High Responsivity, Large-Area Graphene/MoS2 Flexible Photodetectors

We present flexible photodetectors (PDs) for visible wavelengths fabricated by stacking centimeter-scale chemical vapor deposited (CVD) single layer graphene (SLG) and single layer CVD MoS2, both wet transferred onto a flexible polyethylene terephthalate substrate. The operation mechanism relies on injection of photoexcited electrons from MoS2 to the SLG channel. The external responsivity is 45.5A/W and the internal 570A/W at 642 nm. This is at least 2 orders of magnitude higher than bulk-semiconductor flexible membranes. The photoconductive gain is up to 4 × 105. The photocurrent is in the 0.1–100 μA range. The devices are semitransparent, with 8% absorptance at 642 nm, and are stable upon bending to a curvature of 1.4 cm. These capabilities and the low-voltage operation (<1 V) make them attractive for wearable applications.

M odern electronic and optoelectronic systems, such as smart phones, smart glasses, smart watches, wearable devices, and electronic tattoos, increasingly require ultrathin, transparent, low-cost, and energy efficient devices on flexible substrates. 1 The rising demand for flexible electronics and optoelectronics requires materials that can provide a variety of electrical and optical functionalities, with constant performance upon application of strain. 2 A wide range of optoelectronic devices on flexible substrates have been reported to date, such as photodetectors (PDs), 3,4 light emitting diodes (LEDs), 5 optical filters, 6 optical interconnects, 7,8 photovoltaic devices, 9,10 and biomedical sensors. 11,12 Major challenges in the development of flexible optoelectronic devices stem from the limitations associated with the high stiffness of bulk semiconductors. 13,14 In the case of flexible PDs, the current approaches primarily rely on thin (μm-thick) semiconductor membranes 4,15 and compound semiconductor nanowires (NWs), 3,16−18 mainly because of their ability to absorb light throughout the whole visible range (0.4−0.7 μm) and the possibility to adapt their fabrication techniques from rigid to plastic, or deformable substrates. 1 One of the key parameters for PDs characterization is the responsivity. This is defined as the ratio between the collected photocurrent (I ph ) and the optical power. The responsivity is named external (R ext = I ph /P o ) 19 or internal (R int = I ph /P abs ), 19 whenever the incident (P o ) or absorbed (P abs ) optical power is used in the denominator. Since not all incident photons are absorbed by a PD, i.e., P abs < P o , then R int is typically larger than R ext . 19 In flexible PDs, R ext up to∼ 0.3 A/W was reported for crystalline semiconductor membranes (InP, Ge) 4,15 with integrated p−i−n junctions, showing photocurrent up to∼ 100 μA, with∼ 30% degradation upon bending at a radius r b ∼ 3 cm. 15 PDs made of a single semiconductor NW on flexible substrates 3,16−18 demonstrated R ext up to∼ 10 5 A/W, for r b down to 0.3 cm. 3 Yet, these provide limited I ph in the order of nA 3,16,18 up to <1 μA. 17 For flexible devices exploiting NW arrays by drop-casting, 3,16,18 rather than based on single NWs, R ext degrades significantly from ∼10 5 A/W to the mA/W range, 3,16,18 due to photocurrent loss at multiple junctions in the NW network. 3,16,18 Graphene and related materials (GRMs) have great potential in photonics and optoelectronics. 20−23 A variety of GRM-based devices have been reported, such as flexible displays, 24 photovoltaic modules, 25,26 photodetectors, 22,27−29 optical modulators, 30 plasmonic devices, 31−35 and ultrafast lasers. 23 Heterostructures, obtained by stacking layers of different materials, were also explored, 21,22 e.g., in photovoltaic 36 and light emitting devices. 37 Flexible PDs based on GRMs were studied for ultraviolet, 38,39 visible, 40−45 and near-infrared bands. 46,47 In these devices, different materials and heterostructures produced by mechanical exfoliation, 40,41 Chemical Vapor Deposition (CVD), 42,43,46 and liquid-phase exfoliation (LPE) 44,45,47 were employed. The flexible PDs produced by mechanical exfoliation 40,41 have a small (∼μm 2 ) photoactive area, and they cannot be scaled up to mass production. LPE-based PDs have low (<mA/W) 44,45 responsivity. Ref 47 showed that thick (∼μm) films of chemically modified, charge-transfer optimized, LPE-produced, MoSe 2 and MoS 2 polymer composites can provide ∼ A/W responsivity 47 at near-infrared bands. Nevertheless, these PDs require high (∼10 V) operation voltage and are nontransparent. Flexible PDs at 450 nm using CVD MoS 2 transistors 42 and MoS 2 /WS 2 heterostructures 43 were previously reported, and PDs at 780 nm were prepared from doped SLG p−n junctions. 38 However, these devices have responsivity in the mA/W range. CVD-based SLG/MoS 2 heterostructures 48 showed good photodetection on rigid Si/SiO 2 substrates, with back-gate-dependent R int ∼ 10 8 A/W for optical intensities <0.1pW/μm 2 .
