We demonstrate a large area MoS2/graphene barristor, using a transfer-free method for producing 3–5 monolayer (ML) thick MoS2. The gate-controlled diodes show good rectification, with an ON/OFF ratio of ∼103. The temperature dependent back-gated study reveals Richardson's coefficient to be 80.3 ± 18.4 A/cm2/K and a mean electron effective mass of (0.66 ± 0.15)m0. Capacitance and current based measurements show the effective barrier height to vary over a large range of 0.24–0.91 eV due to incomplete field screening through the thin MoS2. Finally, we show that this barristor shows significant visible photoresponse, scaling with the Schottky barrier height. A response time of ∼10 s suggests that photoconductive gain is present in this device, resulting in high external quantum efficiency.

Graphene and MoS2, 2-dimensional crystals, have drawn attention in recent years due to their exceptional properties such as ultra-high mobility,1 thermal conductivity,2 high on-off ratio and low subthreshold slope in field effect transistors,3,4 and high photosensitivity.5,6 Interestingly, these two materials have certain contrasting properties, for example, graphene based FETs have poor switching performance,7 while MoS2 based FETs can outperform many state-of-the-art ultra-low power transistors.34 Fabricating a Schottky diode made of graphene and MoS2 allows the unique properties of these two materials to be combined and has been shown to be useful.8–12 

A key property of these 2D heterojunctions is that each constituent of the heterojunction is so thin that it may not be able to completely screen an electric field from the second constituent, i.e., the Debye screening length can be greater than the layer thicknesses, so that voltage-induced interfacial tuning is achievable. This capability is unique to thin layers, most practically achieved in 2D heterojunctions,13 and has been exploited in recent barristors,14–20 which are 3-terminal devices with Schottky diodes with barrier heights tuned with a gate. Such a tunable Schottky diode, similar to a triode vacuum tube, is attractive for applications in RF circuits, photodetection, chemical sensing, analog and digital electronics, etc., with all the advantages of solid state devices, such as high speed, low-cost, and compactness.14–20 

In this work, we demonstrate such a graphene/MoS2 barristor using CVD (chemical vapor deposition)-grown graphene transferred onto as-grown pre-patterned MoS2 thin films. Using a degenerately doped Si back gate and thermally grown SiO2 dielectric, we demonstrated the functionality of the barristor. By varying the gate bias between –20 V and +10 V, the barrier height can be modulated by >0.65 eV. We show that the current-voltage (I-V) and capacitance-voltage (C-V) characteristics of this device are used to extract Richardson's coefficient and electronic effective mass in MoS2 using the thermionic emission model, from which the electrostatics of the device are elucidated.

The high quality 3–5 ML (monolayers) MoS2 samples were grown on the 100 nm SiO2/n+-Si substrate by partial oxidation and subsequent sulfidation of Mo, as described in Ref. 21. This method results in a pre-patterned transfer-free MoS2 film and is not detrimental to the quality of the SiO2 substrate. Ti/Au metal pads were fabricated on specific areas to serve as contacts to MoS2 and graphene patterns, followed by a 300 °C annealing in forming gas. High quality 1–2 ML graphene was grown separately on high purity Cu foils using CH4/H2 precursor gases at around 1000 °C in a tube furnace; details on the growth parameters can be found in Refs. 22 and 23. The graphene/Cu bilayer was then coated with polymethyl meth-acrylate (PMMA) for mechanical stability, and Cu was then etched in FeCl3 solution.22,23 After many rinses with HCl solution and deionized water, the PMMA/graphene bilayer was then transferred onto the as-grown MoS2/SiO2 sample. After removing PMMA in acetone, the graphene film was patterned using O2 plasma in a reactive ion etching (RIE) system. A second layer of Ti/Au metallization with larger contact pads was performed on top of the annealed contacts for both MoS2 and graphene to improve the contact resistance. Figure 1 shows the (a) schematic and (b) optical microscopy images of the final device structure, where we see that the four contacts allow measurements not only on the MoS2/graphene heterojunction but also on the MoS2 and graphene films individually. Figure 1(c) shows the Raman spectra of graphene and MoS2 after the final device fabrication. The ratios of peak intensities ID/IG = 0.2 and I2D/IG = 3.2 indicate low defect density and good quality mono- or bi-layer (1–2 ML) graphene. The inset of Fig. 1(c) shows the Raman spectra of MoS2, where the characteristic peaks of E12g and A1g are observed. The separation distance between the peaks is about 23 cm−1, which is indicative of 3–5 ML of MoS2.26 

