Waveguide-integrated mid-infrared photodetection using graphene on a scalable chalcogenide glass platform

The development of compact and fieldable mid-infrared (mid-IR) spectroscopy devices represents a critical challenge for distributed sensing with applications from gas leak detection to environmental monitoring. Recent work has focused on mid-IR photonic integrated circuit (PIC) sensing platforms and waveguide-integrated mid-IR light sources and detectors based on semiconductors such as PbTe, black phosphorus and tellurene. However, material bandgaps and reliance on SiO2 substrates limit operation to wavelengths λ ≲ 4 μm. Here we overcome these challenges with a chalcogenide glass-on-CaF2 PIC architecture incorporating split-gate photothermoelectric graphene photodetectors. Our design extends operation to λ = 5.2 μm with a Johnson noise-limited noise-equivalent power of 1.1 nW/Hz1/2, no fall-off in photoresponse up to f = 1 MHz, and a predicted 3-dB bandwidth of f3dB > 1 GHz. This mid-IR PIC platform readily extends to longer wavelengths and opens the door to applications from distributed gas sensing and portable dual comb spectroscopy to weather-resilient free space optical communications.

Mid-IR absorption spectroscopy is a critical tool for chemical sensing and analysis, especially for inert gases that evade detection by chemical reaction-based sensors.Many such gases derive their inertness from halogenated chemistries and thus exhibit global warming potential due to carbon-halogen stretching modes resonant in the thermal IR [1,2].To facilitate sensor deployment for greenhouse gas leak detection and other chemical sensor application areas, there exists a strong need to transition from co-packaged discrete components to compact and chip-integrated sensors.
To address this challenge, mid-IR photonic integrated circuit platforms have been investigated to reduce optical gas sensors to the size of a chip.Recent work has demonstrated integrated optical methane [3] and volatile organic compound [4] sensing, but required coupling to off-chip sources and detectors.However, integrating the detector on-chip is more compact and can improve sensitivity by reducing the volume of active material able to generate thermal noise.Su et al. achieved integration of a PbTe photoconductor and demonstrated methane sensing at a wavelength of λ = 3.31 µm [5], but their platform is limited to λ 4 µm due to absorption in the SiO 2 substrate [6] and by PbTe's absorption cutoff [7].Waveguide-integrated detectors based on narrow-gap 2D materials black phosphorus [8] and tellurene [9] have also been demonstrated, but they too are bandgap-limited to λ 4 µm.
Here we exceed the wavelength limit of previous demonstrations using graphene-based detectors on an extended-transparency waveguide platform.
While graphene integrated detectors have shown promise at telecom wavelengths [10], the material's advantages are magnified further at longer wavelengths due to the thermal nature of the photothermoelectric (PTE) response mechanism [11,12] and due to the impact of optical plasmon scattering at short wavelengths [13].Integrated photodetection with graphene has been demonstrated at wavelengths up to 3.8 µm [6] and with chalcogenide glass waveguides [14], but on SiO 2 platforms.To access longer wavelength operation and achieve good sensitivity at zero bias, we introduce a Ge 28 Sb 12 Se 60 (GSSe)-on-CaF 2 waveguide platform supporting gated PTE-based graphene photodetectors.
Figs. 1a and 1b illustrate the platform and photodetector design.The device consists of a single-mode GSSe waveguide fabricated on top of a 5.4 µm wide by 300 µm long, CVD-grown graphene channel, flanked on either side by source and drain contacts.Beneath the graphene channel are pair of CVD graphene back-gates, separated by a 400 nm gap and used to electrostatically induce a p-n junction along the center of the channel.We use HfO 2 as the gate dielectric and as an airtight capping layer.The device is fabricated on a CaF 2 substrate, transparent up to λ = 8 µm.Fig. 1c depicts the resulting waveguide mode at λ = 5.2 µm.
