Graphene-black phosphorus printed photodetectors

Photodetectors (PDs) are key components of video imaging [1], optical communications [2], night vision [3], gas sensing [4] and many other devices.

Their responsivity can be expressed as external [5, 6]:

$$\begin{align} \textit{R}_{\textrm {ext}}=\frac{|I_{\textrm {light}}-I_{\textrm {dark}}|}{(P_{\textrm {opt}}. A_{\textrm {PD}}/A_{\textrm {opt}})}, \end{align} \tag{ 1 }$$

or internal [6]:

$$\begin{align} R_{\textrm {int}}=\frac{|I_{\textrm {light}}-I_{\textrm {dark}}|}{(P_{\textrm {abs}}. A_{\textrm {PD}}/A_{\textrm {opt}})}, \end{align} \tag{ 2 }$$

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. $A_{\textrm {PD}}/A_{\textrm {opt}}$ 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 = $\textrm {abs} \times P_{\textrm {opt}}$ is the absorbed optical power, where 0$\lt \textrm {abs}\lt$1 is the optical absorption in the PD. Typically, $\textrm {abs}\lt$1, since not all incident photons are absorbed (P $_{\textrm{opt}}\gt \textit{P}_{\textrm{abs}}$) [6], therefore R $_{\textrm{int}}\gt \textit{R}_{\textrm{ext}}$ [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]:

$$\begin{equation} R_{\textrm {ext}}= R_{\textrm {int}}.\textrm{abs}=\frac{{\eta_{\textrm {int}}}q\lambda \textrm {abs}(\lambda)}{hc}, \end{equation} \tag{ 3 }$$

where η_int is the internal quantum efficiency, i.e. the ratio of the number of charge carriers collected from the photoactive layer to the number of absorbed photons [6], q is the electron charge, λ is the incident light wavelength, h is the Planck constant, and c the speed of light. $\textrm{abs}(\lambda)$ is wavelength dependent, therefore the spectral response in quantum-type PDs (whereby photons generate electron–hole, e-h, pairs) typically follows the absorption spectrum of the light-absorbing material [6].

The response time (τ_life) is the lifetime of the photogenerated charges in the light-absorbing layer [5]. This determines the PD speed, defined as [5, 6]:

$$\begin{equation} \tau_{\textrm {life}}=\frac{\Delta{n}}{QE \times \phi_{\textrm {in}}}, \end{equation} \tag{ 4 }$$

where $\Delta{n}$ is the light-induced change in carrier density, QE is the external quantum efficiency, defined as QE = $\eta_{\textrm {tran}}\times\eta_{\textrm {abs}}$ where η_tran is the charge transfer efficiency (i.e. the ratio between the flux of charges that contribute to the current and the total light flux that reaches the surface), η_abs is the light absorption efficiency (i.e. the percentage of light absorbed by the sample), and φ_in is the incoming photon flux. The operation wavelength range is the spectral range where the PD is sensitive to incident light [6]. For cameras and video imaging, detection in the visible (∼400–700 nm) with $\tau_{\textrm {life}}{\sim}$10–50 ms is desired [5]. R $_{\textrm {ext}}\gt$0.1 A W⁻¹ can remove the need of amplifiers (to increase the output with respect to the input signal (i.e. current)) [7], thus decreasing costs [7].

PDs currently in the market are mainly based on Si complementary metal-oxide-semiconductor (CMOS) technology [8]. For applications in the short-wave infrared (SWIR) (1000–2500 nm/1.24–0.5 eV), beyond the Si bandgap (1.1 eV) [6], current technology relies on III-V InGaAs PDs [9]. However, these require complex manufacturing steps (epitaxial growth) [10], cooling to liquid nitrogen [10], and they are rigid [10].

Graphene and related materials (GRMs) are promising for PDs [5, 11], and have demonstrated R $_{\textrm{ext}}{\sim}$10⁸ A W⁻¹ at 532 nm [12], with response time ${\sim}10^{-4}\,\mathrm{s}$ [13], 110 GHz speed [14], operation wavelength covering visible to the mid-IR ∼3.2 µm [15] and THz [16, 17], and CMOS integrability [18]. Many GRM-based PDs fabricated based on scalable chemical vapor deposition (CVD) approaches [19, 20] were also reported, with R $_{\textrm{ext}}{\sim}$121 A W⁻¹ at 532 nm [20]. R $_{\textrm {ext}}\gt10^{5}$ A W⁻¹ was achieved integrating graphene flakes [12] and/or layered materials (LMs), such as MoS₂, [21] with PbS [22, 23] and HgTe quantum dots (QDs) [24], with spectral coverage determined by the absorption of the added material (e.g. QDs) [22].

In graphene-based PDs (e.g. metal-graphene-metal PDs [25]), $\textrm {abs}(\lambda)$ is governed by the wavelength dependent optical conductivity of SLG [26], doping [26], Pauli blocking [26], mobility [27], scattering time [28], device architecture, and substrate, which affects the optical path and the interference of the incident light [25]. In graphene PDs based on photogating (e.g. graphene/QDs [12], graphene/semiconductor [29]), abs(λ) depends on the absorption coefficient profile (4πK/λ) [6] of the light-absorbing material, where K is the imaginary part of the photoactive material [6].

