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M. Massicotte, P. Schmidt, F. Vialla, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), K. J. Tielrooij, F. H. L. Koppens

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[Photo-thermionic effect in vertical graphene heterostructures](https://mdr.nims.go.jp/datasets/ab7e1612-45ca-42be-b060-a318fb824513)

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Photo-thermionic effect in vertical graphene heterostructuresARTICLEReceived 7 Jan 2016 | Accepted 8 Jun 2016 | Published 14 Jul 2016Photo-thermionic effect in vertical grapheneheterostructuresM. Massicotte1, P. Schmidt1,*, F. Vialla1,*, K. Watanabe2, T. Taniguchi2, K.J. Tielrooij1 & F.H.L. Koppens1,3Finding alternative optoelectronic mechanisms that overcome the limitations of conventionalsemiconductor devices is paramount for detecting and harvesting low-energy photons.A highly promising approach is to drive a current from the thermal energy added to the free-electron bath as a result of light absorption. Successful implementation of this strategyrequires a broadband absorber where carriers interact among themselves more strongly thanwith phonons, as well as energy-selective contacts to extract the excess electronic heat. Herewe show that graphene-WSe2-graphene heterostructure devices offer this possibility throughthe photo-thermionic effect: the absorbed photon energy in graphene is efficiently transferredto the electron bath leading to a thermalized hot carrier distribution. Carriers with energyhigher than the Schottky barrier between graphene and WSe2 can be emitted over the barrier,thus creating photocurrent. We experimentally demonstrate that the photo-thermionic effectenables detection of sub-bandgap photons, while being size-scalable, electrically tunable,broadband and ultrafast.DOI: 10.1038/ncomms12174 OPEN1 ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain. 2 National Institute forMaterials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 3 ICREA—Institució Catalana de Recerça i Estudis Avancats, Barcelona 08010, Spain. * Theseauthors contributed equally to this work. Correspondence and requests for materials should be addressed to F.H.L.K. (email: frank.koppens@icfo.eu).NATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunications 1mailto:frank.koppens@icfo.euhttp://www.nature.com/naturecommunicationsSince the discovery of the photoelectric effect in the latenineteenth century1, a great number of photodetectors thatrely on the emission of photoexcited charge carriers havebeen proposed. These carriers—sometimes referred to as hotcarriers, although they are not thermalized with the electronbath—are typically injected over a Schottky barrier between ametal and a semiconductor, allowing detection of photons withenergy lower than the semiconductor bandgap (see Fig. 1a). Thisprocess, called internal photoemission, has led to thedevelopment of visible and near-infrared photodetectors2,3,which have recently been combined with plasmonicenhancement schemes4–8. However, the efficiency of thismechanism drops for photon energy lower than the Schottkybarrier height FB (ref. 9) and is limited by the ability to extractthe carriers before they lose their initial energy, which in metalstypically occurs on a timescale of B100 fs (ref. 10).A promising way to overcome these limitations is to make useof the excess thermal energy contained in the electron bath. Thisenergy arises from the thermalization of photoexcited carrierswith other carriers, which results in a hot carrier distribution witha well-defined temperature Te. For increasing Te, a larger fractionof carriers can overcome the Schottky barrier, creating a currentvia thermionic emission (Fig. 1b). In this scheme, even photonswith energies below FB can lead to an increase in Te andsubsequently to carrier emission. However, in order to reach highTe, the hot carriers must be weakly coupled to the surroundingphonon bath11.Graphene, which has recently emerged as an excellent platformfor converting photons into hot carriers12, has the ideal propertiesto implement this scheme. Graphene presents strong electron–electron interactions leading to carrier thermalization withinB50 fs (refs 13,14), where a large fraction (450%) of the initialenergy of photoexcited carriers is transferred to the electronicsystem15. This efficient carrier heating creates a thermalized hotcarrier state that is relatively long-lived (longer than 1 ps)16,owing to weak coupling