M Massicotte

P Schmidt

F Vialla

K G Schädler

A Reserbat- Plantey

K Watanabe

T Taniguchi

K J Tielrooij

F H L Koppens

Picosecond photoresponse in van der Waals heterostructures

Two-dimensional (2D) crystals, such as graphene and transition metal dichalcogenides 1 (TMDs), present a collection of unique and complementary optoelectronic properties 2,3 . Assembling different 2D materials in vertical heterostructures 4 enables the combination of these properties in one device, thus creating multi-functional optoelectronic systems with superior performance. Here we demonstrate that graphene/WSe2/graphene heterostructures ally the high photodetection efficiency of TMDs 5,6 with a picosecond photoresponse comparable to that of graphene 7-9 , thereby optimizing both speed and efficiency in a single photodetector. We follow in time the extraction of photoexcited carriers in these devices using timeresolved photocurrent measurements and demonstrate a photoresponse time as short as 5.5 ps, which we tune by applying a bias and by varying the TMD layer thickness. Our study provides direct insight into the physical processes governing the detection speed and quantum efficiency of these van der Waals (vdW) heterostuctures, such as out-of-plane carrier drift and recombination. The observation and understanding of ultrafast and efficient photodetection demonstrate the potential of hybrid TMD-based heterostructures as a platform for future optoelectronic devices.

The optoelectronic response of 2D crystals is currently the subject of intense investigation [1][2][3][5][6][7][8][9][START_REF] Eda | Two-dimensional crystals: Managing light for optoelectronics[END_REF][START_REF] Furchi | Mechanisms of photoconductivity in atomically thin MoS2[END_REF][START_REF] Klots | Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy[END_REF][START_REF] Lee | Atomically thin p-n junctions with van der Waals heterointerfaces[END_REF][START_REF] Lopez-Sanchez | Ultrasensitive photodetectors based on monolayer MoS2[END_REF][START_REF] Ross | Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions[END_REF][START_REF] Youngblood | Waveguide-integrated black phosphorus photodetector with high responsivity and low dark current[END_REF] prompted by the need for next-generation photodetectors with superior performance in terms of efficiency, detection speed, as well as flexibility and transparency [START_REF] Ferrari | Science and technology roadmap for graphene, related twodimensional crystals, and hybrid systems[END_REF] . High photon absorption 5,[START_REF] Carvalho | Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides[END_REF] and large photoconducting gain [START_REF] Furchi | Mechanisms of photoconductivity in atomically thin MoS2[END_REF][START_REF] Klots | Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy[END_REF][START_REF] Lopez-Sanchez | Ultrasensitive photodetectors based on monolayer MoS2[END_REF] have been observed in devices based on semiconducting 2D crystals. Yet, the observed response time typically ranges from nanoseconds [START_REF] Youngblood | Waveguide-integrated black phosphorus photodetector with high responsivity and low dark current[END_REF] to seconds [START_REF] Furchi | Mechanisms of photoconductivity in atomically thin MoS2[END_REF][START_REF] Lopez-Sanchez | Ultrasensitive photodetectors based on monolayer MoS2[END_REF] , with faster devices often displaying lower responsivity [START_REF] Furchi | Mechanisms of photoconductivity in atomically thin MoS2[END_REF] . Therefore, the main challenge is to develop and assess photodetectors based on 2D semiconductor crystals that simultaneously possess a large active area, high internal efficiency, and fast response time.

A promising approach to create such versatile devices is to sandwich a TMD layer between two graphene sheets serving as charge extraction contacts. In contrast to lateral photodetectors, such vertical van der Waals (vdW) heterostructures 4 have the advantage of possessing a large, scalable active area and an atomically short charge extraction channel, potentially enabling both efficient and fast photodetection. Whereas the quantum efficiency of these vdW devices 5,6,[START_REF] Lee | Atomically thin p-n junctions with van der Waals heterointerfaces[END_REF] and the dynamics of photocarrier creation and relaxation in TMDs [START_REF] Cui | Transient absorption microscopy of monolayer and bulk WSe2[END_REF][START_REF] He | Electron transfer and coupling in graphene-tungsten disulfide van der Waals heterostructures[END_REF][START_REF] Mouri | Nonlinear photoluminescence in atomically thin layered WSe2 arising from diffusion-assisted exciton-exciton annihilation[END_REF][START_REF] Nie | Ultrafast carrier thermalization and cooling dynamics in few-layer MoS2[END_REF][START_REF] Shi | Exciton dynamics in suspended monolayer and few-layer MoS2 2D crystals[END_REF][START_REF] Strait | High intrinsic mobility and ultrafast carrier dynamics in multilayer metal-dichalcogenide MoS2[END_REF][START_REF] Sun | Observation of rapid exciton-exciton annihilation in monolayer molybdenum disulfide[END_REF][START_REF] Wang | Ultrafast Dynamics of Defect-Assisted Electron-Hole Recombination in Monolayer MoS2[END_REF][START_REF] Borzda | Charge Photogeneration in Few-Layer MoS 2[END_REF] have been addressed, the response time of TMD-based photodetectors, as well as the dynamic processes governing their quantum efficiency remain elusive.

Here, we report on the intrinsic processes that limit the performance of photodetectors based on high-quality G/WSe2/G (with G representing graphene) vdW heterostructures encapsulated in hexagonal boron nitride (hBN) [START_REF] Wang | One-dimensional electrical contact to a two-dimensional material[END_REF] . We perform time-resolved photocurrent measurements 7,[START_REF] Gabor | Ultrafast Photocurrent Measurement of the Escape Time of Electrons and Holes from Carbon Nanotube p-i-n Photodiodes[END_REF] on devices consisting of WSe2 flakes with a range of thicknesses (monolayer and multilayers from 2.2 to 40 nm). This technique, which combines electronic detection with subpicosecond optical excitation, allows probing of the extraction (Figure 1a) and loss dynamics of the photoexcited charge carriers in the photoactive TMD layer. We use WSe2 as the photoactive material because of its high optical quality [START_REF] Ross | Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions[END_REF][START_REF] Zhao | Evolution of electronic structure in atomically thin sheets of WS2 and WSe2[END_REF] , and monolayer graphene flakes, placed below and above the TMD layer, as source and drain electrodes with gate-tunable work functions (Figure 1b). Figure 1c shows an optical image of a typical device comprising a WSe2 flake with a thickness of 2.2 nm (3 atomic layers).

Unless otherwise specified, all measurements presented in Figures 1 and2 are obtained from this particular device.

We first characterize the photoresponse of our devices at room temperature using a scanning photocurrent microscope (see Methods). The photocurrent (PC) map displayed in Figure 1d shows that the photosensitive region corresponds to the area where the three main layers (G/WSe2/G) are superimposed. The photocurrent spectrum (Figure 1e) measured in this area exhibits three main peaks (labelled A, B and A') whose positions match well with the exciton absorption peaks of WSe2 [START_REF] Zhao | Evolution of electronic structure in atomically thin sheets of WS2 and WSe2[END_REF][START_REF] Wilson | The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties[END_REF][START_REF] Beal | Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination[END_REF] . This confirms that the photocurrent originates from the generation of photoexcited charge carriers upon light absorption in the WSe2 layer, followed by the transfer of these charges to the graphene electrodes. The polarity and efficiency of the photocurrent are driven by the potential drop across the WSe2 layer (ΔV), which can be tuned by applying a bias (VB) or gate (VG) voltage 5,6 (see Supplementary Section I).