Liquid phase exfoliation (LPE) is a promising route for production of LM-based inks [30–35]. These have been used for printed solar cells [36], sensors [37], transistors [32], supercapacitors [38, 39], and PDs [40]. LPE inks were used to prepare PDs on rigid (e.g. Si) [41] and flexible (e.g. PET(polyethylene terephthalate)) [42] substrates. Challenges in the development of inkjet-printed LPE based PDs stem from the limitations associated with the presence of traps (surface [43, 44] and interface sites [43, 44] formed during LPE), resulting in photocurrent loss [44].

PDs based on solution-synthesized MoS₂ on Si/SiO₂ were demonstrated [44]. These were prepared by dissolving (NH₄)₂MoS₄ in dimethylformamide:butylamine:aminoethanol (volumetric ratio of 4.5:4.5:1), followed by spin coating on Si/SiO₂ and conversion to MoS₂ via annealing at 750 ^∘C and 1000 ^∘C under Ar/H₂ and Ar/S [44]. The MoS₂ channel was defined by photolithography (PHL) and dry etching using O₂ plasma. The electrodes were fabricated via e-beam evaporation of Au/Ti. However, the PDs in reference [44] showed R$_{ext}$ limited to ∼63 µ A W⁻¹ at 405 nm [44], due to the presence of defects [44]. These acted as trap states and resulted in a slow (few s) τ_life. The current (∼10⁻⁹A when the light was turned on) did not recover to the initial level (∼3×10⁻¹²A with light off [44]). τ_life improved to ∼20 ms by applying a gate pulse ∼100 V to discharge the trapped charges [44]. Lateral heterostructures based on LPE MoS₂ flakes as photoactive material and ∼4 layer graphene (4LG) flakes [40, 45] or Ag paste [46] as electrodes were reported [40, 45, 46], with R $_{\textrm {ext}}{\sim}$36 µ A W⁻¹ and $\tau_{\textrm {life}}{\sim}$60 ms at 532 nm [46], and 300 mA W⁻¹ under white light. Reference [47] reported LPE MoS₂ based PDs with R $_{\textrm {ext}}{\sim}$50 mA W⁻¹ at 515 nm and $\tau_{life}{\sim}$5 ms, using ethyl cellulose to make percolating films with conductivity ∼1.72×10⁻²S m⁻¹ [47]. Water-based $\lt$7LG and WS₂ inks were used in reference [42] to make vertical heterostructures, resulting in PD arrays. However, these PDs mostly cover visible (405–532 nm) [40, 42, 44–47] with R $_{\textrm {ext}}\leqslant$50 mA W⁻¹, due to photocurrent loss mainly due to traps [43, 44].

Black phosphorus (BP) is a LM interesting for broad-band PDs because of its thickness dependent direct bandgap varying from ∼0.3 eV in bulk [48] to ∼2 eV in 1LBP [49]. Micro-mechanical cleavage (MC) has been the main approach used to make BP PDs [50–57]. Reference [56] demonstrated PDs based on BP flakes with thickness ∼10 nm [56], working from ∼532 to 3390 nm, with R$_{ext}{\sim}$ 82A W⁻¹ at 3.39 $\mu m$ and $\tau_{\textrm {life}}{\sim}$0.13 ms. BP was exfoliated on Si/SiO₂. A resist layer was patterned via e-beam lithography (EBL) for metallization and evaporation of Cr/Au as contacts [56]. Reference [53] used MC BP (∼8 nm thickness), EBL, and electron-beam evaporation to form arrays of metal contacts. Reference [53] demonstrated BP-based PDs for 400–900 nm, with R $_{\textrm {ext}}{\sim}4.3\times$10⁶A W⁻¹ at 400 nm, ∼10³ A W⁻¹ at 900 nm and $\tau_{\textrm {life}}{\sim}$5 ms. Reference [50] used a 225 nm thick BP film stacked between two SLGs as top and bottom contacts. To prevent exposure to the environment, this was encapsulated in 18 nm hBN [50]. The PDs had broadband response ∼632–3400 nm, with R $_{\textrm {ext}}{\sim}$0.15 A W⁻¹ at 632 nm, ∼1.43 A W⁻¹ at 3400 nm, and $\tau_{\textrm {life}}{\sim}$1.68 ns [50]. However, MC usually produces flakes $\lt$1 mm [58], without thickness control (random locations of 1L to tens nm flakes) [59, 60], and lacks reproducibility in terms of amount of material, flake size, and number of layers [61–65]. Reference [41] used LPE BP inks to print BP/CVD SLG/Si Schottky junction PDs, with R $_{\textrm {ext}}{\sim}$164 mA W⁻¹ at 450 nm, ∼1.8 mA W⁻¹ at 1550 nm, and $\tau_{\textrm {life}}{\sim}$0.55 ms [41]. Si/SiO₂ was patterned with EBL, followed by e-beam evaporation of Au and lift-off. The devices were further patterned to make a window to etch SiO₂. CVD SLG was then transferred, covering the Au electrode and the Si window [41]. BP was inkjet-printed on the SLG/Si Schottky junction. This process is complex and requires expensive fabrication tools (EBL and e-beam evaporator). Reference [66] reported SLG/LPE BP PDs. Two Au electrodes were evaporated through a shadow mask on Si/SiO₂. CVD SLG was wet transferred on the printed LPE BP. The resulting SLG/BP film was transferred on Si/SiO₂ with Au electrodes [66]. These PDs had R $_{\textrm {ext}}{\sim}7.7\times$10³ A W⁻¹ at 360 nm at 5 V bias, with $\tau_{\textrm {life}}{\sim}$7 s and operation wavelength ∼360–785 nm [66]. Table 1 compares the results of MC BP and inkjet-printed BP PDs with different device structures [41, 42, 44–47, 50, 52, 53, 56, 67–71, 182–185]. To the best of our knowledge, there are no reports of inkjet-printed PDs with broadband operation from visible (∼400–700 nm) to SWIR (∼2500 nm), with R $_{\textrm {ext}}\gt$1 A W⁻¹ in visible and $\tau_{life}{\sim}$10–50 m, suitable for video imaging [72].