Here we demonstrate a polymer electrolyte (PE) gated, CVD-based, flexible PD, for visible wavelengths, with large (∼mm 2 ) photoactive area combined with high responsivity (∼hundreds A/W), high (>80%) transparency, gate tunability, low (<1 V) operation voltage, and stable (±12%) I ph upon multiple (>30) bending cycles. The device is assembled by stacking on a PET substrate a centimeter-scale CVD single layer graphene (SLG) on top of a CVD-grown single layer MoS 2 (1L-MoS 2 ). In this configuration, 1L-MoS 2 acts as visible light absorber, while SLG is the conductive channel for photocurrent flow. 48 We show that R ext can be increased by promoting carrier injection from 1L-MoS 2 to SLG using PE gating, or by increasing the source-drain voltage. This is achieved in devices with∼ 82% transparency, twice that reported for semiconductor membrane devices. 15 We get R int ∼ 570A/W for ∼0.1nW/μm 2 at 642 nm, similar to SLG/MoS 2 PDs 48 on rigid substrates operating at the same optical power. This shows that SLG/MoS 2 heterostructures on PET retain their photodetection capabilities. We note that the devices from ref 48 have at least 2 orders of magnitude smaller photoactive area with respect to ours, and they are not flexible, not transparent, and require tens of volts operation, unlike the <1 V of ours. Upon bending, our PDs have stable performance for r b down to ∼1.4 cm. This is comparable to r b measured in semiconductor membranes PDs, 4,15 which show lower (<0.3 A/W) responsivities. 4,15 Although our r b is 1 order of magnitude larger than for flexible single NWs, 3,16−18 the latter had at least 3 orders of magnitude smaller device areas (<5 μm 2 ) 3,16−18 compared to our PDs (>0.2 mm 2 ). Given the responsivity, flexibility, transparency, and low operation voltage, our PDs may be integrated in wearable, biomedical, and lowpower optoelectronic applications. 11,12,17 RESULTS Figure 1a plots a schematic drawing of our PDs. We fabricated 4 PD arrays with 10 devices each, with channel lengths of 100 μm, 200 μm, 500 μm, and 1 mm. Each device consists of a 1L-MoS 2 absorber covered by a SLG channel, clamped between source and drain electrodes. We chose PET as a flexible substrate due to its ∼90% transparency in the visible range 49 and ability to withstand solvents (e.g., acetone and isopropyl alcohol) 50 commonly used in the transfer processes of layered materials grown by CVD (e.g., transfer of SLG grown on Cu). 51 A 1L-MoS 2 is used as absorber in order to preserve >80% transparency, considered suitable by industry for wearable applications, 52 Figure 1b. The SLG/1L-MoS 2 heterostructure is gated using a PE. 53,54 The operation principle of our devices is depicted in Figure  2. For energy bands alignment, the electron affinity of 1L-MoS 2 and the Dirac point of SLG are assumed to be ∼4−4.2 eV 55,56 and ∼4.6 eV, 57,58 respectively. We also assume SLG to be initially p-doped (Figure 2a), as reported in previous works involving SLG transferred on PET. 59,60 At zero voltage the device is in thermodynamic equilibrium with a constant Fermi level (E F ) and zero current flow between the layers. During illumination and photon absorption in MoS 2 , part of the photogenerated electrons would be injected from the 1L-MoS 2 conduction band into the lower energy states in p-doped

