Graphene-black phosphorus printed photodetectors

Layered materials (LMs) produced by liquid phase exfoliation (LPE) can be used as building blocks for optoelectronic applications. However, when compared with mechanically exfoliated flakes, or films prepared by chemical vapor deposition (CVD), LPE-based printed optoelectronic devices are limited by mobility, defects and trap states. Here, we present a scalable fabrication technique combining CVD with LPE LMs to overcome such limitations. We use black phosphorus inks, inkjet-printed on graphene on Si/SiO2, patterned by inkjet printing based lithography, and source and drain electrodes printed with an Ag ink, to prepare photodetectors (PDs). These have an external responsivity (R ext)∼337 A W−1 at 488 nm, and operate from visible (∼488 nm) to short-wave infrared (∼2.7 µm, R ext∼ 48 mA W−1). We also use this approach to fabricate flexible PDs on polyester fabric, one of the most common used in textiles, achieving R ext∼ 6 mA W−1 at 488 nm for an operating voltage of 1 V. Thus, our combination of scalable CVD and LPE techniques via inkjet printing is promising for wearable and flexible applications.

Their responsivity can be expressed as external [5,6]: or internal [6]: where I light and I dark are the currents of the PD under illumination and in dark conditions. A PD and A opt are the PD area and the laser spot size. A PD /A opt is a scaling factor that takes into account the fact that only a fraction of optical power impinges on the PD. P opt is the incident optical power, and P abs = abs × P opt is the absorbed optical power, where 0< abs <1 is the optical absorption in the PD. Typically, abs <1, since not all incident photons are absorbed (P opt > P abs ) [6], therefore R int > R ext [6]. R ext describes the overall PD responsivity, including device-related considerations, such as PD design and architecture, light absorption and reabsorption (i.e. the absorption of radiatively recombined photons in the PD photoactive materials), optical reflection from interfaces, optical path in the photoactive area, materials quality, etc [6]. On the other hand, R int provides an estimate of the photodetection efficiency, characterizing the optical-to-electrical conversion process of the absorbed photons [6]. R ext is related to R int as [6]:
Here we use inkjet printing to fabricate SLG/BP PDs. CVD SLG is patterned by inkjet printing polyvinylpyrrolidone (PVP) as mask, followed via reactive ion etching (RIE). PVP is rinsed with water. Source-drain Ag electrodes are then inkjet-printed at the end of the SLG channel. LPE BP is inkjetprinted on the channel, followed by encapsulation using Parylene C to prevent BP oxidation [96].
Our PDs have R ext up to ∼337 A W −1 at 488 nm for 1 V bias, the highest reported to date for inkjetprinted LPE LMs, to the best of our knowledge, see table 1. Our PDs work in the range ∼488 nm−2.7 µm, the broadest for inkjet-printed based PDs, to the best of our knowledge, see table 1. Instead of TMDs, which have tuneable indirect band gap in bulk crystals [97] and direct band gap in 1L [98], we use BP, which exhibits thickness dependent direct bandgap from ∼0.3 eV in bulk [48] to ∼2 eV in 1L [49]. R ext is proportional to the mobility, µ, as [6]: with τ life the response time, V ds the bias applied between source and drain, and L the channel length. The term τ life µV ds L 2 is called gain [6]. By increasing µ, the gain increases, which results in higher R ext . Therefore, we use CVD SLG with µ∼1700 cm 2 V −1 s −1 , instead of solution-processed graphene with µ∼300 cm 2 V −1 s −1 as in reference [99].
To demonstrate the viability of our approach for flexible and wearable electronics, we fabricate SLG/BP PDs on polyester fabric, with R ext ∼6 mA W −1 at 1 V and 488 nm, higher than CVD SLG PDs (R ext ∼ 0.11 mA W −1 ) on flexible (acrylic) substrates [100], and comparable to CVD MoS 2 PDs (R ext ∼20 mA W −1 at 405 nm) with inkjet-printed poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) on polyethylene naphthalate (PEN) [69], but with surface roughness lower than our fabric. Thus, inkjet lithography is promising for LMs-based optoelectronic devices on textiles.

Inkjet printing
BP bulk crystals are sourced from Smart-elements GmbH. These are then exfoliated as follows. 15 mg are transferred to a mortar and ground for ∼20 min to  [ 64,101]. The supernatant is collected and used for characterization and printing. All procedures are carried out in a glove box (inert atmosphere to minimise BP exposure to the environment or air), except the centrifugation.