Table 1. PDs based on MC BP and LPE BP. IP (inkjet printing), EBL , PHL, UVL (UV lithography). t: average LM film thickness.

	Properties
Fabrication	Spectral range (nm)	Rext(A W−1)	Response time (s)	NEP ($WHz^{-1/2}$)	D$^{*}$(Jones)	References
IP (LPE BP t∼200 nm)	488–2700	337–0.048 (488–2700 nm)	50 × 10−3	1.68 × 10−10	1011	this work
IP (LPE MoS2 t∼1.9  µm)	white light	0.3	–	–	3.6 × 1010	[45]
IP (LPE MoS2 t∼700 nm)	515	0.05 (515 nm)	5×10−3	–	3.2 × 109	[47]
IP (LPE MoS2 t∼1.3 mm)	405–980	63$\times10^{-6}$ (520 nm)	20 × 10−3	–	4.2×108	[44]
IP (LPE MoS2 t∼50 nm)	532	36$\times10^{-6}$(532 nm)	60×10−3	–	–	[46]
IP (LPE WS2 t∼100 nm)	514	0.001(514 nm)	–	–	–	[42]
IP (CVD MoS2 t=1L)	405–780	0.02–0.01 (405–780 nm)	1.7	–	4.8 × 107	[69]
IP (LPE WS2 t∼30 nm)/PHL	632	10−4(632 nm)	–	–	–	[70]
IP (LPE BP)/EBL	450–1550	0.164(450 nm)	550 × 10−6	–	–	[41]
EBL (MC BP t∼8 nm)	640–940	4.8 × 10−3 (640 nm)	4 × 10−3	–	–	[52]
EBL (MC BP t∼10 nm)	532–3390	82 (3390 nm)	130 × 10−6	5.6 × 10−12	–	[56]
EBL (MC BP t∼10 nm)	830	53(830 nm)	–	–	–	[71]
EBL (MC BP t∼30 nm)	400–3750	0.35 × 10−3(1200 nm)	40 × 10−6	–	–	[67]
UVL (MC BP t∼60 nm)	635–1550	594–3300(635–1550 nm)	3 × 10−3	–	–	[68]
EBL (MC BP t∼8 nm)	400–900	4.3 × 106–103(400–900 nm)	5 × 10−3	–	–	[53]
EBL (MC BP t∼225 nm)	632–3400	0.15–1.43(632–3400nm)	1.8 × 10−9	7×10−12	–	[50]
Abration (WS2 t∼30 nm)	625	144$\times10^{-3}$(625 nm)	70 × 10−6	–	108	[181]
Sputtered (WS2 t∼4 nm)	450–635	1.68$\times10^{-3}$(450 nm)	–	–	–	[182]
EBL (WS2 t∼7.2 nm)	405–635	160$\times10^{-3}$(405 nm)	21×10−3	–	1.4 ×1011	[183]
MLL (Carbon QDs/MoS2 t=1L)	300–700	377(360 nm)	7.5	–	1.6 × 1013	[184]
Abration (MoS2 t=15–25 µm)	365–940	1.5 × 10−6(660 nm)	20–30	–	–	[185]

Printing can be used for large-scale($\gt$1 m²) [73] fabrication of optoelectronic devices on both rigid [74] and flexible [75] substrates. A variety of printed devices have been reported [76], such as radio-frequency identification tags on paper [77, 78], sensors [79], displays [80], memories [81], and thin-film transistors [32]. Printing was performed with different methods, such as screen [82, 83], gravure [84], flexography [85], and inkjet [32, 86]. Amongst those, inkjet printing is one of the most promising, because of attractive features such as direct patterning (mask-free) [87, 88] and resolution [89, 90]. The typical printing resolution is ∼100 µm for gravure [91], ∼100–200 µm for flexo [91], ∼100 µm for screen printing [91]. Inkjet printing offers resolution down to ∼50 µm [92], which can be made$\lt$500 nm by pre-patterning [93]. Inkjet printers can also be used to dispense etching [94] or patterning agents [95].

