CVD Graphene Contacts for Lateral Heterostructure MoS2 Field Effect Transistors

Intensive research is carried out on two-dimensional materials, in particular molybdenum disulfide, towards high-performance transistors for integrated circuits 1 . Fabricating transistors with ohmic contacts is challenging due to the high Schottky barrier that severely limits the transistors’ performance. Graphene-based heterostructures can be used in addition to, or as a substitute for unsuitable metals. We present lateral heterostructure transistors made of scalable chemical vapor-deposited molybdenum disulfide and chemical vapor-deposited graphene with low contact resistances of about 9 kΩ·µm and high on/off current ratios of 10 8 . We also present a theoretical model calibrated on our experiments showing further potential for scaling transistors and contact areas into the few nanometers range and the possibility of a substantial performance enhancement by means of layer optimizations that would make transistors promising for use in future logic circuits.

Two-dimensional (2D) semiconducting materials from the group of transition metal dichalcogenides (TMDCs) are promising for aggressively scaled transistors for next-generation integrated circuits that are largely unaffected by short-channel effects [2][3][4][5] .By now, stable waferbased deposition techniques have been achieved for the most studied TMDC molybdenum disulfide (MoS2) [6][7][8][9] .Also, MoS2 has been demonstrated as a suitable channel material for n-type field-effect transistors (FETs) with high performance [10][11][12] and has been successfully used in circuits [13][14][15] .Low-voltage and low-power applications require transistors that not only exhibit sufficiently high mobility and high current on/off ratio but also low contact resistance between the metal electrodes and the 2D channel.Direct contacting of MoS2 with metals can lead to the formation of Schottky barriers and Fermi-level pinning at the interfaces.The results are undesirably high contact resistances and therefore limited carrier injection and, ultimately, reduced device performance 16,17 .For this reason, various contact methods were evaluated.The use of MoS2 phase-transformed from semiconducting 2H into metallic 1T has been proposed as a contact region 18 .However, it should be noted that stable 1T contact regions have not yet been reproducibly demonstrated with chemical vapor deposited (CVD)-grown MoS2.Others have demonstrated that ultra-high vacuum-deposited Au contacts can also lead to very low contact resistance 12,19,20 .However, gold is typically not suitable for monolithic integration due to the lack of silicon CMOS compatibility.A further approach is chloride molecular doping, which leads to a significant reduction of contact resistance but is also unstable over time 21 .
Recently, McLellan et al. 22 presented a stable doping process that can lead to very low contact resistance through aluminum oxide (AlOx) capping, but also induces strong n-doping and cannot easily be limited to the contact regions 22 .Another approach to achieving very low contact resistances to 2D materials is to use semimetals like bismuth and antimony 23,24 , although they are relatively scarce, which may limit their long-term use as contact metals. 25aphene, on the other hand, has excellent electrical conductivity and is chemically stable, making it a promising candidate for low-resistance contacts to MoS2 [26][27][28][29][30][31][32][33][34] .Several reports have already proven the versatility of graphene as a contact due to the tunability of its work function by electrostatic doping, which minimizes the Schottky barrier height at the graphene-semiconductor interface 26,32,[35][36][37] .Using the semimetal graphene as contacts provides an atomically sharp interface without dangling bonds, so the Fermi-level pinning 38 at the contact interface to TMDCs can be prevented 33 .The mechanical strength, flexibility, transparency, and thermal stability of 2D materials make them highly desirable for flexible electronics applications 39 .
Here, device bendability is a significant concern.Graphene contacts can offer an excellent alternative to traditional metals, which are often the limiting factor in high strain levels.Although the advantages of graphene are apparent, the graphene sheet resistance and the metalgraphene contact resistance contribute to the total resistance in addition to the graphene-TMDC contact resistance and, therefore, must be co-optimized in the contact design and fabrication.Furthermore, the employment of graphene contacts required an additional metallization layer for electrical characterization due to the inherent thinness of graphene as an electrode.An intrinsic limitation of these contacts is the high van der Waals gap, which is, in some cases, higher than the metal-MoS2 gap 40 .This issue can, however, be addressed by achieving a perfect edge contact between the metal and the graphene 41 .
In this work, we experimentally demonstrate a scalable technique for low contact resistance to MoS2 using CVD-grown SLG.We further show that metal one-dimensional edge contacts between single-layer graphene (SLG) and nickel (Ni) are a suitable method for achieving low contact resistances 42,43 .The results are corroborated through simulations that explore the scalability potential of further contact resistance optimization based on this approach.