to the lattice and the environment. Thesethermalized carriers can thus reach temperatures significantlyhigher than the phonon bath temperature (Te4Tph) even undercontinuous-wave (CW) excitation17 (see Supplementary Note 1and Supplementary Fig. 1). Moreover, the tunability of thegraphene Fermi energy gives control over the height of theSchottky barrier. For these reasons, graphene was recentlyproposed as a promising material for efficient and tunablethermionic emission of hot carriers18–20.Here, we use graphene/WSe2/graphene van der Waals hetero-structures to detect low-energy photons (with a wavelength up to1.5 mm) through photo-thermionic (PTI) emission. Figure 1bshows in detail how the PTI photocurrent is generated: photonsare absorbed by graphene, creating electron–hole pairs, whichthen rapidly equilibrate into a thermalized carrier distributionwith an elevated electron temperature Te compared with thetemperature of the lattice Tph and the environment T0; carrierswithin this distribution with an energy larger than the Schottkybarrier height FB at the graphene/WSe2 interface can be injectedinto the WSe2 and travel to the other graphene layer. The numberof carriers with sufficient energy scales with e�fBkB Te , where kB is theBoltzmann constant.ResultsDevice structure. In our device, WSe2—a transition metaldichalcogenide with a bandgap EgB1.3 eV—provides an energybarrier between the two graphene sheets with low interfacialdefects and reduced Fermi-level pinning. The active device(depicted schematically in Fig. 1c) is encapsulated between layersof hexagonal boron nitride (hBN) which provides a clean,charge-free environment for the graphene and WSe2 flakes21.The device is equipped with an electrostatic bottom gate (VG)that enables control of the Fermi energy m and thereby FB of(mainly) the bottom graphene. All measurements presentedin the main text are obtained from one particular devicecomprising a 28-nm-thick WSe2 flake (see Fig. 1d) and areperformed at room temperature with a quasi-CW laser source,unless otherwise mentioned (see Methods). We have studieddevices with WSe2 flakes of various thicknesses (L¼ 2.2–40 nm)and obtained similar results, consistent with the PTI effect(see Supplementary Note 2 and Supplementary Figs 2 and 3).Photocurrent measurements. The PTI process is driven by thelight-induced increase of the thermal energy of the electron gas(kBTe). Signatures of this mechanism are readily visible in the datapresented in Fig. 2. First, the photocurrent spectrum of Fig. 2ashows a sizable, spectrally flat response for photon energies wellbelow the bandgap of WSe2 (EphotonoEg). That is expected froma thermally driven photocurrent, given the uniform absorption ofgraphene in the visible, near-infrared range and the fact that kBTeis independent of Ephoton for constant power15,22. Furthermore,the photocurrent generated in this sub-bandgap regime exhibits astriking superlinear dependence on laser power P (Fig. 2b,c). Thisis a direct consequence of the thermal activation of carriers overthe Schottky barrier, which, in first approximation, scalesexponentially with P (see Methods). In contrast, thephotocurrent in the above-bandgap regime (Ephoton4Eg) variesstrongly with Ephoton and scales linearly with P. Thisphotoresponse is characteristic of light absorption in WSe2 andtransfer of photoexcited carriers to the graphene electrodes, aprocess driven by the potential drop across the WSe2 layer23–25.Alternative photocurrent generation mechanisms are less likelyto contribute to the observed sub-bandgap photocurrent. Toverify this, we measured a device with a Au/WSe2 interface, wherephotocurrent is generated by internal photoemission of non-thermalized photoexcited carriers (see Supplementary Note 3 andSupplementary Fig. 4). This device shows a strong dependence onEphoton along with a cutoff energy at Ephoton¼FB, and a linearpower dependence—clearly at odds with our observations forG/WSe2/G (where G stands for graphene) devices. We note thatmulti-photon absorption followed by charge transfer could alsolead to a superlinear power dependence, but the laser intensityrequired to induce significant two-photon absorption in eithergraphene or WSe2 is at least 1–2 orders of magnitude higher thanthe one used in our experiment (smaller than 1 GWcm� 2)(refs 26,27). Similarly, the photo-thermoelectric and bolometriceffects could generate sub-bandgap photocurrent, but both wouldhave a sublinear—rather than the observed