A Aubin

B Ouerghi

Dubertret
email: benoit.dubertret@espci.fr.

A Robin¹2

E Lhuillier²3̛

X Z Xu¹

S Ithurria¹

H Aubin¹

A Ouerghi´

B Dubertret¹

Engineering the Charge Transfer in all 2D Graphene-Nanoplatelets Heterostructure Photodetectors

  L'archive ouverte pluridisciplinaire

Introduction

Colloidal quantum dots (CQD) are attracting growing interest since their recent use in displays as narrow luminescence fluorophores. One of the promising next steps is their integration in optoelectronic devices such as photodetectors or photovoltaic cells. [START_REF] Kim | 25th Anniversary Article: Colloidal Quantum Dot Materials and Devices: A Quarter-Century of Advances[END_REF][START_REF] Wang | Recent advances in solution-processed inorganic nanofilm photodetectors[END_REF][START_REF] Talapin | Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications[END_REF] In a CQD array, the transport occurs through a hopping process which tends to limit the mobility below ≈ 1 cm 2 .V -1 .s -1 . [START_REF] Morgan | Electronic transport in films of colloidal CdSe nanocrystals[END_REF][START_REF] Yu | Electronic transport of n-type CdSe quantum dot films: Effect of film treatment[END_REF] As a consequence, the carrier diffusion length remains limited: 100 -200 nm, [START_REF] Carey | Record Charge Carrier Diffusion Length in Colloidal Quantum Dot Solids via Mutual Dot-To-Dot Surface Passivation[END_REF] which is a decade below the absorption depth of the nanocrystals thin film. Various strategies have been explored to overcome the transport bottleneck, such as building phototransistors [START_REF] Lhuillier | Electrolyte-Gated Colloidal Nanoplatelets-Based Phototransistor and Its Use for Bicolor Detection[END_REF] to fill majority carrier traps or reducing the electrode spacing using a nanotrench geometry to get rid of hopping transport. [START_REF] Lhuillier | Nanoplatelets Bridging a Nanotrench: A New Architecture for Photodetectors with Increased Sensitivity[END_REF][START_REF] Lam | Programmable definition of nanogap electronic devices using self-inhibited reagent depletion[END_REF] As an alternative, van der Waals heterostructures can be used to decouple the photogeneration from the transport. Such devices can be built by coupling CQD with efficient transport layer such as graphene. [START_REF] Withers | Heterostructures Produced from Nanosheet-Based Inks[END_REF][START_REF] Roy | Field-Effect Transistors Built from All Two-Dimensional Material Components[END_REF][START_REF] Buscema | Photocurrent generation with two-dimensional van der Waals semiconductors[END_REF] Hybrid graphene/CQDs photoconductors with CQDs of various composition including PbS, [START_REF] Konstantatos | Hybrid graphene-quantum dot phototransistors with ultrahigh gain[END_REF][START_REF] Sun | Infrared Photodetectors Based on CVD-Grown Graphene and PbS Quantum Dots with Ultrahigh Responsivity[END_REF] ZnO, [START_REF] Chang | A highly sensitive ultraviolet sensor based on a facile in situ solution-grown ZnO nanorod/graphene heterostructure[END_REF] CdSe [START_REF] Geng | Aqueous-Processable Noncovalent Chemically Converted Graphene-Quantum Dot Composites for Flexible and Transparent Optoelectronic Films[END_REF] and CdS 17 have been realized. A photoconductive gain of 10 8 and responsivity of 10 7 A.W -1 can be achieved [START_REF] Konstantatos | Hybrid graphene-quantum dot phototransistors with ultrahigh gain[END_REF] at very low irradiance (10 -14 W.cm -2 ), thanks to the high mobility of the graphene channel and the long carrier lifetime of the photogenerated carriers in the CQD layer.