Material Characterization
Confocal Raman measurements were performed on the SLG/MoS2 lateral heterostructure (LH) (Figure 1a) to analyze the transferred 2D films.A Raman map with 400 points taken after the transfer of SLG on SiO2 in Figure 1b shows the 2D (2692 cm -1 ) and G (1589 cm -1 ) modes of SLG.A defect peak around 1350 cm -1 was not detected, indicating high quality graphene after the transfer.The thickness of MoS2, as measured by atomic force microscopy in a prior growth process, is approximately 0.7 nm and aligns with the Raman data confirming its monolayer structure. 9A spatially resolved Raman map of a µm-scale FET was performed (red box in Figure 1c).The strong intensity of the A1g mode of MoS2 in Figure 1d confirms that the MoS2 channel uniformly covers the entire region between the Ni contacts, while SLG is in contact with the Ni and the MoS2.

Device Characteristics
The contact resistance Rc of Ni edge contacts to SLG is typically in the range of only a few hundred Ω µm and the sheet resistance Rs of SLG is ~1 kΩ/square 43 (Supplementary Fig. 4), more than 100x lower than that of MoS2. Figure 2a shows the transfer characteristic for Vds = 1 V with measured maximum on current of Ion/W = 43 µA/µm for a device with Lch = 100 nm and Vgs = 40 V.
The transfer characteristics of a LH-FET with Lch = 1 µm is shown in Figure 2b.This device reached a high current on/off ratio of more than 10 8 with a low off-current of order 10 fA/µm at Vgs = -30 V (a graph with a wider Vgs sweep is shown in Supplementary Fig. 3).The transfer curves show a kink at Vgs = -20 V, which can be attributed to acceptor-like interface states in S/D regions 44 .The output curves of the 1 µm-long LH-FET in Figure 2c demonstrate an ohmic behavior of the drain currents, indicating the suitable contacting scheme with graphene.The drain current's saturation range is limited by the relatively thick gate oxide (90 nm SiO2), which hinders the build-up of a strong electrostatic potential across the channel.The oncurrents of the device increase continuously as the channel length decreases with approximately a 1/# !" relationship, as shown in Figure 3a for Vds = 100 mV (red) and Vds = 1V (black) at Vgs = 40V.The transmission line method (TLM) was used to extract a contact resistance from the total resistance Rtotal = 2•Rc + Rch (1)   where Rch is the channel resistance.Figure 3b shows the linear fit of Rtotal for different Lch, and the point at which the line intersects the Y-axis corresponds to a value of 2•Rc.Here, a Rc = 9 ±2 kΩ µm was extracted for the LH-FET, which is more than one order of magnitude lower than reference MoS2 FETs with pure Ni side contacts (Supplementary Fig. 5 and a comparison of transfer characteristics of LH-FETs and Ni contacted FETs in Supplementary Fig. 6).For both types of devices, a sheet resistance of Rs ~60 kΩ /square was extracted.To demonstrate the scalability of our approach, we conducted measurements on 10 LH-FETs for each channel length (Supplementary Fig. 8), revealing minimal device-to-device variability.A benchmarking plot of literature data compares contact resistances of multilayer CVD and exfoliated MoS2 FETs contacted with graphene (Figure 3c).The comparison has been made among graphene-contacted MoS2-FETs to emphasize the importance of this scalable approach, which still has a margin of improvement in the quality of the materials.Even though flakebased MoS2 and graphene have previously achieved lower contact resistances, this work stands out by utilizing scalable materials and demonstrating the lowest reported contact resistance on a CVD monolayer MoS2 channel, narrowing the gap with the superiority with flakes-based materials.(c) Benchmarking plot of contact resistance of graphene-contacted MoS2 FETs [26][27][28][29][30]32,33,45 as a function of MoS2 layers (blue: CVD MoS2; red: exfoliated MoS2).