We use lock-in measurement to characterize our detectors, focusing light from a λ = 5.2 µm QCL source into our chip's input facet.Light exiting the chip is focused onto an InAsSb photodetector and amplified for transmission measurement.Supplementary Fig. 1a depicts this beam-path in more detail.We operate the device under zero bias voltage to avoid introducing electronic shot noise and to prevent channel conductivity fluctuations from manifesting as 1/f noise [15].For the following low-frequency measurements we use a lock-in amplifier to measure the photovoltage directly with no preamplification.
Figs. 2a, b and c plot the photovoltage, resistance, and transmission lock-in signals versus both gate voltages for one such photodetector ("Device A").Here, we modulate the λ = 5.2 µm QCL source at 3.78 kHz with a guided "on" power of 11 µW at the detector input.From our photovoltage and resistance maps, alongside the power and waveguide loss calibrations described in Supplementary Section A, we infer the gate voltage pairs that optimize the voltage responsivity, current responsivity, and NEP with respect to Johnson noise, indicated with green markers in Fig. 2. For these, we arrive at 1.5 V/W, 10. mA/W, and 1.1 nW/Hz 1/2 , respectively.The observed photovoltage gate map indicates a PTE response mechanism, evidenced by the six-fold sign change pattern around the graphene channel's charge neutral point [11].Figs.2d, e and f show line slices of the voltage maps as indicated by the dashed lines in Figs.2a, b and c of the same color.Fig. 2d, in particular, highlights the changes in slope associated with PTE-based detectors [11].
To confirm our understanding of device operation and elucidate the prospects for performance improvement, we apply the formalism introduced in Song et al. [12] to cal- culate the electronic temperature distribution and Seebeck photovoltage in the graphene channel under illumination.Figs.3a and 3b compare our measured and modelled voltage responsivities using calculations described in the Methods section.The performance of our device depends on several fitting parameters, whose definitions and approximate values (derived from our measured data) we provide in Table I.We describe our fitting process in Supplementary Section C. Critically, all features of the modelled responsivity map in Fig. 3b up to an overall scale factor from τ eph are established a priori from fitting parameters extracted from the device transmittance and resistance maps, with only τ eph obtained by matching the scales of the measured and modelled responsivities.The resemblance between Figs. 3a and 3b thus reflects the validity of our PTE model and is not due to over-fitting.In Fig. 3c, we plot the solution to Eqn. 6, ∆T el (x), as well as the source term Q(x).The thermal transport model predicts that 9 µW of guided power raises the temperature of the graphene channel's electron gas by as much as 1 K along the center of the device.
Current modulation of our QCL source permits frequency response measurements up to its modulation bandwidth of 1 MHz.To account for the modulation response of our laser, we measure the photovoltage of Device A alongside that of a fast InAsSb photodiode.The comparison shown in Fig. 4a indicates that our device is faster than our laser's modulation bandwidth.We thus use a COMSOL model to find the actual RC contribution to our device's frequency response, plotted in the inset of Fig. 4a.We also plot the product of the RC-limited frequency response and the τ eph -limited frequency response with an assumed (1 + (2πτ eph f ) 2 ) −0.5 dependence, which applies as the electron-phonon cooling length = κτ eph /C el ≈ 230 nm is narrower than our device channel [12].We thus predict a 3-dB cutoff frequency of f −3dB ≈ 1.3 GHz, dominated by the capacitance between the graphene back-gates.
To investigate our device's noise performance, we modulate the QCL current at 30 kHz, amplify the photovoltage with a low-noise preamplifier and inspect using a signal analyzer.We observe in Device A no broadening of the 30 kHz photoresponse peak at offset frequencies as low as 0.1 Hz, indicating long-term responsivity stability, and we observe no illumination-dependence of the noise floor.We then measure the un-illuminated noise spectral density and resistance versus both gate voltages.Fig. 4b shows the resulting data for a Device B of identical design to Device A, organized by resistance and compared to the expected Johnson noise spectral density.We observe excellent consistency between the measured and predicted noise, with a 2-4 dB discrepancy consistent with the specified noise figure of our preamplifier, corroborating our earlier claim of Johnson-noise-limited NEP.
