Coulomb drag transistor using a graphene and MoS2 heterostructure

Two-dimensional (2D) heterostructures often provide extraordinary carrier transport as exemplified by superconductivity or excitonic superfluidity. Recently, a double-layer graphene (Gr) separated by few-layered boron nitride demonstrated the Coulomb drag phenomenon: carriers in the active layer drag carriers in the passive layer. Here, we propose high-performance Gr/MoS2 heterostructure transistors operating via Coulomb drag, exhibiting a high carrier mobility (∼3700 cm2 V−1 s−1) and on/off-current ratio (∼108) at room temperature. The van der Waals gap at the Gr/MoS2 interface induces strong interactions between the interlayer carriers, whose recombination is suppressed by the Schottky barrier between p-Gr and n-MoS2, clearly distinct from the presence of insulating layers. The sign reversal of lateral voltage clearly demonstrates the Coulomb drag in carrier transport. Hole-like behavior of electrons in the n-MoS2 is observed in magnetic field, indicating strong Coulomb drag at low temperature. Our Coulomb drag transistor thus provides a shortcut for the practical application of 2D heterostructures. The Coulomb drag effect describes long-range electronic interactions between the charge carriers of two conducting channels separated by an insulating layer. Here, the authors report a graphene/MoS2 heterostructure which operates using the Coulomb drag effect with energy barrier and exhibits high carrier mobility and on/off current ratio at room temperature

A tomically thin two-dimensional (2D) van der Waals layered materials are chemically inert with no dangling bonds. This allows for exploring a unique facet of science as well as expanding the realm of practical applications to soft and wearable electronics, with high transparency 1 and stretchability 2,3 . The recently developed wafer-scale 2D materials, such as graphene (Gr) [4][5][6] , transition-metal dichalcogenides (TMdCs) 7,8 , and their heterostructures 9 , combined with the stateof-the-art top-down technology, further allow for integration of the complementary metal-oxide-semiconductor components.

Results and discussion
Energy barrier between graphene and MoS 2 . Monolayer Gr and MoS 2 were grown separately by chemical vapor deposition (CVD). Later, monolayer MoS 2 was transferred onto a SiO 2 (300nm)/p + -Si substrate, followed by Gr transfer to yield the heterostructure (see Supplementary Fig. 1). This stacking process leads to slight p-doping effect on MoS 2 in Gr/MoS 2 heterostructure due to charge transfer from MoS 2 to Gr, resulting in the formation of a vertical energy barrier (EB) at the heterointerface (see Supplementary Note 1). EB is effectively controlled by dualgate modulation. Figure 1a illustrates a schematic for dual-gated Gr/MoS 2 heterostructure to control the carrier type and density in each layer as a function of top V TG ð Þ and bottom gates (V BG ). Electrical contacts for the Gr and MoS 2 layers were separately constructed after stacking both layers (see Supplementary Fig. 1). Ambipolar Gr with a charge-neutrality point (V CNP ) and n-MoS 2 characteristics is clearly probed via these electrodes (Fig. 1b), similar to the electrical properties of individual layers.
EB is determined by each transfer curve of Gr and MoS 2 in the heterostructure under dual-gate modulation 24 . The electrostatic displacement field has been suggested for EB as evidence for electrical isolation. The net vertical displacement field (ΔD) is defined from displacement fields of top (D TG , 30-nm Al 2 O 3 ) and bottom gate (D BG , 300-nm SiO 2 ) as given below 25 : where V th , ε, and t are threshold voltage of MoS 2 , dielectric constant, and thickness for each dielectric material, respectively.