Device Simulation
To better understand device operation and the potential of downscaling to nanometer size, we performed a multiscale simulation of the LH-FET.
In our model, we describe the top contact as a ladder of resistors and current generators, as shown in Figure 4a.The horizontal (in-plane) resistors have a resistance proportional to the layers' sheet resistances and the vertical current generators provide the vertical current per unit area due to ballistic transport, which is nonlinearly dependent on the electrochemical potentials of the two nodes and on the vertical electrostatic potential profile.Since we can define local electrochemical potentials for each layer  #$ () and  %&' !() on the horizontal direction, the nonlinear current generators are described through a modified Landauer formula where, in order to use measurable quantities, we use the in-layer applied potentials defined as instead of the chemical potentials: Assuming that the electrostatic potential varies smoothly in the horizontal direction, we can compute the electrostatic potential for every horizontal position  through a vertical 1D Poisson simulation dependent the on the gate voltage Vgs and the applied potentials.In general, the interlayer transmission coefficient (, ) depends on the detailed shape of the electrostatic potential in the vertical direction.Assuming that the difference between the electrochemical potential of the two layers is small, we can approximate (, ) as a ( + ()), where () is the average of the electrostatic potentials of the two layers for the same horizontal coordinate x: This corresponds to considering that the shape of the barrier in the vertical direction is negligibly dependent on the electrochemical potential of the layers and that the transmission coefficient in the vertical direction is only affected by the average shift of the barrier.We computed () through a multiscale approach considering two infinite layers at equilibrium following the procedure described in the methods section.
The solution of the Poisson equations enables us at the same time to use the aforementioned approximation to shift () to ( + ()), and to compute the carrier densities in the two layers, which in turn affect the sheet resistances , where  +,-() is the majority carrier density and  ! is the carrier mobility in the layer denoted by , where ( = , MoS 7 ).
The model parameters are the materials' mobilities  !,#$ ,  !,%&'7 , and the corresponding doping densities  #$ ,  %&' ! .We estimated  #$ on the SiO2 substrate to be 4.5 × 10 .7 cm 87 from the position of the charge neutral point in an analogous structure in Ref. 43 , while for the MoS2 we assume it to be 2 × 10 .7  87 .Using the estimated doping densities, we could use carrier densities obtained from Poisson simulations to estimate  !,#$ and  !,%&'7 respectively from the sheet resistance of Ref. 43 and the channel sheet resistance obtained from the TLM depicted in Supplementary Fig. 7 by inverting for MoS2 we estimated it to be  !,%&'7 ≈ 1 cm 7 V 8. s 8. for sample 1 and  !,%&'7 ≈ 7 cm 7 V 8. s 8. for sample 2, and for graphene we estimated it to be  !,#$7 ≈ 629 cm 7 V 8. s 8. .We also introduced a single fitting parameter: the interface quality factor , defined as which represents the missing knowledge on the actual distance between the planes and the overall interface quality.
We cast our model in a non-linear transmission line model structure, where we solved a system of differential equations describing horizontal transport with source terms representing vertical transport 43 .Our model allowed us to obtain the applied potentials  #$,%&' !() and the horizontal currents  #$,%&' !() profiles in the two layers.From these current profiles, we could extract two main quantities describing the performance of the top contact i) contact resistance ( ! ) and ii) transfer length ( < ).The former is the main figure of merit of a contact.With our calculation we confirm the experimental result by obtaining  != 9 Ω ⋅  for the estimated mobility of sample 2. As for the latter, which represents the characteristic length over which the current goes from one layer to the other, and therefore the minimum length for the top contact, we obtain  < = 27 , showing potential for contact length scaling and integration.
Low resistance is achieved by inserting the semimetal graphene between the metal and the 2D semiconductor.As demonstrated in Shen et al. 23 , this partially avoids the formation of the hybridized states in the gap of the semiconductor that lead to the Fermi pinning phenomenon.
The relatively low Schottky barrier between graphene and MoS2 of ~0.5 eV can be further reduced electrostatically via the gate voltage, since graphene is a semimetal, and we cannot assume it to have an infinite density of states 26,35,36,47 .Furthermore, the gate voltage introduces a large carrier density in the contact, further improving conductivity.The use of an advanced fabrication process also ensures a clean heterostructure with a low density of impurities and defects.
The main confirmation of the validity of our model is the correct scaling of contact resistance  ! with  !,%&'7 .As we can see in Figure 4d, by increasing  !,%&'7 while keeping every other parameter constant implies a nonlinear decrease in  ! .Our mobility scaling can describe  ! in two samples with different mobilities by using the same value for .This suggests that  is a general parameter, depending only on materials choice and interface quality, not on the quality of the materials.Therefore, obtaining the value of  for one value of  !,%&'7 allowed us to extrapolate the contact resistance for contacts made with higher quality materials, assessing the potential of the Ni-graphene/MoS2 contact for future practical applications.We can see that even if the contact would have been made of materials with record mobilities (∼10000 cm 7 V 8. s 8. ) for graphene 44 and ∼200 cm 7 V 8. s 8. for MoS2 10 ), with the current interface quality  = 0.17 the minimum contact resistance would have been  !~2 Ω ⋅  with a transfer length of  < ~80 .For an ideal interface quality  = 1, we can estimate the minimum achievable contact resistance to be  !∼ 0.5 Ω ⋅  with  < ∼ 35 .Figure 4d also shows that interface quality is even more important than the 2D-materials mobilities since the contact resistance quickly saturates because of the effective resistance of the vertical interface.In summary, we have experimentally demonstrated lateral SLG/MoS2 heterostructures based on scalable materials, with low contact resistances down to ~9 kΩ µm at current ON/OFF ratios of 10 8 .The proposed theoretical model, calibrated with experiments, shows a charge transfer length down to 27 nm, indicating the scaling potential of the SLG approach for ultra-scaled 2D FETs.Furthermore, our model shows that TMDCs with higher mobility and an optimized interface can lead to a very promising contact resistance of 0.5 kΩ µm.Here, direct growth processes or cleaner transfers of large area grown 2D materials are necessary to improve the interfaces of heterostructures and thus lower contact resistance in future scalable devices.