In order to investigate the dynamics of the photoexcited charges, we perform timeresolved photocurrent measurements 7,[START_REF] Gabor | Ultrafast Photocurrent Measurement of the Escape Time of Electrons and Holes from Carbon Nanotube p-i-n Photodiodes[END_REF] by exciting the photodetector with a pair of ultrashort pulses (~200 fs, centered at 1.55 eV) separated by a variable time delay Δt (Figure 1b, see Methods). Also known as photocurrent autocorrelation measurements -in analogy to autocorrelation measurements using non-linear optical crystals -this technique exploits the nonlinear power dependence of the photocurrent to extract the photocurrent dynamics. Figure 2a shows that this nonlinear power dependence is significant for average laser pulse intensities exceeding 10 kW/cm 2 . The observed sublinearity likely originates from saturable absorption [START_REF] Nie | Ultrafast carrier thermalization and cooling dynamics in few-layer MoS2[END_REF][START_REF] Wang | Ultrafast saturable absorption of two-dimensional MoS2 nanosheets[END_REF] (phase space filling), but we cannot exclude possible contributions from increased interactions between photocarriers (such as electron-hole recombination [START_REF] Gabor | Ultrafast Photocurrent Measurement of the Escape Time of Electrons and Holes from Carbon Nanotube p-i-n Photodiodes[END_REF] , exciton-exciton annihilation [START_REF] Mouri | Nonlinear photoluminescence in atomically thin layered WSe2 arising from diffusion-assisted exciton-exciton annihilation[END_REF][START_REF] Sun | Observation of rapid exciton-exciton annihilation in monolayer molybdenum disulfide[END_REF] and carrier-carrier scattering [START_REF] Nie | Ultrafast carrier thermalization and cooling dynamics in few-layer MoS2[END_REF] ), or from screening of the external bias (see Supplementary Section II). As a result of this sublinearity, photocurrent autocorrelation measurements, such as the one presented in Figure 2b, exhibit a symmetric dip around Δt = 0. We ascribe the dynamics of the dip to depletion of photocarriers from the active region [START_REF] Gabor | Ultrafast Photocurrent Measurement of the Escape Time of Electrons and Holes from Carbon Nanotube p-i-n Photodiodes[END_REF] , which we can describe (see Methods) with a characteristic time constant τ that corresponds to the photoresponse time of our WSe2-based photodetector. We will show that regardless of the mechanism that leads to the sublinear power dependence, the extracted time constant is representative for the photophysics that takes place in the device.

We determine τ for five devices with different WSe2 layer thicknesses L (Figure 3a) and find that τ increases with L and varies by more than two orders of magnitude: from 10 ns (40 nm device) down to 5.5 ps (monolayer and 2.2 nm devices). Figure 3b furthermore shows that τ scales quadratically with the thickness L (except the monolayer, which we discuss later). The highest response rate of Γ = τ -1 = (5.5 ± 0.1 ps) -1 , corresponding to a bandwidth of f = 0.55/τ = 100 GHz, is comparable to the intrinsic photo-switching speed of typical graphene detectors (~260 GHz) 7 . We note that in general ultrafast devices may have an operating speed limited by their resistance-capacitance (RC) time. In our devices the relevant capacitance is that of the WSe2 channel and the resistance is the sum of the graphene resistance and graphene-metal contact resistance. We indeed expect the photoresponse time to be RC-limited to τ > 0.4 ns for the thinnest devices (L < 10 nm, see Supplementary Section III). Using real-time electronic measurements, we find an instrument-limited higher bound of ~1.6 ns. This is already significantly faster than any TMD-based photodetectors reported to date 6,[START_REF] Furchi | Mechanisms of photoconductivity in atomically thin MoS2[END_REF][START_REF] Klots | Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy[END_REF][START_REF] Lopez-Sanchez | Ultrasensitive photodetectors based on monolayer MoS2[END_REF] and can further be improved by optimizing the circuit design, graphene resistance and contact resistance, up to the intrinsic limits that are reported in this work.

To address the underlying physics governing the dynamics and efficiencies in more detail, we study the dependence of τ on the bias voltage VB (Figure 3c) and observe that τ decreases with VB (Figure 3c, inset), indicating that photocarriers escape the active region more quickly as the electric field across the WSe2 layer increases. For devices made of a relatively thick WSe2 layer (L ≥ 7.4 nm), the response rate Γ depends linearly on VB (Figure 3d). This observation and the scaling of τ with L 2 suggests out-of-plane drift-diffusive transport: to reach the graphene contact, photocarriers generated in the middle of the WSe2 layer travel a distance L/2 with a drift velocity vd = μE where μ is the out-of-plane photocarrier mobility and E is the electric field across the WSe2 layer. Assuming that E ≈ VB/L (see Supplementary Section IV), the time τd it takes for photocarriers to drift out of the active region is τd = L 2 /2μV. This simple expression, represented by the dotted line in Figure 4a, captures the trend of Γ at low VB/L 2 (<10 -2 V/nm 2 ), yielding μ = 0.010 ± 0.003 cm 2 /Vs. This value is similar to the one recently reported for thick MoS2 flakes obtained from transport measurements [START_REF] Li | Electric-field-induced strong enhancement of electroluminescence in multilayer molybdenum disulfide[END_REF] , and is consistent with the strong conductivity anisotropy observed in TMDs (the in-plane conductivity is typically 2-3 orders of magnitude larger than the out-of-plane conductivity) [START_REF] Kautek | Electronic mobility anisotropy of layered semiconductors: transversal photoconductivity measurements at n-MoSe2[END_REF] .

Interestingly, for higher values of VB/L 2 (>0.1 V/nm 2 ) the response rate reaches a limit. For L = 2.2 nm (trilayer), this occurs for high VB (VB > 0.6 V), whereas the monolayer device reaches this limit without any applied bias. This saturation behaviour indicates the existence of an additional process that occurs in series with the drift process, thus prolonging the carrier extraction process. We find that the timescale τs of this additional process is bias-independent and is about 3-5 ps. This value is similar to the transfer time of photocarriers at the interface between WSe2 and graphene (~1 ps) [START_REF] He | Electron transfer and coupling in graphene-tungsten disulfide van der Waals heterostructures[END_REF] and to the hot exciton dissociation time in few-layer MoS2 (~0.7 ps) [START_REF] Borzda | Charge Photogeneration in Few-Layer MoS 2[END_REF] , which were both recently measured in all-optical pump-probe experiments. We thus argue that the response rate at high VB/L 2 has a higher bound that is determined by these two processes rather than by drift (Figure 4b); this constitutes an intrinsic limitation for this device geometry.

We also observe a lower bound for the response rate, occurring at low VB, which we attribute to a loss mechanism that occurs in parallel to the photocurrent generation process (Figure 4b). We find that this process presents a strong thickness dependence, with time constant τr ranging from 40 ps (2.2 nm device) up to >10 ns (40 nm device). We attribute this effect to radiative and non-radiative recombination of photocarriers [START_REF] Cui | Transient absorption microscopy of monolayer and bulk WSe2[END_REF][START_REF] Shi | Exciton dynamics in suspended monolayer and few-layer MoS2 2D crystals[END_REF][START_REF] Strait | High intrinsic mobility and ultrafast carrier dynamics in multilayer metal-dichalcogenide MoS2[END_REF][START_REF] Wang | Ultrafast Dynamics of Defect-Assisted Electron-Hole Recombination in Monolayer MoS2[END_REF] and energy transfer via dipole-dipole interaction to the graphene sheets [START_REF] Swathi | Resonance energy transfer from a dye molecule to graphene[END_REF] -two processes that have been shown to depend on TMD layer thickness. The latter interpretation is corroborated by the quenching of the WSe2 photoluminescence observed in the trilayer (10-fold quenching) and monolayer (300-fold quenching) devices (see Supplementary Section V).

We now show that the internal quantum efficiency (IQE, defined as the ratio between the number of extracted photocarriers and the number of absorbed photons) of the photodetector is the direct result of the competition between the photocarrier extraction time (τd + τs) and recombination loss (τr). Figure 4c shows the IQE as a function of ΔV (the potential drop across the WSe2 layer) that can be controlled by both VG and VB (inset in Figure 4c). We find that the experimental IQE matches well the extraction efficiency τr/( τd + τs + τr) derived from the dynamic model illustrated in Figure 4b. This concordance confirms that the dynamic processes identified in our time-resolved study correspond to the relevant physical mechanisms that govern the photoresponse of the device in the linear response regime (low-power, quasi-continuous excitation). It further demonstrates that the high IQEs observed in TMD-based vertical photodetectors (>85%) 6 This suggests that the IQE can be optimized by reducing the channel length, and thus minimizing the TMD thickness. Interestingly, for the most extreme case of a WSe2 monolayer, we observe a very low IQE (~6%, assuming 5% absorption) despite of a very short response time. This indicates that the observed dynamics in this device, as opposed to thicker ones, correspond to the losses, rather than to the extraction of charges. This is supported by the observation that the response time is bias-independent. The two loss mechanisms mentioned previously (intrinsic recombination and energy transfer) should indeed both occur much faster for a monolayer: recombination is facilitated by the direct nature of the bandgap of monolayer WSe2 [START_REF] Cui | Transient absorption microscopy of monolayer and bulk WSe2[END_REF][START_REF] Zhao | Evolution of electronic structure in atomically thin sheets of WS2 and WSe2[END_REF] , and loss through energy transfer exhibits a strong power law dependence with the inverse dipole-dipole distance [START_REF] Swathi | Resonance energy transfer from a dye molecule to graphene[END_REF] .

