Strong light-matter interactions in heterostructures of atomically thin films 
L. Britnell1, R. M. Ribeiro2,3, A. Eckmann4, R. Jalil5, B. D. Belle5, A. Mishchenko1, Y.-J. Kim1,6, R. V. Gorbachev1, T. Georgiou1, S. V. Morozov7, A. N. Grigorenko1, A. K. Geim5, C. Casiraghi4,8, A. H. Castro Neto2? , K. S. Novoselov1
1School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
2 Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546.
3 Departamento de F?sica and Centro de F?sica, Universidade do Minho, P-4710-057, Braga, Portugal.
4School of Chemistry and Photon Science Institute, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
5Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
6Department of Chemistry, College of Natural Sciences, Seoul National University, Seoul, 151-747, Korea
7Institute for Microelectronics Technology, 142432 Chernogolovka, Russia.
8Department of Physics, Freie University, Berlin, 14195, Germany.
Abstract
The isolation of various two-dimensional (2D) materials, and the possibility to combine them in vertical stacks, has created a new paradigm in materials science: heterostructures based on 2D crystals. Such a concept has already proven fruitful for a number of electronic applications in the area of ultrathin and flexible devices. Here we expand the range of such structures to photoactive ones by utilizing semiconducting transition metal dichalcogenides (TMDC)/graphene stacks. Van Hove singularities in the electronic density of states of TMDC guarantees enhanced light-matter interactions, leading to enhanced photon absorption and electron-hole creation (which are collected in transparent graphene electrodes). This allows development of extremely efficient flexible photovoltaic devices with photo-responsivity above 0.1 A/W (corresponding to an external quantum efficiency of above 30%). 
The advent of graphene  and subsequent discovery of its multitude of superior properties  has led to the identification of many other two-dimensional (2D) crystals  through both chemical modification of graphene and exfoliation of other layered compounds. This new area of research and progress in precise transfer of the crystals whilst maintaining their quality  has resulted in the emergence of a new class of materials: heterostructures based on 2D atomic crystals . More specifically, there is the possibility to create hybrid materials, by stacking combinations of 2D crystals with differing properties. These structures are interesting from both fundamental and application points of view. It has, for instance, been shown that layering sheets of graphene and hexagonal boron nitride (hBN), molybdenum disulfide (MoS2) or tungsten disulfide (WS2) allows operation of tunneling transistors  and permitted the observation of phenomena such as Coulomb drag  and the fractional quantum Hall effect .
Many other crystals have been found to exfoliate to monolayer by both mechanical  and chemical methods . TMDC is a group of layered materials that has attracted a lot of interest . They are structured such that each layer consists of a three atomic planes: a triangular lattice of transition metal atoms sandwiched between two triangular lattices of chalcogen atoms (S, Se, or Te). There is strong covalent bonding between the atoms within each layer and predominantly weak van der Waals bonding between adjacent layers. Many of these materials? NbSe2, MoS2, WS2, TaS2 to name a few?are structurally similar but have an array of electronic properties ranging from semiconducting , to metallic , from charge density waves to superconducting , depending on their exact composition, electronic density, geometry, and thickness . 
Besides the traditional applications of TMDC films as solid state lubricants and industrial surface protection , films of these materials have long been considered for photovoltaic devices, due to their large optical absorption, which is greater than 107 m-1 across the visible range, meaning that 95% of the light can be absorbed by a 300 nm film. A further advantage of WS2 is its chemical stability  and band gaps in the visible part of the spectrum . 
Previously, planar WS2  and MoS2  structures were studied for photovoltaic applications. However, efforts to extract photocurrent have been hampered by the need to create a p-n junction to separate the electron-hole (e-h) pairs, created by incoming photons. Here we show that, with the arrival of vertical 2D-crystal based heterostructures, a beneficial combination of each material?s properties emerges: TMDC as good photoactive materials and graphene as a good transparent electrode. Using a Gr/TMDC/Gr stack (here Gr stands for graphene) with appropriately positioned Fermi levels and simply doping the two graphene layers differently (either by electrostatic gating or chemical methods) leads to large photocurrent. The layered nature of our structures and exceptional mechanical strength of graphene and TMDC crystals  also allowed us to fabricate flexible devices. Without illumination, such devices act as tunneling transistors .
While we concentrate the experimental data on the properties of Gr/WS2/Gr heterostructures, our results are generic for a large class of systems where semiconducting TMDC are the key element. 
Our devices comprise of three principal elements?top and bottom graphene electrode layers (both micro-mechanically cleaved and CVD-grown graphene were tested) sandwiching a photoactive TMDC layer (Fig. 1). In the fabrication procedure, the flakes were transferred with the ?dry transfer? technique (in the case of micro-mechanically cleaved graphene)  with thorough annealing  at each stage to ensure minimal contamination between the layers  and low level doping of the graphene layers. We also chose to use hBN as both a substrate and an encapsulating layer to achieve a higher doping homogeneity . Thus, the final structure of a typical device, on top of an oxidized silicon wafer or flexible PET film, was hBN/Gr/WS2/Gr/hBN. In case of non-flexible devices on Si/SiO2, the doped silicon could be used as a back gate and SiO2/hBN (typically 300nm of SiO2 and 20nm of hBN) the gate dielectric. A series of such structures was produced where the thickness of the TMDC layer was varied from ~5-50 nm. 
The IV characteristics of our samples strongly depended on illumination (Fig. 2A, left axis). Without illumination, the devices displayed strongly non-linear IV curves (Fig. 2A, right axis). Comparing the two sets of IV curves, there is strong contrast to when they were illuminated: the resistance drops by more than 3 orders of magnitude and the curves are linear around zero bias. At higher bias (~?0.2 V) they began to saturate, as the number of available charge carriers in the photoactive region becomes limited.
The photocurrent generated in our devices was mapped by scanning photocurrent microscopy, where a laser spot was scanned over the sample, and the resultant photocurrent displayed as a function of laser spot position. Photocurrent is generated only in the region where all three principal layers overlap (Fig. 1C). The origin of the photocurrent can be explained by examining the collective band diagram. In the idealized case the structure is symmetric (Fig. 2B) and the electrons/holes generated in TMDC (by absorption of a photon with sufficient energy) have no preferred diffusion direction and, hence, no net photocurrent is measured. However, in the presence of a built-in electric field (Fig. 2C) across the TMDC (either due to a difference in the initial doping between the graphene sheets or by gating ), the e-h pairs are separated and a photocurrent measured.
Immediately after fabrication (which involves the annealing stage) in the undoped state, the devices showed a minimum in the integrated photocurrent close to zero gate voltage (Fig. 1D). For any finite Vg (either positive or negative) the photocurrent increased proportionally to Vg but began to saturate at ~?20 V, again due to the finite number of generated charge carriers. We also intentionally doped the top graphene electrode in one of our non-encapsulated samples to become p-type by exposing it to high-concentration water vapor. The photocurrent (Fig. 1E) at zero gate voltage became finite (positive) and the response with gate voltage was shifted by ~20 V. The effect is also seen in Fig. 2A where the intercept of the IV curves is shifted due to movement of the chemical potential in graphene. Our devices also showed strong gate dependence without illumination, demonstrating transistor behavior. The ON/OFF ratio (highest to lowest current modulation) of such tunneling transistors exceeds that of previously reported devices . Devices made from micro-mechanically cleaved and CVD graphene demonstrate very similar photovoltaic and transistor behavior, opening a way for scale-up.
The photocurrent observed in these devices is surprisingly strong for only a few atomic layers of TMDC, but this strong light-matter interaction can be understood from the nature of the electronic states in this material. Ab initio calculations  for the density of states (DoS) and the joint density of states (JDoS) of three single layer semiconducting TMDC (WS2, WSe2, and MoS2) show strong peaks in the visible range (Fig. 3A) associated with van Hove singularities in the DoS. This leads to enhanced light absorption, and importantly this is a feature that is universal to TMDCs. These van Hove singularities come from the nature of the electronic wave functions: while the valence band is essentially composed of states coming from the d orbitals of the transition metal (TM), the conduction band is characterized by a linear superposition of d orbitals of the TM and p orbitals of the chalcogen atoms. The d-orbitals have a localized nature with enhanced interaction effects. The p-orbitals generate  the ? bands which in turn are responsible for the structural stability of these materials (analogous to what happens in graphene ). The localized character of the electronic bands (that is, the large effective mass of the carriers) leads to the peaks, i.e., van Hove singularities, in the DOS which are responsible for the enhanced photo-responsivity of these materials from the nanoscopic down to atomic scale. A direct measure of the effect of the van Hove singularities in the optical response of TMDC is given by the JDoS, defined as:

		
where V and C are the valence and conduction bands, respectively. The JDoS is a direct measure of the so-called joint critical points, that is, the van Hove singularities in the Brillouin zone around which a photon of energy, 
, is very effective in inducing electronic transitions over a relatively large region in momentum space. The large contribution to the transition probability for joint critical points gives rise to the structure observed in the frequency dependence of the optical properties of the TMDC. Thus, the photocurrent, 
, at some light frequency 
 is proportional to 
 . There is a sharp rise in the photo-absorption in the 
 in the visible range of all TMDC studied (Fig. 3B). In order to further confirm that our results are not dependent on the thickness of the TMDC, we calculated the DoS and JDoS for bulk (3D) semiconducting TMDCs . The peaks in the DoS and the sharp rise of the JDoS is comparable with the values found for a single layer in Fig.3B, and are consistent with the previous measurements on bulk MoS2 . Hence, the strong light-mater interaction in semiconducting TMDCs is not a unique feature of the bulk material and it can be extended to monolayers.
The effect discussed here has a similar, albeit with a different physical origin, to the strong Raman absorption in 1D semiconducting carbon nanotubes. In that case, the 1D nature of the material leads to 1/
 singularities in the DoS at the top (bottom) of the valence (conduction) bands, leading also to strong light-matter response .
We have also computed the work function, ?, for the semiconducting TMDCs studied here. We find that the work functions vary considerably depending on the transition metal used (for monolayer, ?WS2 ~ 4.6 eV, ?WSe2 ~ 4.3 eV, ?MoS2 ~ 5.1 eV) and their thickness (for bulk, ?WS2 ~ 4.2 eV, ?WSe2 ~ 3.9 eV, ?MoS2 ~ 4.5 eV). Notice that as the work-function of graphene is not significantly different (?G ~ 4.5 eV), it has been shown  that it has a very minimal effect on the band structure of TMDC, and the Dirac point of graphene stays within the gap, facilitating efficient extraction of both electrons and holes from TMDC. 
We investigated the performance of our prototype photovoltaic devices in detail. An important parameter is the extrinsic quantum efficiency (EQE), defined as the ratio of the number of charge carriers generated to the number of incident photons. This can be expressed in terms of the photocurrent I, incident power per unit area P and excitation wavelength ? by


