Introduction

The two-dimensional (2D) layered materials such as graphene and semiconducting transition-metal dichalcogenides (TMDs) can exhibit peculiar electronic properties depending on their exact composition, thickness and geometry1,2,3,4,5. Furthermore, the broad possibility to combine different materials in van der Waals heterostructures (vdWHs) can create a new paradigm in materials science with unprecedented flexibility to integrate highly disparate materials and enable unique functions, as exemplified by the recent demonstration of vertical tunnelling transistors and vertical field-effect transistors for ultra-thin and flexible devices6,7,8,9,10,11,12,13 Graphene/multi-layer (ML)-TMD/graphene stack has also been shown to function as a unique photodiode for photocurrent generation or photodetection7,12. With a direct band gap in monolayer TMD and ultra-fast carrier transfer (∼1 ps) rate14, vdWHs with ultra-thin TMDs have attracted considerable interest for photovoltaic applications15,16 and ultra-fast photodetection17. However, classical charge transport theory for bulk semiconductors was often employed to interpret the electron transport in ultra-thin vdWHs even though it is well expected to exhibit completely different photocurrent generation characteristics7,12. Notably, an atomically thin graphene/WSe2/MoS2/graphene p–n heterojonction has been investigated for photocurrent generation. However, Shockly–Read–Hall recombination and Langevin recombination in the WSe2/MoS2 p–n junction could compromise the carrier extraction performance13. The unique characteristics of ultrathin vdWHs are insufficiently explored to date. In particular, a systematic investigation of layer-number-dependent studies is lacking due to complications from highly variable nature of the van der Waals interfaces and extrinsic factors in creating vdWH devices.

Here we report a layer-number-dependent photocurrent generation in graphene/MoS2/graphene vdWHs by creating a device with two distinct regions containing one-layer (1L) and seven-layer (7L)-MoS2 to exclude extrinsic device factors. Significantly, we discover a surprisingly higher photoresponsivity and internal quantum efficiency (IQE) by going from ML MoS2 device to a monolayer device. The discretized electrostatic potential barriers were introduced to interpret the photocarrier tunneLling and extracting in ultrathin vdWHs.

Results

Photocurrent generation in graphene /1L-MoS2/graphene stack

Figure 1 shows the schematic illustration of graphene/1L-MoS2/graphene heterostructure device on Si/SiO2 substrate. A focused laser was used to generate electron-hole pairs in the MoS2 layer, which can be separated by the asymmetric potential between the top graphene (GrT)/MoS2 and the bottom graphene (GrB)/MoS2 junction to produce photocurrent (Fig. 1a). Figure 1b shows an optical image of a typical graphene/1L-MoS2/graphene vdWH device. The 8 μm strip of GrB is located below 1L-MoS2 flake (vertical strip). The GrT layer is located directly on the MoS2 flake (horizontal strip) to overlap with MoS2 flake and the GrB.The photocurrent generation in our devices was mapped by scanning photocurrent microscopy, where a focused laser beam was raster-scanned over the sample, while the photocurrent was being measured (Fig. 1c). The spatially resolved photocurrent map reveals pronounced photocurrent generation in the overlapping region in the vertical stack. The current–voltage (Ids–Vds) data obtained in the dark (blue line, Fig. 1d) and under 514 nm laser irradiation (red line, Fig. 1d) show a clear photoresponse in the vdWH. In contrast to typical diode characteristics observed in graphene/ML-MoS2/metal vdWHs due to asymmetric contact between top and bottom junction7,12, a linear transport curve is observed in the graphene/1L-MoS2/graphene heterostructure device, which can be attributed to direct tunnelling (IDT) through ultrathin tunnelling barrier of 1L-MoS2

Figure 1: Photocurrent generation in the vertical heterostructure of graphene/monolayer MoS2/graphene stack.
figure 1