Here, the threshold voltage of MoS 2 is extracted from the transfer curves of MoS 2 as a function of top gate and calculated from the relation (ΔV BG /ΔV TG ) between top V TG and bottom gates (V BG , see Supplementary Note 2). Once electrons and holes prevail at MoS 2 and Gr, respectively, the net vertical displacement across Gr and MoS 2 is positive and the displacement is applied from MoS 2 to Gr, resulting in the energy barrier for each carrier in MoS 2 and Gr. In the opposite case (negative vertical displacement), the displacement promotes carrier transfer between two layers without the energy barrier. The vertical energy barrier from the displacement field is finally obtained from the following equation: ΔD Á d GM Á q, where d GM denotes interlayer distance between Gr and MoS 2 (~0.4 nm) (Fig. 1c, d). When Gr is p-type near V CNP (V TG = −6.2 V) and MoS 2 is n-type (V BG = 40 V) at Gr/MoS 2 , the established vertical displacement energy is over 0.55 eV and becomes larger (~0.72 eV) at higher V TG = −8.2 V, exceeding previously reported e-h separation energy of 0.25 eV at Gr/ MoS 2 26 . This is again confirmed by the Schottky barrier concept; Schottky barrier height ranges from 0 to 0.72 eV at Gr/MoS 2 heterostructure 27,28 (see Supplementary Note 2). Consequently, the enhanced EB between Gr and MoS 2 plays a key role as an electrical insulator in vertical direction, thus mimicking the conventional Coulomb drag configuration [29][30][31][32][33][34][35] .
Coulomb drag effect at graphene/MoS 2 heterostructure. To verify the Coulomb drag effect and strong interaction at Gr/MoS 2 heterointerface, two representative devices were fabricated without an insulating layer. Gr/MoS 2 stacks for both devices are fabricated in the same way by transferring monolayer MoS 2 onto SiO 2 /Si substrate, followed by monolayer Gr transfer onto MoS 2 (see "Methods"). Channel definition and metallization were performed at larger Gr and smaller MoS 2 for the first case (Fig. 2a).
To ensure data reliability, various electrical properties were investigated at high current regime (I > 10 nA, see Supplementary Note 3). A drive current flows along Gr (active layer), while the resulting longitudinal potentials in MoS 2 (passive layer) and Gr are separately monitored (Fig. 2a). For data analysis, the electrical properties of ambipolar Gr and n-MoS 2 are confirmed using the transfer curves in Coulomb drag configuration (Fig. 2b), similar to the electrical properties at the Gr/MoS 2 heterostructure (Fig. 1b). The longitudinal potentials of both Gr and MoS 2 are almost identical (Fig. 2c), where EB is relatively shallow at the gate biases for n-Gr/n-MoS 2 and p − -Gr/n-MoS 2 near V CNP ( Fig. 1 and see Supplementary Note 2). Meanwhile, the potential of MoS 2 rapidly drops and approaches to zero in electrically isolated conditions at p-Gr/n-MoS 2 heterostructure with a sufficiently high EB, which is clearly distinct from the positive potential at the Gr side. Yet, interlayer carrier transport at Gr/MoS 2 edge takes place by interlayer tunneling induced by drain bias through EB, so that the injected carriers move laterally along Gr and MoS 2 (schematic in the inset of Fig. 2c). Thanks to the ideally narrow gap at Gr/MoS 2 , holes in Gr (gray arrow) strongly drag electrons in MoS 2 (red arrow) without recombination, resulting in zero or negative potential as a counterflow geometry 36 . In addition, the thermoelectric effect appears particularly at high drain (drive) current of Gr (active layer), but potential difference between the positive-and negative-current regime is distinct, confirming the presence of Coulomb drag effect in our device (see Supplementary Fig. 6 and Supplementary Note 4). A similar behavior is observed in the opposite structure with MoS 2 (active layer) and Gr (passive layer) with respect to V BG ( Fig. 2d-f). The second device was fabricated at larger MoS 2 and smaller Gr (Fig. 2d). When a drive current I active MoS 2 is applied through source/drain onto MoS 2 (active layer), longitudinal potentials of MoS 2 V active MoS 2 and Gr V passive Gr at the heterostructure are measured (Fig. 2d). Nearly zero and negative potentials are observed for MoS 2 , while the positive potential is observed for Gr, although the signature is rather weak compared to the previous case ( Fig. 2a-c). This clearly indicates that most carriers flow along the MoS 2 -Gr (at Gr/MoS 2 )-MoS 2 path and holes inside Gr drag electrons inside MoS 2 at the heterointerface. It is of note that this anomalous V XX behavior in Gr/MoS 2 heterostructure device persists even at T = 2 K with I = 10 μA (see more details later).