FIG. 1.

(a) Schematic of the simultaneously fabricated MoS2 FET, the MoS2/graphene heterojunction device, and the graphene FET on the same SiO2/n+ Si substrate. (b) Optical microscopy image of the fabricated device showing the partially overlapping MoS2 and graphene films with their metal contacts (contrast enhanced for better visibility). (c) Raman spectra of graphene and (inset) MoS2. (d) Individual transfer characteristics of the MoS2 and graphene based FETs at a drain bias of 0.1 V.

FIG. 1.

(a) Schematic of the simultaneously fabricated MoS2 FET, the MoS2/graphene heterojunction device, and the graphene FET on the same SiO2/n+ Si substrate. (b) Optical microscopy image of the fabricated device showing the partially overlapping MoS2 and graphene films with their metal contacts (contrast enhanced for better visibility). (c) Raman spectra of graphene and (inset) MoS2. (d) Individual transfer characteristics of the MoS2 and graphene based FETs at a drain bias of 0.1 V.

Close modal

A temperature controlled chuck and cryostat were used to study the effect of temperature on the I-V and C-V (at 100 kHz) characteristics of the devices. Figure 1(d) shows the transfer characteristics of the constituent MoS2 and graphene field effect transistors at VDS= 0.1 V. These FETs were formed on the extended parts of MoS2 and graphene layers outside the heterojunction and probed by the additional contacts fabricated on them [Fig. 1(a)]. The field effect mobility of graphene was 950 cm2/V s, while for MoS2, the ON-state mobility was ∼80 cm2/V s, comparable to our previously reported values.21,27

Figure 2(a) shows the I-V curves for the MoS2/graphene barristor for three different gate voltages, and the measurements were taken at a temperature of ∼180 K in a dark environment, with the graphene contact being used as the drain electrode. The current was >103 times lower in the reverse bias when compared to the forward bias, demonstrating the clear rectifying behavior of the junction. The effective junction area of this device was 5 × 100 μm2, and the distance between the edge of the junction and the MoS2/graphene contact was 5 μm. Since MoS2 is n-doped21 and graphene is p-doped22 at VBG = 0 V [Fig. 1(d)], VBG < 0 V will cause depletion in MoS2 and accumulation in graphene, while VBG > 0 V will do the opposite.

FIG. 2.

(a) I-V curves for three different back-gate biases for the MoS2/graphene barristor device at ∼180 K (dark) with the drain contact being on graphene. (b) Arrhenius plots of J0/T2 as a function of 1/T for different back-gate biases used for calculating the effective Schottky barrier height and Richardson's coefficient for each case using the thermionic emission model. (c) 1/C2 vs reverse bias for the MoS2/graphene barristor at room temperature for three different back-gate biases with and without illumination. (d) Calculated dark current at VDS = –1 V and barrier heights from C-V and I-V measurements of MoS2 without illumination for different back-gate biases.

FIG. 2.

(a) I-V curves for three different back-gate biases for the MoS2/graphene barristor device at ∼180 K (dark) with the drain contact being on graphene. (b) Arrhenius plots of J0/T2 as a function of 1/T for different back-gate biases used for calculating the effective Schottky barrier height and Richardson's coefficient for each case using the thermionic emission model. (c) 1/C2 vs reverse bias for the MoS2/graphene barristor at room temperature for three different back-gate biases with and without illumination. (d) Calculated dark current at VDS = –1 V and barrier heights from C-V and I-V measurements of MoS2 without illumination for different back-gate biases.