In spite of all these progresses, the performances of photoconductors are limited by several parameters. Some of them have already been addressed, [START_REF] Konstantatos | Nanostructured materials for photon detection[END_REF] such as the carrier mobility of the CQD film, CQD surface chemistry, [START_REF] Barkhouse | Thiols Passivate Recombination Centers in Colloidal Quantum Dots Leading to Enhanced Photovoltaic Device Efficiency[END_REF] and the doping of the CQD layer. [START_REF] García De Arquer | Tailoring the Electronic Properties of Colloidal Quantum Dots in Metal-Semiconductor Nanocomposites for High Performance Photodetectors[END_REF] But other parameters, including the effect of the CQD environment (the gas for example), the number of charges that can be trapped on the CQDs, the lifetime of these trapped charges, the effect of heterostructures on charge separation, are still largely undocumented. In particular, purely 2D heterostructures strongly differ from nanocrystalgraphene hybrid systems due to their large exciton binding energy which potentially prevents charge transfer to other layers. [START_REF] Zhu | Exciton Binding Energy of Monolayer WS2[END_REF][START_REF] Komsa | Effects of confinement and environment on the electronic structure and exciton binding energy of MoS${}_{2}$ from first principles[END_REF][START_REF] Ugeda | Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor[END_REF][START_REF] Borzda | Charge Photogeneration in Few-Layer MoS2[END_REF] In this paper, we highlight and propose some strategies to reduce the impact of this large binding energy by forming in-plane heterostructures. To do so and rather than using conventional Transition Metal DiChalcogenide (TMDC) material such as MoS 2 or WS 2 , we use colloidally grown CdSe nanoplatelets (NPL). In addition to their 2D character, [START_REF] Pelton | Carrier Cooling in Colloidal Quantum Wells[END_REF][START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] the NPL offer the possibility to be grown under a heterostructured core/shell and core-crown aspect to tune their carrier localization. [START_REF] Ithurria | Colloidal Atomic Layer Deposition (c-ALD) using Self-Limiting Reactions at Nanocrystal Surface Coupled to Phase Transfer between Polar and Nonpolar Media[END_REF][START_REF] Pedetti | Type-II CdSe/CdTe Core/Crown Semiconductor Nanoplatelets[END_REF] These NPL-graphene hybrid systems are studied in an electrolyte gated phototransistor configuration to finely probe the carrier density within the graphene and evidence the charge transfer from the semiconductor layer. Moreover, we also studied how the dynamic of transport is affected and show that the 1/f noise intensity in the graphene layer is only moderately affected by the graphene functionalization by nanocrystals.

All 2D nanoplatelets-graphene heterostructure in an electrolytic gating configuration

Colloidal metal-chalcogenides nanoplatelets (NPL) such as CdSe offer excellent optical properties originating from the control of their thickness at the atomic level. [START_REF] Ithurria | Quasi 2D Colloidal CdSe Platelets with Thicknesses Controlled at the Atomic Level[END_REF][START_REF] Lhuillier | Two-Dimensional Colloidal Metal Chalcogenides Semiconductors: Synthesis, Spectroscopy, and Applications[END_REF] As synthetized, [START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF] they exhibit sharp excitonic features (see a and b) which make them appealing candidates for photodetectors with welldefined cut-off wavelength. The initial long capping ligands are exchanged for atomically short sulfide ligands [START_REF] Nag | Metal-free Inorganic Ligands for Colloidal Nanocrystals: S2-, HS-, Se2-, HSe-, Te2-, HTe-, TeS32-, OH-, and NH2-as Surface Ligands[END_REF] to reduce the interlayer spacing and favour the charge transfer (see Supplementary Information S1 for additional details on synthesis and ligand exchange). In the meanwhile, a monolayer of epitaxial graphene has been grown and gently hydrogenated to reduce the coupling with the substrate [START_REF] Pallecchi | High Electron Mobility in Epitaxial Graphene on 4H-SiC(0001) via post-growth annealing under hydrogen[END_REF] (see Supplementary Information S2 for detail about the preparation of the graphene layers). Epitaxial graphene is chosen because it offers large scale layers on an insulating and transparent substrate.

Backside illumination of the device is thus possible, and contrary to CVD grown graphene, no transfer step to a metal dielectric substrate is necessary. As seen from the Raman spectrum and the STM map (see c and d), a high quality mono-layer of graphene is obtained (see Supplementary Information S2 for details about characterization).

As a probe for the charge transfer, we choose to use an electrolytic transistor configuration [START_REF] Lhuillier | Electrolyte-Gated Field Effect Transistor to Probe the Surface Defects and Morphology in Films of Thick CdSe Colloidal Nanoplatelets[END_REF][START_REF] Froehlicher | Raman spectroscopy of electrochemically gated graphene transistors: Geometrical capacitance, electron-phonon, electron-electron, and electron-defect scattering[END_REF] (see Supplementary Information S3 for details about the device fabrication). Compared to usual solid state gating method this strategy allows larger carrier density [START_REF] Kominkova | Extreme electrochemical doping of a graphene-polyelectrolyte heterostructure[END_REF] up to 10 14 cm -2 which will be of utmost interest to evidence a strong charge transfer. We use a fast sweep rate (50 -100 mV.s -1 ) only allowing the gating of graphene why leaving the charging state of the NPL unaffected. [START_REF] Lhuillier | Investigating the n-and p-Type Electrolytic Charging of Colloidal Nanoplatelets[END_REF]