We conclude that G/WSe2/G devices made of trilayer WSe2 (2.2 nm) offer the best compromise for optimizing the IQE as they exhibit both a fast photoresponse (down to 5.5 ps) and a high internal quantum efficiency (>70%). Moreover, the device can be efficiently operated without dark current, and thus with low noise level, by applying a large gate voltage and no bias voltage (Noise-equivalent Power down to ~5x10 -12 W/Hz 1/2 , see Supplementary Section VI). Further improvement of the external quantum efficiency (EQE = 7.3% in our 2.2-nm-thick device) can be achieved by enhancing the light-matter interaction in the TMD layer with, for instance, optical waveguides 9,[START_REF] Furchi | Mechanisms of photoconductivity in atomically thin MoS2[END_REF] and cavities or plasmonic nanostructures 5,[START_REF] Eda | Two-dimensional crystals: Managing light for optoelectronics[END_REF] .

Stacking multiple semiconducting 2D crystals with different bandgaps is also a promising way to extend the spectral absorption range 2 without compromising much the photoresponse time. Our comprehensive understanding of the photocurrent dynamics in G/TMD/G heterostructures paves the way for designing vdW heterostructures for fast and efficient optoelectronic applications, such as highspeed integrated communication systems. Photocurrent (PC) vs. laser pulse power (P) for VB = 0.2 V. The transition from the linear to sublinear regime takes place at P ~ 100 μW (~10 kW/cm 2 ). The dotted line corresponds to a linear relationship between PC and P. Inset: the same data presented on a linear scale. b) Photocurrent as a function of time delay between two pulses (illustrated above the plot) with P = 300 μW, at VB = 1.2 V (blue dots). The photocurrent is normalized by the value of the photocurrent saturating at long Δt. The solid black line is a fit to the data using the model described in Methods, yielding a time constant τ = 5.5 ± 0.1 ps. Inset: Schematics of the photoresponse time in a G/WSe2/G heterostructure, here represented by a band diagram with a bias voltage VB applied between the graphene layers. The red sinusoidal arrows, blue dot and blue circle symbolize photons, photoexcited electron and hole, respectively. The photoresponse time τ, which corresponds to the time that photocarriers reside in the photoactive area, is represented by the black arrows. 3d). The dotted line corresponds to the diffusive transport model discussed in the main text with photocarrier mobility μ = 0.010 ± 0.003 cm 2 /Vs. The uncertainty in μ is estimated from the small variations in the mobility of each device, which, among other things, could stem from extrinsic factors (e.g. unintentional doping) or variations in the laser power employed to measure each device (see Supplementary Section VII). The solid black lines correspond to the equation τ -1 = (τd + τs) -1 + τr -1 with μ = 0.01 cm 2 /Vs, τs = 3 ps and the values of τr indicated for each line. b) Schematic of the processes contributing to the response time. Radiative and nonradiative photocarrier recombination (τr) leads to losses, whereas photocurrent is generated by photocarrier drift (τd) in combination with exciton dissociation and/or charge transfer at the G/WSe2 interface (τs). c) IQE as a function of the potential drop across the WSe2 layer ΔV for devices with L = 2.2, 7.4 and 28 nm. The black lines correspond to the expression τr/(τd + τs + τr), where τd = L 2 /2μΔV, using the values indicated in a. The experimental IQE (data points) is obtained by measuring the photocurrent generated at low power (P = 1 μW) with a quasi-continuous laser (λ = 759 nm) and by using the absorption as a fit parameter. The fitted absorption values are shown in the top left inset and compare well with the absorption expected from Beer-Lambert's law (solid black line) using the bulk absorption coefficient of WSe2 (3 x 10 5 cm -1 ) [START_REF] Beal | Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination[END_REF] . Bottom right inset: IQE vs VB measured on the 7.4-nm-thick device under the same illumination conditions as the main figure, with VG from 0 to 60 V in steps of 20 V.

Figure captions

Methods:

Device fabrication. Our vdW heterostructures are prepared using a layer assembly technique similar to that reported by Wang et al. [START_REF] Wang | One-dimensional electrical contact to a two-dimensional material[END_REF] . First, hBN is exfoliated onto a polymer (PMMA or PPC) and one of the flakes is employed to successively pick up graphene, WSe2, graphene and hBN flakes from their substrate (oxidized silicon). hBN flakes are typically 15 to 50 nm thick, depending on the device. The resulting stack is deposited onto a degenerately doped silicon substrate covered with a 285 nm thick SiO2 layer, which we use as a back gate (VG). Top and bottom graphene flakes are electrically connected by one-dimensional contacts [START_REF] Wang | Ultrafast saturable absorption of two-dimensional MoS2 nanosheets[END_REF] made of 2 nm Ti/ 100 nm Au.

Optoelectronic measurements. Photocurrent is generated by focusing a laser beam (close to diffraction limit) with a microscope objective (Olympus LUCPlanFLN 40x) on the device, and measured with a preamplifier and a lock-in amplifier synchronized with a mechanical chopper. A supercontinuum laser (NKT Photonics SuperK extreme) with tunable wavelength (from 500 to 1500 nm), pulse duration of ~40 ps and repetition rate of 40 MHz is employed to characterize the devices. Timeresolved photocurrent measurements are performed with ~200 fs pulses (at the sample, not Fourier-transform-limited) centered at 800 nm (1.55 eV) with a spectral bandwidth of ~200 nm. Since the laser spectrum overlaps with the A exciton peak (Figure 1e), we expect a significant contribution from these excitons to the photocurrent generated with this laser. Laser pulses are generated by a Ti:Sapphire laser (Thorlabs Octavius) with a repetition rate of 85 MHz. The optical beam is split into two arms and recombined using 50/50 beamsplitters. One arm contains a motorized translation stage that allows for the generation of a computer-controlled time delay Δt between the two pulses.

Extraction of the photoresponse time.

Global fitting of the time-resolved photocurrent signals is done using the following equation:

𝑃𝐶(Δ𝑡) 𝑃𝐶(Δ𝑡 → ∞) = 1 -𝐴 exp ( -|Δ𝑡| 𝜏 ) + 𝐵 exp ( -|Δ𝑡| 𝜏 𝐺 )
where amplitudes A and B, and time constants τ and τG are the fitting parameters. The exponential with time constant τG is an empirical term introduced to reproduce the flattening of the signals at low time delay (│Δt│≤ 2.2 ps) which is observed on the thinnest devices (L < 5 nm). This contribution is always small compared to the other exponential term (|A| >> |B|) and slightly faster (τG ~ 2-5 ps). We attribute this signal to the optoelectronic response of the top and bottom graphene layers 7 . We emphasize that this small correction to the global exponential decay is introduced for the sake of generality of the fitting procedure, and in any case does not influence the extracted response time τ and subsequent conclusions. Here we show that the photocurrent is driven by the out-of-plane potential drop inside WSe 2 .

For this we use an electrostatic model, similar to the one used by Yu et al. [1], that predicts the band alignment of the graphene-WSe 2 -graphene heterostructures.

The studied devices are deposited onto a substrate made of two different dielectrics, the thermally grown SiO 2 with thickness D SiO2 = 285 nm, and a hBN flake (15 nm < D hBN < 50 nm). Therefore, we add the capacitances per unit area C G , C SiO2 and C hBN of graphene, SiO 2 and hBN

1 C G = 1 C SiO2 + 1 C hBN = D SiO2 hBN + D hBN SiO2 0 SiO2 hBN . ( 1
)
Here 0 is the vacuum permittivity and SiO2 = 3.9 and hBN = 4.2 [2] are the relative permittivities of SiO 2 and hBN.