(a) A schematic illustration of the side view of the device, with a monolayer MoS2 sandwiched between the top (GrT) and bottom (GrB) graphene electrodes. Hole (red particle) and electron (blue particle) are generated in the monolayer MoS2 layer by 514 nm laser and transferred to top and bottom graphene electrodes. (b) Optical image of the vertical heterostructures with monolayer MoS2 sandwiched between the top (GrT) and bottom (GrB) graphene electrodes. The scale bar is 4 μm. (c) Scanning photocurrent image taken under a 514 nm laser with an excitation power of 400 μW and a spot size of 1 μm. The dotted and solid lines indicate the edge of the bottom and top graphene electrodes, respectively. (d) I-V characteristics of the device under laser illumination of 514 nm laser (red line) and dark (blue line). (e) Photoresponsivity of 1L-MoS2 heterostructures in various illuminated photon energies.

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where Aeff, ϕB, q, m, m, d and h are effective contact area, barrier height, electron charge, free electron mass, effective electron mass, barrier width (MoS2 thickness) and Plank’s constant, respectively18.

Based on the photocurrent response and input laser power, we can determine the photoresponsivity (A W−1) of the device. The photoresponsivity of 1L-MoS2 increases with decreasing the laser power could be attributed partly to absorption saturation in MoS2 and partly to the screening of a built-in electric field by the excited electrons in the conduction band of MoS2 (ref. 7). Importantly, the photoresponsivity of 1L-MoS2 increases with increasing the laser wavelength and a maximum photoresponsivity of 68 mA W−1 in 1L-MoS2 vdWHs was achieved at the wavelength of 633 nm and the laser power of 100 nW (Fig. 1e), which exceeds that of previous studies on graphene/ML-MoS2/graphene vdWHs device (∼30 mA W−1 without plasmonic enhancement)7,12. This performance difference is attributed to the number of layer difference between this work (monolayer MoS2) and previous reports (5∼30 nm MoS2), which will be further discussed by comparison of external quantum efficiency (EQE) and IQE between 1L-MoS2 and 7L-MoS2 vdWHs in Fig. 2g,h.

Figure 2: Comparison of photocurrent generation in monolayer and ML MoS2 heterostructures.
figure 2

(a) Optical image of the 1L MoS2 vertical heterostructures with partially 7L MoS2 sandwiched between the GrT and GrB electrodes. The dotted line and solid lines indicate the edges of the GrB and GrT electrodes, respectively. Scale bar, 5 μm. (b) The PL image of the same device. (c) Scanning photocurrent image of the same device taken under a 514 nm laser with an excitation power of 400 μW and a spot size of 1 μm. Dashed line indicates the boundary of 1L- and 7L-MoS2.

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Quantum efficiency between 1L-MoS2 and 7L-MoS2

To further unambiguously illustrate the difference between monolayer and ML MoS2 device, we have created a vdWH device with two distinct regions with 1L- and 7L-MoS2 in the same device (Fig. 2a). The 8 μm strip of GrB is located below the MoS2 flake (inside the dotted line) and the GrT layer is located directly above the MoS2 flake (inside the solid line), to overlap with MoS2 flake and the GrB. The number of layers of MoS2 was then confirmed by Raman spectra measurements (Supplementary Fig. 1) and atomic force microscopic measurement. Figure 2b display the photoluminescence (PL) mapping image of 1L-MoS2 and 7L-MoS2 portion in Fig. 2a under an excitation wavelength of 532 nm (2.33 eV). The monolayer-MoS2 exhibited a much stronger PL compared with 7L-MoS2, which is consistent with the direct band gap nature of 1L-MoS2 (band gap ∼1.82 eV)15,16 and the indirect band gap nature of 7L-MoS2 (band gap ∼1.3 eV)16. Two prominent PL peaks can be identified at 630 nm (1.96 eV) and 680 nm (1.82 eV) in the spectrum (Supplementary Fig. 2), corresponding to A1 and B1 direct excitonic transitions15.