superlinear—powerdependence16,28.To further verify that the sub-bandgap photocurrent stemsfrom the PTI effect, we perform time-resolved photocurrentmeasurements by varying the time delay Dt between two sub-picosecond laser pulses generated by a Ti:sapphire laser (seeSupplementary Note 4 and Supplementary Fig. 5). From thedynamics of the positive correlation signal (due to the superlinearpower dependence) in Fig. 2d, we extract a characteristic decaytime tcool of 1.3 ps, which is on the order of the cooling time ofhot carriers in graphene16,22. All together the observationspresented in Fig. 2 suggest that the sub-bandgap, superlinear,picosecond photocurrent is governed by the PTI effect.Electrical tuning of the PTI effect. In contrast to bulk metal–semiconductor systems, this graphene-based heterostructureoffers the possibility to tune the Schottky barrier, and thereforethe magnitude of the PTI photocurrent, using the interlayer biasARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms121742 NATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsvoltage (VB) and gate voltage (VG). Applying these voltages isnecessary in order to generate a finite photocurrent, as it breaksthe symmetry of our device, which is composed of two G/WSe2Schottky barriers with opposite polarity. As the infrared photo-current maps (Ephoton¼ 0.8 eV) in Fig. 3a,b indicate, the inter-layer voltage VB essentially controls over which of the twoSchottky barriers hot carriers are injected: for VB¼ � 0.6 V(Fig. 3a), the photoactive region corresponds to the area wherethe top graphene overlaps with the WSe2 layer (GT/WSe2),whereas the interface with the bottom graphene (GB/WSe2) isphotoactive for VB¼ þ 0.6 V (Fig. 3b). In Fig. 3c,d, we examinethe photocurrent originating from regions containing a singleG/WSe2 interface, thus allowing us to assess each Schottky barrierindividually. To create a current, hot carriers need to be emittedover the G/WSe2 interface and subsequently transported alongthe WSe2 layer and collected by the other graphene electrode, asillustrated in the insets of Fig. 3c,d. When the interlayer bias VBmakes this process energetically favourable, each Schottky barriergives rise to a photocurrent with a specific sign. The photocurrentgenerated in the G/WSe2/G region (Fig. 3e) exhibits both signs asit stems from charge injection over both top and bottom Schottkybarriers. From the photocurrent sign associated with each layer,we deduce that hot electrons, rather than holes, are pre-dominantly emitted over both Schottky barriers. This is expectedgiven the work functions of graphene and electron affinity ofWSe2 (ref. 29).One of the hallmarks of thermionic emission is its exponentialdependence on the Schottky barrier height. In our device, the gatevoltage VG provides a crucial way of enhancing the photocurrentby controlling the height of the GB/WSe2 Schottky barrier via thetuning of the Fermi energy of GB. As Fig. 3f demonstrates, dopingthe bottom graphene layer with electrons by applying a positivegate voltage VG effectively lowers FB and results in a strongincrease in photocurrent. At high VG (low FB), the device reachesa responsivity of up to 0.12 mAW� 1 at wavelength l¼ 1,500 nm,which, for 0.5% light absorption in graphene30, translates into anWSe2hBNVBWSe2GThBNSiO2n++-SiVGAhBNdcGB––Metalbn(E)WSe2�B�–+GBhot e–an(E)�BSemi-conductor�0GBGTFigure 1 | The photo-thermionic effect and device structure. (a) Simplified band diagram illustrating the internal photoemission process taking place at ametal–semiconductor interface. Non-thermalized photoexcited carriers in metal with sufficient energy to overcome the Schottky barrier FB can be injectedinto the semiconductor before they lose their initial energy (within 100 fs for conventional metals10). The portion of the energy band filled by electrons andthe bandgap of the semiconductor are shaded in blue and pale orange, respectively. Low (high) energy photon and the electronic transition following theirabsorption are represented by red (green) sinusoidal and vertical arrows. The out-of-equilibrium electron distributions n(E) resulting from these processesare illustrated on the left-hand side with the corresponding colours. Photoexcited electrons are depicted by blue dots and their possible transfer path isrepresented by blue dashed arrows. (b) Simplified band diagram of the PTI effect at a G/WSe2 interface. The ultrafast thermalization of photoexcitedcarriers in graphene gives rise to a hot-electron distribution