To demonstrate our device's utility, we analyze its predicted gas-sensing performance, summarized from Supplementary Section F. The minimum detectable gas concentration for a given waveguide platform and photodetector is given by [16]: where I 0 is the source power, α base is the waveguide attenuation coefficient in the absence of gas, a is the specific attenuation coefficient of the gas, n g is the guided mode group index, Γ E is the confinement factor of electric field energy within the gaseous medium, and e = exp (1).For detection of nitric oxide (NO), with an absorption peak at λ = 5.24 µm and a specific attenuation of approximately a ≈ 70 m −1 atm −1 at low concentrations [17], we arrive at p gas,min = 74 µatm/ √ Hz for a 1 mW illumination source.
Assuming a measurement bandwidth of 0.1 Hz over which we have measured our photoresponse to be stable, we find p gas,min = 23 ppm, roughly equal to the National Institute of Occupational Safety and Health (NIOSH) recommended exposure limit (REL) of 25 ppm [18].Removing the slightly lossy HfO 2 dielectric underneath the gaslight interaction waveguide could decrease p gas,min considerably, as waveguide losses down to 0.7 dB/cm have been demonstrated at the same wavelength using a similar chalcogenide glass and liftoff process [19].
Although our demonstration is limited to λ = 5.2 µm by light source availability, the optical conductivity of our graphene inferred from the fitting parameters in Table I remains relatively constant and even increases at longer wavelengths due to intraband absorption as shown in Supplementary Fig. 7.We thus expect our platform to scale to λ = 10 µm and beyond, perhaps requiring a BaF 2 substrate for extended transparency, with little reduction in performance owing to the PTE effect's thermal nature.In Table II we compare our device's performance with various off-the-shelf detectors.Although its NEP is not yet on par with commercial options, its predicted bandwidth may be useful for dual-comb spectroscopybased integrated gas analyzers [22].Additionally, the vacuum requirement of VO x bolometers may complicate copackaging and introduce coupling losses, and the high cost of HgCdTe may preclude use in broadly deployed sensor networks.
In conclusion, we have demonstrated a PTE-based graphene photodetector, integrated in a scalable chalcogenide glass waveguide platform with an NEP of 1.1 nW/Hz 1/2 and a bandwidth exceeding f −3dB = 1 MHz.We have modeled the bandwidth to approach 1.3 GHz and we predict similar performance at longer wavelengths for scaled-up devices enabled by the transparency of GSSe beyond λ = 10 µm [23].Finally, we have shown that our device and waveguide platform would enable NO detection at concentrations comparable to its REL.Substantial improvements are likely using metalinsulator-metal [10] or dielectric slot waveguides to concentrate the optical mode to within a cooling length of the pn-junction, which would also reduce the detector length and thus device footprint needed to absorb an optical signal.Gapped bilayer graphene may also be investigated as an alternative to monolayer graphene to reduce thermal noise [24].The PIC platform further promises to support a full toolkit of mid-IR active devices including on-chip quantum cascade light sources [25], and may even leverage the same graphene material platform for devices such as graphene modulators [14] and hot-electronbased [26] [20]) and a VO x bolometer (from [21]) available off the shelf.For the photodiodes, the NEP is extrapolated from the specified detectivity for a detector scaled down to match the size of a diffraction-limited spot with NA = 0.3, which is the acceptance NA of these detectors.For the bolometer, we give the NEP of a single 17 µm × 17 µm bolometer pixel as calculated from the specified noise-equivalent temperature difference as described in Rogalski [7].
platform could also be adapted to alternative mid-IR waveguide platforms, such as suspended Ge, as necessary to reach longer wavelength ranges [27].This research represents the first foray into waveguide-integrated detectors operating beyond λ = 4 µm, paving the way towards 2D-material-enabled integrated mid-IR microsystems for gas sensing, spectroscopy [22] and free-space optical communications [28].