Evidence for photogating

The Dirac point of the as-prepared pristine graphene channels lies below -0.3 V (a), meaning that the SiC substrate induces an n doping of the channel (b). Upon back-side illumination with a 532 nm Laser with optical power density ranging from 10 µW/cm 2 to 10 W/cm 2 , no current modulation is observed regardless of the gate voltage, see a. This is consistent with previous works reporting the electrical insensitivity of graphene toward light because of its low 2% absorption [START_REF] Nair | Fine Structure Constant Defines Visual Transparency of Graphene[END_REF] and the sub-picosecond recombination of the electron-hole pair. [START_REF] Urich | Intrinsic Response Time of Graphene Photodetectors[END_REF][START_REF] Yee | Ultrafast modulation of optical transitions in monolayer and multilayer graphene[END_REF] CdSe core NPLs are drop-casted on a bare graphene channel, and the electrolyte is then subsequently brushed (see c for a scheme of the device). Compared to pristine graphene, the Dirac point of the NPL-graphene hybrid shifts toward positive voltage, meaning that electrons from graphene are transferred to the NPL owing to the n type of these nanocrystals, the presence of electron surface traps [START_REF] Lhuillier | Electrolyte-Gated Field Effect Transistor to Probe the Surface Defects and Morphology in Films of Thick CdSe Colloidal Nanoplatelets[END_REF] and the quasi-resonance of NPL conduction band versus graphene Fermi level (d and Supplementary Information Table S1 and Table S3). The positive shift of the Dirac point reflects a carrier density injection in the NPL film around 10 13 charges.cm -2 (see Supplementary Information S4 for details about the calculation). Upon illumination, the Dirac point shifts back toward negative voltages (e). This evidences a charge transfer from the nanoplatelets to graphene upon illumination (f). Because the conduction band of the NPL (-4.4 eV, see Supplementary Info Table S3) is almost resonant with the Fermi level of graphene (-4.5 eV, see Supplementary Info Table S1), the photogenerated electrons are transferred to the graphene channel while the holes remains trapped inside the nanocrystals. This selective charge transfer thus prevents the recombination of the electronhole pair inside the NPL or in the graphene channel, which increases dramatically the gain of the photodetector. [START_REF] Konstantatos | Nanostructured materials for photon detection[END_REF] According to reference [START_REF] Das | Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor[END_REF] S1). Thus, upon 10 W/cm 2 illumination, the negative Dirac point shift corresponds to a Fermi level change from -4.5 eV to -4.3 eV, that is to say that about 10 12 electrons.cm -2 are transferred from the NPL to the graphene channel. As a comparison, under the same illumination condition, 10 9 charges.cm -2 are generated in a film of NPL (see Supplementary Information Table S1). This 3 orders of magnitude difference for photogenerated charges density in comparison with the graphene hybrid evidences a photogating mechanism. [START_REF] Konstantatos | Hybrid graphene-quantum dot phototransistors with ultrahigh gain[END_REF] From the inset of e, it is observed that the displacement of the Dirac point versus the optical intensity Opt P follows a power law , and tends to saturate at powers higher than 1 W/cm 2 .

Charge transfer mechanism

In a steady state regime, the number of photocarriers Δn injected from the NPL to graphene can be written as: 44 τ k

k hν P = Δn rec CT Opt abs



where abs α is the nanoplatelet integrated absorption coefficient, Opt P the optical power density, h the Planck constant, ν the photon frequency, CT k the charge transfer rate from nanoplatelet to graphene, rec k the recombination rate inside the nanoplatelet (radiative and non-radiative 45 ), and τ the lifetime of the injected carriers in the graphene (which is the same as the lifetime of trapped photocarriers in the nanoplatelets). The strength of the photogating effect thus depends on the three parameters CT k , τ and rec k . The lifetime τ is related to the nanocrystal surface chemistry and its environment, while the charge transfer rate CT k can be efficiently magnified by controlling the exciton binding energy. We would like to emphasise that rec k and τ themselves are depending on the carrier density Δn . The overall transferred carrier density is thus self-limited upon high irradiance or particularly efficient charge transfer. In other words, if

CT k or

Opt P increases, electrons are more promptly transferred to the graphene and the supplementary remaining holes in the NPL behave as additional recombination centers, leading also to a rise of

rec k . 46,47
To elucidate the mechanism determining τ, time-resolved photoresponse recovery measurements for a CdSe NPL decorated graphene were performed under various environment conditions (a). Under vacuum, the photoresponse is persistent upon extinction of the laser, with s τ 100 ≫ (a -black curve).