Apart from the electric field induced by the backgate voltage V G , there are additional fields at the graphene-WSe 2 interfaces, which are induced by charge transfer from WSe 2 to graphene. We call them E B for the bottom graphene flake and E T for the top graphene flake. Taking these fields into account, the charge densities in bottom and top graphene are given by

en B = C G V G -WSe2 0 E B ( 2
)
en T = WSe2 0 E T , (3)
where WSe2 = 4.2 is the relative permittivity of WSe 2 [3]. The fields at the top and bottom graphene-WSe 2 interfaces have the following relationship

E T = E B + N eL WSe2 , ( 4
)
where N is the donor density in WSe 2 and L is the thickness of WSe 2 . We assume that WSe 2 is fully depleted. From the electric fields we calculate the electric potential and a potential drop ∆V inside WSe 2 :

∆V = 1 2 (E B + E T )L. ( 5
)
Finally, we calculate the chemical potential in each of the two graphene flakes as

µ = hv F π|n + n 0 |, (6)
where n 0 is the intrinsic charge density of the graphene flakes. When a bias voltage V B is applied, the sum of the difference in Fermi levels between the top and bottom graphene layers and the potential drop inside WSe 2 has to be equal to the applied bias voltage: eV

B = e∆V + µ T -µ B . ( 7
)
The resulting potential drop ∆V is plotted in Supplementary Figure 1a. Its bias and gate voltage dependences follow very well that of the measured photocurrent (Supplementary Figure 1b), with the only fitting parameters being the donor density of WSe 2 (N = 8x10 17 cm -3 ) and the initial doping of the two graphene flakes (n 0,B = 8x10 11 cm -2 for the bottom graphene and n 0,T = 0 for the top graphene for the device with a WSe 2 flake thickness of L = 7.4 nm -these values vary slightly for each device). From the measured and simulated data we deduce that the photocurrent is proportional to the potential drop inside WSe 2 and that this potential drop can be controlled by V G and V B [1, 4].

We now look closer at the short-circuit current I SC and open-circuit voltage V OC . I SC is defined as the current at V B = 0 and we assume it to be proportional to ∆V, I SC = α∆V , with the proportionality constant α = 2 MΩ -1 used as a fitting parameter. The open-circuit voltage V OC is defined as the bias voltage at which the photocurrent vanishes. This happens when there is no net electric built-in potential inside WSe 2 . We find an excellent agreement between theory and experiment (Supplementary Figures 2a and2b), further confirming that the potential drop ∆V inside WSe 2 drives the photocurrent.

II Power dependence of photocurrent

We perform measurements of the power dependence for every G/WSe 2 /G device. For this we sweep the excitation power over 4 orders of magnitude at different excitation wavelengths using a supercontinuum laser (superK). Supplementary Figures 3a and3b present the results for devices with WSe 2 thicknesses of L = 2.2 and 7.4 nm. We observe similar behaviors with clear sublinearity at high excitation power. We find an identical trend with power when excitation is done with the pulsed Ti:Sapphire laser used in the time resolved measurements of the main text.

Remarkably, if we consider each device separately, we find an identical power dependence for the different probed excitation wavelengths when the excitation power is normalized by a wavelength dependent factor that stands for the different absorption coefficients. This is evidenced by the horizontally translated curves in the log-log scale and the unique photocurrent value where the non-linearity begins. If we compare the different devices with excitation at the A exciton resonance (Supplementary Figures 3c and3d), we find that the nonlinear regime starts for slightly different powers, with a global trend of a less marked nonlinearity the thinner the WSe 2 flake. Interestingly, we get very similar saturation thresholds when the excitation power is normalized by the absorption values extracted from the final analysis in the main text (Figure 4c inset). These observations are compatible with the different mechanisms mentioned in the main text and do not allow to discriminate between each one of them. However, we note that the actual origin of the sublinearity does not influence our claim that the time-resolved photocurrent measurements directly reflect the dynamics of photocarriers in the system.

III Real-time photoresponse and RC-time constant

We directly measure the photo-switching rate of our photodetectors by probing their response to a short light pulse in real time. Using a fast oscilloscope (Agilent MSO9404A, 4 GHz), we monitor the voltage across a 50 Ω load resistance (R L in Supplementary Figure 4d). We find a similar bias-independent response time of 1.6 ns (1/τ ∼ 0.6 GHz) for both the 2.2 and 7.4 nm devices (Supplementary Figures 4a to c). These experimental values, which are limited by our electrical setup, give us a lower bound for the actual photo-switching rate of our devices, which we expect to lie in the GHz regime.

We can indeed evaluate the actual photo-switching rate of our detector. To this end, in addition to the photoresponse time discussed in the main paper, we have to take into account the resistance-capacitance (RC) time constant of the device equivalent circuit (Supplementary Figure 4d). In this vertical geometry, we expect that the RC time constant is largely determined by the large capacitance of the Gr/WSe2/Gr heterostructure, C W Se2 = 0 W Se2 A/L. The resistance to take into account corresponds to the two graphene sheets and the following contacts and circuits (R S in Supplementary Figure 4d). The high resistance of the WSe 2 channel R W Se2 acts here as a shunt resistance so it does not affect the RC time constant. We estimate R S = 1 kΩ in our devices, yet this value can be further reduced by optimizating the circuit design, contact resitance and graphene charge density. These considerations give RC rates in the Ghz regime, which is consistent with the instrument limited photo-switching rates observed experimentally and discussed previously (Supplementary Figure 4e). We finally note that for the reasonably optimized device we propose (smaller active area A = 5 µm 2 and lower graphene and contact resistance R = 100 Ohm), we find much higher photo-switching rates which are RC limited only for thicknesses L lower than 2 nm. (e) Thickness dependence of the photoresponse rate (black, the data points are measured by time-resolved photocurrent -from Figure 3b in the main text -and the dotted line is a guide to the eye), the RC time constant (evaluated for our actual devices in blue and for an optimized device in red) and the measured decay time limited by the probing setup (green, also shown in c).

IV Dependence of the photoresponse time on the potential drop in WSe2

Here we show that the results we obtained from the photoresponse time model described in the main text are not affected if we consider the effective potential drop ∆V inside WSe 2 (Supplementary Figure 5) in our analysis instead of V B (see main text for comparison). In a first approximation ∆V, which we derive from the previously presented electrostatic analysis (section I), is comparable to the applied electrical bias voltage V B . We clearly observe the same trend, with a global linear dependence, and the two saturations of the response rate 1/τ at high and low V B /L 2 or ∆V /L 2 . Moreover, the time constants (τ s and τ r ) and mobility (µ) values we extract in Supplementary Figure 5 are very similar to those reported in the main text. Therefore, the different discussions and conclusions of the main text hold true even when these small electrostatic deviations are taken into account.

V Photoluminescence quenching

We perform spatial mapping of the photoluminescence from WSe 2 on the 1L and 3L devices on a different experimental setup than the one for photocurrent measurements. We use 532 nm excitation light (diffraction limited excitation spot with power 50 µW) and a detection with either a single photon counter module (coupled with longpass filters) or a spectrometer (coupled to an EMCCD camera), in a confocal geometry. Spatial maps of the photoluminescence intensity are presented in Supplementary Figure 6, as well as corresponding photoluminescence spectra at given laser positions. Relative intensity and spectral lineshape from the two devices confirm the respective 1L and few-layers WSe 2 geometry [5].

We clearly observe a strong reduction of the luminescence from the areas where WSe 2 is in contact with the top and/or bottom graphene layers. This emission quenching is a strong evidence for an energy transfer from the WSe 2 to the graphene, by the addition of a highly efficient non-radiative relaxation pathway for the photogenerated excitons [6]. A quantitative evaluation of the quenching ratios shows on average a 300-fold and 10-fold reduction of the luminescence in the 1L and 3L device respectively. This strong thickness dependence is indicative of an energy transfer mechanism. For instance in a Förster resonant energy transfer formalism, where dipole-dipole interaction between a point-like emitter and a plane is evaluated, the induced decay time of the emitter scales with the distance to the power of 4 [6, 7]. Moreover, the photoluminescence intensity being driven by the lifetime of the excitons in the WSe 2 , the quenching ratio directly gives the ratio between the intrinsic lifetime (without graphene) and the reduced lifetime due to the energy transfer to graphene. Exciton lifetimes in WSe 2 have already been evaluated to be hundreds of ps from several optical pump-probe studies [8]. This gives reduced lifetimes of roughly tens of ps for the 3L device and a few ps for the 1L device. This timescale should correspond to the zero-bias photoresponse time of the device, introduced as τ r in the main text. It appears to be in good agreement with the values extracted from the time-resolved photocurrent measurements. (3, black) and spectrally broad luminescence from the 3-layer flake (4, pink). We note the inclusion of a strongly luminescent monolayer flake on the bottom edge of the 3-layer flake.

  arise from the short extraction time of the photocarriers out of the thin TMD channel, thereby outcompeting the loss mechanisms.