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 inkjet-printed 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 inkjet-printed 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]:

$$\begin{equation} R_{\textrm {ext}}= \frac{\Delta{I}}{P_{\textrm {opt}}} \frac{\tau_{\textrm {life}} \mu V_{ds}}{L^{2}}, \end{equation} \tag{ 5 }$$

with τ_life the response time, V $_{ds}$ the bias applied between source and drain, and L the channel length. The term $\frac{\tau_{\textrm {life}}\mu V_{ds}}{L^{2}}$ is called gain [6]. By increasing µ, the gain increases, which results in higher R_ext. Therefore, we use CVD SLG with $\mu{\sim}$1700 cm² V⁻¹s⁻¹, instead of solution-processed graphene with $\mu{\sim}$300 cm² V⁻¹s⁻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 $_{\textrm{ext}}{\sim}$6 mA W⁻¹ at 1 V and 488 nm, higher than CVD SLG PDs (R $_{\textrm{ext}}{\sim}$ 0.11 mA W⁻¹) on flexible (acrylic) substrates [100], and comparable to CVD MoS₂ PDs (R $_{\textrm{ext}}{\sim}$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.

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 facilitate subsequent sonication. BP powders are then mixed with 15ml anhydrous isopropyl alcohol (IPA) (Sigma-Aldrich) in a Schlenk flask, sealed with parafilm, and sonicated for 3 h in a 900 W ultrasonic bath (Fisherbrand Elmasonic S 300 Ultrasonic). The BP solution is then centrifuged (H-641 swinging bucket rotor in a Sorvall WX-100) at 4000 rpm (∼6000 g) for 20 min to let the unexfoliated flakes sediment [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 $\lt$0.5 mW, to exclude heating effects, figure 1. Bulk BP (red) has three main peaks, figure 1(b). One out-of-plane A$_g^1$ mode, with position Pos(A$_g^1$) ∼362.6 cm⁻¹ [60, 96, 102–104] and two in-plane B$_{2g}$ and A$_g^2$ modes, Pos(B$_{2g}$) ∼439.5 and Pos(A$_g^2$) ∼467.1 cm⁻¹ [60, 96, 102–104]. The corresponding full width at half maximum (FWHM) are FWHM(A$_g^1$) ∼2 cm⁻¹, FWHM(B$_{2g}$) ∼3.5 cm⁻¹, FWHM(A$_g^2$) ∼2.5 cm⁻¹. 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 [105–107].

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The ground BP sample (blue curve in figure 1) has Pos(A$_g^1$) ∼362.6 cm⁻¹, FWHM(A$_g^1$) ∼2.1 cm⁻¹, Pos(B$_{2g}$) ∼439.4 cm⁻¹, FWHM(B$_{2g}$) ∼3.8 cm⁻¹, Pos(A$_g^2$) ∼466.9 cm⁻¹ with FWHM(A$_g^2$) ∼2.7 cm⁻¹, figure 1(b). We observe $\lt$0.3 cm⁻¹ change in FWHM and Pos(A$_g^1$, B$_{2g}$, A$_g^2$) compared to bulk BP, indicating the presence of flakes with number of layers, N$\gt\gt$6 [96].

The LPE BP flakes (green in figure 1) have Pos(A$_g^1$) ∼362.6 cm⁻¹, FWHM(A$_g^1$) ∼2.3 cm⁻¹, Pos(B$_{2g}$) ∼439.3 cm⁻¹, FWHM(B$_{2g}$) ∼3.9 cm⁻¹, Pos(A$_g^2$) ∼466.9 cm⁻¹, FWHM(A$_g^2$) ∼2.8 cm⁻¹, figure 1(b). We observe $\lt$0.5 cm⁻¹ change in FWHM and Pos(A$_g^1$, B$_{2g}$, A$_g^2$) compared to bulk BP, indicating N$\gt$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 ($\mu m$) [109]. A dimensionless figure of merit (FOM) $Z = (\gamma\rho\textit{D})^{1/2}/\eta$ was suggested to characterize the stability of inkjetting [108, 109]. [110] reported that if $Z\lt{1}$ the ink would not jet, $Z\gt{14}$ would result in secondary droplets. Therefore, $1\lt Z\lt{14}$ 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 $Z\gt{14}$ 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 ${\sim}1/50-1/20$ 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$\lt{100\,}^{\circ}$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 $\eta{\sim}$0.55 mPas, $\gamma{\sim}$26 mNm⁻¹ and $\rho{\sim}$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].

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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] Abs = $c\times\epsilon_{ext}\times l$, where c [gL⁻¹] is the concentration, _ext [Lg⁻¹m⁻¹] the extinction coefficient, and l[m] is the cuvette length [126]. Reference [64] experimentally derived the BP _ext at 660 nm from the slope of Abs per length versus the concentration of BP, $\epsilon_{ext}{\sim}$267 Lg⁻¹m⁻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].

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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/SiO₂, followed by N₂ 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].

The design of our SLG/BP PD is shown in figure 5(a). SLG is the channel on Si/SiO₂, Si is the bottom gate, SiO₂ is the dielectric, BP is the photoactive material, Ag is used for the electrodes, and Parylene C as encapsulation layer. Upon illumination, electron–hole (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.