where h is the Planck constant, c the speed of light in vacuum and e the electron charge. Using the relation for EQE we calculate the efficiency (Fig. 4), where the data were collected for several wavelengths at zero bias and Vg = -40 V.  The extrinsic quantum efficiency did not appear to be dependent on wavelength, as expected from the approximately constant optical absorption, over this range . It is likely that the decrease in quantum efficiency with increasing power is due to screening of the built-in electric field by the excited electrons in the conduction band of WS2.
The already good performance and high EQE of our devices (ensured by the peculiar band structure of TMDC used) can be further improved by optimizing light absorption in the active layer. One possible way ? the use of optical resonators  -  is already partly realized in our devices on SiO2, where light interference in SiO2 layer  enhances the optical electric field in TMDC (this is one of the reasons of better performance of our devices on SiO2 in comparison with those on flexible substrates). Another strategy is the utilization of plasmonic nanostructures  or metamaterials . To test the idea we applied gold nano-spheres,  Fig. 4C on top of one of our hBN/Gr/MoS2/Gr heterostructures, which enhances optical field in the active layer and allowed for 10-fold increase in the photocurrent,  Fig. 4D, E (see  for further details and other examples of the use of plasmonic nanostructures).
Atomically thin heterostructures of semiconducting TMDC present strong light-matter interactions that can lead to large photon absorption and photocurrent production. We are able to reach an extrinsic quantum efficiency of 30%, due to the localized character of the electronic wave functions in TMDCs that leads to large peaks in the DoS associated with van Hove singularities. The same devices demonstrate transistor behavior with ON/OFF ratios exceeding those in previously reported devices. The use of various TMDCs, as well as their combinations, would allow one to create new transparent and flexible photonic and optoelectronic structures and devices with unique properties which surpass current technologies. 
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This work was supported by the Royal Society, European Research Council, US Army, EPSRC and European Science Foundation (ESF) under the EUROCORES Programme EuroGRAPHENE (GOSPEL). A.M. acknowledges support from the Swiss National Science Foundation. AHCN acknowledges NRF-CRP award "Novel 2D materials with tailored properties: beyond graphene" (R-144-000-295-281). Y.-J. Kim's work was supported by the Global Research Laboratory (GRL) Program (2011-0021972) of the Ministry of Education, Science and Technology, Korea. RMR is thankful for the financial support FEDER through
 the COMPETE Program and by the Portuguese Foundation for Science and Technology
 (FCT) in the framework of the Strategic Project PEST-C/FIS/UI607/2011 and grant nr. SFRH/
BSAB/1249/2012.