Photodetector Fabrication
A continuous monolayer graphene film was grown on Cu foil (99.8%,Alfa Aesar, annealed, uncoated, item no.46365) cut to a size of 15 × 2 cm 2 in a 1-inch-diameter quartz tube furnace under atmospheric pressure.The furnace was heated to 1060 • C over 30 minutes under 500 sccm of Ar flow; afterwards, 15 sccm of H 2 and 10 sccm of dilute CH 4 (1% in Ar) were introduced as reducing gas and carbon source, respectively, and flowed for 4 hours to ensure the continuity of the graphene film.Finally, the furnace was allowed to cool to 100 • C without modifying the gas flow before the CVD graphene was removed from the chamber.Our devices were fabricated on a 1" diameter by 1.0 mm thick (111)-cut CaF 2 substrate (MTI Corporation, item CFc25D10C2).We first coated our substrate with a PMMA bilayer for liftoff (495 PMMA A6 followed by 950 PMMA A2), which features a slightly re-entrant sidewall profile after developing.We then performed e-beam lithography us-ing an Elionix FLS-125 125 keV electron beam lithography system to pattern alignment marks on our substrate, followed by room-temperature development in 3:1 isopropanol:methyl isobutyl ketone, e-beam evaporation of 5 nm Ti/100 nm Au (Temescal VES2550), and liftoff.To transfer the first layer of graphene, we first coated one side of the CVD graphene-on-Cu sheet with PMMA and removed the graphene from the other side using 90 seconds of oxygen RIE (16 sccm He and 8 sccm O 2 at a pressure of 10 mTorr and an RF power of 100W, "oxygen RIE process").We then etched away the Cu using a FeCl 3 -based etchant, followed by 2 DI water rinses, a 30minute clean in 5:1 DI water:HCl 37% in water to reduce metal ion contamination, and two more DI water rinses.After letting the graphene film sit overnight in the final evaporating dish of water, we scooped it out with our CaF 2 substrate, blew N 2 on the film to eliminate most of the trapped water, and then baked the sample at 80 • for 30 minutes followed by 160 • for 2 hours.We then removed the PMMA from the graphene using acetone at room temperature, rinsed it in isopropanol and blew it dry, and baked the sample in N 2 for 1 hour to improve adhesion.To pattern the graphene back-gates, we spun on a layer of 950 PMMA A6, patterned the gates in the Elionix and developed as described previously, etched away the exposed graphene using "oxygen RIE process", and removed the PMMA as described previously.We then repeated the Ti/Au liftoff process described above to define the contacts to the graphene gates, after which we evaporated 1.5 nm Al (Temescal VES2550) as an ALD seed layer, allowed the thin Al layer to oxide in ambient, and deposited 300 cycles ≈ 30 nm of HfO 2 ALD at 200 • C (Cambridge Nanotech Savannah 200).To define the graphene channel and channel contacts, we performed another graphene transfer as described above and repeated the subsequent graphene patterning and contact metallization steps, followed by another Al seed layer and 150 cycles of HfO 2 ALD to protect the graphene channel.Finally, to pattern the GSSe waveguides, we coated the chip with 495 PMMA A11, used the Elionix to define the waveguides, developed as described previously and evaporated 750 nm of Ge 28 Sb 12 Se 60 , followed by a quick liftoff in boiling acetone, IPA rinse and N 2 blow-dry, and cleaving of the chip to expose waveguide facets.