MoS2 deposition
A continuous single-layer MoS2 film was grown by metal-organic chemical vapor deposition (MOCVD) on 2" sapphire wafer using molybdenum hexacarbonyl (Mo(CO)6) and hydrogen disulfide (H2S) precursors 9 .Extensive characterization of the material has been performed in reference 9 , including transmission electron microscopy (TEM) to assess the quality of the material.

Material Characterization
Confocal Raman and PL measurements were performed with a laser wavelength of 532 nm and a power of 1 mW on MoS2 in detail, both on its growth substrate sapphire and after being transferred onto 90 nm silicon oxide on silicon substrates (Supplementary Fig. 1).PL measurements of MoS2 and Raman measurements of SLG were conducted with a 300 lines/mm grating and Raman measurements of MoS2 with a 1800 lines/mm grating.The step height of ~0.7 nm of MoS2 was measured by atomic force microscopy.

Device Fabrication
Commercially available CVD grown SLG on copper (Cu) was transferred onto a 90 nm SiO2/Si substrate with pre-patterned alignment marker via PMMA supported wet transfer.Electron beam lithography (EBL) and Oxygen (O2) plasma reactive ion etching (RIE) were used to pattern the SLG contact areas.CVD-MoS2 was then transferred onto the entire chip by wet transfer 48 .FET channels were defined by EBL and subsequent RIE using a gas mixture of tetrafluoromethane (CF4) and O2.Finally, self-aligned sputtered Ni edge contacts to SLG were defined by EBL and a subsequent CF4/O2 plasma RIE process using the same resist mask.The back-gated FETs with different channel lengths from 100 nm to 1 µm were used to determine the contact resistance by Transfer-Line-Method (TLM).The relatively large device channel width of 100 µm was used to compensate single material defects in the 2D layers or residues caused by the transfers 49 .A sketch of the fabrication process of lateral heterostructure (LH)-FETs is shown in Figure S2.Although graphene and MoS2 are vertically stacked, the term 'lateral heterostructure 'refers to the lateral transistor configuration wherein the MoS2 channel can be modulated between two graphene contacts.

Computational Methods
The device model required a correct description of the physics and the two largely different length scales in the horizontal direction (~1 µm) and in the vertical direction (~1 nm).For this reason, we assume diffusive transport in the horizontal direction and ballistic transport in the vertical direction across the van-der-Waals gap of the heterojunction.These two very different transport regimes were described with a single multiscale model.As for the ballistic transport, we compute the vertical transmission coefficient between graphene and MoS2 following the procedure detailed in Ref. 50     A schematic device cross-section is shown in Supplementary Fig. 2. All devices were designed with a channel width of 100 µm.The length of the graphene contacts (LSLG) are 1 µm and are not included in the actual transistor channel lengths (Lch).Lch is defined by the gap between the SLG contacts, vary between 100 nm (Fig. 1b) and 1 µm.
Supplementary Figure 2: Fabrication process and device schematic of LH-FETs.Pre-structured graphene contacts at the bottom serve as low ohmic contacts to MoS2.The 2D-heterostructure is contacted by nickel edge contacts.The contact length of graphene is denoted as L and the MoS2 channel in between as Lch.