The dark signal is only recovered under ambient air (a -red curve). Without shutting the laser off, the dark current can even be recovered with the introduction of moisture in the system (a -green curve).

This suggests that water is directly responsible for the recombination of trapped holes in the nanocrystals. Upon illumination and in the absence of moisture, the photogenerated holes are permanently trapped, thus increasing their lifetime and the photogating gain. [START_REF] García De Arquer | Tailoring the Electronic Properties of Colloidal Quantum Dots in Metal-Semiconductor Nanocomposites for High Performance Photodetectors[END_REF][START_REF] Konstantatos | Engineering the Temporal Response of Photoconductive Photodetectors via Selective Introduction of Surface Trap States[END_REF] However, in presence of water provided by air, the surface holes get de-trapped by water, thus decreasing τ (see last step of b&c). In the extreme case of very moist air (a -green curve), no photoresponse is measured. This surface-assisted mechanism indicates that the hole traps are likely located in the sulfide-rich surface of the nanoplatelets. We would like to emphasise that this behaviour is fully consistent with previously reported transport and spectroscopic studies on the air/moisture effect on fluorescence. [START_REF] Shao | Organic-Inorganic Heterointerfaces for Ultrasensitive Detection of Ultraviolet Light[END_REF][START_REF] Javaux | Thermal activation of non-radiative Auger recombination in charged colloidal nanocrystals[END_REF][START_REF] Gómez | Exciton-Trion Transitions in Single CdSe-CdS Core-Shell Nanocrystals[END_REF][START_REF] Zhang | Dynamic Charge Carrier Trapping in Quantum Dot Field Effect Transistors[END_REF] Apart from increasing τ, stronger photogating effect is possible by increasing the charge transfer rate CT k process between illuminated NPL and graphene. This requests a deeper understanding of the coupling between the semiconductor NPL and the graphene. According to Marcus Theory, [START_REF] Marcus | Electron transfer reactions in chemistry. Theory and experiment[END_REF][START_REF] Tvrdy | Photoinduced electron transfer from semiconductor quantum dots to metal oxide nanoparticles[END_REF] the charge transfer rate of an electron (resp. hole) to the graphene channel can be estimated by

T k E e T πλ k H π = k B a B CT  4 2 2 
where H is the matrix element of the Hamiltonian coupling between an electron (resp. hole) in the conduction band (resp. valence band) of the NPL and the graphene, λ the reorganization energy and a E the activation energy. The latter can be written structures, we demonstrate that the use of a heterostructure is well suited to achieve charge displacement within the semiconductor. [START_REF] Rosencher | Giant nonlinear optical rectification at 8-12 μm in asymmetric coupled quantum wells[END_REF] We eventually used these heterostructures as a way to enhance the electronic coupling between graphene and the nanocrystals.

CdSe NPLs with their 2D aspect and limited static dielectric (ε = 10) constant [START_REF] Benchamekh | Tight-binding calculations of image-charge effects in colloidal nanoscale platelets of CdSe[END_REF] have a large exciton binding energy (250 meV typically [START_REF] Benchamekh | Tight-binding calculations of image-charge effects in colloidal nanoscale platelets of CdSe[END_REF][START_REF] Achtstein | Electronic Structure and Exciton-Phonon Interaction in Two-Dimensional Colloidal CdSe Nanosheets[END_REF] ) which prevents an efficient charge dissociation. [START_REF] Lhuillier | Electrolyte-Gated Colloidal Nanoplatelets-Based Phototransistor and Its Use for Bicolor Detection[END_REF][START_REF] Lhuillier | Nanoplatelets Bridging a Nanotrench: A New Architecture for Photodetectors with Increased Sensitivity[END_REF] A key advantage of colloidal grown 2D nanoplatelets compared to other transition metal dichalcogenides system is the possibility to further grow at the atomic scale some heterostructures perpendicular to the plane (core/shell structure) or into the plane (core-crown structure). On a 4 monolayers (ML) CdSe core we use the c-ALD procedure [START_REF] Lhuillier | Electrolyte-Gated Field Effect Transistor to Probe the Surface Defects and Morphology in Films of Thick CdSe Colloidal Nanoplatelets[END_REF] to grow a CdS shell (0.9 nm of CdS on each side). In this core/shell structure, there is a complete delocalization of the electron wavefunction over the whole thickness, while the hole stays confined into the CdSe core, see a. We also grow CdSe-CdTe core-crown NPL. The CdSe core is expanded laterally by growing a 10 nm large CdTe crown, while keeping the thickness unchanged. [START_REF] Pedetti | Type-II CdSe/CdTe Core/Crown Semiconductor Nanoplatelets[END_REF] In this material, the electron wavefunction is localized within the CdSe core, while the holes get localized into the crown (type II band alignment), see b. This heterostructure thus enables the exciton dissociation at the nanocrystal scale before charge transfer to graphene, [START_REF] Wu | Efficient and Ultrafast Formation of Long-Lived Charge-Transfer Exciton State in Atomically Thin Cadmium Selenide/Cadmium Telluride Type-II Heteronanosheets[END_REF]