Figure 1

 1 Figure 1 Photocurrent generation in G/WSe2/G heterostructure. a) Schematic representation of photoexcited charge carrier dynamics in a hBN/G/WSe2/G/hBN heterostructure. Graphene and hBN layers are respectively coloured in black and green, W and Se atoms in blue and orange. Upon pulsed-laser excitation, excitons or electron-hole pairs are created, separated and transported to the graphene electrodes. b) Schematic illustrating the experimental time-resolved photocurrent setup and cross-sectional view of the device. Two ultrashort pulses, delayed by a controllable distance cΔt (c denotes the speed of light), are focused on the device, which comprises a backgate (VG). A bias voltage (VB) can be applied between the top (GT) and bottom (GB) graphene layers through which photocurrent is measured (see Methods). c) Optical image of a heterostructure comprising a 2.2 nm thick WSe2 flake. The graphene and WSe2 flakes are outlined and shaded for clarity. d) Photocurrent (PC) map obtained by scanning a focused laser beam with a wavelength λ = 759 nm and a power P = 5 μW on the device shown in c with VG = 0 V and VB = 0.4 V. The photocurrent is mainly generated in the region where graphene layers (delimited by grey dotted lines) overlap. e) Responsivity spectrum of the device shown in c measured at a constant power P = 5 μW, with VG = 0 V and VB = 0.4 V. The exciton peaks are labelled according to the convention of Wilson and Yoffe 31 for WSe2 and confirm that the PC stems from the vertical extraction of carriers generated in the WSe2 layer. The orange shading indicates the spectral range of the pulsed excitation (illustrated in b) employed for time-resolved measurements.

Figure 2

 2 Figure2Extraction of the photoresponse time of a G/2.2-nm WSe2/G heterostructure by time-resolved photocurrent measurements. a) Photocurrent (PC) vs. laser pulse power (P) for VB = 0.2 V. The transition from the linear to sublinear regime takes place at P ~ 100 μW (~10 kW/cm 2 ). The dotted line corresponds to a linear relationship between PC and P. Inset: the same data presented on a linear scale. b) Photocurrent as a function of time delay between two pulses (illustrated above the plot) with P = 300 μW, at VB = 1.2 V (blue dots). The photocurrent is normalized by the value of the photocurrent saturating at long Δt. The solid black line is a fit to the data using the model described in Methods, yielding a time constant τ = 5.5 ± 0.1 ps. Inset: Schematics of the photoresponse time in a G/WSe2/G heterostructure, here represented by a band diagram with a bias voltage VB applied between the graphene layers. The red sinusoidal arrows, blue dot and blue circle symbolize photons, photoexcited electron and hole, respectively. The photoresponse time τ, which corresponds to the time that photocarriers reside in the photoactive area, is represented by the black arrows.

Figure 3

 3 Figure 3 Tuning of the photoresponse time τ by variation of the WSe2 layer thickness L and bias voltage VB. a) Time-resolved photocurrent measurements on heterostructures with different L (curves are offset for clarity). All measurements are obtained using a laser pulse power P ~ 300 μW and a bias voltage VB = 0.5 V, except the monolayer which was measured at VB = 0 V. Solid black lines are fits to the data. b) Photoresponse rate Γ = 1/τ vs. L. Data points represent the averaged values of Γ for different VB (typically from 0.1 to 1 V), whereas the error bars correspond to the minimum and maximum value of Γ. The solid black line is a power law fit (excluding the monolayer device), yielding Γ ∝ L -1.9±0.3 . c) Time-resolved photocurrent measurements on a heterostructure with L = 7.4 nm at various bias voltages VB and P = 300 μW (curves are offset for clarity). Inset: photoresponse time τ extracted from this heterostructure as a function of VB. d) Photoresponse rate Γ as a function of VB for various values of L. The solid black line corresponds to a linear relationship between Γ and VB, whereas the dotted line labels the effective minimum response time τ = 5.5 ps.

Figure 4

 4 Figure 4 Dynamic processes governing the photoresponse of G/WSe2/G heterostructures. a) Response rate Γ = 1/τ vs. VB/L 2 (same data as Figure3d). The dotted line corresponds to the diffusive transport model discussed in the main text with photocarrier mobility μ = 0.010 ± 0.003 cm 2 /Vs. The uncertainty in μ is estimated from the small variations in the mobility of each device, which, among other things, could stem from extrinsic factors (e.g. unintentional doping) or variations in the laser power employed to measure each device (see Supplementary Section VII). The solid black lines correspond to the equation τ -1 = (τd + τs) -1 + τr -1 with μ = 0.01 cm 2 /Vs, τs = 3 ps and the values of τr indicated for each line. b) Schematic of the processes contributing to the response time. Radiative and nonradiative photocarrier recombination (τr) leads to losses, whereas photocurrent is generated by photocarrier drift (τd) in combination with exciton dissociation and/or charge transfer at the G/WSe2 interface (τs). c) IQE as a function of the potential drop across the WSe2 layer ΔV for devices with L = 2.2, 7.4 and 28 nm. The black lines correspond to the expression τr/(τd + τs + τr), where τd = L 2 /2μΔV, using the values indicated in a. The experimental IQE (data points) is obtained by measuring the photocurrent generated at low power (P = 1 μW) with a quasi-continuous laser (λ = 759 nm) and by using the absorption as a fit parameter. The fitted absorption values are shown in the top left inset and compare well with the absorption expected from Beer-Lambert's law (solid black line) using the bulk absorption coefficient of WSe2 (3 x 10 5 cm -1 )[START_REF] Beal | Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination[END_REF] . Bottom right inset: IQE vs VB measured on the

G

  Photocarrier generation

Supplementary Fig 1 :

 1 (a) Potential drop ∆V in WSe 2 , calculated from the electrostatic model presented in the text. (b) Photocurrent as a function of bias and backgate voltages for the device with a WSe 2 flake thickness L = 7.4 nm. The data was taken at a temperature of 26 K, an illumination wavelength of 575 nm and an illumination power of 10 µW.

Supplementary Fig 2 :

 2 (a) Measured short-circuit current I SC and fit to theory I SC = α∆V , where α = 2 MΩ -1 is a fitting parameter. (b) Measured open-circuit voltage V OC and simulated values for the bias voltage at which the electric field inside WSe 2 vanishes. The data shown were taken at the same experimental conditions as described in Figure 1b.

Supplementary Fig 3 :

 3 Photocurrent vs optical excitation power, for devices with a (a) 2.2 nm and (b) 7.4 nm thick WSe 2 layer. For each device, excitation with different wavelengths gives identical trends considering the different absorptions. (c) Photocurrent vs optical excitation power for different WSe 2 thicknesses at a wavelength λ = 759 nm. (d) Same data as in (c) with the excitation power normalized by the absorption of the different WSe 2 flake thicknesses.

Supplementary Fig 4 :

 4 (a,b) Real-time traces of the photoresponse to a short optical pulse (55 ps pulse duration , λ = 532 nm) for different bias voltage V B and devices with 7.4 (a) and 2.2 nm (b) thick WSe 2 . The solid black lines are fits to the data corresponding to decay rates 1/τ = 610 and 590 GHz in a and b, respectively. Insets show the same data in semilog scale. (c) Extracted decay rates of both devices (red for 2.2 nm and blue for 7.4 nm thick WSe 2 ) as function of bias voltage. (d) Schematics of the equivalent circuit of our devices.

1 )μ

 1 = 0.03 cm 2 /Vs τ r = 20 ps μ = 0.01 cm 2 /Vs τ r = 100 ps μ = 0.01 cm 2 /Vs τ r = 750 ps τ s = 5 ps μ = 0.01 cm 2 /Vs τ r = ∞ Supplementary Fig 5: Response rate 1/τ vs ∆V /L 2 . The potential drop in WSe 2 (∆V) was calculated using the electrostatic model described in the text. The solid black lines correspond to the time response model τ -1 = (L 2 /2µ∆V + τ s ) -1 + τ -1 r . The fitted values are indicated on the figure for each curve.

Supplementary Fig 6 :

 6 WSe 2 photoluminescence intensity (in log scale) spatial maps measured on the devices with a WSe 2 flake (drawn with solid black lines) consisting of (a) a monolayer and (b) 3 layers. Strong quenching is observed in the area in contact with the graphene flakes (drawn with dashed lines). (c) Photoluminescence spectra obtained on the marked spots in the maps, showing strong and spectrally narrow luminescence from the monolayer (1, red), quenched luminescence from the same monolayer (2, blue), scattering or luminescent defects

Acknowledgements:

The authors are grateful to Qiong Ma and Pablo Jarillo-Herrero for their instruction on the layer assembly technique, and Mark Lundeberg for valuable discussions. MM thanks the Natural Sciences and Engineering Research Council of Canada (PGSD3-426325-2012). FV acknowledges financial support from Marie-Curie International Fellowship COFUND and ICFOnest program. F.K. acknowledges support by the Fundacio Cellex Barcelona, an ERC Career integration grant (294056,GRANOP) and ERC starting grant (307806, CarbonLight) and support by the EC under the Graphene Flagship (contract no. CNECT-ICT-604391).