n(E) with a lifetime longer than 1 ps. As the number of electrons in the hot tail (yellow shadedarea) of n(E) increases, more electrons are emitted over the Schottky barrier FB, which generates a larger thermionic current (represented by the horizontalarrow). The colour gradient from blue to yellow illustrates the heat contained in the electron distribution. The offset between the graphene neutrality pointand WSe2 conduction edge is denoted by F0 and was experimentally determined to be 0.54 eV (ref. 28). (c) Schematic representation of theheterostructure on a 285-nm-thick SiO2/Si substrate, to which a gate voltage (VG) is applied to modify the Fermi-level m of the bottom graphene. Aninterlayer bias voltage (VB) between the top (GT) and bottom (GB) graphene flakes can be applied, and current or photocurrent flowing through GB ismeasured. (d) Optical image of a heterostructure composed of a 28-nm-thick WSe2 flake. The top and bottom hBN flakes are 10 and 70 nm thick,respectively. For clarity, graphene flakes are shaded in grey and outlined by a black dashed line, whereas WSe2 is coloured in orange and outlined by anorange line. Scale bar, 5mm.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12174 ARTICLENATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationsinternal quantum efficiency (IQE) of 2%. These figures of meritare similar to those obtained in devices using the in-plane photo-thermoelectric effect31 and can be further improved by adjustingthe relevant physical parameters as discussed below.Theoretical model of the PTI effect. The gate tunability of thePTI process and its distinct power dependence allow for aquantitative comparison of our measurements with a Schottkybarrier model based on the Landauer transport formalism32 (seeMethods). In this model, the photocurrent depends on thefraction of carriers with enough energy to overcome the barrier,governed by Te and FB, and on the carrier injection time tinj. Thevalues for FB(VG) are extracted from temperature-dependentdark current measurements (Fig. 4a) and are consistent with aband offset F0 of 0.54 eV (ref. 29). For simplicity, we assume thatheat in the electronic system dissipates through a single, rate-limiting cooling pathway characterized by a thermal conductanceG, such that under steady-state conditions the increase intemperature is proportional to P/G (see Supplementary Note 1).Figure 4b compares the measured and fitted PC as a function ofFB(VG) and laser power. This two-dimensional fit yields a carrierinjection time tinj¼ 47±10 ps and a thermal conductanceG¼ 0.5±0.3 MWm� 2 K� 1. This value of tinj is almost identicalto the one found for ideal G/Si Schottky barriers32, while the oneobtained for G matches the predicted thermal conductance ofG/hBN interfaces due to electron coupling with SPP phonons33and is also consistent with disorder-enhanced supercollisions withacoustic phonons16 (see Supplementary Note 1). The excellentagreement between model and experiment is clearly visible inFig. 4c,d. We note that the same measurements were performedat other ambient temperatures (T0¼ 230 and 330 K) and theanalysis yields very similar results (see Supplementary Note 5 andSupplementary Fig. 6).DiscussionThe device modelling and extracted physical parameters provideimportant insights into how to improve the efficiency of the PTIprocess. They also explain why this mechanism dominates thephotoresponse of graphene/semiconductor heterostructures,while being absent for metal/semiconductor devices. The reasonis that the thermal conductance G of our graphene-based device ismore than 2 orders of magnitude smaller than the thermalconductance due to electron–phonon coupling in thin (B10 nm)metal films10 (see Supplementary Note 3). Hence, thermalized hotcarriers in metals do not reach a sufficiently high temperature togenerate significant PTI photocurrent. Strategies to substantiallyincrease the device efficiency include further reduction of thethermal conductance in graphene-based devices, for example, byusing a nonpolar encapsulating material33. Likewise, theefficiency of the process can be readily improved by lowering–2 0 2 4 6 8 1000.511.52Δt (ps)ΔPC (nA)0 0.04 0.08 0.1200.250.50.751Power (mW)PC (normalized)Ephoton (eV): 1.311.070.960.900.83VB = 0.6 VT0 = 300 KVB = 0.6 VT0 = 300 K VB = 0.04 VT0 = 30 K−4 −2 0 2 40.11Δt (ps)ΔPC (nA)�cool = 1.3 psEg1.5 1.4 1.3 1.2λ (μm)0.8 0.9 1 1.1 1.2 1.3 1.4 1.5Ephoton (eV)Power law index �PC (nA)-+-+-+-Graphene absorption WSe2 