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To fabricate the SLG/BP PD, SLG is grown on a 35 $\mu m$ Cu foil, as for reference [128]. The substrate is annealed at 1000 ^∘C for 30min in the presence of 20sccm H₂. To initiate growth, 5sccm CH₄ 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]. Pos(G) is ∼1586 cm⁻¹, with FWHM(G) ∼14 cm⁻¹. Pos(2D) is ∼2703 cm⁻¹, I(2D)/I(G) and A(2D)/A(G) are ∼3.1 and ∼6.4. No D peak is observed, indicating negligible defects [131].

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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 SiO₂, followed by overnight drying and PMMA removal with acetone and IPA, figure 7(a).

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The Raman spectrum of SLG transferred on Si/SiO₂ is in figure 6. The 2D peak retains its single-Lorentzian line shape with FWHM(2D) ∼31.6 cm⁻¹. Pos(G)∼1594 cm⁻¹, FWHM(G)∼11.6 cm⁻¹ and Pos(2D)∼2693.1 cm⁻¹, I(2D)/I(G) and A(2D)/A(G) are ∼1.2 and 3.2, indicating a p-doping with Fermi energy, E$_F,{\sim}$450 meV [132, 133], which corresponds to a carrier concentration ∼12.3×10¹²cm⁻² [132]. I(D)/I(G)∼0.06 corresponds to a defect density of ∼3.54 × 10¹⁰cm⁻² [134, 135] for excitation energy 2.41 eV and E$_F{\sim}$450 meV.

Pos(G) and Pos(2D) are also affected by the presence of strain. For uniaxial(biaxial) strain, Pos(G) shifts by ΔPos(G)/Δ $\epsilon_{strain}{\sim}$23(60) cm⁻¹/$\%$ [136, 137]. Pos(G) also depends on doping [132, 133]. The average doping as derived from A(2D)/A(G) should correspond to Pos(G)∼1599.2 cm⁻¹ for unstrained SLG [132]. However, in our experiments Pos(G)∼1594 cm⁻¹, which implies a contribution from uniaxial (biaxial) strain ∼0.22$\%$ (0.08$\%$) [136]. Local variations in strain and doping manifest as a spread in Pos(G) and Pos(2D), which in our sample vary from 1592 to 1597 cm⁻¹ and from 2688 to 2696 cm⁻¹, figure 8(a). In presence of uniaxial (biaxial) strain, and in the absence of doping, ΔPos(2D)/ΔPos(G)∼2.2 [136, 137]. In our samples ΔPos(2D)/ΔPos(G)∼0.87 (figure 8(a)), which indicates that most of the variation of Pos(G) is due to doping [136, 137]. This is also confirmed by the inverse correlation of FWHM(G) with Pos(G) in figure 8(d) [132, 138, 139].

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To pattern the CVD SLG, we use an IPA based PVP ink as mask, to protect SLG during RIE etching. PVP is used due its solubility in IPA [140], stable jetting [92] and ease of removal with water [141]. To make the ink, 5mg PVP (Sigma-Aldrich) is dispersed in 5 ml IPA. The PVP ink has $\eta{\sim}$1.25 mPas, as measured with Rheometery (Discovery HR-1), $\gamma{\sim}$69 mNm⁻¹, as determined with a FTA100 series contact angle and surface tension measurement system (First Ten Angstroms), and $\rho{\sim}$1 gcm⁻³, as derived by weighting a known volume of PVP ink via microbalance (Sartorius). For D = 22 µm, Z = 30. We use a Fujifilm Dimatix DMP-2800 to inkjet print PVP, while Si/SiO₂ is kept at ∼60 ^∘C to promote ink drying. To pattern SLG, PVP is printed on SLG to mask selected SLG regions, figure 7(b). Then, the sample is placed in a RIE to etch the uncovered SLG, figure 7(c). PVP is then removed by adding droplets of water, figure 7(d).

The Raman spectrum of etched SLG after PVP removal is in figure 6. The 2D peak retains its single-Lorentzian shape with FWHM(2D) ∼33.7 cm⁻¹. Pos(G)∼1588.1 cm⁻¹, FWHM(G)∼15.6 cm⁻¹, Pos(2D)∼2689.6 cm⁻¹, I(2D)/I(G) and A(2D)/A(G) are ∼1.7 and 3.8, indicating a p-doping with E$_F{\sim}$380 meV [132, 133], corresponding to a carrier concentration ∼8.7×10¹²cm⁻² [132]. I(D)/I(G)∼0.08 corresponds to a defect density ∼4.3×10¹⁰cm⁻² [134, 135] for excitation energy 2.41 eV and E$_F{\sim}$380 meV, thus no significant additional defects are induced during inkjet-lithography. The doping estimated from A(2D)/A(G) should correspond to Pos(G)∼1596.4 cm⁻¹ for unstrained graphene [132]. In our experiments Pos(G)∼1588.1 cm⁻¹, which implies a contribution from uniaxial (biaxial) strain ∼0.36$\%$ (0.13$\%$) [136]. ΔPos(2D)/ΔPos(G)∼0.34 (figure 8(b)), which indicates that most of ΔPos(G) is due to doping [136, 137], as confirmed by the inverse correlation of FWHM(G) with Pos(G) in figure 8(e) [132, 138, 139].