The photocurrent map of the entire device clearly demonstrates that 1L-MoS2 region exhibited much more pronounced photocurrent than the 7L-MoS2 region (Fig. 2c). The current–voltage (Ids–Vds) data obtained in the dark (black line, Fig. 3a) and under 514 nm laser irradiation (red line for 1L-MoS2 region and blue line for 7L-MoS2 region; Fig. 3a) show a clear photoresponse in the vdWH. The open-circuit voltage and a short-circuit current obtained in the 1L-MoS2 region are 110 mV and 0.8 μA, both about one order of magnitude higher than those observed in the 7L-MoS2 (10 mV and 0.08 μA, respectively). This is a rather surprising and counter-intuitive discovery, considering that the 7L-MoS2 should have significantly higher optical absorption than 1L-MoS2 (Fig. 3b and Supplementary Note 1).

Figure 3: Quantum effieciency between monolayer and ML MoS2 heterostructures.
figure 3

(a) Ids–Vds characteristics of the device under laser illumination of 514 nm laser (red line for 1L-MoS2, blue line for 7L-MoS2) and dark (black line). (b) Absorption spectra of a 7L-MoS2 flake (red line) and 1L-MoS2 flake (black line). (c) Calculated imaginary part of the dielectric function (k2) of 1L- and bulk MoS2 (as a model for thick ML). The effective thickness for the 1L-MoS2 was taken to be the inter-layer separation in ML-MoS2. (d) EQE of 1L-MoS2 stack and 7L-MoS2 stack at a laser power of 100 μW. (e) Photon energy dependence of IQE at a laser power of 100 μW (black line: 1L-MoS2; red line: 7L-MoS2). (f) Calculated density of states of 1L- and ML-MoS2.

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The enhanced photoresponsivity of 1L-MoS2 may be attributed to two potential factors: higher photocarrier generation rate in the monolayer MoS2 and higher photocarrier extraction/collection efficiency. We will discuss the influence of each factor below, first by modelling the transition probability and subsequently by comparing the internal and external quantum efficiencies. These two lines of reasoning will show that at peak IQE (633 nm and 1.96 eV), the second factor (that is, the improved collection) dominates in our device.

In general, the spectral dependence of the photocarrier generation rate can be estimated from first principles, using the Fermi golden rule. The probability of transition from a valence band state (υ) to a conduction band state (c) is thus given (in 2D) by

where k2 is the imaginary part of the dielectric function, ħ is the plank constant, ω is the frequency of the incident radiation, me and q are the electron mass and charge. In MoS2, k2 diverges because the conduction and valence bands run nearly parallel in some regions of the reciprocal space (that is, band nesting19). This can be noticed in Fig. 3c where we compare the imaginary part of the dielectric function, obtained from relativistic first-principles calculations, for 1L and thick multilayer (bulk) MoS2. Thus, W increases with the excitation energy up to the energy of the first peak, which is at ∼2.4 eV for the bulk and 2.8 eV for the monolayer, respectively19. The effect of band-nesting is more pronounced in monolayer, because this system is closer to the 2D limit and is responsible for a raise in the absorption coefficient in that spectral region.

To separate the effects of enhanced photon absorption from carrier collection, we have also conducted the photocurrent studies under difference excitation photon energies and determined the corresponding EQE (, as defined by the number of carriers produced per incident photon20). The wavelength-dependent studies indicate the EQE of 1L-MoS2 increases with decreasing photon energy and can reach as high as 2.5% at 633 nm (1.96 eV; Fig. 3d), whereas the EQE of 7L-MoS2 maintains a relatively low value of 0.3–0.4% throughout the entire measured wavelength range (Fig. 3d). Thus, the increased EQE does not follow the trend of k2 that increases with increasing photon energy. This indicates that the enhanced absorbance is not the primary factor responsible for the maximum EQE. Other factors such as carrier collection should be considered.