The BP crystals are characterized by Raman spectroscopy using a LabRAM HR Evolution equipped with a 100× objective with power on the sample <0.5 mW, to exclude heating effects, figure 1. Bulk BP (red) has three main peaks, figure 1(b). One out-ofplane A 1 g mode, with position Pos(A 1 g ) ∼362.6 cm −1 [60,96,[102][103][104] and two in-plane B 2g and A 2 g modes, Pos(B 2g ) ∼439.5 and Pos(A 2 g ) ∼467.1 cm −1 [60,96,[102][103][104]. The corresponding full width at half maximum (FWHM) are FWHM( The peaks ∼194 and ∼230 cm −1 are assigned to B 1g and B 3g modes [105]. These are expected to appear when the incident light has a polarization component along the axis orthogonal to the BP layers [106]. However, we detect both, although we are in backscattering, as for previous reports [105][106][107]. The ground BP sample (blue curve in figure 1) the presence of flakes with number of layers, N>>6 [96]. The LPE BP flakes (green in figure 1 figure 1(b). We observe <0.5 cm −1 change in FWHM and Pos(A 1 g , B 2g , A 2 g ) compared to bulk BP, indicating N>6 [96]. Stable jetting happens when a single droplet is produced for each electrical impulse, with no secondary droplet formation [92]. This depends on ink viscosity η (mPas) [108], surface tension γ (mNm −1 ) [108], density ρ(gcm −3 ) [108] and nozzle diameter D (µm) [109]. A dimensionless figure of merit (FOM) Z = (γρD) 1/2 /η was suggested to characterize the stability of inkjetting [108,109]. [110] reported that if Z < 1 the ink would not jet, Z > 14 would result in secondary droplets. Therefore, 1 < Z < 14 is generally considered as the optimal range for stable drop-on-demand [108,109]. However, we previously showed that drop-on-demand inkjet printing of LM inks with Z > 14 is possible [32]. By changing η, γ, and ρ, we are able to tune Z across and outside the conventionally optimal range, and modify our inks for drop-on-demand printing. The size of flakes in solution should be ∼1/50 − 1/20 smaller than the nozzle diameter to prevent clogging [32], and clustering of the particles at nozzle edge [32].
Flakes tend to concentrate at the droplet edge during evaporation, resulting in a ring-like deposit, the so-called coffee-ring effect [111], leading to printing non-uniformity [111]. Adding polymer binders into the LPE dispersion [39,46,112] might prevent [39] or alleviate [39] the formation of coffee-rings [39,46,112]. However, binders decrease electrical conductivity [39], and must be annealed for removal (e.g. baking on a hot plate at 300 • C-400 • C for ∼1 h [39]). Solvents like N-Methyl-2-pyrrolidone (NMP) are generally the preferred option to disperse BP because of NMP's surface tension and Hansen solubility parameters [31,113]. However, a temperature close to the NMP boiling point (204 • C) [114]) is required to remove NMP residuals [91], but this can cause oxidation [64,96] and degradation [64,96] of air-sensitive BP [41]. NMP is also toxic [115] and can affect the central nervous system [116], so LMs inks dispersed in NMP cannot be used in an open environment [39]. Therefore, it is better to formulate BP inks in nontoxic solvents, with boiling point< 100 • C.
We prepare our BP ink in anhydrous IPA (not as toxic as NMP [121], and commercially available as a 70% solution in rubbing alcohol and hand sanitizers [121]), with a boiling point ∼83 • C [114]. The surface tension and viscosity are characterized via contact angle, surface tension (First Ten Angstroms) and rheometery (Discovery HR-1) measurements at room temperature (RT) and ambient pressure. The BP ink has η∼0.55 mPas, γ∼26 mNm −1 and ρ∼0.8 gcm −3 . For printing we use a Fujifilm Dimatix DMP-2800 with D = 22 µm, resulting in Z = 35, outside the conventional optimal range [110]. We aim for BP flake sizes∼1 µm to prevent nozzle clogging [32]. Scanning tunneling electron microscopy (STEM) (Magellan 400 L) is used to measure the flakes lateral size.