Figure 1 Device structure and photocurrent mapping
(A) A schematic of the device with the principal layers shown. hBN is not shown. (B) An optical micrograph of one of our devices. The shading of the three constituent layers denotes the regions of the respective materials?top and bottom graphene electrodes shown in red and blue, while WS2 is shown in green. (C) A photograph of one of our flexible devices placed on an electroluminescent mat. (D-E) photocurrent maps taken before (D) and after (E)  doping the top graphene layer with water vapour. A signal is only seen in the area where all three layers overlap. The two graphene layers were connected via 1k? resistor, on which the photocurrent was measured. No bias was applied and for both (E) and (D), the maps were taken at gate voltages from -20 V to + 20 V. The scale of the maps is given by their width 20 ?m.


Figure 2 Gate dependent IV characteristics

(A) Left axis: IV curves for a device on Si/SiO2 taken under illumination at gate voltages from -20 (red) to +20 V (blue) in 10 V steps, after doping. The laser illumination energy was 2.54 eV and the power 10 ?W. The curves are linear at low bias but saturate at higher bias due to limited available charge carriers. Right axis: IV curves for the same device taken in dark at gate voltages from -20 (black) to +20 V (green) in 20 V steps, after doping. (B, C) Schematic band diagram for Gr/WS2/Gr heterostructure with (C) and without (B) a built-in electric field to separate the generated e-h pairs.




Figure 3 Electronic DoS for single layer TMDCs. 

(A) The DoS for monolayer TMDCs: MoS2, WS2 and WSe2. Strong peaks are present in all three materials which lead to a strong light-matter interaction. (B) The JDoS with the same three TMDC materials. 





	 On leave from the Department of Physics, Boston University, USA.
	? Corresponding author



Figure 4 Quantum efficiency
(A) The external quantum efficiency of the devices is the ratio of the number of measured e-h pairs to absorbed incident photons. Due to the small variation in optical absorption across this wavelength range the data for different wavelengths collapse onto a single curve. (B) Photocurrent measured with a 1.95 eV laser as a function of intensity and follows a sublinear dependence. This results in the largest quantum efficiency values at low intensities. Open symbols ? for a device on Si/SiO2 substrate and crossed symbols are for device on a flexible substrate. (C) Schematic representation of hBN/Gr/MoS2/Gr (layers bottom to top) photovoltaic device with gold nanoparticles spattered on top of the top graphene layer for plasmonic enhancement of light absorption. (D-E) photocurrent maps of one of our hBN/Gr/MoS2/Gr device taken before (D) and after (E) spattering of gold nanoparticles for plasmonic enhancement (illumination parameters: 633nm, 10?W; scan size 14?m?14?m; note the logarithmic scale chosen to represent the 10-fold increase in the photocurrent on (E)).