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Article SLG, 48 leaving behind the uncompensated charge of photogenerated holes. The latter would be trapped in 1L-MoS 2 and act as an additional positive gate voltage, V GS , applied to the SLG channel, resulting in a shift of the charge neutrality point (V CNP ) to more negative voltages. The injected electrons from 1L-MoS 2 would occupy energy states above E F (Figure 2b), thus reducing the hole concentration and decreasing the hole current in the SLG channel. Electron injection can be further promoted by gating. When a negative V GS is applied, higher pdoping of the SLG channel would induce a stronger electric field at the SLG/1L-MoS 2 interface, 48 thus favoring electron transfer from 1L-MoS 2 ( Figure 2b). Hence, for negative V GS , R ext is expected to increase, due to injection of more photoelectrons to SLG and consequent more pronounced current reduction. The opposite should happen for positive V GS , where the gate-induced negative charge in SLG would reduce the p-doping and shift E F toward the Dirac point. In this case, the photogenerated electrons in 1L-MoS 2 would experience weaker electric fields at the SLG/1L-MoS 2 interface 48 and would become less attracted by the SLG channel. Thus, we expect R ext to decrease. For high enough positive V GS , E F would cross the Dirac point, and SLG becomes n-doped ( Figure 2c). As a result, only a weak electron injection from 1L-MoS 2 would be possible, if E F in SLG remains below the 1L-MoS 2 conduction band, retaining a weak electric field at the interface. In this regime, the transferred electrons would increase the free carrier concentration in the n-doped channel, hence only minor increments of R ext and I ph are expected.
Our devices are built as follows: 1L-MoS 2 is epitaxially grown by CVD on c-plane sapphire substrates, 61 while SLG is grown on a 35 μm Cu foil, following the process described in refs 51 and 62 (see Methods for details). Prior to assembling the SLG/ MoS 2 stack, the quality and uniformity of MoS 2 on sapphire and SLG on Cu are inspected by Raman spectroscopy and photoluminescence (PL), using a Horiba Jobin Yvon HR800 spectrometer equipped with a 100× objective. The laser power is kept below 100 μW (spot size <1 μm) to avoid possible heating effects or damage. Figure 3a (green curve) plots the Raman spectrum of CVD MoS 2 on sapphire for 514 nm excitation. The peak at ∼385 cm −1 corresponds to the in-plane (E 2g 1 ) mode, 63,64 while that at ∼404 cm −1 is the out of plane (A 1g ) mode, 63,64 with full width at half-maximum FWHM (E 2g 1 ) = 2.5 and FWHM(A 1g ) = 3.6 cm −1 , respectively. The E 2g 1 mode softens, whereas the A 1g stiffens with increasing layer thickness, 65,66 so that their frequency difference can be used to monitor the number of layers. 65 The peak position difference ∼20 cm −1 is an indicator of 1L-MoS 2 . 65 The peak at∼ 417 cm −1 (marked by an asterisk in Figure 3a) corresponds to the A 1g mode of sapphire. 67

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The Raman spectrum measured at 514 nm of SLG on Cu is shown in Figure 3b (magenta curve). This is obtained after the removal of the background PL of Cu. 68 The two most intense features are the G and the 2D peak, with no significant D peak. The G peak corresponds to the E 2g phonon at the Brillouin zone center. 69 The D peak is due to the breathing modes of sp 2 rings and requires a defect for its activation by double resonance. 69−72 The 2D peak is the second order of the D peak. 69 This is always seen, even when no D peak is present, since no defects are required for the activation of two phonons with the same momentum, one backscattering from the other. 69 In our sample, the 2D peak is a single sharp Lorentzian with FWHM(2D) ∼26 cm −1 , a signature of SLG. 70 Different (∼20) measurements show similar spectra, indicating uniform quality throughout the sample. The position of the G peak, Pos(G), is ∼1588 cm −1 , with FWHM(G) ∼6 cm −1 . The 2D peak position, Pos(2D) is ∼2705 cm −1 , while the 2D to G peak intensity and area ratios, I(2D)/I(G) and A(2D)/A(G), are ∼2.6 and ∼5.8, respectively, indicating a p-doping ∼300 meV, 53,73,74 which corresponds to a carrier concentration ∼6 × 10 12 cm −2 .