Figures 2(a) and (b) are a representative STEM image and a statistical analysis on 140 flakes, indicating mean length ∼220 nm and mean width ∼96 nm. The thickness distribution is estimated by Atomic Force Microscopy (AFM, Bruker Dimension Icon). Figure 3(a) is a typical AFM image of one flake, with thickness ∼5.4 nm, figure 3(b), corresponding to N ∼11. The AFM statistics on 140 flakes shows an average thickness ∼6.7 nm, figure 3(c), corresponding to N ∼13, given a 1 L-BP thickness ∼0.5 nm [122]. Figure 4(a) plots the absorbance, Abs = −log10(Tr) [123], with Tr the transmittance of the BP ink measured with a Cary 7000 UV-VIS-NIR Spectrometer. The BP concentration is estimated from the Beer-Lambert Law [124,125] the extinction coefficient, and l[m] is the cuvette length [126]. Reference [64] experimentally derived the BP ε ext at 660 nm from the slope of Abs per length versus the concentration of BP, ϵ ext ∼267 Lg −1 m −1 , with c calculated by measuring the weight difference of the collected BP flakes on an anodic aluminum oxide membrane before and after vacuum filtration [64]. From this, we estimate c ∼0.36 gL −1 for our ink, similar to reference [64].
High-resolution transmission electron microscopy (HRTEM) images are obtained via a FEI Tecnai F20 FEG TEM operated at 200 keV on BP flakes transferred on holey carbon grids. Figures 4(b) and (c) indicate a crystal plane spacing ∼0.21 nm, corresponding to the (002) plane of orthorhombic phosphorus [117], with N ∼15, and overall thickness ∼7.5 nm, consistent with the flake distribution range obtained by AFM in figure 3(c).
X-ray photoelectron spectroscopy (XPS) (Thermo Fisher ESCALAB 250Xi) is then performed to assess the chemical composition of the BP flakes. The samples for XPS are prepared in an Ar glove box by drop-casting the BP dispersion onto Si/SiO 2 , followed by N 2 gas flushing on a hot plate (60 • C) for ∼5 min. Figure 4(d) shows the 2p 3/2 and 2p 1/2 spin-orbit split doublet ∼129.7 [64,118] and ∼130.5 eV [64,118], consistent with previous XPS measurements on bulk BP [119,127]. The sub-bands ∼134 eV are attributed to surface suboxides introduced during LPE, as for [64,118].

SLG/BP on Si/SiO 2
The design of our SLG/BP PD is shown in figure 5(a). SLG is the channel on Si/SiO 2 , Si is the bottom gate, SiO 2 is the dielectric, BP is the photoactive material, Ag is used for the electrodes, and Parylene C as encapsulation layer. Upon illumination, electronhole (e-h) pairs are photogenerated in BP. Due to the band alignment ( figure 5(b)) h are transferred from the BP valence band (VB) into SLG, leaving behind uncompensated e, acting as an additional negative gate bias, leading to a photogating effect [12]. A schematic band diagram of the SLG/BP interface is in figure 5(b). A built-in field is formed at the SLG/BP interface. Upon BP photoexcitation, h are transferred to SLG under the built-in field, leaving e trapped in BP. Figure 5(c) is a false color SEM image of the SLG/BP PD.
To fabricate the SLG/BP PD, SLG is grown on a 35 µm Cu foil, as for reference [128]. The substrate is annealed at 1000 • C for 30min in the presence of 20sccm H 2 . To initiate growth, 5sccm CH 4 is added. After growth, the sample is cooled to RT at 1mTorr.
The SLG quality is monitored at each step of the fabrication process by Raman spectroscopy. The Raman Spectrum of as grown SLG on Cu is in figure 6, after Cu photoluminescence (PL) removal [129]. The 2D peak is a single Lorentzian with FWHM(2D) ∼29 cm −1 , signature of SLG [130]. 1 and ∼6.4. No D peak is observed, indicating negligible defects [131].
The fabrication process flow for SLG/BP PD is outlined in figure 7. To transfer SLG, poly(methyl methacrylate) (PMMA) is spin coated on SLG/Cu, followed by oxygen etching of SLG on the Cu backside, using a RIE-NanoEtch (3 W 30 s). Cu/SLG/PMMA is then left in ammonium persulfate (APS) in DI water for ∼6 h until Cu is etched. The resulting SLG/PMMA membrane is placed in DI water to clean the APS residuals and then transferred onto Si+90 nm SiO 2 , followed by overnight drying and PMMA removal with acetone and IPA, figure 7(a).