absorption+0.91.1 110010121.51abcdFigure 2 | Experimental signatures of photo-thermionic emission. (a) Photocurrent (PC) spectrum measured at room temperature in the G/WSe2/Gregion with laser power P¼90mW, VB¼0.6 V and VG¼0 V (same conditions for b,c). The insets illustrate the absorption process taking place in thedifferent photoresponse regimes: absorption in WSe2 for Ephoton4Eg and absorption in graphene for EphotonoEg. The transition between these two regimesis represented by the background colour gradient, where red (blue) corresponds to the graphene (WSe2) absorption regimes. The vertical orange dashedline corresponds to the energy of the bulk WSe2 bandgap. (b) Power dependence of the photocurrent for various values of photon energy Ephoton. The dotsrepresent experimental data and the solid lines are power law fits (PCpPa) obtained with a fit range P¼ 70–120mW. (c) Fitted power law index a versusphoton energy, showing the transition from linear to superlinear power dependence. This transition occurs around Ephoton¼ Eg, the indirect bandgap ofWSe2. The error bars correspond to the s.d. obtained from the linear fit. (d) Time-resolved photocurrent change DPC(Dt)¼ PC(Dt)� PC(Dt-N),measured using the setup and technique described in ref. 24 with an average laser power of 260mW (wavelength 800 nm), at low temperature (30 K) andbias (VB¼0.04 V) in order to suppress the contribution of the photocurrent originating from WSe2 absorption. Experimental data are represented byorange dots and the solid black line is a decaying exponential fit with time constant tcool¼ 1.3 ps. Inset: same data and fit in logarithmic scale.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms121744 NATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsFB. Indeed, we find that the PTI efficiency increases by one orderof magnitude (up to 20%) by extrapolating the IQE to higher Te(B1,000 K) or lower FB (B0.06 eV, see Supplementary Note 6and Supplementary Fig. 7). Moreover, our model suggests that theefficiency can be greatly enhanced by reducing the carrierinjection time tinj, which is related to the coupling energybetween adjacent layers. The long tinj obtained from our fitappears to be one of the main factors limiting the observed IQEand is presumably due to momentum mismatch betweenelectronic states in the two adjacent materials. The interlayertransfer of charge carriers and heat in van der Waalsheterostructures is currently not well understood and furtherstudies are needed in order to unveil the limits of the PTIefficiency.We finally note that the PTI effect shows some similarities tophoton-enhanced thermionic emission (PETE), with the impor-tant differences that for PETE the photoexcited carriers are inthermal equilibrium with the lattice of a hot semiconductor andare emitted over a vacuum energy barrier34,35. There are alsoimportant resemblances between the PTI mechanism and theconcept of hot carrier solar cells, since both require decoupling ofthe electron and phonon baths and energy-selective contacts11,36.Both PETE devices and hot-solar cells have an interestingpotential for power conversion, but harvesting low-energyphotons is limited by the bandgap of the semiconductingabsorber. Interestingly, in our PTI device, which has a verysimple geometry and operates at room temperature, we alsofind a gate-dependent open-circuit voltage (of the photocurrent)of up to 0.17 V with a fill factor of 38%. This effect, observablein Fig. 3e, opens up a promising avenue for infraredenergy harvesting using graphene as the active material37.Furthermore, the PTI mechanism should work over anextremely broad wavelength range, including the mid-infraredand far-infrared (terahertz) regions and can be used for ultrafastphotodetection, given that the signal recovery time is on theorder of picoseconds. Finally, these vertical thermionic deviceshave a scalable active area and can be easily integrated withconventional and flexible solid-state devices. These features make–206040200–40–60VB = –0.6 Va–50510VB = 0.6 VbPC (nA)VG (V)–0.6 –0.3 0 0.3VB (V)d–0.3 0 0.3 0.6VB (V)40200e–0.6 –0.3 0 0.3VB (V)0.6 –0.6VG (V)VB = 0.6 V5PC (nA)00.6c60f10 15WSe2GBGTWSe2GBGT�B�BFigure 3 | Tunable photo-thermionic response. (a,b) PC maps of the device shown in Fig. 1d measured with an interlayer bias voltage VB of (a) �0.6 Vand (b) 0.6 V, and VG¼0 V. The graphene flakes are outlined by black dotted lines and the WSe2 flake by solid orange lines, as in Fig. 1d. Scale bar, 3mm.