Another evidence for 1L-MoS 2 comes from the PL spectrum [ Figure 4a (green curve)], showing a peak at ∼658 nm (∼1.88 eV), due to band-to-band radiative recombination in 1L-MoS 2 . 75 Then, the MoS 2 film is transferred onto a PET substrate from sapphire using a KOH-based approach. 61 The samples are first spin coated with ∼100 nm poly(methyl methacrylate) (PMMA). This is detached in a 30% KOH solution, washed in deionized (DI) water, and transferred onto PET. The PMMA is then dissolved in acetone. Subsequently, SLG is transferred on the 1L-MoS 2 on PET. PMMA is spin coated on the SLG/Cu substrate and then placed in a solution of ammonium persulfate (APS) in DI water until Cu is etched. 51,76 The PMMA membrane with attached SLG is then transferred to a beaker filled with DI water for cleaning APS residuals. The membrane is subsequently lifted with the target PET substrate, having 1L-MoS 2 on top. After drying, PMMA is removed in acetone leaving SLG on 1L-MoS 2 .
Raman and PL characterizations are performed at each step of the SLG/1L-MoS 2 assembly on PET, i.e., on 1L-MoS 2 transferred on PET and on SLG on 1L-MoS 2 . This is to confirm no degradation during the fabrication process. Figure  3a (red curve) plots the Raman spectrum of 1L-MoS 2 on PET. The frequency difference between E 2g 1 and A 1g and the FWHMs are preserved on PET, suggesting no degradation. The PL spectrum of 1L-MoS 2 on PET is shown in Figure 4b  . Prior to subtraction, the spectra are normalized to the intensity of the Raman peak at ∼1615 cm −1 (corresponding to the peak at ∼560 nm in Figure 4b), due to the stretching vibrations of benzene rings in PET. 77 As a result, the PL signal of 1L-MoS 2 can be seen in Figure 4a  We then characterize the SLG transferred on 1L-MoS 2 /PET. The intense Raman features of the underlying PET substrate 77 [ Figure 3c (black curve)] mask the SLG peaks. In order to reveal the Raman signatures of SLG, we first measure the reference spectrum, shown in Figure 3c (black curve), of a PET substrate, using identical conditions as those for SLG/1L-MoS 2 /PET. We then implement a point-to-point subtraction, normalized to the intensity of the PET peak at ∼1615 cm −1 , of the PET reference spectrum, Figure 3c (black curve), from the total spectrum, Figure 3c (blue curve). The result is in Figure

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Article 3b (blue curve). The 2D peak retains its single-Lorentzian lineshape with FWHM(2D) ∼28 cm −1 , validating the transfer of SLG. The negligible D peak indicates that no significant defects are induced during transfer. Pos(G) is ∼1583 cm −1 , FWHM-(G) ∼ 17 cm −1 , Pos(2D) ∼ 2683 cm −1 , and A(2D)/A(G) ∼ 4.8, indicating a p-doping ∼4 × 10 12 cm −2 (∼250 meV). 53,73 We then measure the absorptance and transmittance of SLG/1L-MoS 2 using a broadband (400−1300 nm) white light from a tungsten halogen lamp. The transmitted light is collected by a 10× objective lens (NA = 0.25) with a Horiba Jobin Yvon HR800 spectrometer equipped with a 300 grooves/ mm grating, charged coupled device (CCD) detector and a 50 μm pinhole. Figure 75,78 Their positions remain unchanged after SLG transfer. The absorptance difference between the two curves (red and blue) is ∼2.6%, consistent with the additional SLG absorption. 79 The PD area is shaped by etching, whereby SLG extending beyond the 1L-MoS 2 flake is removed in an oxygen plasma. The source, drain and gate electrodes are then defined by patterning the contacts area, followed by Cr/Au (6 nm/60 nm) evaporation and lift-off. PDs with different channels lengths (100 μm to 1 mm), 2 mm channel width, and common sidegate electrodes (1 × 0.5 cm) are built (Figure 1b). Ref 48 showed that the responsivity of SLG/MoS 2 PDs can be enhanced by gating. This induces a stronger electric field at the SLG/MoS 2 interface and promotes charge transfer. Various gating techniques have been exploited for GRM-based devices, including conventional Si/SiO 2 back-gates, 80 high-k dielectrics (Al 2 O 3 , HfO 2 ), 81 chemical dopants, 82 ionic liquids, 83 and PEs. 53,74 In order to gate our SLG/1L-MoS 2 on PET, we employ the latter due to its compatibility with flexible substrates 84 and the ability to substantially dope SLG (±0.8 eV) 53,74 using small gate voltages (up to 4 V), unlike other gating techniques, which would require considerably higher biases to reach the same doping. 80,82 We use a PE consisting of LiClO 4 and poly(ethylene oxide) (POE). 53,74 We place the PE over both the SLG channel and the side-gate electrode. To evaluate the effect of PE deposition on the SLG channel doping, we use Raman analysis. We get Pos(G) ∼ 1583 cm −1 , FWHM(G) ∼ 19 cm −1 , Pos(2D) ∼ 2686 cm −1 , and A(2D)/ A(G) ∼ 5.3, consistent with a small reduction of p-doping to ∼230 meV. 53,73 For electrical measurements we apply −1 V < V GS < 1 V in order to avoid electrochemical reactions, such as hydrolysis of residual water in the electrolyte. 85,86 These may permanently modify the graphene electrode 85,86 and compromise the stability and performance of the device. To control the stability of the PE gating, we continuously monitor the gate leakage current (I gate ), keeping I gate < 1 nA throughout the experiments. The devices are tested ∼30 times, showing no degradation in the leakage current over at least six months.