Source and drain electrodes are then prepared by inkjet printing an Ag ink from Sigma-Aldrich (Ag dispersion, 736465), figure 7(e), with resistivity ${\sim}11.2\,\mu\Omega$cm, 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/SiO₂, measured using a 4-point probe method, is R$_S{\sim}$600 $\Omega/\square$. In SLG, R_S = ($\sigma_{2d}$)⁻¹ [26], with $\sigma_{2d}$ the SLG conductivity. In SLG, $\sigma_{2d}$ = $n\mu q$ [142] where n is the carrier density per unit area and q is the e charge. From n∼8.7 × 10¹²cm⁻² derived from our Raman measurements, we get R$_{S}{\sim}$450 $\Omega/\square$, consistent with our R_S measurements.

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We then gate modulate the current between SLG source and drain. SLG shows ambipolar behavior with $\mu{\sim}$1700 cm$^{2}V^{-1}s^{-1}$, figure 9(b), from [6]:

$$\begin{equation} \mu = \frac{\triangle I_d.L}{\triangle V_g.C_{ox}.V_{ds}.W}, \end{equation} \tag{ 6 }$$

where $\triangle I_d$ is the change in drain current, $\triangle V_g$ 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 = $\epsilon_{0}\epsilon$/t$_{ox}$, where $\epsilon_{0}{\sim}8.85\times10^{-14}$F/cm is the vacuum permittivity, $\epsilon{\sim}3.9$ is the dielectric constant of SiO₂ [6] and $t_{ox}{\sim}$90 nm is the SiO₂ thickness. We use 90 nm SiO₂ in order to have a larger electric field at lower gate voltages. The SLG quantum capacitance (C_Q ) can be calculated as [132, 143]:

$$\begin{equation} C_{Q} {\sim} \frac{2q^{2}}{\hbar v_{f} \sqrt{\pi}} \sqrt{p_{ch}+{n_{i}}}, \end{equation} \tag{ 7 }$$

where $\hbar$ is the reduced Planck constant, $v_{f} = 1.1\times10^{6}\textrm {m/s}$ 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, 145–147]. From the Raman analysis we estimate $n_{i}{\sim}$8.7$\times10^{12}\textrm{cm}^{-2}$. This gives $C_{Q}{\sim}6\times10^{-6}\textrm{F/cm}^{2}$. Thus, the total capacitance C$_{Tot}$ = (1/C$_{ox}$+1/C$_{Q})^{-1}{\sim}$C$_{ox}$.

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 K$\Omega.\mu$m (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 $\gt$30 days under ambient conditions. Parylene dimers are vaporized at ${\sim}80^{\circ}$C. In a separate chamber, they are pyrolysed into monomers at ${\sim}690^{\circ}$C. The PD is held at RT, so that parylene polymerizes on contact with the surface, forming a conformal film [41].

The Raman spectra of SLG coated with BP and sealed with Parylene C are in figure 6, and, after subtraction of the parylene C signal, in figures 10(a)–(c). In the Raman spectrum of Parylene C, the peaks ∼1207, 1337, 1610 cm⁻¹, figure 10(b), are attributed to CH in-plane vibrations [150, 151], CH₂ wagging and twisting vibrations [150, 151], CH scissoring in CH₂,and/or C-C skeletal in-plane vibrations of the aromatic rings [150, 151], respectively. The 2D peak retains its single-Lorentzian line shape, and narrows from FWHM(2D) ∼33.7 cm⁻¹ to FWHM(2D)∼23.6 cm⁻¹, figures 6 and 10(c). FWHM(G) narrows from ∼15.6 cm⁻¹ to ∼9.2 cm⁻¹, figures 6 and 10(b). FWHM(2D) and FWHM(G) narrow due to the homogeneous distribution of doping in SLG channel. Pos(G) is ∼1585.4 cm⁻¹, Pos(2D)∼2684.8 cm⁻¹, I(2D)/I(G) and A(2D)/A(G) are ∼2 and 5.3, indicating a n-doping with E$_F{\sim}$360meV [132, 133] which corresponds to carrier concentration ∼7.7×10¹² cm⁻² [132]. I(D)/I(G)∼0.25 corresponds to a defect density ∼13.0×10¹⁰ cm⁻² [134, 135] for excitation energy 2.41 eV and E$_F{\sim}$360 meV. E_F , as calculated from A(2D)/A(G), should correspond to Pos(G)∼1590.2 cm⁻¹ for unstrained graphene [132]. We have Pos(G)∼1585.4 cm⁻¹, which implies a contribution from uniaxial (biaxial) strain ∼0.21$\%$ (0.08$\%$) [136]. ΔPos(2D)/ΔPos(G)∼0.38 (figure 8(c)), which indicates that most of the variation of Pos(G) is due to doping [136, 137]. This is also confirmed by the inverse correlation of FWHM(G) with Pos(G) in figure 8(f) [132, 138, 139].