Measurement conditions
The maps in Figs.2a, b, and c were measured by sequentially measuring each data point column by column, bottom to top from left to right.SR830 lock-in amplifiers were used for all measurements.Prior to each data point collection, both gate voltages were reset to −7 V for 80 ms to reset the gate dielectric hysteresis (see Supplementary Section B), then set to the desired gate voltages and allowed to dwell for 200 ms for the lock-in signal to stabilize.The lock-in filter was set to a 30 ms time constant with a 12 dB/octave falloff.The detector photovoltage in Fig. 2a was measured directly by the lock-in amplifier with no additional amplification.For the resistance map in Fig. 2b, we used our lock-in amplifier to bias the device with a 1 VRMS sine wave at 3.78 kHz through a 100 kΩ resistor to act as a current source and measured the voltage across the device with the lock-in.To produce the frequency response plots in Fig. 4a, we apply a sinusoid of variable frequency to the current modulation input of our QCL and measure the calibration and photoresponse signals with a SR844 RF lock-in amplifier.For the laser modulation response (indicated in red in Fig. 4a), we couple the laser light through a single-mode waveguide on our chip with no devices on it and directly measure the amplified transmission signal produced by the fast InAsSb detector on the output side of our chip.For the photovoltage signal (blue curve in Fig. 4a), we amplify the photovoltage produced by our detector by 40 dB using a preamplifier and measure this amplified signal with our lock-in.In all cases, we used a dwell time of 1.5 s, and the filter of our lock-in was set to 100 ms with a 12 dB/octave falloff.To measure the un-illuminated noise spectral density in Fig. 4b, we amplify the noise produced by the device using a 60 dB preamplifier and analyze the output on an FFT signal analyzer while controlling the gate voltages applied to the device.We choose to measure the averaged noise spectral density between 22 and 32 kHz where we find no electromagnetic interference-related spectral peaks.We also use a lock-in amplifier to simultaneously measure the device resistance as described above for Fig. 2b, albeit at a higher frequency so as to not produce a signal in the noise measurement range.We use our signal analyzer's band averaging feature to measure the noise spectral density for each data point.To produce the final plot, we manually record the resistance and noise spectral density for all gate voltage pairs from −6 V to 6 V in steps of 2 V.

Device modelling
We use the Kubo formula adapted from Hanson [29] to model graphene's conductivity at DC and infrared frequencies (albeit with different values of the Drude scattering time τ for the different frequency ranges): where e is the elementary charge, is the Fermi-Dirac distribution and k B is Boltzmann's constant.As I will show below, graphene's low frequency conductivity σ DC and infrared conductivity σ IR affect various intermediate model parameters; σ DC and σ IR themselves depend strongly on E F , which features spatial variation due to the backgates.For the graphene channel, we assume a constant N c = N 0,c + e −1 C g V g in the region above each gate, where N c is the carrier concentration in the channel (positive for positive E F , negative for negative E F ), N 0,c is the native carrier concentration at zero gate voltage, C g is the capacitance per area of the gate dielectric, and V g is the voltage applied to the gate in question.(Using a set of test devices, we measure C g = 34.fF/µm 2 on our chip, corresponding to a back-gate dielectric constant of K ≈ 12; this is described in more depth in Supplementary Section D.) In the part of the graphene channel above the gap between the two gates, we assume a linear slope between N c,1 and N c,2 .For the gates, N g = N 0,g − e −1 C g V g , with N g and N 0,g defined similarly to N c and N 0,c .In general, the graphene's Fermi level and carrier concentration are related by E F = v gr π|N | sign(N ), where v gr is graphene's Fermi velocity.To incorporate the blurring of the graphene's Fermi level-dependent properties due to spatial carrier concentration variations, we convolve the Kubo formula with a Gaussian as follows: and similarly for σ IR (N ) using ω = 2πc/λ instead of 0 and τ IR instead of τ DC .Finally, we have B T 0 σ DC /3e 2 via the Wiedemann-Franz law, and S = −d(log σ DC )/dE F [30].C el is obtained by convolving the heat capacity of pristine graphene with a Gaussian of standard deviation σ N as in Eqn. 3, where the pristine heat capacity is given by [30,31]: We use a waveguide eigenmode solver to find the mode profile of our waveguide at λ = 5.2 µm, using refractive indices of 1.4, 2.6, and 1.88 for the CaF 2 , GSSe, and HfO 2 , respectively.The resulting mode profile enters into our expression for Qel as follows [32]: Here y c is the y-coordinate of the graphene channel, and y g would be the y-coordinate of the graphene gates.We may then write α c = P −1 W/2 −W/2 Qel (x) dx.Similar expressions hold for α g in terms of σ IR,g (x), noting of course that σ IR,g (x) = 0 for x within the gap between the gates where there is no graphene.Finally, ρ Ω = W/2 −W/2 R(x) dx.Having thus obtained expressions for κ(x), C el (x), Qel (x), S(x), Π(x), α c , α g and ρ Ω as a function of the gate voltages as well as τ DC , τ IR , σ n , E Fc , E Fg , τ eph , α e , and ρ c , we then solve for the increase in electronic temperature per guided power ∆T el (x)/P = (T el (x) − T 0 )/P using the equation: where κ is the 2D electronic thermal conductivity of the graphene, τ eph is the electron-phonon cooling time, Qel is the absorbed optical power per area, η is the conversion efficiency of absorbed optical power to electronic heat after initial electron-phonon scattering [12], J x is the line current density in the x-direction, and Π is the Peltier coefficient.We are approximating the electric field to run exclusively in the x-direction, valid for sufficiently gradual light absorption.We assume η = 1 as has been previously reported in pump-probe experiments at this wavelength range [13].The thermal electromotive force (EMF) arising from the Seebeck effect is then given by: where W = 5.4 µm is the channel width and S is the Seebeck coefficient.In Eqns.6 and 7, κ, C el , S, and Π = ST el ≈ ST 0 (for small ∆T el ) are all dependent on the local Fermi level E F of the graphene, and thus have a gate-tunable x-dependence, which we account for in our calculations.Combining the equations, the η Qel source term in Eqn.6 gives rise to a proportional photoinduced EMF, whereas the Peltier term J x dΠ dx gives rises to a current-dependent EMF which appears as a resistance in series with the Ohmic and contact resistances of the channel.We can thus write: where V is the voltage across the contacts, R v is the photovoltage per absorbed power per length of a cross-sectional slice of the device (i.e., dimensions of V/(W/m)), α c is the component of the waveguide power attenuation coefficient arising from absorption in the graphene channel, P (z) is the guided power at a position along the waveguide, and ρ Ω , ρ Π , ρ c are the Ohmic, Peltier, and contact line resistivities (dimensions of Ω•m), respectively.Averaging over z along the length of the waveguide we obtain: where I is the current produced by the photodetector, thus describing a Thévenin equivalent source.Here, α tot = α c + α g + α e is the total guided power attenuation coefficient within the detector, including contributions not only from the graphene channel but also from the graphene gates (α g ) as well as a gate-independent excess loss α e associated with scattering and absorption from organic or metallic impurities attached to or trapped underneath the graphene sheets.Thus the total device resistance is equal to R = R Ω + R Π + R c , and the voltage responsivity is given by: which we plot versus both gate voltages in Fig. 3b for the best-fit device parameters given in Table I

DATA AVAILABILITY
The datasets generated during and/or analysed during the current study are available in the FigShare repository at https://doi.org/10.6084/m9.figshare.c.5514759.v1.

ACKNOWLEDGMENTS
We would like to thank the MIT.Nano and MIT Nanostructures Laboratory staff for maintaining the cleanroom facilities used to fabricate these devices, in particular Mark Mondol, Jim Daley, and Dave Terry.We also would like to thank Sebastián Castilla of ICFO for helpful discussions.This research was funded in part by a grant from the Army Research Office via the MIT Institute for Soldier Nanotechnologies University-Affiliated Research Center (ISN UARC) (award number W911NF-18-2-004), the NSF Graduate Research Fellowship Program (award number 1122374), and NSF Award #2023987.Any opinions, findings, and conclusions or recommendations ex-pressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Supplementary Figure 4: Transmission line method (TLM) device used for gate capacitance and contact resistance measurements.measure, we perform a measurement with both pads contacted and with only one pad contacted to compensate for any stray capacitance in our setup.We then subtract the measured capacitances in the "connected" and "disconnected" cases to obtain the actual device capacitance as a function of frequency, which we plot in Supplementary Fig. 5. Excluding the orange curve as an outlier, we measure a capacitance of C ≈ 30 pF corresponding to a capacitance per area of C g = 3.4 fF/µm 2 and a dielectric constant of K ≈ 12.