In order to estimate the S value, we use a two bands k.p. model. [START_REF] Harrison | Quantum wells, wires, and dots: theoretical and computational physics of semiconductor nanostructures[END_REF][START_REF] Lhuillier | Quantum transport in weakly coupled superlattices at low temperature[END_REF] More details are given in the Supplementary Information S6 and Table S4 give the parameters used for this modelling. Compared to the core NPL, the core/shell heterostructure has an overlap integral reduced by ≈ 10 %, while for Type II the overlap decreases by about two orders of magnitude. Since the exciton lifetime is 2.5 times longer for the core/shell structure (see c), we can roughly estimate that the Exc E value is twice smaller than for core only structure (Supplementary Information S6).

To confirm that the charge transfer to graphene can be tuned by engineering a heterostructure at the nanoplatelet scale, hybrid graphene-NPL phototransistors involving these objects have been fabricated using an identical procedure than for core-only NPL-graphene hybrids. As expected from the reduction of the binding energy, we notice that under illumination, the Dirac point shifts toward negative gate bias (a) and that the magnitude of the shift is larger for core/shell NPL than for core-only NPL (c).

The amount of transferred electrons is about 3 times larger for the heterostructure (see Supplementary Information Table S1).

Knowing the exciton binding energy

Exc E , the self-exchange reorganization energy λ and the energy difference between the NPL conduction band the graphene Fermi level ΔE , we can quantify the improvement of the charge transfer rate CT k for core/shell NPL in comparison to core only NPL. The self- exchange reorganization energy was recently evaluated [START_REF] Xu | Effects of size polydispersity on electron mobility in a two-dimensional quantum-dot superlattice[END_REF] for a film of colloidal quantum dot and was shown to poorly depend on nanoparticle geometry. The NPL contribution to the λ is thus estimated to be 0.1 ± 0.05 eV. Since the reorganization energy for graphene nanoribbons and for graphene-like πconjugated systems sharply decreases as a function of the number of carbon atoms, [START_REF] Torres | Electronic structure of graphene nanoribbons doped with nitrogen atoms: a theoretical insight[END_REF][START_REF] Sancho-García | Charge-transport properties of prototype molecular materials for organic electronics based on graphene nanoribbons[END_REF][START_REF] Brédas | Charge-Transfer and Energy-Transfer Processes in π-Conjugated Oligomers and Polymers: A Molecular Picture[END_REF] the graphene contribution to λ is largely smaller than 0.1 eV and can be neglected. The energy level difference ΔE remains equal to 0.1 eV since the 0.2 eV Fermi level shift between core-only and core/shell NPL decorated graphene reflects the confinement energy reduction of 0.2 eV between the two types of NPL (see Supplementary Information S4 and S5). The reduction of Exc E from 0.2 eV to 0. with op n the sheet density optically generated in the covering semiconductor, we expect that the increase of the charge transfer rate is partially compensated by the opposite evolution of rec k τ / at steady state. However, the net increase of the injected carriers Δn in graphene by switching from core- only to core/shell NPL validates the exciton binding energy engineering strategy.

In the case of core-crown NPL decorated graphene under illumination higher than 100 mW.cm -2 , the Dirac point shift reverses toward positive voltages, meaning that holes are being injected to the graphene (b and c). This is consistent with the rise in absolute energy of the valence band of CdTe compared to CdSe (see Supplementary Information Table S3). When the electron injection from the CdSe core saturates, holes from the CdTe crown are efficiently injected into the graphene channel. For all materials, the shift of the Dirac point with illumination is sublinear and follows approximately a power law with a 0.23 exponent. This behaviour is also a consequence of the dependence of the recombination rate rec k and the trapped carrier lifetime τ on the number of injected carriers in graphene Δn . A higher photon flux means a higher optically generated electron-hole pairs density op n . As for CT k , the resulting increase of injected carriers Δn is moderated by the opposite evolution of rec k τ / . This leads to the observed sublinear dependence of the charge transfer on incident light power at steady state.