The I DS −V GS measurements in Figure 6a are done at room temperature using a probe station and a parameter analyzer (Keithley 4200). The PD is illuminated at normal incidence by a collimated laser with P o ranging from 100 μW to 4 mW. At these P o and with V DS = 0.1 V we measure a positive V CNP ranging from ∼0.39 to 0.47 V, indicating an initial SLG pdoping ∼220 meV, consistent with the Raman estimate. Figure 6a shows that for −1 V < V GS < 0.5 V, where SLG transport is hole dominated, the current decreases under illumination (∼10 μA at V GS = −1 V), as anticipated from the band-diagram of Figure 2. For V GS > 0.5 V, where SLG is electron-doped, the PD shows a small (up to ∼0.2μA) current increase under illumination. Figure 6b plots R ext as a function of V GS , as derived from transconductance measurements using: 19 where I light and I dark are the PD current under illumination and in dark, |I light − I dark | = I ph is the photocurrent defined as the absolute change in the device current upon illumination, A o is the laser spot area, A PD is the PD area, and A PD /A o is a scaling factor that takes into account the fact that only a fraction of optical power impinges on the PD. As expected from the banddiagram in Figure 2, R ext tends to increase for more negative V GS , up to ∼5.5 A/W at V GS = −1 V, V DS = 0.1 V for P o = 100 μW. By taking into account that only 8% of light is absorbed

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Article (P abs = 0.08 × P o ), we derive R int = R ext /0.08 = 69A/W. Figure  6b implies that the higher P o , the lower R ext . This can be explained considering that the more photogenerated electrons are injected into the p-doped channel, the lower the electric field at the SLG/1L-MoS 2 interface, therefore a reduced injection of electrons causes R ext to decrease. Given that R ext ,R int > 1A/W, we expect a photoconductive gain (G PD ), 19,87 whereby absorption of one photon results in multiple charge carriers contributing to I ph . Our PDs act as optically gated photoconductors, where the SLG conductance is modulated by optical absorption in the 1L-MoS 2 . In this configuration, the presence of G PD implies that the injected electrons in SLG can recirculate multiple times between source and drain, before recombining with trapped holes in 1L-MoS 2 . Consequently, G PD can be estimated as the ratio of electrons recombination (τ rec ) and transit (t tr ) times in the SLG channel: G PD = τ rec /t tr . 19,21,22,87 For higher V DS , the free carriers drift velocity υ d in the SLG channel increases linearly with bias (ohmic region) until it saturates, because of carriers scattering with optical phonons. 88 The linear increase in υ d results in shorter t tr , with t tr = L/υ d , where L is the channel length. 19,21,22,87 Therefore, G PD is also expected to grow linearly with V DS , providing higher R ext . To confirm the photoconductive nature of G PD in our devices and test the dependence of R ext on V DS , we measure I DS −V DS under illumination at P o = 100 μW for V GS = −1 V and calculate R ext using eq 1. The I DS −V DS characteristics of the PD show linear dependence, confirming ohmic behavior of the metal-SLGmetal channel. 89 We use V DS < 1 V to keep the device operation in the linear (ohmic) regime and minimize the effects of the nonlinear dependence of υ d on V DS (such as velocity saturation) that might appear for V DS > 1 V. 88 As shown in Figure 7, R ext scales with V DS and reaches ∼45.5A/W (R int ∼ 570A/W) at V DS = 1 V. This is almost 1 order of magnitude higher than at V DS = 0.1 V, consistent with the similar increase in V DS . These results are at least 2 orders of magnitude higher than semiconductor flexible membranes. 4,15 Furthermore, such a combination of high responsivity with μA range photocurrent surpasses that found in other GRM-based PDs in the visible range. [40][41][42][43][44][45]47 We also fabricate a control device with a 1L-MoS 2 channel only, without SLG. This has R ext ∼ 2 mA/W, which is 4 orders of magnitude smaller than that of our SLG/ 1L-MoS 2 heterostructure. We thus conclude that SLG/1L-MoS 2 heterostructures are necessary to achieve high (hundreds A/W) responsivity, due to the presence of photoconductive gain.