Source and drain electrodes are then prepared by inkjet printing an Ag ink from Sigma-Aldrich (Ag dispersion, 736465), figure 7(e), with resistivity ∼11.2 µΩcm, as measured via a Keithley source meter at the two ends of the channel layer. The linear relation between current and source-drain voltage, V ds , indicates an Ohmic contact between Ag and SLG channel, figure 9(a). The resistance of the channel is ∼2.07 kΩ. The average sheet resistance, R S , of CVD SLG on Si/SiO 2 , measured using a 4-point probe method, is R S ∼600 Ω/□. In SLG, R S = (σ 2d ) −1 [26], with σ 2d the SLG conductivity. In SLG, σ 2d = nµq [142] where n is the carrier density per unit area and q is the e charge. From n∼8.7 × 10 12 cm −2 derived from our Raman measurements, we get R S ∼450 Ω/□, consistent with our R S measurements.
We then gate modulate the current between SLG source and drain. SLG shows ambipolar behavior with µ∼1700 cm 2 V −1 s −1 , figure 9(b), from [6]: where △I d is the change in drain current, △V g is the change in gate voltage, L is the channel length, W is the channel width, and V ds is source-drain voltage. C ox is the gate oxide capacitance = ϵ 0 ϵ/t ox , where ϵ 0 ∼8.85 × 10 −14 F/cm is the vacuum permittivity, ϵ∼3.9 is the dielectric constant of SiO 2 [6] and t ox ∼90 nm is the SiO 2 thickness. We use 90 nm SiO 2 in order to have a larger electric field at lower gate voltages. The SLG quantum capacitance (C Q ) can be calculated as [132,143]: where ℏ is the reduced Planck constant, v f = 1.1 × 10 6 m/s is the SLG Fermi velocity [59,144], p ch is the charge carrier concentration per unit area in the channel, and n i is the intrinsic carrier concentration in SLG near the Dirac point induced by defects and impurities [143,[145][146][147]. From the Raman analysis we estimate n i ∼8.7×10 12 cm −2 . This gives C Q ∼6 × 10 −6 F/cm 2 . Thus, the total capacitance C Tot The contact resistance (R c ) of the Ag printed ink on SLG is estimated from the transfer length method [6], making 6 Ag/SLG/Ag contacts at SLG channel lengths ∼60, 160, 175, 300, 305, 430 µm, figure 9(c). R c of the Ag printed ink on SLG is ∼11 KΩ.µm ( figure 9(c)). From the linear relation between current and voltage in figure 9(c), we derive an Ohmic contact between Ag and SLG for all 6 samples.
The BP ink is then printed to a thickness ∼200 nm to cover the whole SLG channel, as measured with a DektakXT Stylus Profilometer. To prevent BP oxidation and degradation during electrical and photodetection characterizations, the SLG/BP PD is sealed under vacuum using Parylene C dimers (Curtiss-Wright) with a parylene coater (SCS coating). This forms a barrier to moisture and gas permeability [148,149]. References [41,96] encapsulated BP flakes with parylene C to prevent BP degradation. Following encapsulation, our SLG/BP PDs are stable for >30 days under ambient conditions. Parylene dimers are vaporized at ∼80 • C. In a separate chamber, they are pyrolysed into monomers at ∼690 • C. The PD is held at RT, so that parylene polymerizes on contact with the surface, forming a conformal film [41].