Author contributions:

M.M. and F.H.L.K. conceived and designed the experiments. M.M., P.S. and F.V. fabricated the samples, carried out the experiments and performed the data analysis. K.W. and T.T provided boron nitride crystals. K.G.S. and A.R.P. provided assistance for the photoluminescence measurements. M.M., F.V., K.J.T., P.S. and F.H.L.K co-wrote the manuscript, with the participation of K.G.S. and A.R.P.

Additional information:

Supplementary information accompanies this paper at www.nature.com/naturenanotechnology. Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/. Correspondence and requests for materials should be addressed to F.H.L.K.

Competing financial interests:

The authors declare no competing financial interests.

VI Characterization of the photodetectors

In this section we present an overall characterization of our devices as photodetectors by presenting their responsivity ( ), external quantum efficiency (EQE), noise equivalent power (NEP) and specific detectivity (D*) in Supplementary Table 1.

We calculate the EQE (the number of electrons contributing to the photocurrent per incident photon) as EQE = P C P hc eλ with P C being the measured photocurrent, P the illumination power at the sample, λ the illumination wavelength and h, c and e the Planck constant, speed of light in vacuum and electron charge. The EQE of the device with a WSe 2 flake thickness of L = 7.4 nm is presented as function of the bias voltage V B in Supplementary Figure 7. In Supplementary Table 1, we note that higher values for responsivity and EQE can be reached for the device with L = 40 nm when applying very high bias and backgate voltages. However, we did not apply these high voltages in order to protect the device.

L (nm)

(mA/W) EQE (%) NEP (W/Hz

We can optimize the NEP by taking advantage of the electrical tunability of our devices with bias V B and gate voltage V G . As seen in the previous section, applying a gate voltage V G increases the open circuit voltage. It is therefore possible to reach high photocurrent efficiency without applying any bias V B . In this configuration, we minimize the dark current I d and the noise of the detector is no longer dominated by the shot noise but only by the thermal contribution (Supplementary Figures 8ab). We evaluate the NEP as NEP = 1 2eI d + 4k B T R d , where k B is the boltzmann constant, T the temperature and R d the equivalent resistance extracted from the dark current I-V curve at the operating bias [9]. For the device with L = 7.4 nm, we find values lower than 10 -11 W/Hz 1/2 even at high bias where the highest efficiency is reached (Supplementary Figure 8c). Using a gate voltage V G = 30 V, the NEP goes down to 10 -12 W/Hz 1/2 at zero bias voltage while the IQE remains high (∼40%). These values of NEP are similar to those of typical commercial photodetectors.

The specific detectivity is defined as D* = √ A N EP where A is the photoactive area of the device and is also reported in Supplementary Table 1.

VII Dependence of photocarrier mobility on laser power

For sake of completeness, we study the effect of laser power on the extracted photoresponse time τ of the devices and the underlying photocarrier dynamic processes. As a general rule, we observe that higher power leads to slower photoresponse time. Supplementary Figure 9 shows this effect for 4 different laser powers measured on the device with WSe 2 layer thickness L = 7.4 nm.

Using the photoresponse time model described in the main text, we find that laser power mostly affects the mobility µ of the photocarriers, which varies from 0.002 to 0.017 cm 2 /Vs as the average laser pulse power decreases from 1000 to 55 µW. The reduction of the mobility with increasing power (and therefore higher photocarriers densities) suggests that photocarriers mobility is limited by carrier-carrier scattering. This interpretation is consistent with the assumption that carrier-carrier interactions are responsible for the sublinear power dependence. Since the photocurrent autocorrelation technique relies on this sublinear effect, a sufficiently high laser power is required in order to reach the sublinear regime and extract a reliable response time. Hence, the values of mobility (response time) reported in the main text should be regarded as lower (upper) bounds.


Dominique Deneux
email: dominique.deneux@uphf.fr

Christian Goëtz

Katja Kuhn

Lisa Raab

Jorma Säteri

Robin Westacott

Innovative Engineering Teaching Unit in International Context

Keywords: Coop-education, International context, Digital transformation, Massive data

This communication is intended to disseminate the first learnings and outcomes of an Erasmus+ Strategic Partnership project (2018-1-DE1-KA203-00423) realized between Sept. 2018 and Aug. 2021 by 4 European applied science universities. The InT#Tech (International Transfer of cooperative study programmes in Europe: Scientific expectations, challenges and potentials) project's aim is the development of an international module for coop-students (apprentices), focusing on the digital transformation of engineering, i.e. the use of massive electronic data in design, manufacturing, mobility and facility management. After comparing the different models of coop-studies and identifying common requirements among the partners, after achieving a first level of cooperation during a Summer School, the most challenging task of the project was to imagine, develop, implement and analyse the execution of an innovative teaching unit, constituted of autonomous and supervised work, individual and team-based tasks in international context, theory and practice, distant and local lectures, academic and industrial inputs, so as to be able to grant ECTS credits to the participating coop-students. The paper includes recommendations to universities willing to implement a similar programme.

INTRODUCTION

The digital transformation of society is now obvious to everybody, even the elderly. Online shopping, banking, service sourcing and even interaction with the public administration have become the standard. In engineering, virtual reality is used to optimize the performance of future products based on their digital mock-up, while augmented reality increases the information carried out by physical artefacts of the real world. The physical and the digital worlds interact with each other more and more, under the concept of the digital twin. Products, vehicles, machines and facilities are all affected. In industry, robots take over the tasks in smart factories, manufacturing execution systems control the planning and supervision of automated processes distributed onto flexible cells monitored by smart sensors. The industrial world is focused on digital transformation. In this context, universities try to train the engineers of tomorrow, so that they can meet the upcoming demands in industry: "Skills 4.0". Many countries, especially across Europe, opt for the concepts of coop-education in higher education. This special system, combining academic lectures and industrial experience has great future potential for all stakeholders: companies, students, universities, but also for the territories where this happens. For companies, coop-study programmes are a response to demographic change and skilled worker shortages. For students, coop-study programmes offer practice-oriented higher education combined with paid work in companies and valuable evidence of experience. For universities, it offers the opportunity to develop new study programmes and curricula tailored to the regional needs. Regions increase their attractiveness for young people, if a branch of a coop-university in close connection with local companies is available. The globalization of companies however results in a new challenge to internationalize coop-programmes. It may seem easy to develop joint international programmes among universities in this context, since coop-study programmes are generally not controlled by the central education policy, but rather by regional cooperation between universities and industry. However, the first tasks of the Erasmus+ InT#Tech project, revealed many challenges.

INTERNATIONALIZATION OF COOP-EDU-CATION CHALLENGES

Coop-education in engineering

The steps to implement dual study programmes and the cooperation between companies and academia are different in different countries. In Europe, 3 models of dual study currently predominate. Dual programmes with a work experience component combine a course of study with extended practical phases with an employer. Students obtain a university degree, but not a recognised vocational qualification. A dual programme with employment component is primarily aimed at people who have already done vocational or professional training and/or already have a number of years of professional experience. It is designed to offer further professional development and combines a course of study with professional experience that is directly relevant to the academic contents. Students can enrol on this type of course without a general university entrance qualification. A dual programme with training component combines a course of study with training in a recognised occupation. In addition to the degree, students will obtain an official vocational qualification. In this model, the cooperation between academia and companies is increased. This is the model considered in the current communication, especially at the Bachelor 3 or Master 1 levels, when both the academic profile and the vocational skills have reached a sufficient level of maturity for considering internationalization.

Internationalization of coop-studies

Independent of the study model, there are several difficulties in developing and implementing coop-courses of study at the international level. On the one hand, the period that students spend abroad has to be discussed not only within universities, but also with participating companies. This results in several constellations between universities and companies in different European countries. A suitable cooperation model must be found in each case and be regulated in a compatible manner by a cooperation agreement. In addition, students must consider the requirements and expectations of their company in their homeland when choosing their stay abroad. Not all companies show an interest and understanding for stays abroad of their dual students. They may fear uncontrolled outflow of professionals and intellectual property. The duration of the stay abroad in the dual study programmes is usually limited to a few weeks. As a result, the students are overwhelmed with the theory phase, but above all, with the very intensive practical phase. Another problem is the financial aspect of the students' mobility. There is currently no special scholarship programme across Europe tailored to the needs of coop-students. Another relevant point is the recognition of academic achievements from abroad. Again, there is no standardized procedure at the EU level, except the ECTS (European Credit Transfer System). Furthermore, there are significant differences between universities in terms of rhythm of alternation and teaching agenda. International cooperation requires synchronization.