Close modal

The current through the heterojunction is controlled by the Schottky barrier height and the ideality factor at small biases. For this particular measurement, we found the ideality η < 1.3, which is reasonably good given the difficulties of forming a low-impurity interface between MoS2 and graphene. We repeated the I-V measurements for gate voltages ranging between –20 V and +10 V at different temperatures from 160 K to 350 K (with ±2 K accuracy). The reverse saturation current (I0) is obtained by finding the Y-axis intercept of the log(I) vs V curves and expressed as current density, J0. Using the thermionic emission model, we express the diode current as follows:

J=J0expqVηkBT1,
(1)
J0=A*T2expqΦkBT.
(2)

Richardson's coefficient (A*) is related to the effective mass of electrons (m*) by the following equation:

A*=4πqkB2m*/h3,
(3)

where η is the ideality factor, kB is Boltzmann's constant = 1.3806 × 10−23 J/K, h is Planck's constant = 6.626 × 10−34 J s, q is the electronic charge = 1.609 × 10−19 C, while Φ is the Schottky barrier height. In this work, graphene is modeled as an equipotential semi-metallic surface with no significant drop of voltage across it, and the small voltage drop across the MoS2 film, partially overlapped by graphene for only 5 μm length, is also small especially at low injection. That is why, until the series resistance starts to dominate (diode fully on), the effect of such a small potential difference can be ignored, which is the case in the studies that follow. There are many reports on the thermionic emission model being effectively employed for different graphene/semiconductor vertical heterojunctions with a similar structure as ours, such as the ones in Refs. 8, 14, 19, and 23–25.

In Fig. 2(b), we plot ln(J0/T2) vs q/(kBT), where we show the linear fit for each gate voltage, drawn through the data points for which η was less than 1.3. For VBG = –10 V and −20 V, η < 1.2 even for the high temperature measurements, and all data points matched closely with the linear fit. However, for VBG = 0 V and +10 V, the data points at higher temperature started to show saturation behavior, and η started to rise above 1.3 quickly. This can be attributed to the series resistance that played a dominant role in limiting the current at its already high value and thus significantly increasing the ideality factor. The slope of each fitted straight line indicates Φ, which is shown in Fig. 2(d). Also, the Y-axis intercepts of these fitted lines indicate mean Richardson's coefficient A* = 80.3 ± 18.4 A/cm2/K, and the mean electron effective mass, m*/m0 = 0.66 ± 0.15, accurately describes the transport over all temperature and VBG ranges measured, supporting the starting assumption of thermionic emission [Eq. (1)]. These values are consistent with those previously reported for exfoliated MoS2 based MoS2/graphene heterojunctions and with theory (Table I).

TABLE I.

Comparison of barrier heights and Richardson coefficients with other works on the graphene/MoS2 heterojunction.

WorkA* (A/cm2/K)m*/m0Φ (eV)MoS2 preparationOxide/Substrate
This work 80.30±18.4 0.66±0.15 0.24–0.91 CVD SiO2 
Tian et al.8  … … 0.23–0.57 Exfoliated SiO2 
Kwak et al.9  … … 0.23 Exfoliated SiO2 
Peelaers et al.28  45.86–117.07a 0.38–0.97 … Theoretical … 
Yu et al.29  56.72a 0.47 … Theoretical … 
WorkA* (A/cm2/K)m*/m0Φ (eV)MoS2 preparationOxide/Substrate
This work 80.30±18.4 0.66±0.15 0.24–0.91 CVD SiO2 
Tian et al.8  … … 0.23–0.57 Exfoliated SiO2 
Kwak et al.9  … … 0.23 Exfoliated SiO2 
Peelaers et al.28  45.86–117.07a 0.38–0.97 … Theoretical … 
Yu et al.29  56.72a 0.47 … Theoretical … 
a

Calculated from m* using Eq. (3).