Since device fabrication comprises many steps, monitoring the quality of graphene is essential, as it could affect µ. The Raman analysis provides information on doping, defects, and strain, which affect µ, thus R ext , as for equation (5). Both compressive and tensile strains can affect µ [152]. [152] reported that a change in strain ∼0.012% in CVD SLG resulted in a ∼3 times decrease of µ. Our Raman analysis shows a change of strain ∼0.01%, from transferred SLG on Si/SiO 2 , to patterned and BP coated SLG. Thus, we expect µ to decrease ∼2 times when going from SLG on Si/SiO 2 to patterned and BP coated SLG. This is consistent with field-effect measurements, giving µ∼1200 cm 2 V −1 s −1 for SLG on Si/SiO 2 , reduced to ∼650 cm 2 V −1 s −1 for patterned and BP coated SLG. Figure 11(a) plots the drain current (I d ) as a function of back gate voltages (V g ),under different optical powers, ranging from ∼612 µW to 620 nW. We do not observe light sensitivity<620nW, due to no photocurrent generation (photocurrent generation in our SLG/BP PD requires absorption and generation of e-h pairs in BP as photoactive material). Following illumination, V D shifts to higher V g , and I d increases for V g < V D , where carrier transport is h dominated. Therefore, h transfer from BP to SLG is further promoted by gating. Under illumination, light is absorbed by BP and part of the photogenerated h are transferred from the BP VB into lower energy states in SLG, leaving behind uncompensated photogenerated e [68]. The latter are trapped in BP and act as an additional negative gate on the SLG channel, altering the electric field at the SLG/BP junction [68].  Figure 11(b) plots the photocurrent as a function of V ds , defined as [6]: where I light is the current under illumination, and I dark is that in dark conditions. To derive R ext , we measure I photo for powers from ∼490 to 1.1 µW, figure 11(c). Figure 11(c) gives R ext ∼337 A W −1 for 488 nm, when V g = -20 V (V g < V D ) and V ds = 1 V. For V ds >1 V, the free carriers drift velocity ν d = µE 1+µE/νsat [153], with ν sat the saturation velocity of the carriers in the SLG channel and E the applied electric field to SLG, increases linearly, until saturation, due to carrier scattering with optical phonons [154]. Therefore, all measurements are done at V ds ⩽ 1V to keep the device operation in the linear (Ohmic) regime, thus eliminating the nonlinear dependence of ν d on V ds . Figure 11(c) shows that R ext saturates for incident optical power<1 µW. For P opt ∼1.1 µW the number of photogenerated carriers decreases, resulting in an increases of the built-in field at the SLG/BP interface [12,68], which explains the enhancement of R ext at lower optical powers [12,68]. Figure 12 plots the spectral R ext for SLG/BP PDs. These show broadband R ext from visible (488 nm, ∼ 300A W −1 ) to mid-infrared (2700 nm, ∼48 mA W −1 ) at 1 V.
Metal-SLG-metal PDs were reported with R ext of few mA W −1 at 633 nm [155] and 1550 nm [156].
The difference in R ext between these and our SLG/BP PDs is attributed to the contribution of the BP photoactive layer. To get a better understanding of spectral response versus wavelength, we perform optical simulations. We extract the BP refractive index from the solution absorbance of LPE BP, figure 4(a). Specifically, transmission in solution can be defined either by the absorbance (Abs = c × ϵ ext × l as T r = 10 −cϵextl ) or by the optical depth as e −al [157,158], where l is the cuvette length and a = a BP c/ρ, a BP = 4πK BP /λ is the BP bulk absorption coefficient, K BP is the imaginary part of the BP refractive index, ρ is the BP density (2340 gL −1 [159]), and λ is the incident wavelength. We assume BP flakes randomly oriented, thus seek to extract the average refractive index [160]. Then, K BP = ϵ ext λρ/4πlog 10 (e) and the real part of the average refractive index is found by applying the Kramers-Kronig (KK) relation [160], n BP (w) where P denotes the principal value of the integral and w is angular frequency. The absorbance data of figure 4(a) are truncated at UV = 300 nm, due to the cuvette absorbance ∼300 nm [161], making our n BP extraction qualitative, because of the finite integration range. We use the extracted BP refractive index in Fresnel equation calculations [162] to estimate the absorption of SLG/BP on Si/SiO 2 . The SLG refractive index is modelled by the Kubo conductance [163] at RT and E F = 0.38 eV, as estimated by the Raman measurements in figure 6. Due to the fluctuations in absorbance beyond 1700 nm, figure 4(a), we do not extract refractive index for BP beyond 1700 nm. The experimental absorption of inkjet-printed BP/SLG on quartz is plotted in figure 12. This follows the experimental and theoretical absorption spectra of SLG/BP films, i.e. drop of both R ext and absorption with increasing wavelength, indicating R ext follows the absorption spectra of the light-absorbing photoactive material. The temporal response of our PDs is then measured with a MSO9404A Mixed Signal Oscilloscope, figure 13(a). The time response in figure 13(a) reaches saturation at ∼3.8 µA, as shown by the horizontal dashed line. We thus fit the temporal response decay  in figure 13(a) with [72]: I(t) = A 0 .exp(-t/τ life ) + B, where A 0 is the initial current, τ life is the response time and B a constant. We get a response time ∼50 ms, two orders of magnitudes faster than the LPE BP/CVD SLG PD of reference [66], consistent with other LPE based PDs [44,164], but two orders of magnitude slower than the Schottky junction PDs of reference [41], with lower R ext ∼164 mA W −1 at 450 nm, due to lack of photoconductive gain, but faster response time ∼550 µs, because of the Schottky diode characteristics at the Si/SLG/BP interfaces [41].