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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/SiO₂, to patterned and BP coated SLG. Thus, we expect µ to decrease ∼2 times when going from SLG on Si/SiO₂ to patterned and BP coated SLG. This is consistent with field-effect measurements, giving $\mu{\sim}$1200 cm² V⁻¹s⁻¹ for SLG on Si/SiO₂, reduced to ∼650 cm² V⁻¹s⁻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$\lt$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 $V_{g}\lt V_{D}$, 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]:

$$\begin{equation} I_{\textrm{photo}}=I_{\textrm{light}}-I_{\textrm{dark}}, \end{equation} \tag{ 8 }$$

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).

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Figure 11(c) gives R $_{\textrm{ext}}{\sim}$337 A W⁻¹ for 488 nm, when V_g = -20 V ($V_{g}\lt V_{D}$) and V$_{ds}$ = 1 V. For $V_{ds}\gt$1 V, the free carriers drift velocity ν_d = $\frac {\mu E}{1+\mu E/\nu_{\textrm{sat}}}$ [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 $V_{ds}\leqslant 1V$ 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$\lt$1 µW. For P$_{\textrm{opt}}{\sim}$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.

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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 ($\textrm{Abs}$ = $c\times\epsilon_{\textrm{ext}}\times l$ as T_r = 10$^{-c\epsilon_{\textrm{ext}}l}$) 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 = $\epsilon_{ext}\lambda\rho$/4πlog₁₀(e) and the real part of the average refractive index is found by applying the Kramers–Kronig (KK) relation [160], $n_{BP}(w)$ = 1 + 2π⁻¹ $\mathcal{P}$ $\int_{0}^{\infty}\, w^{^{^{\prime}}}\, K_{BP}(w^{^{^{\prime}}})/(w^{^{^{\prime}}2}-w^{2})\, dw^{^{^{\prime}}}$, where $\mathcal{P}$ 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/SiO₂. 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) = A₀.exp(-t/τ_life) + B, where A₀ 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}{\sim}$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].

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By applying V$_{ds}$, transferred photogenerated h drift to the drain with a timescale τ_transit [6]:

$$\begin{equation} \tau_{\textrm{transit}}=\frac{L^{2}}{\mu V_{ds}}, \end{equation} \tag{ 9 }$$

where L = 60 µm is the length of channel, and $\mu{\sim}$1700 cm²V⁻¹s⁻¹. We thus get $\tau_{\textrm{transit}}{\sim}$37 ns, resulting in a photoconductive gain [6]:

$$\begin{equation} \textrm{Gain}=\frac{\tau_{\textrm{life}}}{\tau_{\textrm{transit}}}{\sim} 10^{6}. \end{equation} \tag{ 10 }$$

The dependence of R_ext on $\frac{\tau_{\textrm{life}}}{\tau_{\textrm{transit}}}$ 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]:

$$\begin{equation} \textrm{Gain}=\frac{|I_{\textrm{light}} - I_{\textrm{dark}}|}{q.A_{\textrm{PD}}.\triangle p_{ch}}, \end{equation} \tag{ 11 }$$

where $\triangle p_{ch}$ is the concentration per unit area and per unit time of the injected h. $\triangle p_{ch}$ is equal to the trapped e concentration per unit area and per unit time in BP, related to a charge neutrality point shift $\triangle V_{g} = \triangle V_{D}$ in the transfer characteristics (I_d versus V_g ). To calculate $\triangle p_{ch}$, 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]:

$$\begin{equation} V_{g}=V_{ch}+V_{\textrm{diel}}=\frac {E_{f}}{q}+\frac {Q_{G}}{C_{ox}}, \end{equation} \tag{ 12 }$$

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:

$$\begin{equation} \frac{dV_{g}}{dQ_{g}}=\frac{1}{C_{ox}}+\frac {dV_{ch}}{dQ_{g}} \end{equation} \tag{ 13 }$$

which results in:

$$\begin{equation} \triangle Q_{g}=\left(\frac{1}{C_{ox}} + \frac{1}{C_{Q}}\right)^{-1}. \triangle V_{g}. \end{equation} \tag{ 14 }$$

To find Q_G and $\triangle p_{ch}$, C_ox and C_Q are needed. $C_{ox}{\sim}38.35\times10^{-9}F/cm^{2}$. From equation (7), we get $C_{Q}{\sim}$6$\times10^{-6}F/cm^{2}$. Therefore, $\triangle p_{ch}$ varies from ∼2.6$\times10^{11}cm^{-2}$ to $1.1\times10^{12}cm^{-2}$ for optical power 620nW to 612 µW at $V_{ds} = 0.5V$. Then, from equation (11), we get Gain ${\sim}2\times 10^{6}$, 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]:

$$\begin{equation} D^* =\frac{(A_{\textrm{PD}}B)^{1/2}}{\textrm{NEP}} \end{equation} \tag{ 15 }$$

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]):

$$\begin{equation} \textrm{NEP}=\frac{i_n}{\textit{R}_{\textrm{ext}}}, \end{equation} \tag{ 16 }$$

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/$\sqrt{Hz}$] 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 ${\sim}1.8\times10^{-10}WHz^{-1/2}$ and D$^{*}{\sim}$2×10⁷Jones. 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]:

$$\begin{equation} D^* =\frac{R_{\textrm{ext}}(AB)^{1/2}}{[2qI_{\textrm{dark}(SLG)}]^{1/2}}. \end{equation} \tag{ 17 }$$

Equation (17) gives $D^{*}{\sim}$10¹¹ Jones, ∼3 times higher than reference [45] for inkjet-printed graphene/MoS₂ PDs. It is also ∼3-4 orders of magnitude higher than reference [47] for PDs based on inkjet-printed MoS₂. 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].