Device performances

Being the best candidate for photodetection among the tested materials, we made a photodetector by depositing CdSe/CdS core/shell nanoplatelets on a graphene channel. Current versus voltage characteristics are measured under increasing illumination power Opt P , see a. An increase of the current is measured under increasing illumination, arising from the conductance modulation of the graphene channel due to photogating (a). We verified that no significant modulation is measurable for bare graphene devices (Supplementary Information Figure S2a). The responsivity figure of merit  is mainly driven by the illumination power (b). This is due to the weak dependence of the photocurrent to the optical intensity, allowing the measurement of weak optical signals. [START_REF] Konstantatos | Hybrid graphene-quantum dot phototransistors with ultrahigh gain[END_REF] The responsivity under modulated illumination is also measured (c and Supplementary Information S7 for details about the measurement procedure). For modulation frequencies ranging from 1 Hz to 100 Hz, the responsivity decreases with the modulation frequency. These behaviours are consistent with the fact that the system is a photogating-based graphene photodetector. This strategy indeed allows enhanced made possible by the high mobilityµ ≈ 1000 cm 2 .V -1 .s -1 of graphene [START_REF] Pallecchi | High Electron Mobility in Epitaxial Graphene on 4H-SiC(0001) via post-growth annealing under hydrogen[END_REF] . It comes at the price of a lowered bandwidth, the latter being inversely proportional to the carrier lifetime τ .

The photodetection performances of photodetectors can be compared by calculating the specific detectivity * D figure of merit. Since it can be expressed as

n S A R = D *
where A the optical area and n S the current noise spectral density, a measurement of the noise is required. We emphasise that the latter could not be estimated by the Johnson-Nyquist (thermal) noise nor by the Shot noise because graphene possesses 1/f excess noise at frequencies below a few kHz. [START_REF] Balandin | Low-frequency 1/f noise in graphene devices[END_REF] It is still an open question whether the presence of nanocrystals decorating the graphene may lead or not to a dramatic enhancement of the noise. In order to measure the noise arising from a graphene channel, we chose a Wheatstone bridge configuration comprising of 4 identical graphene channels biased using a battery (see Supplementary Information S3 scheme S1). [START_REF] Demolder | The measuring of 1/f noise of thick and thin film resistors[END_REF] The fluctuations of the voltage difference V between the middle of the two branches are the averaged noise coming from the 4 graphene channels,

i.e. 4 / 4 1  = i i V, measured V,

S = S

. This strategy suppresses the upstream noise arising from the source and common-mode noise arising from environmental perturbations. The square-voltage noise spectral density is measured for a bare graphene channel under increasing bridge excitation voltage I V and presented in d. A 3 parameters fit according to the equation , consistent with previous report of 1/f noise in graphene. [START_REF] Balandin | Low-frequency 1/f noise in graphene devices[END_REF] The square voltage noise spectral density 2 V S thus scales quadratically with the applied bias. In the framework of the Hooge model, knowing the total number of carriers involved in transportN, we can calculate the α parameter characterizing the intrinsic noise of a sample:

γ Thermal V, V f β + S = S
fN α = V S DS V 2 2
The channel area being 270 × 30 µm 2 and the carrier density of bare graphene on SiC being 8.10 12 cm -2 (Supplementary Information Table S1), we estimate the value of the Hooge parameter

1 4 ± = N × A = α .
CdSe/CdS core/shell nanoplatelets are then deposited on the four channels of the Wheatstone bridge, and the same noise measurements are performed (see Supplementary Information Figure S2b and e -red curve). The 1/f behaviour is still maintained and the thermal noise floor is reached. However, the noise level is increased by a factor 3, meaning that (Supplementary Information Table S1), this gives a Hooge parameter

5 ≈ α
. Given the accuracy of the α parameter estimation, this parameter is barely affected by the deposition of nanoplatelets on graphene.