To assess the photoresponse uniformity in our SLG/1L-MoS 2 heterostructures, we perform photocurrent mapping using the same laser source (642 nm) as for optoelectronic characterizations. We scan areas of 80 × 140 μm (pixel size 3 × 3 μm) at different locations. At each position (pixel) the device photocurrent is measured for V DS = 0.3 V (Figure 8a). We also collect the backscattered light to give a reflection map ( Figure  8b). Figure 8a indicates that the entire channel area confined between the source-drain electrodes is photoactive, and shows uniform photocurrent photoresponse with standard deviation ±15%. We thus conclude that interface imperfections (e.g., bubbles, polymer residuals, etc.) have minor effect on the charge transfer process from MoS 2 to graphene.
We define G PD as the ratio between electrons recirculating in the SLG channel, thus sustaining I ph , and the initial electron concentration injected into SLG from 1L-MoS 2 : 48 where q is the electron charge and Δn ch is the concentration per unit area and per unit time of the injected electrons. Δn ch is equal to the trapped-hole concentration per unit area and per unit time in 1L-MoS 2 , which is related to a charge neutrality point shift ΔV GS = ΔV CNP in the transfer characteristics. To calculate Δn ch , we first write the potential balance in the metaldielectric-SLG structure. When V GS is applied, it creates a gateto-channel potential drop (V diel ), and it induces a local electrostatic potential in the graphene channel (V ch = E F / q): 19,53 where Q G and C G are the charge concentration and the geometrical capacitance per unit area associated with the gate electrode, respectively. |Q G | = |q·n ch |, reflecting the charge neutrality of the gate capacitor, with n ch the charge carrier concentration per unit area in the channel induced by V GS . Any variations of n ch change Q G and V GS . From eq 3 we get: which leads to where C Q = dQ G /dV ch is the SLG quantum capacitance 90,91 that characterizes the changes of the channel potential ΔV ch as a result of additional gating ΔQ G , and (1/C G + 1/C Q ) −1 is the total capacitance C tot . To calculate Q G and Δn ch , we first need to find C G and C Q . In PE gating, C G is associated with the electric double layer (EDL) at the SLG/electrolyte interface. 53,90,92,93 The EDL acts like a parallel-plate capacitor with a dielectric layer thickness of the order of the Debye length λ D , so that C G = C EDL = ϵϵ 0 / λ D , where ϵ is the PE dielectric constant, and ϵ 0 is the vacuum permittivity. In principle, for a monovalent electrolyte, λ D can be explicitly calculated 94 if the electrolyte concentration is known. However, in the presence of a polymer matrix, the electrolyte ions can form complexes with polymer chains, 95 therefore the precise ion concentration is difficult to measure. For PE gating, different EDL thicknesses in the range ∼1−5 nm have been reported. 53,54,92,93 To estimate C EDL in our devices,

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Article we take λ D ∼ 2 nm 53 and the dielectric constant of the poly(ethylene oxide) matrix to be ϵ ∼ 5, 96 as done in ref 53. As a result, we obtain C EDL = 2.2 × 10 −6 F/cm 2 . This is the same order of magnitude as the SLG C Q . 90 Therefore, the latter cannot be neglected in eq 5. C Q is given by 90 where ℏ is the reduced Planck constant, υ F = 1.1 × 10 6 m/s is the SLG Fermi velocity, 80,97 and n i is the intrinsic carrier concentration in SLG near the Dirac point induced by charge impurities, defects and local potential fluctuations in the SLG channel. 