Coulomb drag transistor at graphene/MoS 2 heterostructure. We took advantage of a platform of Coulomb drag to demonstrate the high performance of our unique field-effect transistor; this is achieved by connecting MoS 2 to the source and drain (and the inner four-probe electrodes) with a dual gate, while Gr is deliberately isolated from other electrodes (Fig. 3a-c). The transfer curve of Gr/MoS 2 transistor was measured as a function of V TG at room temperature (Fig. 3d). In Gr/MoS 2 transistor, the observed high on-current is attributed to Gr, while the low offcurrent is ascribed to MoS 2 , ultimately resulting in a large on-/offcurrent ratio of~10 8 . The longitudinal potential of Gr/MoS 2 device is positive when V TG > −13 V. More intriguingly, the potential approaches to zero and becomes negative when V TG < −13 V, resembling the Coulomb drag effect (Fig. 2). This is contrasted with the no negative-potential regions in individual Gr and MoS 2 devices fabricated by identical procedures on the same wafer ( Fig. 3e and see Supplementary Fig. 7).
We further calculated the four-probe field-effect mobility (μ FE ) using the following relationship: where C ox , g m , L, and W denote net-oxide capacitance per unit area, transconductance, channel length, and width, respectively 37 .
In particular, Gr/MoS 2 mobility values were analyzed at V XX ∼5 mV (below V CNP ) to improve data reliability (Fig. 3d). The twoprobe-measured μ FE is compared with four-probe-measured μ FE for Gr and MoS 2 at room temperature (see Supplementary Fig. 8).
As a whole, the mobility of the Gr/MoS 2 device exceeds that of MoS 2 and Gr, and more importantly, the divergence in mobility is distinct at V TG < −13 V (Fig. 3f), resulting from the nearly zero potential shown in Fig. 3d. We define two distinct regimes in the Gr/MoS 2 device, based on V CNP~− 11 V (white line, Fig. 3f), similar to the individual Gr device. Such a high mobility at p/n regime can be ascribed to the suppressed effective carrier density and carrier-carrier scattering inside MoS 2 at a given conductivity. At the n/n regime for heavily n-doped MoS 2 and n-type Gr, the electrical properties of the heterostructure are dominated by Gr as the energy barrier at Gr/MoS 2 becomes smaller and carrier transfer occurs. Furthermore, MoS 2 at Gr/MoS 2 reduces the substrate effect from SiO 2 , so that Gr at the heterostructure gives better mobility, compared to that of individual Gr device.  We further investigate the temperature (T)-dependent transfer curves and threshold voltage from 2 to 300 K. Metal-insulator transition (MIT) also appears in both Gr/MoS 2 at V TG~2 V (Fig. 4a) and MoS 2 at V TG~1 3 V (Fig. 4b), which is the cross-over point of the conductivity at different temperatures. In general, metallic behavior in MoS 2 is observed at high carrier density, which is typical for poor-quality samples with impurities and disorders 17 . To evaluate the interface quality of our devices, the carrier density (n) is calculated at the MIT point in dual-gate configuration. The carrier densities of the Gr/MoS 2 and MoS 2 devices at the MIT point are 1.6 × 10 13 m −2 and 3.3 × 10 13 m −2 at 300 K and 1.1 × 10 13 m −2 and 1.2 × 10 13 m −2 at 2 K, respectively, with the corresponding threshold voltages (Fig. 4c). This confirms high quality of the Gr/MoS 2 interface, which is necessary for the Coulomb drag effect.  