(c–e) PC versus VB and VG measured on single Schottky barriers formed by (c) top or (d) bottom graphene and WSe2, as well as (e) double G/WSe2/Ginterfaces. The coloured circle (green, red and blue) in the upper right corner of each measurement corresponds to the position of the focused laser beamwhich are indicated on the PC maps (a,b). The black dashed line in e indicates where PC is null. All measurements are scaled to the same colour bar. Insetsof c,d: side view of the heterostructure illustrating the generation and transport of hot carriers from one graphene flake to the other. Insets of e: banddiagrams depicting the PTI effect in G/WSe2/G for VBo0 (left) and VB40 (right). (f) PC versus VG taken from (e) at VB¼0.6 V. Inset: band diagrams ofthe GB/WSe2 Schottky barrier at low (bottom) and high (top) VG illustrating the increase of PTI emission resulting from the lowering of FB. Allmeasurements are performed at room temperature, with Ephoton¼0.8 eV and P¼ 110mW.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12174 ARTICLENATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunications 5http://www.nature.com/naturecommunicationsthe photo-thermionic effect a highly promising mechanism for aplethora of optoelectronic applications38.MethodsDevice fabrication and optoelectronics measurements. The heterostructuresare fabricated the same way as described in ref. 24. Photocurrent is generated byfocusing a supercontinuum laser (NKT Photonics SuperK extreme, repetition ratef¼ 40 MHz and pulse duration dt¼ 100 ps) with a microscope objective (OlympusLCPlanN � 50) on the device. The photocurrent is measured using a preamplifierand a lock-in amplifier synchronized with a mechanical chopper at 117 Hz.PTI emission model. In the reverse-bias regime, the Schottky barrier model basedon the Landauer transport formalism32 (see Supplementary Note 7) predicts thatthe current density J thermionically emitted over a Schottky barrier of height FB attemperature T isJ Tð Þ ¼ 2pe0tinjkBT‘ vF� �2 F0kBTþ 1� �exp�FBkBT� �; ð1Þwhere e0 is the elementary charge, kB is the Boltzmann’s constant, : is the reducedPlanck’s constant, vF is the graphene Fermi velocity, F0 is the band offset at theG/WSe2 interface (0.54 eV) and tinj is the charge injection time. In our experiment,the thermionic photocurrent (PC) we measure is produced by the increase ofelectronic temperature DT¼Te�T0 upon illumination of the device with a quasi-CW laser at l¼ 1,500 nm. Hence, it follows that the photocurrent isPC¼AD J T0 þDTð Þ� J T0ð Þ½ �, where A is the area of the laser beam (laser spot sizeof 1.75 mm), D is the duty cycle (D¼ dt � f¼ 0.04%) and T0 is the ambienttemperature. Using these equations and assuming T0cDT, one can show thatPC / DT þ fB2kBT20DT2 þ . . . , which makes evident the superlinear behaviour ofthe photocurrent. Finally, we assume that the rise in electronic temperature createdby each pulse is DT¼aZheatP=ADG, where a is the light absorption in graphene(0.5%), Zheat is the fraction of absorbed energy that is transferred to the electronbath (B70%) (ref. 15), P is the average power of the laser and G is the thermalconductance of the rate-limiting thermal dissipation step (see Supplementary Note 1).Data availability. The data that support the findings of this study are availablefrom the corresponding author upon request.References1. Hertz, H. Ueber einen Einfluss des ultravioletten Lichtes auf die electrischeEntladung. Ann. Phys. Chem. 267, 983–1000 (1887).2. Peters, D. W. An infrared detector utilizing internal photoemission. Proc. IEEE55, 704–705 (1967).3. Scales, C. & Berini, P. 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Rev. 38, 45–56 (1931).10. Qiu, T. Q. & Tien, C. L. Heat transfer mechanisms during short-pulse laserheating of metals. J. Heat Transfer 115, 835–841 (1993).0 20 40 60 800.10.140.180.22�B (eV)VG = 10 – 70 V35 40 45 50−30−28−26−24−220 0.05 0.10 0.05 0.10.20.180.160.14�B (eV)0 5 10 15PC (nA)Experiment Modela b0.12 0.14 0.16 0.18 0.2 0.220481216�B (eV)Power (mW):0.1 0.13 0.06 0.016 PC (nA)0 0.04 0.08 0.120481216PC (nA)70 56 42 28 14 VG (V):60 900 30ΔT (K)0.12 0.16 0.2110�B (eV)PC (nA)0.10.001 0.01110PC (nA)0.01Power (mW)0.1c dPower (mW) Power (mW)Power (mW)ln(I/T) (A/K)1/kBT (eV–1)VG (V)Figure 4 | Comparison between data and photo-thermionic model. (a) Schottky barrier height FB versus VG extracted from the temperature-dependenceof dark current measurements. Inset: Arrhenius plot of the dark current at different VG and VB¼0.36 V. Experimental data are represented by blue dots andthe solid black lines are linear fits. The error bars in the main panel correspond to the standard deviation obtained from these fits. (b) PC versus FB andlaser power P, measured (left plot) and according to our PTI model (right plot). PC is measured at room temperature, with Ephoton¼0.8 eV and VB¼0.36 V.