Further insight is given by the IQE, which can be obtained by dividing the EQE by the optical absorbance of 7L- and 1L-MoS2 (Fig. 3e). Importantly, the maximum IQE in 1L-MoS2 can reach up to 65%, far exceeding to IQE in 7L-MoS2 (<7%). It is also noted that the IQE in 1L-MoS2 region steadily increases when the photon energy is reduced to approach the bandgap of 1L-MoS2 (1.82 eV (ref. 15)). The highest IQE reached ∼65% at 633 nm (1.96 eV), very close to the optical absorption edge of 1L-MoS2 (1.82 eV). It is noteworthy that in this region k2 is nearly independent on the thickness. According to the theoretical calculations, 1L-MoS2 has a much larger density of states near the band edges, at the valence band top due to the heavier hole masses, and near the conduction band edge, due to the presence of the 2D van-Hove singularities (Fig. 3f), increasing the probability of transfer to the graphene electrodes.

Photocarrier extraction mechanism

Photocarrier transport in bulk MoS2 is driven by diffusion and drift process, which is dictated by different band bending at GrT and GrB MoS2 interface (originated from the difference of GrT and GrB doping densities)7,12 (Supplementary Fig. 3a). The photo-carrier extraction in atomically thin vdWHs is predicted to be completely different from that in bulk heterojunctions. Unlike bulk MoS2 having a continuous band bending (Supplementary Fig. 3a), atomically thin vdWH has discrete energy states in the vertical direction (Supplementary Fig. 3b). The classical semiconductor charge transport model—the charge drifts downhill following the band slope—cannot describe photocurrent generation phenomena via such discrete energy states in vdW heterojunctions. To this end, we introduce a tunnelling transport model to describe the photocarrier tunnelling through electrostatic potential barriers formed at the atomically thin vdW heterojunctions. Electrostatic potential barriers of 1L-MoS2 heterostructures are calculated by density functional theory (DFT; Supplementary Fig. 4 and Supplementary Note 2). Large electrostatic potential barriers are discretely constructed between GrT/GrB and MoS2 interface. The barrier heights at the top and bottom junctions are symmetric because of symmetric environmental conditions imposed in the DFT calculations. In real device, the different environmental conditions of GrT and GrB result in asymmetric doping between GrT and GrB. Doping characteristics of GrT and GrB were confirmed by 2D peak shift in Raman spectrum of another graphene/1L-MoS2/graphene heterostructure device (Supplementary Fig. 5 and Supplementary Note 3). With n- or p-type doping, the 2D Raman band exhibits a red or blue shift, respectively. In our device, the GrT is more p-type doped than GrB. Such doping difference generates internal field, leading to asymmetric barrier height between top and bottom junctions (Supplementary Fig. 6). In this way, the photo-excited electrons can effectively tunnel to lower barrier at GrT/MoS2 interface, whereas higher barrier at GrB/MoS2 interface can block the electron tunnelling. Asymmetric tunnelling to top and bottom barrier thus generates photocurrent in vdWH device. It is noteworthy that the delta-function potential barriers for hole carriers are formed at the graphene/MoS2 interface, allowing hole tunnelling from MoS2 to GrB by built-in electric field21.

Furthermore, the different dielectric environment at the GrT and GrB /MoS2 interface can significantly alter the electrostatic potential. Figure 4a shows the schematic illustration of the dielectric environment of the device. The GrB is sandwiched between SiO2 substrate and 1L-MoS2, and the GrT between 1L-MoS2 and air. The dielectric constant of GrB (4.2) and GrT (2.7) are determined by the standard approximation of ɛGrB=(ɛ1L-MoS2+ɛSiO2)/2=4.2 and ɛGrT=(ɛ1L-MoS2+ɛair)/2=2.7, respectively22,23, where ɛ1L-MoS2=4.5 (ref. 24).