90,98−100 From our Raman and transconductance measurements we estimate n i ∼ 3 × 10 12 cm −2 . From eq 6 we then get C Q = 4 × 10 −6 F/cm 2 at V CNP . From Figure 6a, and extracting ΔV CNP between the dark current and the transfer curves measured under illumination, and with eq 5, we get Δn ch ranging from 4 to 8 × 10 11 cm −2 for P o going from 100 μW to 4 mW. As a result, we obtain G PD ∼ 5 × 10 4 at V DS = 0.1 V for different P o as shown in Figure 9. As discussed previously, G PD becomes larger for higher V DS . Thus, we measure an increase of almost 1 order of magnitude (G PD ∼ 4 × 10 5 at P o = 100 μW) for V DS going from 0.1 to 1 V. Finally, we test I ph as a function of bending using a Deben Microtest three-point bending setup (Figure 10a). In this case, r b = [h 2 + (L/2) 2 ]/2h, where L is the chord of circumference connecting the two ends of the arc, and h is the height at the chord midpoint. The plotted values of I ph in the bent state at each r b (I ph,bend ) are normalized to the values of I ph measured at rest with the sample in the flat position (I ph,rest ). Figure 10b plots the normalized I ph,bend /I ph,rest for different r b , showing

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Article deviations within 15% for r b down to 1.4 cm. This r b is comparable to that reported for semiconductor membrane PDs, 4,15 yet the latter have 2 orders of magnitude lower (<0.3 A/W) responsivities. 4,15 Although our r b is five times larger than that reported for flexible single NW devices, 3,16−18 the area of our PDs (>40 mm 2 ) is at least 6 orders of magnitude larger than that of the NW devices (<5 μm 2 ). To test the device performance upon bending cycles, we first measure the photocurrent at rest (I ph,rest , flat position) and then at the smallest r b (I ph,bend , r b ∼1.4 cm), repeating these measurements for 30 bending cycles. Figure 10c plots I ph,bend /I ph,rest as a function of bending cycles. This shows that our PDs retain stable photocurrent after multiple bending tests with a I ph,bend / I ph,rest standard deviation ±12%.

CONCLUSIONS
We reported polymer electrolyte gated, flexible photodetectors, for visible wavelengths with external responsivity up to ∼45.5 A/W, photoconductive gain ∼4 × 10 5 , operation voltage <1 V, and optical transparency >82%. The responsivity is at least 2 orders of magnitude higher than in semiconductor flexible membranes. The devices show stable performance upon bending for radii of curvature larger than ∼1.4 cm. Owing to their responsivity, flexibility, transparency, and low operation voltage, our photodetectors can be attractive for wearable, biomedical, and low-power optoelectronic applications. 11,12,17 METHODS 1L-MoS 2 is epitaxially grown by CVD on c-plane sapphire substrates. 61 These are annealed at 1000°C in air for 1 h after consecutive cleaning by acetone/isopropyl alcohol/DI water. They are then placed facedown above a crucible containing ∼5 mg MoO 3 (≥99.998% Alfa Aesar). This is loaded into a 32 mm outer diameter quartz tube placed in a split-tube three-zone furnace. A second crucible containing 350 mg sulfur (≥99.99% purity, Sigma-Aldrich) is located upstream from the growth substrates. Ultrahigh-purity Ar is used as carrier gas at atmospheric pressure. The procedure is to ramp the temperature to 300°C with 200 sccm Ar flow, set to 300°C for 10 min, ramp to 700°C (50°C/min increase temperature rate) with 10 sccm Ar flow, set at 700°C for 10 min, cool to 570°C with 10 sccm of Ar, increase the gas flow to 200 sccm and open the furnace for rapid cooling. 61 SLG is grown on a 35 μm Cu foil, following the process described in ref 51. The substrate is annealed in hydrogen atmosphere (H 2 , 20 sccm) up to 1000°C for 30 min. Then, 5 sccm CH 4 is added to initiate growth. 51,62 The sample is then cooled in vacuum (1 mTorr) to room temperature and removed from the chamber.
Author Contributions §