literature, we carried out DFT calculations also in the case of defect-free MoS 2 . In the absence of S-vacancies, we demonstrate that no asymmetry is obtained between electron and hole doping by field effect.
In fact, in the neutral case the Dirac cone lies deep in the gap of MoS 2 (as shown in Fig. S11a) and the charge induced by field effect in the proximity of E F is not influenced by the MoS 2 layer. To confirm such a conclusion, we studied the system under multiple gate potentials S-12 (V G > 0 and V G < 0). In particular, in Fig. S11b-c we show results for the V G = ∓45 V cases: the charge induced by field effect is n ≈ ±1.2×10 13 cm −2 , respectively, and is spatially localized only on the graphene monolayer. Also the electronic band structures for such cases, as shown in Fig. S11d-e, confirm this picture. In fact, the field-induced charge is simply associated with the filling (or depletion) of the Dirac cone in the graphene monolayer.
Conversely, in the presence of S-vacancies, the field-effect response of the electronic band structures, as shown in Fig. S13a-b, is asymmetric on the hole (S13a, V G < 0) or electron (S13b, V G > 0) side of the field effect response. Comparing Fig. S13b  we can see that graphene behaves in an equivalent way regardless the presence/absence of S-vacancies: in both cases they do not affect the field effect on the hole side of the Dirac cone.
We performed our calculations with a density of S-vacancies of ρ v ≈ 1.8 × 10 13 cm −2 , which corresponds to one S-vacancy in the simulation cell, i.e. we removed one sulfur atom in a 8 × 8 MoS 2 supercell. In the plots, the vacancy is located in the sulfur plane closest to the graphene layer, but the position (closer or further away from graphene) of the vacancy is not found to affect the conclusions of our calculations. We also verified how this result depends on the density of S-vacancies. In particular we repeated the analysis with ρ v ∼ 2.5 × 10 13 cm −2 , ρ v ∼ 3.8 × 10 13 cm −2 and ρ v ∼ 7.5 × 10 13 cm −2 . The field-effect induced charge distributions do not change with increasing density of S-vacancies, in fact in Fig. S12 we can see that, despite the increasing density of S-vacancies, almost the same fraction of electrons goes on the MoS 2 monolayer.

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Figure S12: Field-effect induced charge distribution with an increasing density of S-vacancies. Field-effect induced charge distribution as a function of gate voltage V G , evaluated as the difference between the gated (V G = 0) and ungated case (V G = 0); the topological analysis of the electron density was done by means of the Bader theory as discussed in the main text. The colored solid (dashed) lines indicate the excess electrons (holes) on the graphene monolayer, while the color density of S-vacancies. In order to mimic the experimental values, the values of V G are rescaled considering that there is a 300 nm thick layer of SiO 2 between the metal gate and the Graphene-MoS 2 interface.
S-14 Figure S13: Field effect on the electronic band structure and the charge distribution. (a) Electronic band structure of the graphene-MoS 2 interface with S-vacancies. a field-induced charge n ≈ 1.2 × 10 13 cm −2 is obtained for V G ≈ −45 V (see Fig 3b). In this configuration, the S-vacancy state is far from the Fermi energy and it does not contribute to the transport nor it affects the gating. (b) The same situation for V G ≈ +45 V leads to a total field-induced charge of n ≈ −1.2 × 10 13 cm −2 . In this case, the proximity of the Fermi energy to the S-vacancy state implies a significant part of the field-induced charge ends on mid-gap states created by the S-vacancy, in the MoS 2 . The red dashed lines indicate the Fermi energy E F . (c-d) Side view of the gated graphene-MoS 2 interface. In the two panels, the charge isosurface for V G < 0 (left) and V G > 0 (right) is evaluated as the difference between the charge densities for the gated and ungated limit; the location of the S-vacancy is marked by the green ball. The isosurface corresponds to a charge density of ≈ 6.7 × 10 −4 eÅ −3 . To compare these results with the ones in Fig. S11, the impact of sulfur vacancies was simulated by removing one S atom from a 4 × 4 MoS 2 supercell placed on a 5 × 5 supercell of graphene which corresponds to a density of S-vacancies of ρ v ∼ 7.5 × 10 13 cm −2 . These results do not depend on the density of S-vacancies, in the range we have explored.

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Figure S14: Charge isosurfaces of the field-effect induced charge accumulation with a decreasing density of S-vacancies.
Top view of the charge isosurfaces for and V G > 0 are evaluated as the difference between the charge densities for the gated (V G = 0) and ungated case (V G = 0). The blue (red) isosurfaces are for negative (positive) accumulated charge. It is evident that the induced charge accumulates around the S-vacancy and the radius of the induced charge distribution increases with decreasing the density of S-vacancies, while the integral is almost the same (see the right side of Fig. S12). To properly compare the three cases, the charge isosurface level has been chosen the same for all the cases.