By applying V ds , transferred photogenerated h drift to the drain with a timescale τ transit [6]: where L = 60 µm is the length of channel, and µ∼1700 cm 2 V −1 s −1 . We thus get τ transit ∼37 ns, resulting in a photoconductive gain [6]: The dependence of R ext on τ life τ transit explains the decrease in R ext when the optical power increases. The decrease in R ext suggests an increase of τ transit and/or decrease of τ life . The increase of τ transit is likely due to increase in scattering of photogenerated carriers in the channel with increase in optical power [165]. Auger recombination induced by increasing power can also increase the photogenerated charges recombination rate, reducing τ life [165]. The gain can be further defined as the ratio of photogenerated currents recirculating in the SLG channel to the injected h from BP to SLG [68]: where △p ch is the concentration per unit area and per unit time of the injected h. △p ch is equal to the trapped e concentration per unit area and per unit time in BP, related to a charge neutrality point shift △V g = △V D in the transfer characteristics (I d versus V g ). To calculate △p ch , we consider the potential balance in the metal-dielectric-SLG structure. V g creates a potential drop (V ch = E f /q) so that [6,132]: where Q G is the charge concentration. |Q G | = |q.p ch |, with p ch the charge carrier concentration per unit area in the channel induced by V g . Any variation in p ch changes Q g and V g . The derivative of V g with respect to Q g gives: which results in: To find Q G and △p ch , C ox and C Q are needed. C ox ∼38.35 × 10 −9 F/cm 2 . From equation (7), we get C Q ∼6×10 −6 F/cm 2 . Therefore, △p ch varies from ∼2.6×10 11 cm −2 to 1.1 × 10 12 cm −2 for optical power 620nW to 612 µW at V ds = 0.5V. Then, from equation (11), we get Gain ∼2 × 10 6 , in agreement with equation (10).
We then evaluate the detectivity (D * ) [cm.Hz 1/2 /W or Jones]. This relates the performance of PDs in terms of R ext to A PD , allowing the comparison of PDs with different A PD [6]: where B is the electrical bandwidth(Hz), defined as difference between the upper and lower frequencies of R ext , and NEP is the noise equivalent power (i.e. the power that gives a signal to noise ratio of one in a 1 Hz output bandwidth [6,166]): where i n is the dark noise current, i.e. the current that exists when no light is incident on the PD [6]. The noise [A/ √ Hz] is measured in the time domain, by collecting the trace on an oscilloscope, with subsequent Fourier transform in order to analyze the data in the spectral domain. Figure 13(b) plots the 1/f noise (where f is the frequency). 1/f is the noise density (noise power per unit of bandwidth [dBm.Hz −1/2 ] [6]), due to charge traps and defects [6]. At 4 Hz, ∼5 times less than the cut off f, i.e. the f at which the detector R ext decreases by 3 dB [6], we get NEP ∼1.8 × 10 −10 WHz −1/2 and D * ∼2×10 7 Jones. The noise current in the shot noise limit (due to generation-recombination of e-h pairs and resistive current paths in PDs [6]) is defined as i n = (2qI dark ) 1/2 [166], where the total dark current combines the contribution of the unamplified SLG current I dark(SLG) , and the amplified injection current from BP, I dark(BP) , due to the thermal excitation of charge carriers in dark. The latter is orders of magnitube smaller compared to I dark(SLG) ∼200mA. Therefore, following the methodology presented in reference [166], in our devices the shot noise limited noise current is i n = (2qI dark(SLG) ) 1/2 . Thus, in the shot noise limit, we can write D * as [6]: Equation (17) gives D * ∼10 11 Jones, ∼3 times higher than reference [45] for inkjet-printed graphene/MoS 2 PDs. It is also ∼3-4 orders of magnitude higher than reference [47] for PDs based on inkjet-printed MoS 2 . We note that gain was not included in the D * calculations in references [46,47], which may have led to a D * overestimation. Thus, our inkjet-printed PDs are suitable for detecting weak light intensities which compete with the detector noise [6].