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 non-conductive 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 $\mu m$ to $\lt5\mu m$. We then transfer SLG on PU coated polyester fabric using a similar procedure as for Si/SiO₂. After removing PMMA, a PVP ink is inkjet-printed as mask on SLG to pattern a $400\,\mu m \times 400\,\mu m$ 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 CH₂ 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 CH₂ groups [173, 176] and that ∼1251 cm⁻¹ to coupled C-N and C-O vibrations of urethane [173, 176], figure 14(b). The spectrum of SLG on fabric has Pos(G)∼1596.9 cm⁻¹, FWHM(G)∼14.4 cm⁻¹, figure 14(b), Pos(2D)∼2693.3 cm⁻¹, FWHM(2D)∼56.6 cm⁻¹, figure 14(c). I(2D)/I(G) and A(2D)/A(G) are ∼1.5 and 5.8, indicating a p-doping of E$_{F}{\sim}$270 meV [132, 133], which corresponds to a carrier concentration ∼4.33×10¹² cm⁻² [132]. I(D)/I(G)∼1.03 corresponds to defect density ∼4.6×10¹¹cm⁻² [134, 135] for excitation energy 2.41 eV and E_F = 270meV. For the E_F derived from A(2D)/A(G), Pos(G) should be ∼1589.2 cm⁻¹ for unstrained SLG [132]. In our experiments, Pos(G)∼1596.9 cm⁻¹, which implies a contribution from uniaxial (biaxial) strain ∼0.33$\%$ (0.12$\%$) [136], comparable to the uniaxial (biaxial) strain ∼0.36$\%$ (0.13$\%$) of SLG on Si/SiO₂.

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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}{\sim}$2.1 KΩ, comparable to transferred CVD SLG previously reported for polypropylene coated fabrics [172]. BP is then inkjet-printed on the channel layer. Figures 15(a) and (b) are optical and SEM images of PDs on polyester fabric. Figure 15(c) plots the current–voltage characteristic in dark, which shows an Ohmic resistance ($R = 2.09\,K\Omega$) between inkjet-printed electrodes and SLG channel. We then characterize R$_{ext}$ at 488 nm for P = 1.1 mW. Figure 15(c) shows that the current increases under illumination. We get R$_{ext}{\sim}$6 mA W⁻¹ at 488 nm.

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The Raman spectrum of BP coated on SLG on fabric is in figure 14(a). Pos(G)∼1587.4 cm⁻¹, FWHM(G) broadens from ∼14.4 cm⁻¹ to ∼15.6 cm⁻¹, figure 14(b), Pos(2D)∼2687.5 cm⁻¹, FWHM(2D) narrows from ∼56.6 cm⁻¹ to ∼32.5 cm⁻¹, figure 14(c). I(2D)/I(G) and A(2D)/A(G) are ∼5.1 and 10.7, indicating n-doping with E$_F{\sim}$100meV [132, 133] which corresponds to a carrier concentration ∼0.7×10¹²cm⁻² [132]. I(D)/I(G) ∼5.2 gives a defect density ∼1.4×10¹²cm⁻² [134, 135] for excitation energy 2.41 eV and E$_F{\sim}$100 meV. E_F estimated from A(2D)/A(G) would imply Pos(G)∼1583.8 cm⁻¹ for unstrained SLG [132]. However, in our experiments Pos(G)∼1587.4 cm⁻¹, which would imply a contribution from uniaxial (biaxial) strain ∼0.15$\%$ (0.05$\%$) [136].

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]:

$$\begin{equation} R_{b}=\frac{y^{2}+(x/2)^{2}}{2y}, \end{equation} \tag{ 18 }$$

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 ($I_{\textrm{Photo Bend}}$) is normalized to that measured in flat conditions ($I_{\textrm{Photo Rest}}$). Figure 15(d) shows a change ${\sim}17\%$ of $\frac{I_{\textrm{Photo Bend}}}{I_{\textrm{Photo Rest}}}$ 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 ∼11×10⁴ (I$_{d}{\sim}$120nA) under ∼4.5 mWcm⁻² of UV light (R$_{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}{\sim}$35 mm, is in figure 15(e). Our PDs retain ${\sim}82\%$ of $\frac{I_{\textrm{Photo Bend}}}{I_{\textrm{Photo Rest}}}$ for up to 30 cycles, comparable to what previously reported for CVD based MoS₂/SLG PDs on PET [180], making our approach promising for wearable and flexible applications.