Figure 1 :
Figure 1: Overview of the sample design and 2D-layers arrangement.(a) Device schematic of LH-FETs.LSLG describes the length of the SLG/MoS2 heterostructure and Lch defines the channel of the transistor.(b) Raman spectrum of SLG on Si/SiO2 before the transfer of MoS2.(c) Optical microscope image of a LH-FET.The Raman area scan shown in (d) was performed in the area marked by the red box.(d) A spatially resolved Raman map shows the intensity of the 2D mode of SLG (left) and the intensity of the A1g mode of MoS2 (right).Dark areas indicate not present mode while brighter areas indicate a stronger intensity.

Figure 2 :
Figure 2: Transistor performance characteristics of the devices.(a) Transfer characteristic of a MoS2 LH-FET with Lch = 100 nm for Vds = 1 V in log scale (black line) and linear scale (red line).(b) Transfer

Figure 3 :
Figure 3: Additional performance data and benchmarking of the contact resistances.(a) Ion is plotted against Lch for Vds = 1 V (black line) and Vds = 100 mV (red line) in double-logarithmic scale.(b) Total device resistance vs channel length of different LH-FETs and the extracted contact resistance by TLM.

Figure 4 :
Figure 4: Multiscale simulation of transport.(a) Simulated horizontal current for each layer in the whole device for typical device operation conditions.Horizontal current transfer between the graphene layer (1) and the MoS2 layer (2) shows presence of vertical carrier transport over a few transfer lengths  !.(b)Circuit-like schematization of device, a non-linear Transmission Line Model setup.Vertical ballistic transport between the two resistive layers is represented by nonlinear current generators (c) Depiction of vertical ballistic transport.Carriers propagate through the interlayer barrier () from the local Fermi distributions generated by local electrostatic potentials  ",$ ().(d) Simulated dependence of contact resistance  % on MoS2 mobility  &'( ! for different interface quality  and graphene mobility  )* .Our simulation correctly predicts the difference in contact resistance between two samples (S1 and S2) with different  &'( ! .(e) Simulated transmission length  !dependence on  &'( ! for different  and  )* (same legend as (d) ). !does not depend strongly on  )* .
, which consists in performing i) a density functional theory (DFT) simulations of the infinite graphene-MoS2 heterostructure, ii) a transformation of the DFT Hamiltonian into the basis of maximally localized Wannier function (MLWF) using proper projection in order to clearly identify the top and bottom flake, i.e.MoS2 and graphene, iii) non-equilibrium Green's function (NEGF) simulation to compute the vertical transmission, creating a proper MLWF Hamiltonian with monolayer and bilayer regions 50 .DFT calculations have been carried out using Quantum Espresso suite 51 .We have considered a supercell consisting of 5 × 5 graphene and 4 × 4 MoS2 elementary cells, applying 3% of strain on the graphene and no strain on MoS2, with an interlayer distance of 3.4 A. We use GGA-PBE pseudopotentials and grimme-D2 correction to consider van der Waals forces.Calculations are performed on a 3 × 3 × 1 grid.The Hamiltonian in terms of the MLWF has been obtained exploiting Wannier90 code 52 projecting on the pz orbital of each C atom and on the three sp2 orbitals every two C atoms while on the d-orbitals for the Mo and on the sand the p-orbitals for the S atoms.The transmission coefficient has been obtained using NanoTCAD ViDES 53 DATA AVAILABILITY STATEMENT (d) A spatially resolved Raman map shows the intensity of the 2D mode of SLG (left) and the intensity of the A1g mode of MoS2 (right).Dark areas indicate not present mode while brighter areas indicate a stronger intensity.

Figure 2 :
Figure 2: Transistor performance characteristics of the devices.(a) Transfer characteristic of a MoS2

Figure 3 :
Figure 3: Additional performance data and benchmarking of the contact resistances.(a) Ion is plotted

Figure 4 :
Figure 4: Multiscale simulation of transport.(a) Simulated horizontal current for each layer in the whole