Figure 4: Electrostatic potentials of monolayer MoS2 heterostructure under different environments and photocarrier extraction mechanism.
figure 4

(a) Schematic images of graphene/1L-MoS2/graphene heterostructures with SiO2 substrate and air environment. Dielectric constant of each layers is indicated in brackets. (b) Electrostatic potentials of graphene/1L-MoS2/graphene heterostructures including environmental condition (Supplementary Note 3). Green coloured areas are the potential energy barriers. Ef is the Fermi level of graphene. CB, VB and Eg are conduction band, valence band and band gap of MoS2, respectively. (c) Electrostatic potentials near the conduction band of 1L-MoS2 heterostructures with three different potential barrier states. (d) Schematic images of photo-carrier tunnelling probabilities at the three different potential barrier states. (e) Calculated photocarrier extraction rate (I=(TT–TB)/(TT+TB)).

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The calculated electrostatic potentials with these dielectric constants are shown in Fig. 4b,c (calculation is shown in Supplementary Note 4)25. Asymmetric electrostatic barriers are formed between the bottom (∼3.5 eV) and top (∼4.05 eV) junctions (Fig. 4b,c). The photocarrier extraction rate (I) can be determined by the difference of electron tunnelling probabilities between bottom and top junction barriers, which is normalized by the sum of tunnelling probability to top (TT) and bottom junction barrier (TB) (I)=(TT–TB)/(TT+TB)). The potential barrier was sliced to thin square barriers with width of 0.01 nm and then the tunnelling probability was calculated through overall square barriers (Supplementary Fig. 7).

Based on this model, the photocarrier extraction rate (I) strongly relies on the excitation photon energy (Fig. 4c,d). The tunnelling behaviour of excited electrons can be separated to three states, depending on the energy of excited electron, fully confined between TT and TB, partially confined at the TB and no confinement.

For fully confined between TT and TB (Fig. 4d–i), the excited electrons in MoS2 can be transported to GrT and GrB by tunnelling through both sides of the potential barriers. The tunnelling probabilities through TT or TB is defined to (ref. 26), where a is energy barrier width, m* is electron effective mass, U is electrostatic barrier, E is kinetic energy of electron and h is the Planck’s constant. The top junction allows for higher tunnelling probability due to smaller barrier height compared with the bottom junction. Consequently, electrons can transfer to the GrT with positive I. The photocarrier extraction rate (I) is not altered appreciably in response to the energy of excited electrons (or absorbed photon energy), because effective barrier height (U–E) of the bottom and top junction changes by the similar magnitude (Fig. 4e–i).

For partially confined at the TB (Fig. 4d–ii), the barrier at the bottom junction is higher than the kinetic energy of excited electrons. The tunnelling probability to TB can be defined by . On the other hand, the barrier at the top junction is lower than the energy of excited electron. The excited electrons transfer to GrT over the barrier with a tunnelling probability of , where , , where UCB is conduction band minimum of MoS2 (refs 21, 26). The tunnelling probability through TB increases with increase electron excitation energy (E) because of the decrease of effective barrier height (U–E), whereas the tunnelling probability to the TT remains almost at 1 regardless of the electron energy. Consequently, the photocarrier extraction rate (I) decreases in proportion to electron excitation energy (Fig. 4e–ii).

For no confiment case (Fig. 4d–iii), both TB and TT heights are lower than the energy of excited electrons; therefore, the tunnelling probability to TT and TB are defined by . The photocarrier extraction rate (I) decreases in proportion to the electron excitation energy (or absorbed photon energy; Fig. 4e–iii).

MoS2 layer-dependent electrostatic potentials

The electrostatic potentials were calculated in terms of the number of MoS2 layers (Fig. 5). The region of fully confined between TT and TB case is expanded in response to the number of MoS2 layers due to the increased barrier heights at both sides. On the other hand, the region of partially confined at the TB case is shrunken when the number of MoS2 layers increases due to the reduction of barrier height difference at both junctions. The region of no confinement case is also shrunken by increased barrier heights at both sides. Electrostatic potential is saturated over the 7L-MoS2 and behaves as bulk MoS2. The photocarrier extraction rates (I) were calculated in terms of the electrostatic potentials.