Comparison of 4 European partners' models

Before trying to implement a teaching unit in collaboration, it was necessary for the partners to understand the others' models of coop-education so as to identify obstacles and opportunities. Two project tasks were dedicated to this purpose. The first one was focused on identifying the coop-study models themselves, the second one was focused on the comparison of the cooperation models between companies, universities and students.

Coop-study models

The coop-study models among the partners of the project highly depend on the maturity of coop-study models in the country or in the region where it is observed, as well as the experience of each partner in implementing it. While dual education is a strong tradition in Germany [START_REF]Empfehlung des Hauptausschusses des Bundesinstituts für Berufsbildung vom 21[END_REF], especially in the Baden-Württemberg Land (34,000 coop-students per year at DHBW), while also it is well established in Engineering Higher Institutes in France [START_REF] Cereq | 20 ans d'insertion professionnelle des jeunes: entre permanences et évolutions[END_REF], following the "Decomps report" in 1989 and the initiative, in 1990, of the ITII network (Institut des techniques d'Ingénieurs de l'Industrie: 2500 graduates per year), it is only emerging at Heriot-Watt University (Scotland) [START_REF]Skills Development Scotland website[END_REF] and in Metropolia (Finland) [4]. So as to perform a precise analytic comparison of the 4 partners, several topics were listed in the lines of a large spreadsheet and filled like a questionnaire by each partner. The topics headlines include: identity, legal framework, economic model, financial support, relationship with the government and with the region, impact on the economic development of the region, available data and surveys, insertion of the former students on the labour market, specificity of coop-training models, alternation rhythm, quality and checks, staff, international mobil-ity… This comparative analysis was extremely useful for the partners, as a kick-off survey, mainly to confirm the variety of approaches, but none of the topics was susceptible to be adjusted by any partner to improve the ability to cooperate with each other, since the constraints generally have an external origin.

Cooperation-with-industry models

So as to encompass all the aspects of a coop-student's programme, the student journey according to a Life-Cycle Assessment approach was used: each life phase was analysed separately, so as to iteratively collect all the relevant specifications. Here, for each phase of the coopstudent journey, each partner was asked to describe the role of its university, the role of the coop-student and the role of the company, in the execution of the whole process, from being recruited to becoming a practitioner and possibly a mentor. The life phases of a coop-student include: (1) being recruited: application by candidate coop-students and selection process, (2) being trained: learn theory / learn practice / learn internationalization, supervision method / communication method among the 3 stakeholders, (3) progression and graduation: assessment of teaching units, ~practice, ~sessions, ~semesters, ~graduation, (4) joining the labour market: exerting the engineering job and, optionally, becoming a mentor in turn. (I) the models were compared two by two to highlight similarities and differences that may impact the ability for the partners to collaborate, in the scope of internationalization of programmes. An example is showed hereafter, according to the life-cycle phase "being trained", sub-item "teaching theory". (II) based on a list of criteria that universities, students and companies wish to satisfy at most, the performance of each model was evaluated by the other 3 partners (and by self, for comparison purposes), so as to foster the emergence of recommendations to universities willing to implement international coop-programmes. The following short list of criteria was selected: (for universities) increase the number and quality of students, increase the number of collaborations with companies; (for companies) increase the appeal for new talents, increase the quality of staff and corporate knowhow; (for coop-students) increase their own qualification and employability (experience), increase their monetary benefit (higher salary, reduced fees). The average evaluations of how each model item impacts on the 6 criteria was reported on radar graphs. An example (extract) is shown hereafter, comparing the impact of the "teaching process" of DHBW and INSA-HdF upon the 6 satisfaction criteria. The industrial opinions were collected from practitioners involved in the teaching activity within our 4 universities. The scores on the radar graphs in fig 4 are to be interpreted like this: 5 means that the model has a strong positive impact on the criterion. The number 0 means that the model has no impact at all on the criterion. The scores do not at all correspond to a value judgement about the partners. Nor do they intend to suggest any ranking. If university A gets a score near to 5 on a criterion, while university B gets a score near to 0, it does not mean that university A is performing better than univer-sity B. The context, the regulation, the constraints existing or not in the region or in the country, the financial model, the experience of coop-education are determining what can and cannot be done. The criteria which the authors used to compare their programmes can also be extended or changed. Regarding other evaluation models, the results would look different. A very positive score for an item, however, suggests that the model item can be recommended as good practice for establishing a cooperative study programme, because it provides satisfaction to all the concerned actors (student, company, university). It also means that the cooperation is close. In some cases, close cooperation can cause challenges as well. After comparing all the items and their respective impacts on the satisfaction of the success criteria for universities, companies and coop-students, the consortium was able to synthesize a list of objective recommendations.

Recommendations

The process of recruitment of coop-students can provide equally high satisfaction to all the parties because every actor has influence on it and can make a decision. The university should decide which student it would like to recruit and with which companies it would like to cooperate. The company should decide which student it would like to train and in which university this student should learn theory. The coop-student should decide which university programme to attend and in which company to be trained on-the-job. The rhythm of alternation, which is very different in each university, does not influence the satisfaction levels of the theory teaching process. This process mainly influences the university satisfaction. The implication of practitioners in the theory teaching process, which is generalized in every university, seems to be a good practice. The practice teaching process mainly influences the company's satisfaction, since practice is executed inside the company. The best practice seems to have students carrying out projects with increasing difficulty in the company, under close control by a company mentor and the approval of the practice learning programme by the partner university. The determinant for the satisfaction of all the actors regarding internationalization is the fact that a stay abroad is recommended (or even imposed) by the training programme, with a dedicated period. The student gains a cultural (generally also linguistic) experience, the company improves its corporate expertise in terms of international openness, the university gains attractiveness. The ideal situation is when the placement abroad is consistent with the company's activity and the programmes' major topics. Good practice in supervision is when the university is involved in the control of the student's activity in the company, by means of regular visits, and when the company is also involved in the control of the student's academic progress in the university and regularly invited to visit the university, for informative meetings or attendance at student's oral presentations. Despite different implementations of the communication between actors and different levels of constraints, in the consortium, the coop-student is the key element (student progress is the subject of the exchanges; students generally organize the meetings between the company and the university). The use of an electronic data repository, to ensure the tractability of the exchanges, can be suggested as a good practice. The maximum satisfaction of all the parties, regarding the practice assessment process is when the practical work is assessed by both the company assessing the work and a written and/or an oral presentation of this work, and the university, based on a report and/or an oral presentation of the work. Self-evaluation by the coopstudent may also be recommended, in addition, as a good practice. Most of the time, the students have no role in the semester validation and graduation process and it is difficult to satisfy their criteria, except by offering them a second chance to pass. The university is the main actor for these processes, which can be sometimes considered as automatic, when based on grades with a pass/fail threshold. The company can gain satisfaction if it is granted a role in the graduation process, for example by participating to the jury. The impact of the job finding process is not observable at HWU and Metropolia due to the very recent implementation of coop-programmes. In the two other universities, the satisfaction is high for all the parties. Proposing coop-programmes probably benefits the universities in terms of attractiveness. Graduated from coop-programmes is an excellent factor for employability with monetary benefit for students, while companies benefit from experienced new practitioners, on the condition that they can retain them. Keeping in mind these recommendations, the consortium started to prepare a first level of cooperation regarding the collaborative implementation of an international short educational programme, with teamwork, which was called the "InT#Tech Summer School".