SLG/BP on fabric
In wearable applications, inkjet lithography has advantages over EBL and other lithography techniques for patterning and device fabrications because of textiles' porous [167], rough [167] and nonconductive structure [167], which makes these lithography techniques not suitable. To showcase this, we fabricate PDs on polyester fabric, because of its durability against Sun exposure [168], wrinkling [168] and shrinking [169], and common use (∼52% of the synthetic textile market in 2018 [167,170]). Since the surface roughness of textiles affects the electrical conductivity [171,172], we planarize the surface by reducing the roughness. To do so, we rod coat polyurethane (PU) 10 times to reduce the root mean square (RMS) roughness from ∼50 µm to < 5µm. We then transfer SLG on PU coated polyester fabric using a similar procedure as for Si/SiO 2 . After removing PMMA, a PVP ink is inkjet-printed as mask on SLG to pattern a 400 µm × 400 µm channel. SLG is then etched via RIE, followed by removal of PVP with water. Figure 14 shows the Raman spectra of 2 SLG on PU coated polyester fabric. The PU coated polyester fabric has two bands ∼2935 and ∼2845 cm −1 attributed to asymmetric and symmetric C-H stretching vibrations of CH 2 groups [173,174], figure 14(c). The peak ∼1615 cm −1 can be ascribed to -C = C-stretching vibrations of aromatic rings [175,176], figure 14(b). The peak ∼1442 cm −1 can be assigned to C-H deformation vibrations of CH 2 groups [173,176] and that ∼1251 cm −1 to coupled C-N and C-O vibrations of urethane [173,176], figure 14 [132,133], which corresponds to a carrier concentration ∼4.33×10 12 cm −2 [132]. I(D)/I(G)∼1.03 corresponds to defect density ∼4.6×10 11 cm −2 [134,135] for excitation energy 2.41 eV and E F = 270meV. For the E F derived from A(2D)/A(G), Pos(G) should be ∼1589.2 cm −1 for unstrained SLG [132]. In our experiments, Pos(G)∼1596.9 cm −1 , which implies a contribution from uniaxial (biaxial) strain ∼0.33% (0.12%) [136], comparable to the uniaxial (biaxial) strain ∼0.36% (0.13%) of SLG on Si/SiO 2 .
We then inkjet print electrodes with the Ag ink. The sample is annealed at ∼100 • C for ∼2 h to remove residual solvent (triethylene glycol monomethyl ether). We transfer two SLG to have R s ∼2.1 KΩ, comparable to transferred CVD SLG previously reported for polypropylene coated fabrics [172]. BP is then inkjet-printed on the channel layer.   Figure 15(c) plots the current-voltage characteristic in dark, which shows an Ohmic resistance (R = 2.09 KΩ) between inkjetprinted electrodes and SLG channel. We then characterize R ext at 488 nm for P = 1.1 mW. Figure 15(c) shows that the current increases under illumination. We get R ext ∼6 mA W −1 at 488 nm.
Bendable devices, able to coordinate with body motions, such as arms' and legs' bending or extension, are appealing for wearable electronics. Thus, we test I photo as function of bending using a Deben Microtest setup, figure 15(f). The bending radius R b is defined as [177]: where y is the height at the chord midpoint and x is the chord circumference connecting the two ends of the grips, figure 15(f). To compare the performance at different R b , the photocurrent at each R b (I Photo Bend ) is normalized to that measured in flat conditions (I Photo Rest ). Figure 15(d) shows a change ∼17% of I Photo Bend I Photo Rest for R b from flat to 25 mm. This is comparable to that reported for LMs-based PDs, such as InSe PDs on PET [178], but in reference [178] R ext was ∼50% that of R b = 30 mm [178]. Comparable R b was reported for flexible ZnO nanowires [179], with on/off ratio ∼11×10 4 (I d ∼120nA) under ∼4.5 mWcm −2 of UV light (R ext not reported) [179]. However the operating voltage (1 V) of our PDs is 3 times smaller than that in reference [179], making them more suitable for wearable applications, and lowering power. The SLG/BP PDs performance as a function of bending cycles, where 1 bending cycle is set at R b ∼35 mm, is in figure 15(e). Our PDs retain ∼82% of I Photo Bend I Photo Rest for up to 30 cycles, comparable to what previously reported for CVD based MoS 2 /SLG PDs on PET [180], making our approach promising for wearable and flexible applications.