(c) PC versus FB for different values of P and (d) PC versus P for various values of FB taken from b. The data points correspond to the experiment and thesolid black lines to the model. The upper horizontal axis shows the rise in electronic temperature DT¼ Te� T0 (extracted from the fit of the model to theexperiment). Insets of c,d: same experimental data and theoretical curves in logarithmic scale.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms121746 NATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunications11. Ross, R. T. & Nozik, A. J. Efficiency of hot-carrier solar energy converters.J. Appl. Phys. 53, 3813–3818 (1982).12. 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M.M. thanks the Natural Sciences and EngineeringResearch Council of Canada (PGSD3-426325-2012). P.S. acknowledges financial supportby a scholarship from the ‘la Caixa’ Banking Foundation. F.V. acknowledges the financialsupport from Marie-Curie International Fellowship COFUND and ICFOnest program.K.J.T. acknowledges the financial support from Mineco (FIS2014-59639-JIN). F.H.L.K.acknowledges support by Fundacio Cellex Barcelona, the ERC Career integration grant(294056, GRANOP), the ERC starting grant (307806, CarbonLight), the Mineco grantsRYC-2012-12281 and FIS2013-47161-P and support by the EC under the GrapheneFlagship (contract no. CNECT-ICT-604391).Author contributionsM.M. and F.H.L.K. conceived and designed the experiments. M.M., P.S. and F.V. fab-ricated the samples, carried out the experiments and M.M. performed the data analysis.K.W. and T.T provided boron nitride crystals. M.M., F.V., K.J.T., P.S. and F.H.L.Kdiscussed the results and co-wrote the manuscript.Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting financial interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Massicotte, M. et al. Photo-thermionic effect in vertical gra-phene heterostructures. Nat. Commun. 7:12174 doi: 10.1038/ncomms12174 (2016).This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/r The Author(s) 2016NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12174 ARTICLENATURE COMMUNICATIONS | 7:12174 | DOI: 10.1038/ncomms12174 | www.nature.com/naturecommunications 7http://arxiv.org/abs/1504.0721http://arxiv.org/abs/1504.0721http://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications title_link Results Device structure Photocurrent measurements Electrical tuning of the PTI effect Figure™1The photo-thermionic effect and device structure.(a) Simplified band diagram illustrating the internal photoemission process taking place at a metal-semiconductor interface. Non-thermalized photoexcited carriers in metal with sufficient energy to  Theoretical model of the PTI effect Discussion Figure™2Experimental signatures of photo-thermionic emission.(a) Photocurrent (PC) spectrum measured at room temperature in the GsolWSe2solG region with laser power P=90thinspmgrW, VB=0.6thinspV and VG=0thinspV (same conditions for b,c). The insets illust Figure™3Tunable photo-thermionic response.(a,b) PC maps of the device shown in Fig.™1d measured with an interlayer bias voltage VB of (a) -0.6thinspV and (b) 0.6thinspV, and VG=0thinspV. The graphene flakes are outlined by black dotted lines and the WSe2  Methods Device fabrication and optoelectronics measurements PTI emission model Data availability HertzH.Ueber einen Einfluss des ultravioletten Lichtes auf die electrische EntladungAnn. Phys. Chem.26798310001887PetersD. W.An infrared detector utilizing internal photoemissionProc. IEEE557047051967ScalesC.BeriniP.Thin-film Schottky barrier photodetecto Figure™4Comparison between data and photo-thermionic model.(a) Schottky barrier height PHgrB versus VG extracted from the temperature-dependence of dark current measurements. Inset: Arrhenius plot of the dark current at different VG and VB=0.36thinspV. Ex We are grateful to Qiong Ma, Pablo Jarillo-Herrero, Mark Lundeberg and Ilya Goykhman for valuable discussions. M.M. thanks the Natural Sciences and Engineering Research Council of Canada (PGSD3-426325-2012). P.S. acknowledges financial support by a schola ACKNOWLEDGEMENTS Author contributions Additional information