FIRST LEVEL: SUMMER SCHOOL

The Summer School was organized at Heriot-Watt University in Edinburgh during the last week of May 2019, just after the local finish week of the semester, so that a lot of constraints could be relaxed regarding the availability of classrooms and accommodation on the campus. This week was also the most convenient for the 3 other partners. The session was open to 5 Bachelor3-level coop-students from every university. 2 professors from each university would participate to give lectures and to provide guidance for the teamwork. The focus of the week was on digital contents in the context of "Skills 4.0". These skills include: work independently in international teams on unknown issues, integrate knowledge into new tasks, work on multidisciplinary issues, use and share their scientific and technical knowledge, use and share their practical experience, improve their presentation skills, reflect on international project management and international cooperation, reflect on the input of digitalisation in technical departments, reflect on their own project. The added value for the participating students is of course to gain new expertise and knowledge, but also to work on innovation and project management and to gain international experience. The agenda of the week comprised lectures, visits (local or in the Region), and teamwork for small groups of mixed students regarding their origin and their skills (industrial engg, automotive engg, electrical engg, facility management and energetics). The working language was of course English. The lectures were given either in front of the audience or by means of videoconference, highlighting some challenges in modelling, engineering and manufacturing, mobility or energy saving. The visits highlighted local technical expertise and local culture (including the remarkable labs of HWU, a unique boat-lift and a Scotch whisky distillery). The student activities were focused on unsatisfied societal needs requiring technical knowledge and creative thinking. The final half-day was dedicated to the oral presentation of the propositions from the students. The jury, composed of the partner's professors, voted for the most convincing project. The winner team proposed a prototype of real-time car park sharing app for smartphones. This student's project is currently being continued in the scope of a start-up company. This experience was, obviously, strongly appreciated by all the participants (coop-students and teaching staff), all of them looking forward to continuing the experiment suggested by the InT#Tech project. The topics addressed by the lectures, the mixt of physical presence and online knowledge transmission, the challenge-based teamwork on innovative engineering, the international context with a touch of local culture contributed to this success. It had nevertheless significant drawbacks: the students could get no official recognition of their new knowledge; the Scottish students and staff were not really experiencing an international event, since the summer school took place in their own university. Moreover, this experiment was financially supported by the project budget complemented with the academic partners themselves. So, the participation (travel, lectures, visits, accommodation) was free for all the coop-students, but expensive anyway, which is not sustainable in the long term. Combining the positive features of the Summer School and granting the participants a valuable recognition of the work executed was the challenge of the second level of cooperation: implementing a collaborative teaching unit in international context, with an official recognition.

SECOND LEVEL: TEACHING UNIT IN IN-TERNATIONAL CONTEXT

The requirements were: 5 ECTS for participants who pass the tests, the smallest acceptable reward for a teaching unit within the consortium, a balanced workload between theory and practice, a coherent series of keynote lectures related to the general theme "digital transformation", practical work on outstanding equipment, immersion in the world of work in geographical and technical multiculturalism, assimilation of new knowledge, autonomous work and teamwork, involvement of the 4 institutes, a repeatable scenario and of course a tenable budget. The emergence of the 2020 health crisis brought new constraints and obliged us to think of the whole course as distance learning, which considerably reduced the budget to be allocated to the experimentation. Eras-mus+ agreed to consider the period April'20 / April'21 as a "blank year" for the project. The remainder of this paper focuses on the engineering of the module, taking the distance mode as an explicit constraint, which was not the case initially.

Engineering of the specification for the teaching unit

The experiment was sized to correspond to a typical class of 24 apprentices assembled in 6 international quadrinomials. To justify the award of 5 ECTS, a minimum workload equivalent to 6 to 8 weeks of training was required. But neither the teachers nor the trainees could make themselves available synchronously during weeks in any institute. The very few common intersections of availability in the consortium are in the spring and do not last more than a week (apart from holidays, public holidays and examinations). Therefore, it was decided to mobilise only one week for synchronous teaching, but to spread the duration of the module over two months, so that the workload would be both tenable in an already busy apprentice's schedule, while remaining compatible with the 5 ECTS credits. As the week consists of 5 days for 4 partners, it was decided that each institute should organise one day. A teaching day should combine a lecture and a practical lab involving a remarkable experimental device, generating digital data. A standard duration of 3 hours, for a lecture as well as for a practical lab, was retained, including a median break. The lectures were placed in the morning (9:00 am to 12:00 pm) for a better receptivity of the trainees, and the practical exercises in the afternoon (1:00 pm to 7:00 pm, in two batches of 12 trainees). The fifth day is devoted to giving the floor to representatives of European politics and industrialists close to the consortium's institutes. The first month is dedicated to acquiring the knowledge required to follow the course. The start of the first month and therefore of the course consists of a virtual meeting of a few hours, so that the participants can introduce themselves and the teams can be formed. The week of the course (fig. 7) is placed in the middle of the experiment. The second month is dedicated to the production of deliverables, in the form of posters and written reports. The end of the second month and therefore of the teaching unit consists of a finisher workshop. It was planned to occur in Brussels, but had to be replaced by a distant meeting. Once this framework has been established, the next step was to identify the contents of the course week (themes, resources, organisation and evaluation methods).

Identification of the teaching unit contents

The search for local teachers who could contribute to the module was different for the course and for the practical labs. For the course, a detailed call for tenders was launched and the offer most consistent with the general theme was selected. For the practical labs, a survey of the most remarkable equipments of the institute was carried out, and the teachers in charge of each equipment were invited to contribute. Thus, a group of potential contributors was quickly identified. Bearing in mind that one ECTS represents about 16 hours of teaching but that the international week only involves 30 hours of faceto-face teaching, an additional 50 hours of work was therefore required (i.e. 6.25 hours for each of the 8 contributors during the week), either before the week (preparatory work, suggested readings, mainly for the conference), or after the week (reports, mainly for the practical sessions). These requests were passed on to the group of teachers, particularly with regard to the workload constraint, the organisation of the practical sessions (individual tasks or team work or competition between groups), and the method of evaluation, in order to obtain a precise definition of each contribution. For the question of workload, preparatory readings have been chosen for the course. The lecture will start with an assessed quiz on the reading and understanding of the preparatory material. A second assessed quiz will be given after the lecture to check its assimilation. For the practical exercises, the evaluation depends on the teacher. It can be based on a classical presentation or on a written report. As far as INSA-HdF is concerned, the conference will focus on the impact of Big Data and machine learning in various situations related to production planning and control. As far as the practical lab is concerned, the remarkable devices of INSA-HdF that can be used for a distant practical lab are (1) the sustainable development platform is used for the determination, by means of remote measurements, of a cooling strategy for a building instrumented with more than 1000 sensors, (2) a remote diagnosis device implementing the supervision of controllable breakdowns of a strip unwinding and punching machine. The second one was finally retained because it is more available. The autonomous car and virtual reality equipment, although remarkable, were not selected because they are too difficult to use remotely. From an administrative point of view, a new teaching unit has been created and referenced in the pedagogical information system, so that apprentices can be officially enrolled in this unit and the lecturers and rooms can be officially identified as pedagogical resources. The status of the participating apprentices will be "Erasmus+ incoming students" in short-term virtual mobility. This teaching unit is about to start on 19 th April 2021.

CONCLUSION

InT#Tech is an exciting European project, giving 4 European institutes the opportunity to develop a replicable and low cost teaching unit on innovative engineering in an international context. The first implementation focusses on the digital transformation of skills needed to meet the current needs of Industry 4.0. The partners compared their respective work-study models and models of cooperation with companies. Despite a variety of situations, leading to many obstacles to the implementation of a mutualised teaching unit, a first level of collaboration was reached with a Summer School, which suggested the characteristics that needed to be maintained. One year later (2 because of COVID-19), the actual implementation of the Teaching Unit is imminent. This experience is largely reproducible, both in face-to-face and distance learning. It can easily integrate new international partners and seems to be fully transposable to other consortia and other themes.

ACKNOWLEDGEMENT

The project consortium of InT#Tech is very grateful for being part of the European network of Erasmus+ strategic partnerships. On behalf of all members and participating students, the consortium thanks all representatives of Erasmus+ projects, the German Academic Exchange Service and their universities for valuing the project's ideas and for supporting the internationalisation of cooperative study programmes.

fig 1 :

 1 fig 1 : Life phases of a coop-studentAfter collection and synthesis of copious data from the 4 partners, the 4 models were evaluated in 2 ways: (I) and (II). (I) the models were compared two by two to highlight similarities and differences that may impact the ability for the partners to collaborate, in the scope of internationalization of programmes. An example is showed hereafter, according to the life-cycle phase "being trained", sub-item "teaching theory".

fig 2 :

 2 fig 2 : Synthesis model of "teaching theory"

  fig 4: Compared impacts of teaching processes

Fig 5 :

 5 Fig 5: Schedule of the Summer School '19

  fig 6: Teamwork during the Summer School

fig 7 :

 7 fig 7 : Week of course

fig 8 :

 8 fig 8 : Supporting equipment for labs