Figure 5: MoS2 layer-dependent electrostatic potentials of vdWHs.
figure 5

(a) MoS2 layer-dependent dielectric constant of MoS2, GrT and GrB. (b–h) MoS2 layer-dependent electrostatic potentials of vdWHs. (i) Schematic images of graphene/7L-MoS2/graphene heterostructures with SiO2 substrate and Air environment. Dielectric constant of each layers are indicated in brackets.

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Calculated photocarrier extraction rate

The carrier lifetime in direct gap (1L-MoS2) is shorter than that of indirect gap (7L-MoS2), which should be taken into account in recombination process during carrier drift. We have measured the carrier lifetime in direct gap (1L-MoS2) and indirect gap (7L-MoS2) based on transmission change in pump–probe measurement (Fig. 6a) and then calculated the normalized excited carriers (δnx) by initial excited carriers (δ0) for 1L-MoS2 (direct gap, red line) and ML-MoS2 (indirect gap, black line) along with carrier drift distance (nm; Fig. 6b and Supplementary Note 5). The normalized excited carrier density was then multiplied with photocarrier extraction rate (I) to clarify recombination difference in ML-MoS2. The 1L-MoS2 shows ultra-fast carrier transfer (∼1 ps) rate into graphene layer, much shorter than carrier lifetime in 1L-MoS2 (60 ps), resulting in highly efficient transfer of photo-excited carriers in MoS2 into graphene before recombination. Therefore, we multiplied photocarrier extraction rate (I) in 1L-MoS2 by 100% of normalized excited carrier density. Figure 6c clearly reveals that the photocarrier extraction rate (I) reaches around 65% when the number of MoS2 layers is reduced from 7L-MoS2 to 1L-MoS2 and the photon energy approaches the bandgap (1.82 eV). The calculated I are in good agreements with measured IQE of 1L-MoS2 (black dashed line in Fig. 6d) and 7L-MoS2 heterostructures (red dashed line in Fig. 6d).

Figure 6: Calculated photocarrier extraction rate of vDWHs with various number of MoS2 layers.
figure 6

(a) Normalized dynamics of differential transmission (ΔT/T0) of 1L-MoS2 and 7L-MoS2 for pump fluence (dots) and fitting lines. ΔT is the pump-induced probe transmission change and T0 is the probe transmission without pump excitation for pump fluence. The decay lifetime of 1L-MoS2 (τmono) and 7L-MoS2 (τmulti) obtained from the fitting. (b) Normalized excited electron carriers (δnx) by initial excited electron carriers (δn0) for direct gap MoS2 (black line) and indirect gap MoS2 (red line) along with carrier drift distance (nm). (c) 2D colour plot of photocarrier extraction rate as a function of the number of MoS2 layers and photon excitation energy. (d) Photon energy dependence of IQE (black dots: 1L-MoS2; red dots: 7L-MoS2) and calculated photocarrier extraction rate (black dashed line: 1L-MoS2; red dashed line: 7L-MoS2).