We also performed C-V measurements to estimate the Schottky barrier height between graphene and MoS2 and the carrier concentration of MoS2. The back-gate was used to modulate both parameters to demonstrate the barristor action, and the 1/C2 vs reverse bias (MoS2 contact used as the drain) plots are shown in Fig. 2(c). We see that the 1/C2 vs V plots are linear in the low bias ranges, which allows us to fit the curves to the following equation for an n-Schottky junction:

1C2=2qεMoS2n(ΦV)
(4)

where εMoS2 is the dielectric permittivity of MoS230 and n is the MoS2 carrier concentration. Here, we showed the effect of illumination as well, which has a significant effect on the barristor and will be discussed shortly. Using (4), we can estimate Φ and n for various back gate biases with and without illumination. We compared Φ obtained from C-V and I-V (thermionic emission model) measurements for gate voltages between −20 V and +10 V, and both measurement techniques revealed a similar correlation between Φ and VBG. For a positive gate bias, MoS2 goes into an accumulation mode, which is reflected by the increased ns along with a reduced barrier height with graphene. The opposite result is observed with the negative gate bias. The effective barrier height varied within the range of 0.24–0.91 eV, which is around ∼600 meV, showing that current control over 1010 may be possible. The presence of low intensity light (10 W/m2) lowered the barrier by about 0.04 eV for all VBG, and an increase in n was also observed [Fig. 2(c)].

The extracted barrier heights in Fig. 2 correspond to the graphene/MoS2 barrier heights only as the metal/MoS2 junction does not exhibit Schottky behavior as shown in our previous report.21 The barrier heights are calculated at subthreshold bias conditions (both C-V and I-V), which makes the contact resistance Rc (with a value of 1–4 kΩ21) negligible when compared to the junction resistance, as I × Rc gives ≤5 mV drop across the contact across all temperature ranges, well within the ±0.01 eV resolution reported for the barrier heights. We also note the good ideality of the diodes (η), where if there were a significant barrier contribution from the metal/MoS2 junction, would be significantly higher. When the graphene/MoS2 junction is forward biased (range of barrier extraction from I-V), the tunneling MoS2/metal contact is reverse-biased, where it would simply appear as a series resistance, which we exclude by extracting the barrier height in the sub-threshold exponential regime. Similarly, in the C-V measurements, where the graphene/MoS2 junction is reverse-biased, the MoS2/metal contact is forward biased. This leads to a small series resistance, confirmed by the high Q-factor (≥8), assuming a parallel conduction model for the graphene/MoS2 capacitor, showing that the metal/MoS2 contact is well behaved and does not significantly affect the extracted barrier height within the resolution reported.

Based on the above results, the band diagrams and charge balance of the barristor device are shown in Fig. 3 for VBG ≫ 0 V (a) and VBG ≪ 0 V (b). The Schottky barrier is only considered at the graphene/MoS2 junction as the metal/MoS2 junction was ohmic as shown in Ref. 21. Besides, the ideality of the diode would not be close to unity if there were two Schottky barriers in series in the system—one at the metal/MoS2 junction and the other at the graphene/MoS2 junction. The key difference between the graphene/MoS2 heterojunction and traditional Schottky structures is that the constituent materials of this junction are 2D materials and are thus very thin. This leads to incomplete screening of the back-gate induced electric field in the bottom MoS2 layer from the top graphene layer, leading to electric-field modulation in both components of the Schottky junction. Such functionality, enabled by incomplete field screening, is unique to ultra-thin material systems, most practically realized with 2D materials.13 Since the gate oxide is very thick and does not leak,21 charge neutrality must hold in the structure. From a charge-balance electrostatic analysis in the extreme cases, i.e., VBG ≫ 0 V and VBG ≪ 0 V, treating the degenerately doped Si substrate as a metal, the origin of Schottky barrier modulation can be understood. At these extreme points, much beyond the flat band voltage in either direction,21 the influence of interfacial fixed charge is minimal, simplifying the analysis, i.e., the charge in the silicon back gate completely overwhelms any fixed interfacial sheet charge in the dielectric (Fig. 3).