The strong Coulomb drag effect, however, makes the determination of current in MoS 2 in Gr/MoS 2 device ambiguous, which could consequently lead to over-or underestimation of mobility. In addition, the Gr/MoS 2 device consists of two conducting layers (Gr and MoS 2 ) and vertical tunneling barrier. Therefore, the general planar capacitance model may lead to a large discrepancy in the intrinsic mobility of Gr/MoS 2 . To avoid these ambiguities, the Hall mobility μ Hall À Á was determined using the following relationship: where V XY and B are the transverse potential and magnetic field, respectively. Both the longitudinal and transverse potentials were simultaneously measured for MoS 2 in the Gr/MoS 2 device for determining Hall mobility as a function of B, V TG , and V BG at 2 K (Fig. 5a, b). A nearly zero longitudinal potential is clearly observed compared to room temperature (Fig. 3d), indicating enhanced Coulomb drag effect because of the suppressed phonon scattering. The V TG -dependent Hall mobility is almost identical to the field-effect mobility (reaching up to ∼10 4 cm 2 V −1 s −1 in the Coulomb drag regime) (see Supplementary Note 6). Meanwhile, the field-effect mobility is underestimated by Hall mobility, as the net-oxide capacitance is overestimated by a factor of 3 (Fig. 5c). Another distinct evidence of Coulomb drag phenomenon is the carrier-type conversion in MoS 2 of the Gr/MoS 2 device. The carrier type and density were determined from Hall measurement with a sweeping magnetic field (Fig. 5c and see Supplementary Fig. 10a and b). The suppressed number and sign reversal of effective carriers in MoS 2 at Gr/MoS 2 heterointerface were clearly observed around V TG ∼ −10 V at V BG = 40 V, clearly implying that the electrons in MoS 2 are dragged by the holes in Gr in the p-Gr/n-MoS 2 regime.
Conclusion. We designed and demonstrated Coulomb drag transistors based on Gr/MoS 2 heterostructures for achieving high on-/off-current ratio and mobility. Carrier mobility could be enhanced using a hexagonal boron nitride gate insulator 38,39 instead of Al 2 O 3 that degrades the carrier mobility of 2D materials (see Supplementary Fig. 9 and Supplementary Note 5). Several issues remain to be resolved for the practical applications of Coulomb drag transistors, such as their contact resistance [20][21][22] , carrier-type control 40 , and widening of the operation-voltage window. Nevertheless, our Coulomb drag transistors extend the research fields for dissipation-less devices with 2D heterostructures under ambient conditions.

Methods
Graphene growth via chemical vapor deposition (CVD). To obtain large singlecrystal graphene (Gr) flakes, the following procedure was employed. Initially, a Cu foil was preannealed at 1070°C for 2 h in a H 2 and Ar atmosphere to remove organic residues from its surface and improve its crystallinity. Subsequently, one side of the foil was chemically polished, i.e., the Cu surface was etched with an etchant (FeCl 3 , Taekwang, Korea) and rinsed with deionized (DI) water to obtain a flat and organic residue-free substrate. Before Gr growth, the clean Cu foil was annealed again at 1070°C for 30 min in the growth chamber to remove any remaining residues on the surface. In the next step, a low concentration CH 4 gas (0.1% Ar-based gas) was passed through the chamber. After annealing, the Cu foil was immediately exposed to a flow of 3 sccm CH 4 , 20 sccm H 2 (99.9999%), and 1000 sccm Ar (99.9999%) at the same temperature (1070°C) for 30 min without exposure to air to synthesize high-quality Gr flakes.
MoS 2 growth via CVD. We synthesized monolayer MoS 2 by sulfurizing a solutionbased precursor to improve crystal quality 41,42 . The Mo precursor (12 mM ammonium heptamolybdate in DI water (Sigma-Aldrich, 431346)) and a promoter (10 mM sodium hydroxide in DI water (Sigma-Aldrich, 306576)) were mixed and spin-coated onto a SiO 2 /Si wafer at 3000 rpm for 1 min. To sulfurize the Mo-based precursor on the substrate, sulfur powder (100 mg) and the prepared substrate were placed in zones 1 and 2 of the growth chamber, respectively, and 500 sccm N 2 was passed as a carrier gas during the synthesis process. After a sufficient N 2 purging over 1 h, single-crystal MoS 2 was synthesized over a period of 15 min at atmospheric pressure in different temperature zones, i.e., zone 1 (210°C) and zone 2 (780°C).