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I–V characteristics

Previous studies have demonstrated an external gate voltage can be used to effectively modulate the Fermi energy of graphene and thus the potential offset and the driving force for carrier separation in graphene/MoS2/graphene devices7,12. We have also investigated gate voltage dependency of dark current (Supplementary Fig. 8) and photocurrent generation (Fig. 7) in the 1L-MoS2 and ML MoS2 heterostructures. Overall, the 1L-MoS2 device showed considerably smaller modulation of short circuit current (Isc) and open circuit voltage (Voc) by an external gate voltage (Fig. 7a) than that of ML-MoS2 (Fig. 7b). To understand the weak gate modulation in graphene/1L-MoS2/graphene device, the band diagram of the 1L-MoS2 and ML-MoS2 devices at the positive and negative gate voltage are calculated (Supplementary Fig. 9 and Supplementary Note 6) and schematically illustrated in Fig. 7c,d. It is noted that the electrostatic screening of the GrB layer is dependent on its carrier concentration, which can be varied by applied gate voltage. This factor is considered in the simulation and schematics. In general, the gate voltage can more efficiently modulate the GrB EF than GrT EF due to the partial screening of the gate field by the GrB layer and sandwiched MoS2 layers. The larger gate modulation of the TB than TT can create additional potential offset or band slope that leads to change in Voc. In the ML-MoS2 device, the gate electric field primarily modulates the Fermi level (EF) of the GrB due to the relatively strong electrostatic screening by ML-MoS2 (Fig. 7d), leading to a large modulation of the band slope in ML-MoS2 and thus a substantial modulation of the Voc and photocurrent. In contrast for the monolayer device, the gate electric field can effectively modulate both bottom and GrT EF because of much weaker screening effect by the ultra-thin 1L-MoS2 (Fig. 7c). As a result, both top and bottom potential barrier are modulated together in the graphene/1L-MoS2/graphene device, leading to much smaller dependence of potential offset and photocarrier extraction rate on the gate voltage.

Figure 7: I–V characteristics of monolayer and ML MoS2.
figure 7

(a,d) I–V characteristics of (a) graphene/1L-MoS2/graphene and (b) graphene/ML MoS2 (50 nm)/graphene under laser illumination of 514 nm laser and dark (black line, Vg=0 V). Schematic band diagram for (c) graphene/1L-MoS2/graphene and (d) graphene/ML MoS2/graphene at the negative Vg (dashed line) and positive Vg (solid line).

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Discussion

In summary, we have reported an unusually efficient photocarrier generation from monolayer MoS2 in graphene/MoS2/gaphene vdWHs. Owing to intrinsically slow layer-to-layer charge transport in TMD materials, the carrier mobility in the vertical direction is usually several orders of magnitudes lower than that in lateral direction, which can seriously slow down the charge separation process in the vertical heterostructures, leading to undesired photocarrier recombination in MoS2 before they arrive at the current collector. Importantly, we show that this drawback can be largely overcome by using atomically thin MoS2 to enable an unusually high photoresponsivity up to 68 mA W−1 with 65% of IQE in monolayer MoS2. This was congruent with carrier tunnelling through asymmetric electrostatic potential barriers that exist discretely in vdWHs with monolayer MoS2. Conversely, the symmetric potential barrier in ML MoS2 reduces photocurrent via carrier tunnelling. The proposed quantum mechanical-based tunnelling mechanism provides a new theoretical framework to understand van der Waals interaction in vdWHs and to design the next generation of atomically thin optoelectronics including photodetectors and photovoltaic devices. It is noteworthy that the 2.5% EQE achieved in our graphene/1L-MoS2/graphene devices are comparable to the 2.4% value achieved in graphene/1L-WSe2/1L-MoS2/graphene p–n heterojonctions. Considering the absorbance in two layers stack (MoS2/WSe2) is approximately twice of that in single layer (MoS2), the IQE in our device is about twice higher. The lower IQE in in graphene/1L-WSe2/1L-MoS2/graphene p–n heterojunctions may be partially attributed to Shockly–Read–Hall recombination and Langevin recombination, which is not present in graphene/1L-MoS2/graphene devices.

Methods

The fabrication of the vertical heterostructures

For the fabrication of the vertical heterostructures of graphene/MoS2/graphene device, the graphene was grown with a chemical vapour deposition process27,28 and transferred onto Si/SiO2 (300 nm SiO2) substrate, and patterned into 8 × 30 μm strips as the bottom electrode using a photolithography and oxygen plasma etching process. The MoS2 flakes were then transferred onto the graphene strips through a dry transfer approach27. The GrT electrode was transferred and patterned on the MoS2 flake and GrB. Directly overlapping graphene area was patterned and etched away, to avoid short circuit between the GrT and GrB. The metal electrode, for probe contact or wire bonding purposes, was patterned on the bottom and GrT electrodes by e-beam lithography followed by e-beam deposition of Ti/Au (50/50 nm).