FIG. 3.

Band diagram of the barristor device in thermal equilibrium (VDS = 0 V), showing the Schottky barrier height (φ) for positive (a) and negative (b) gate biases. The charge balance diagrams are shown below each band diagram.

FIG. 3.

Band diagram of the barristor device in thermal equilibrium (VDS = 0 V), showing the Schottky barrier height (φ) for positive (a) and negative (b) gate biases. The charge balance diagrams are shown below each band diagram.

Close modal

For VBG ≫ 0 V, large positive mobile sheet charge in the metallic silicon, QM, is induced. This must be balanced by the negative net mirror charge in MoS2, QMoS2, and graphene, QG, i.e., QMoS2 + QM < 0. For VBG ≫ 0 V, mobile electrons are induced in MoS2 [as seen in the transfer curves in Fig. 1(b)]. Furthermore, since the applied field is incompletely screened in MoS2, the rest of the negative balance charge must be accommodated in the graphene. QG < 0 is achieved by a Fermi level above the graphene Dirac K-point in the band-diagram, similar to that described in Ref. 14. At VBG = +10 V, the electron concentration in MoS2 from C-V [Fig. 2(c)] is ∼4 × 1019 cm−3, corresponding to a Debye screening length31 of ∼0.4 nm. This means that the thickness of MoS2 is ∼3–5× the Debye length, leading to ∼90%–99% screening of the electric field from the back-gate. Thus, only a small portion of the field must be accommodated in the graphene and that is why QG is small in this case [Fig. 3(a)].

Conversely, for VBG ≪ 0 V, QM < 0 is induced, which must be balanced by QMoS2 and QG > 0. Since VBG ≪ 0 V, the electron concentration in MoS2 is reduced to n = 0.4 × 1019 cm−3 at VBG = −20 V [Fig. 2(c), C-V characteristics], corresponding to a Debye length of ∼1.2 nm which is comparable to the MoS2 thickness. It means that only ∼30%–50% of VBG is screened from the graphene. Thus, a significant portion of the mirror charge to negative QM must be accommodated in the graphene, leading to QG ≫ 0, which is achieved by a Fermi level below the graphene Dirac K-point [Fig. 3(b)].

We note that the graphene K-point, i.e., the graphene conduction band edge, does not need to shift with respect to the conduction band edge of MoS2, consistent with the general assumption in the band line-up theory32 and other reports of graphene barristors.14 Finally, the large modulation of Φ from 0.24 to 0.91 eV in this study shows the effective transmission of the electric field from the back-gate to the Schottky junction, showing that the influence of trapped charges in the dielectric is small. Larger modulation of Φ may be achieved by increasing the capacitive coupling of the gate to the Schottky junction, i.e., reducing oxide thickness, and/or using high-k dielectrics, without compromising the quality of the dielectric/semiconductor interfaces. This would enable more of the applied VBG to be transmitted to the Schottky junction, leading to greater modulation of Φ or a reduction in the range of VBG to achieve the same modulation of Φ.