This is compatible with a noise modulation resulting from the graphene carrier density modulation upon NPL deposition. [START_REF] Wang | Charge Transfer and Current Fluctuations in Single Layer Graphene Transistors Modified by Self-Assembled C60 Adlayers[END_REF] Rather than defect centers, nanoplatelets could possibly behave as a passivation layer toward air. [START_REF] Rumyantsev | Selective Gas Sensing with a Single Pristine Graphene Transistor[END_REF] To the best of our knowledge, this is the first time that the effect of particles deposition on graphene is reported in term of noise. Measuring noise in nanocrystal-based devices is of crucial importance since 1/f noise cannot be predicted despite being ubiquitous, thus limiting devices ultimate performances. [START_REF] Balandin | Low-frequency 1/f noise in graphene devices[END_REF][START_REF] Demolder | The measuring of 1/f noise of thick and thin film resistors[END_REF] The detector achieves a specific detectivity 6 *

= D

Jones weakly dependent on the modulation frequency (Supplementary Information S7 and f), owing to the similar dependence of the noise spectral density and responsivity versus frequency of operation. Compared to PbS-graphene devices, our all 2D hybrid achieves relatively low detectivities. [START_REF] Konstantatos | Hybrid graphene-quantum dot phototransistors with ultrahigh gain[END_REF] This is a direct consequence of the reduced exciton binding energy for PbS quantum dots, around 10 meV thanks to their large dielectric constant. [START_REF] Kang | Electronic structure and optical properties of PbS and PbSe quantum dots[END_REF] Since TMDC together with chalcogenides nanoplatelets exhibit high exciton binding energies over hundreds of meV resulting from the material and their monolayer structure, [START_REF] Zhu | Exciton Binding Energy of Monolayer WS2[END_REF][START_REF] Komsa | Effects of confinement and environment on the electronic structure and exciton binding energy of MoS${}_{2}$ from first principles[END_REF][START_REF] Ugeda | Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor[END_REF] this emphasises the need to reduce the exciton binding energy to build efficient monolayer based devices. Our results suggest that it could be practically done by building heterostructures at the monolayer scale.

Conclusions

Heterostructures grown at the nanocrystal scale is a practical strategy to 1) lower the exciton binding energy by delocalizing one type of carrier versus the other one, 2) choose the availability of one or the other type of carrier toward charge transfer. Applied to a photodetector made from CdSe-based nanoplatelets decorated on a graphene channel, the growth of a CdS shell enables a more efficient ntype photogating of the graphene while the growth of a CdTe crown produces a p-type photogating. We expect this strategy to be profitable to other 2D materials, [START_REF] Dogan | Field-effect transistors made of individual colloidal PbS nanosheets[END_REF] especially heterostructures involving TMDC because of their giant exciton binding energies. Noise measurements reveals that the deposition of nanoplatelets on graphene increases the noise magnitude by a factor 2 -3 but does not alter the 1/f behaviour nor the Hooge's parameter α. D is the specific detectivity at 1Hz for a CdSe/CdS core/shell NPL decorated graphene photodetector as a function of frequency. Details about the calculations are given in Supplementary Information S7.

F

  photodetector.[START_REF] Konstantatos | Nanostructured materials for photon detection[END_REF] According to reference[START_REF] Das | Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor[END_REF] , we could relate the Dirac point voltage D V to the graphene

  Fermi level and the conduction (resp. valence) band of NPL. Faster charge transfer consequently requests to combine a weaker exciton binding energy with almost resonant coupling of one type of carrier to graphene. The second band of the semiconductor has to stay out of resonance to avoid charge recombination within the graphene. As proposed for quantum well

m

  see c. Apart from the improved charge dissociation, the introduction of a CdTe is also motivated by its bands shifted closer to the vacuum level. This shift raises the valence band level closer to the graphene Fermi level while the conduction band is getting off resonance, see c. As a consequence, for the CdSe-CdTe core-crown heterostructure, we expect a more favourable hole transfer to graphene. The two types of heterostructures present a reduced overlap of the electron and hole wavefunctions and thus likely a reduced binding energy. Details about the synthesis are given in Supplementary Information S1. The spectra of suspensions of such heterostructures are presented in a.To quantify the reduction of the exciton binding energy, we use time resolved photoluminescence (PL) spectroscopy, see c. We can indeed relate the radiative lifetime to the exciton binding energy Exc E and the oscillator strength f thanks to the relation 58,59 the rest mass of the electron,  the reduced Planck's constant, n the optical index of the medium. The oscillator strength can be estimated as

1

 1 photogain

  the average resistance of the channels kΩ = R 8 . The value of the power exponent is 0.05 1.05± = γ as expected for 1/f noise without generation-recombination bulges. The magnitudeβof the noise is plotted versus the applied voltage bias in the e -black curve. A simple 3 parameters power law fit

  According to a carrier density of graphene after CdSe/CdS NPL deposition of about 3.10 12 cm -2

Figure 1 .