Discussion
Our PDs on Si/SiO 2 have R ext up to ∼337A W −1 at 488 nm for 1 V bias and work in the range ∼488 nm-2.7 µm. Reference [181] prepared PDs by depositing ∼30 nm thick WS 2 by rubbing WS 2 powder against a polycarbonate substrate. Then, Au(100 nm)/Ti(5 nm) electrodes were made using e-beam evaporation through a shadow mask. The WS 2 -based PDs showed R ext ∼144 mA W −1 at 625 nm and V ds ∼10 V, worse than ours, because of the photoconductive gain enhancement in our inkjetprinted hybrid SLG/BP PDs. Reference [182] presented WS 2 -based PDs using ∼4 nm WS 2 fabricated via RF magnetron sputtering, with R ext ∼1.68 mA W −1 at 405 nm [182]. This is worse than ours because of the photoconductive gain mechanism in our hybrid SLG/BP PDs. Reference [183] measured R ext ∼0. 16 A W −1 at 405 nm in self-powered PDs based on oxidized WS 2 (O-WS 2 )/WS 2 heterojunctions, where ∼7.2 nm WS 2 was transferred onto Si/SiO 2 by polydimethylsiloxane (PDMS)-assisted micromechanical exfoliation. Photoresist was then spin-coated on WS 2 via e-beam PHL, followed by oxygen plasma irradiation to form selective oxidation regions. Then, Au(100 nm)/Ti(10 nm) electrodes were prepared by PHL and electron beam deposition [183]. The fabrication process is more complex than ours, and the resulting R ext is ∼2000 times lower, since no bias is applied through source and drain electrodes to dissociate photogenerated charges. Reference [184] used spin-coated carbon QDs on CVD 1 L-MoS 2 to achieve R ext ∼377 A W −1 at 360 nm and 5 V. While R ext is comparable to ours, the PDs in reference [184] operated at 5 V and only between 300-700 nm, due to the spectral coverage of the carbon QDs [184], while our PDs work at 1 V from 488 nm to 2.7 µm. Reference [185] reported MoS 2 -based PDs, prepared by abrasion of MoS 2 crystals (thickness ∼15-25 µm) on the substrate, resulting in R ext ∼1.5 µ A W −1 at 660 nm and V ds ∼20 V. R ext and operation voltage are worse than ours, because of our photoconductive gain, combined with the use of BP as photoactive material. To the best of our knowledge, our SLG/BP PDs on Si/SiO 2 have the highest R ext amongst inkjet-printed LM-based PDs, and our operation wavelength range (488-2700 nm) is the broadest, as summarized in table 1.
For SLG/BP PDs on fabric we get R ext ∼6 mA W −1 at 488 nm, i.e. ∼56 000 less than on SLG/BP PDs on Si/SiO 2 . This R ext decrease is expected, since the photogenerated h in the BP VB experience weaker electric fields at the SLG/BP interface (p-doping ∼270 meV) compared to the SLG/BP interface (n-doping ∼360 meV) on Si/SiO 2 . Moreover, µ for SLG on fabric is lower than that on Si/SiO 2 , and the channel in our PDs on fabric is ∼8 times larger than on Si/SiO 2 . R ext also decreases when the optical power increases, due to the increase in scattering of photogenerated carriers in the channel [165], and Auger recombination induced by increasing power [165].
To the best of our knowledge, there is no report of inkjet-printed textile PDs based on LMs. Our R ext is ∼6 times higher than inkjet-printed SLG/WS 2 PDs on PET [42], and one order of magnitude higher (R ext ∼0.11 mA W −1 at 405 nm [100]) than CVD SLG based PDs on flexible (acrylic) substrates [100].

Conclusions
We reported an inkjet printing-based approach to prepare PDs, combining CVD SLG and binder-free LPE BP. The devices have R ext up to ∼337 A W −1 at 488 nm, and ∼48 mA W −1 at 2700 nm, with operation voltage ⩽ 1V. We used this to make flexible PDs on polyester fabric. These PDs were investigated as function of bending radius and cycles. The responsivity, flexibility, and low operation voltage of our PDs makes them attractive for wearable and low-power optoelectronic applications.