Figure 4 shows the response of the device to light with an optical power of 10 W/m2 or 1 mW/cm2 from a halogen lamp with a color temperature of 3350 K and a peak wavelength of ∼800 nm, close to the MoS2 bandgap of ∼850 nm (1.45 eV).33 Electron-hole pairs are generated in MoS2 by above bandgap light, which are collected by the electric field at the Schottky junction. Three different VBG steps (–5, 0, and 5 V) were used, while the source-drain Schottky junction, VDS, was either forward biased or reverse biased at 0.6 V. The photocurrent was smaller for VDS = +0.6 V as the electric field at the forward-biased Schottky junction was reduced, reducing charge collection, while the converse was true for VDS = –0.6 V. From the C-V measurements, the built-in voltage under illumination decreased by ∼0.04 V [from the 1/C2 intercept, Fig. 2(c) and also in the supplementary material], across all ranges of VBG, indicating that the reverse leakage current of the diode increases under illumination. In this VBG range, the electron density is high enough for the conduction band and the Fermi level to be considered identical,21 indicating that the Schottky barrier changes by ∼0.04 eV as well. For example, Φ is large for VBG = –5 V and VDS = –0.1 V, leading to a decrease in the overall leakage current levels, while the opposite is true for VBG = +5 V. Using the transfer curve from I-V in Fig. 2(d) and the change in Φ estimated from the C-V curves in Fig. 2(c), the expected change in IDS can be predicted and is consistent with the photocurrents actually measured in Fig. 4 (please refer to the supplementary material for more details). Thus, the photocurrent difference due to the variation in VDS can be attributed to the changes in charge collection, whereas that due to the changes in VBG is caused by the variations in reverse leakage in the thermionic emission phenomenon [Equations (1)–(3)], which give opposing photo-response trends.

FIG. 4.

Photoresponse of the barristor device at different gates and drain bias voltages.

FIG. 4.

Photoresponse of the barristor device at different gates and drain bias voltages.

Close modal

The responsivity was estimated by accounting for the device area, i.e., by using the optical power incident on the 5 × 100 μm2 device, and the total measured photocurrent. This gave a peak responsivity of ∼20 A/W at VBG = 10 V and VDS = –0.6 V. Even 100% external quantum efficiency would correspond to a responsivity of ∼0.2 A/W, which indicates that there is gain in this device. Moreover, due to the very thin layers, only a fraction of the incident light will be absorbed, providing further evidence of internal gain. Given the slow response time of this device, ∼10 s, the high optical responsivity is likely due to the photoconductive gain in the Schottky junction,34 as an RC limited response time of <1 ms would have been expected (Fig. 2). Photoconductive gain is also supported by C-V [Fig. 2(c)], where the majority carrier concentration increases under illumination. The good ideality and the photoconductive gain can be explained by the interfacial traps that pin the Fermi level of graphene, and this phenomenon often leads to an ideality of ∼1, as seen, for example, in Ge Schottky diodes.35 The defects at the interface that pin the Fermi level can be responsible for trapping an electron or a hole, leading to photoconductive gain. In our devices, we hypothesize that holes are trapped at the interface, lowering the barrier, injecting many electrons from the contact for each trapped hole. The barrier lowering for electrons under illumination is seen in the C-V characteristics clearly, which is where our hypothesis originates from. This photoconductive effect leads to internal gain. There are many examples of such internal gain in Schottky diode photodetectors.36–38 

In summary, we have demonstrated a graphene/MoS2 barristor on an n+ Si/SiO2 substrate using a transfer-free method of growing MoS2, with barrier height modulation from 0.24 to 0.91 eV, potentially enabling current control over 10 orders of magnitude at room temperature. Through careful capacitance measurements, we show quantitatively that the incomplete screening of an electric field from the degenerately doped Si back-gate through the MoS2 leads to the modulation of the Schottky barrier height at the graphene/MoS2 interface through capacitive coupling to the gate. The optical response of the barristor is consistent with the changes in the Schottky barrier height caused by the back-gate.

See supplementary material for the details of the carrier concentration and barrier height modulation from I-V and C-V measurements and the estimation of photocurrent from dark current.

Financial support for this work from the National Science Foundation (Grants Nos. ECCS 1559711, ECCS 1309466, and CBET 1606882) is thankfully acknowledged.

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