 1 Figure 1. (a) Absorbance spectra of a suspension of CdSe core (green line), CdSe/CdS core/shell (red line) and CdSe-CdTe core-crown (blue line) nanoplatelets. (b) TEM picture of CdSe core nanoplatelets. (c) Raman spectra of a hydrogenated graphene layer on the Si-face of 4H-SiC. (d) STM image (-50 mV, 0.1 nA) of such a graphene sample.

Figure 2 .

 2 Figure 2. (a,b) Epitaxial graphene grown on insulating SiC substrate in electrolytic field effect transistor geometry. (a) Drain current (plain) and gate current (dashed) versus gate voltage at different laser optical powers (see inset). (b) Scheme of the device with gold contacts and side gate. Inset: scheme of the Dirac cone with n doped graphene. (c,d) Graphene decorated with CdSe nanoplatelets in the dark. (c) Transfer curve of undecorated graphene (black) and NPL-decorated graphene (red). The arrow shows the displacement of the Dirac point. (d) Scheme of the device and of the electron transfer from the graphene channel to the NPL. (e,f) Graphene-NPL phototransistor under illumination. (e) Transfer curves of the device under increasing optical intensities (see a). Inset: Absolute value of the Dirac point displacement versus optical intensity averaged over 6 samples (black squares) and a power law fit giving an exponent 0.23 (dashed red line). (f) Scheme of the device and of the electron transfer from NPL to graphene upon illumination.

Figure 3 .

 3 Figure 3. (a) Normalized photoresponse decay of a CdSe core NPL decorated graphene channel under various gas environments. Except for the measure under a moist air flow, the curves represent the current decay just after shutting the laser off under secondary vacuum (dark) and ambient air (red). As no photoresponse is measured under moist air flow, in this case the curve represents the current decay just after turning on the moist air flow (green). For all measurements, the curves are normalized by the photocurrent. (b) Proposed mechanism for electron transfer to graphene and water-assisted hole trapping for CdSe core and CdSe/CdS core/shell NPL decorated graphene upon illumination. (c) Proposed mechanism and associated transfer rates for the exciton dissociation, charge transfer to graphene and water-assisted hole trapping for

29

 29

Figure 4 .

 4 Figure 4. (a) Calculated band structure of the CdSe/CdS core/shell heterostructure. Grey: energy levels of the bulk materials, red (resp. blue): conduction (resp. valence) band of the heterostructures. Holes are confined in the core while electrons are delocalized over the entire structure. (b) Calculated band structure of the CdSe-CdTe core-crown type II heterostructure. Grey: energy levels of the bulk materials, red (resp. blue): conduction (resp. valence) band of the heterostructures. Holes are confined in the crown while electrons are confined in the core. (c) Photoluminescence decay spectra of CdSe core NPL (green), CdSe/CdS core/shell NPL (red), and CdSe-CdTe core-crown NPL (blue).

Figure 5 .

 5 Figure 5. Transfer curves under increasing illumination power (see a for the legend) for (a) CdSe/CdS core/shell NPLgraphene phototransistor; (b) CdSe-CdTe core-crown NPL -graphene phototransistor. (c) Displacement of the Dirac point voltage versus incident optical power for graphene (black), graphene -CdSe core (green), graphene -CdSe/CdS core/shell (red), graphene-CdSe-CdTe core-crown (blue). The points are averaged over 3 to 6 devices, and the error bars represent the standard deviation to the mean.

31

 31

Figure 6 . 2 .

 62 Figure 6. (a-c) CdSe/CdS core/shell NPL decorated graphene samples. (a) Current versus voltage of a single channel

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				P ΔV ∝	α
				D	Opt
	with	α	=	0.23

  1 eV while switching from core to core/shell NPL thus cancels the energy barrier

					E	Exc 	ΔE	. The activation energy	a E is thus
	reduced by a factor 4, leading to a potential increase of the charge transfer rate	k up to a factor 150 at
							CT
	room temperature. Because a more efficient charge transfer from NPL to graphene also means a more
	charged nanocrystal and thus increased Auger recombination, the recombination rate	k is increased
							rec
	and the trapped carrier lifetime τ is lowered. When considering the expression of injected carriers in
	graphene
	Δn	=	n	k	CT	τ
			op
				k
					rec

Acknowledgements

We thank Agence National de la Recherche for funding through grants SNAP and H2DH. This work has been supported by the Region Ile-de-France in the framework of DIM Nano-K.

Author contributions

Additional information

Competing financial interests: The authors declare no competing financial interests. Supplementary Information accompanies this paper at http://www.nature.com/scientificreports