Microscopic and electrical characterization

Electrical transport measurements were conducted with a probe station and a computer-controlled analogue-to-digital converter at room temperature. The scanning photocurrent measurements were conducted with the same electrical measurement system under a SP2 MP Film confocal microscope coupled with Ar/ArKr laser (wavelength 458, 476, 488, 496 and 514 nm) and HeNe laser (543, 596 and 633 nm). All optical measurements were carried out under ambient conditions at room temperature by using an inverted microscope coupled to a grating spectrometer with a charge-coupled device camera. The optical beams were focused on the sample with a spot diameter of ∼1 μm. MoS2 heterostructures were excited with a cw solid-state laser at a wavelength of 405 and 532 nm. A low laser power of ∼100 μW was used to avoid heating and PL saturation. The PL of MoS2 samples were calibrated by using rhodamine 6G molecules as the standard. Raman spectroscopy (RM1000 microprobe; Renishaw) was used to characterize the MoS2 and graphene with a wavelength of 514 nm (2.41 eV) and a Rayleigh line rejection filter. As Raman scattering efficiency has usually little layer thickness dependence, the PL spectra normalized by Raman intensity reflects directly the luminescence efficiency16.

The DFT calculations

The DFT calculations were performed using the Quantum ESPRESSO code29. Geometry optimizations and total energy calculations are non-relativistic. Bandstructures calculated using a fully relativistic formalism are obtained using the atomic coordinates optimized in a similar non-relativistic calculation. The core electrons were described by norm-conserving, full relativistic pseudopotentials28 with nonlinear core-correction and spin–orbit information. The exchange correlation energy was described by the generalized gradient approximation, in the scheme proposed by Bueke et al.30. The energy cutoff was 50 Ry.

The monolayer was modelled using a supercell consisting of 4 × 4 unit cells of the monolayer material, comprising a total number of 48 atoms. The lattice parameter (a) used was optimized for the primitive unit cell. The supercell length along the direction perpendicular to the plane c is taken to be twice the lattice parameter, except for preliminary bandstructure calculations performed using a smaller c, which are identified in the text. The Brillouin zone was sampled using a 2 × 2 × 1 Monkhorst–Pack grid31.

The 7L material was modelled as a bulk crystal, using a 4 × 4 × 1 supercell. The in-plane lattice parameter was taken from the monolayer calculation and the c/a ratio was taken from experimental data32.

Ultrafast optical pump–probe spectroscopy

The femtosecond laser source is based on a 250 kHz Ti:sapphire regenerative amplifier (Coherent RegA 9050), which provides a 1.55 eV photon energy, 50 fs pulse width and 6 μJ per laser pulse. The Reg A output pulse is separated into two pulses by a ratio of 7:3. The 70 % laser pulse is used to generate 3.1 eV pump–photon energy by second harmonic generation in a 1 mm-thick beta barium borate crystal. The other 30% laser beam is focused in an ultra-clean sapphire disk to generate a white-light super-continuum, which serves as a probe pulse. Both the pump and the probe pulses are focused on the 1L-MoS2 and 7L-MoS2 samples by an objective lens (Mitutoyo M Plan Apo × 10) and the delay between the two pulses is controlled by a mechanical delay stage (Newport M-IMS300PP).

Data availability

The data that support the findings of this study are available from the corresponding author upon request.

Additional information

How to cite this article: Yu, W. J. et al. Unusually efficient photocurrent extraction in monolayer van der Waals heterostructure by tunnelling through discretized barriers. Nat. Commun. 7, 13278 doi: 10.1038/ncomms13278 (2016).

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