E. Measurement of TLM structure for gate resistance extraction
In additional to capacitance measurement, we also use the TLM structures for their intended purpose of evaluating the resistance of our graphene-metal contacts.For each of the six channels in each of the five TLM devices, we measure the channel resistance as a function of gate voltage using an upward voltage sweep each time to compensate for the hysteresis discussed in Supplementary Section B.. Since the gate voltage of the charge neutral point may shift slightly between measurements due to trapped charges in the gate, we then shift the measured resistance curves so that their peaks overlap.Finally, for each measured voltage offset from the Dirac peak and for each TLM, we fit the data of resistance versus channel length to a line and plot the resulting y-intercept as a function of voltage offset, manually eliminating any gate voltage sweeps showing malformed (for instanced, flattened or bimodal) resistance peaks.The resulting y-intercept curves are shown in Supplementary Fig. 6.Unfortunately, we find highly inconsistent intercept resistances between the five TLM devices, with the intercept even going negative in several cases.Therefore, we are unable to draw a quantitative conclusion regarding the contact resistance of our devices.We can at least, however, estimate the total contact resistance (summing over both contacts) for our TLM devices to be generally in the ≈ 1 × 10 2 Ω range; therefore, since the TLM channels are 40 µm wide, we would expect the total contact resistance of our actual photodetectors to be in the ≈ 1 × 10 1 Ω range, which is an order of magnitude lower than our measured resistances; therefore we conclude that it can be safely ignored in our modelling as other sources of error (such as the imperfect fit between our measured and modelled resistance and transmittance maps) are much more likely to dominate the uncertainty in our analysis.
FIG. 1: a) Illustration of the device cross-section perpendicular to the waveguide axis.The optical mode supported by the GSSe waveguide evanscently couples to and is absorbed by the graphene channel, which is gated by two graphene back-gates to induce a p-n junction.b) Optical image of the device depicting source, drain and gate contact pads.c) Depiction of the optical guided mode at λ = 5.2 µm.

FIG. 2
FIG. 2: a) Measured zero-bias photovoltage produced by the device as a function of the two gate voltages.b) Total device resistance as a function of the two gate voltages.c) Lock-in signal reflecting power measured by an InAsSb photodetector at the focal point of our output facet collection lens, used to monitor transmission of the device as a function of the gate voltages.The power-normalized transmitted is plotted in Supplementary Fig. 3b.d, e, f) Plots of line sections indicated with dashed lines in figures a, b, and c, respectively.

FIG. 3
FIG. 3: a, b) Contour plots of the a) measured and b) modelled responsivity maps of our device, evaluated with τ DC = 3.5 fs, τ IR = 40 fs, σ n = 2 × 10 12 cm −2 , τ eph = 50 ps, and α e = 2.5 mm −1 .c) Electron temperature increase ∆T el and absorbed optical power per area Q profiles in the graphene channel per guided optical power at gate voltages of {−2.35 V, 0.35 V}, chosen to maximize the modelled photoresponse, and other parameters as above.
FIG. 4: a) Comparison of the frequency response of our photodetector with that of the laser current modulation itself.The consistency between the two indicates that the photodetector frequency response exceeds 1 MHz.Inset: Simulated GHz-range photodetector frequency response, with and without considering the impact of the electron-phonon cooling time τ eph .b) Measured noise spectral density versus resistance and corresponding Johnson noise spectral density of Device B, without illumination, for the 49 pairs of gate voltages {V g1 , V g2 } where each V gn is varied from −6 V to 6 V in steps of 2 V. Measurement was performed at T = 293 K.

TABLE I :
Device parameters and approximate values or gapped bilayer graphene light sources.The

TABLE II :
Comparison of our detector with inferred room-temperature performance metrics for two HgCdTe photodiodes optimized for two different wavelengths (from obtained as described in Supplementary Section C. All calculations are carried out in Mathematica..H., D.E. and J.G. conceived the experiments.J.G. designed, fabricated, and measured the devices, with the exception of chalcogenide glass deposition, performed by H.L. and S.D.-J.under the supervision of J.H., and graphene growth, performed by M.H. and A.-Y.L. under the supervision of J.K. and T.P. K.R. provided the chalcogenide glass sources for thermal deposition.J.G. and D.E. wrote the manuscript.All work was supervised by D.E. J