Device fabrication using graphene/MoS 2 heterostructure. To transfer each material, we spin-coated polymethylmethacrylate (PMMA, Sigma-Aldrich) onto the substrate along with Gr/MoS 2 at 2000 rpm for 1 min. The flexible PMMA film holds the material and minimizes any damage during the transfer process. PMMA-coated MoS 2 was separated from the substrate by dipping into DI water and then transferred onto a SiO 2 (300 nm)/Si target substrate. In our MoS 2 growth conditions, the water-soluble promoter remains near and underneath the MoS 2 layer. We removed PMMA by cleaning with acetone, followed by annealing at 350°C for 2 h in a H 2 /Ar atmosphere. The annealing process enhanced interaction between MoS 2 and SiO 2 as well, resulting in a strong adhesion.
To detach PMMA/Gr from the Cu foil, voltage was applied through a Pt wire to the Cu foil in a 0.1 M NaOH solution (water-electrolysis method) 43 . The effect of chemical doping is largely suppressed by this method, which is a key aspect in enhancing the device performance. To further remove chemical residues, Gr was rinsed several times with DI water. We then transferred and stacked Gr onto the MoS 2 flakes on the target substrate. The same cleaning and annealing processes (350°C for 2 h in H 2 /Ar) were conducted to remove residual PMMA and facilitate strong interlayer coupling.
Gr/MoS 2 devices were fabricated using standard e-beam lithography and metallization with Cr (5 nm)/Au (60 nm). To define the channel area for the sixprobe Hall bar structure, MoS 2 and Gr were patterned and etched using O 2 and SF 6 plasma (10 sccm O 2 and 20 W for 20 s, followed by 20 sccm SF 6 at 10 W for 10 s). Later, Al 2 O 3 (30 nm) was deposited via atomic layer deposition on the Gr/MoS 2 device to serve as the top-gate dielectric. The top gate was fabricated by e-beam patterning and Cr (5 nm)/Au (60 nm) deposition to realize a dual-gating device as the final configuration.  5 Carrier transport in the Gr/MoS 2 heterostructure at low temperatures. a V TG -dependent current (black) and longitudinal potential (V XX ) curves (blue) of Gr/MoS 2 at 2 K. b V TG -dependent field effect μ FE À Á and Hall mobility μ Hall À Á of the Gr/MoS 2 device with respect to V BG . c Effective carrier density (n 2D ) in MoS 2 in the Gr/MoS 2 device as a function of V TG . The net-oxide capacitance C ox À Á is overestimated 3 times when compared to the effective capacitance C eff À Á extracted from the linear fit of V TG -dependent n 2D obtained from Hall measurement. Inset: expanded region of the carrier-type conversion. Hole-like carriers are observed in the p-Gr/n-MoS 2 regime due to Coulomb drag. The error bars are represented by the standard deviation of data.
Optical characterization. To identify each material and confirm its interlayer charge-transfer effect, Raman and photoluminescence (PL) measurements were performed on Gr/MoS 2 and MoS 2 after Al 2 O 3 passivation. To this end, a confocal Raman microscope (NTEGRA Spectra, NT-MDT) equipped with a 532-nm excitation laser and an objective lens (numerical aperture of 0.7) was used.
Electrical characterizations. Device performance was characterized at each step after annealing at 150°C for 2 h in high vacuum (∼10 −6 Torr). Measurements were conducted at room temperature using a standard semiconductor characterization system (4200-SCS, Keithley Instruments). To enhance data reliability, we also measured the device performance with another characterization system (B1500A, Keysight Technologies). The temperature-and magnetic field-dependent performances of the devices were monitored under high vacuum (∼10 −7 Torr) in a cryostat (PPMS, Quantum Design, Inc.).

Data availability
Data are available upon request.
Received: 23 April 2020; Accepted: 16 September 2020; Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.