Optoelectronic mixing with high-frequency graphene transistors

Graphene is ideally suited for optoelectronics. It offers absorption at telecom wavelengths, high-frequency operation and CMOS-compatibility. We show how high speed optoelectronic mixing can be achieved with high frequency (~20 GHz bandwidth) graphene field effect transistors (GFETs). These devices mix an electrical signal injected into the GFET gate and a modulated optical signal onto a single layer graphene (SLG) channel. The photodetection mechanism and the resulting photocurrent sign depend on the SLG Fermi level (EF). At low EF (<130 meV), a positive photocurrent is generated, while at large EF (>130 meV), a negative photobolometric current appears. This allows our devices to operate up to at least 67 GHz. Our results pave the way for GFETs optoelectronic mixers for mm-wave applications, such as telecommunications and radio/light detection and ranging (RADAR/LIDARs.)

M ixers are a key component of modern communication modules 1 . In telecommunications and in radio detection and ranging (RADAR) systems 2 , the receiver analyzes the modulation of a carrier wave (or waveform) with frequencies in the microwave  or mm-wave  GHz) range, to extract information 3,4 . As signal processing is performed at near-zero frequencies (baseband 3,4 ), frequency downconversion is required 3,4 . Downconversion is performed by mixing the modulated high-frequency signal centered around the radio frequency (RF) carrier frequency, f RF , with a local oscillator signal at frequency f LO . This translates the modulation centered around f RF to f IF = f LO − f RF . The local oscillator frequency is typically set near f RF , so that f IF is close to zero 3,4 . Superheterodyne receivers are a common type of radio receivers using frequency downconversion to process the original signal 5 . For multi-antenna systems, it is preferable to use a single optical signal as a local oscillator and distribute it to each antenna 6 , decreasing the receiver complexity and noise. For this purpose, one option is to use photodetectors (PDs) to transfer the local oscillator signal from the optical to the electrical domain 6 . After that, an electrical mixer is used 5 . A second option is to employ optoelectronic mixers (OEMs) 7 , i.e., PDs capable of mixing optical local oscillator with an electrical signal 7 . OEMs are particularly convenient in RADAR and light detection and ranging (LIDAR) applications [7][8][9][10] . State-of-the-art OEMs at 1.55 μm are based on III-V semiconductors epitaxially grown on InP 11,12 . These are efficient, but expensive, and can only be heterogeneously integrated in an Si platform 11,12 . Low cost and complementary metal-oxide-semiconductor (CMOS) compatible OEMs require CMOS-compatible materials absorbing light at 1.55 μm 13 .
Low frequency (2MHz) optoelectronic mixing in single-layer graphene (SLG) was studied in ref. 28 using a transistor structure with an on-chip bias resistor. This reported upconversion of a 2MHz signal, and downconversion of a 0.45 MHz one, in two types of OEMs consisting of a SLG field-effect transistor (GFET) and a bias resistor. For the first, the oscillating electrical signal was applied to the GFET drain (the optical signal illuminated the GFET channel), whereas in the second the signal was applied to the gate, and the mixing was proportional to the on-chip resistance. A 30 GHz bandwidth (BW) OEM based on SLG was reported in ref. 29 , based on an SLG coplanar waveguide (GCPW) integrating a SLG channel grown by chemical vapor deposition (CVD). The RF signal was injected into the GCPW, whereas a 1.55 μm laser illuminated the channel. Optoelectronic mixing was based on the linear dependence of the photocurrent on both optical incident power (P opt ) and voltage drop (V bias ) along the channel. As the photocurrent is proportional to P opt V bias 30 , upconverted and downconverted signals were generated. This GCPW operated up to 30 GHz, with a conversion efficiency, (i.e., ratio of output power at f IF and input power at f RF ), of −85 dB for a 10 GHz modulated signal. The results in ref. 29 are far from state-of-the-art OEM performances achieved with III-V semiconductor-based uni-traveling carrier photodiodes: −22 dB conversion efficiency at 35 GHz 31 , and −40 dB at 100 GHz 12 . However, the CMOS integration of III-V semiconductors is challenging 13 . SLG is CMOS-compatible 16 but, to technologically bridge the gap with III-V-based OEMs, BW, and conversion efficiency need to be improved 29 . Furthermore, the OEM in ref. 29 was a two-contact device operating only in the photoconductive regime, at a fixed Fermi level (E F ).
Here, we present a 67 GHz GFET-OEM (three-contact device), exploiting the modulation of E F , that controls the photoconductivity. At low (equilibrium) E F (<130 meV) the laser power induces interband transitions 32 , thus the charge carrier density, n, and the channel conductance increase (positive photoconductivity). At high E F (>130 meV), the laser heating induces intraband transitions 32 . In this case, the hot carrier distribution reduces the effectiveness of the electronic screening 32 which, in turn, leads to a higher scattering rate (e.g., owing to Coulomb impurities 32 or strain disorder 33 ). The increased scattering decreases the carrier mobility 32 and the resulting photoconductivity is negative 32,[34][35][36] . In our OEMs, an intensitymodulated (up to 67 GHz) laser beam illuminates part of the SLG channel, generating an AC photocurrent, proportional to the product of optical power and photoresponsivity. An RF signal applied to the gate of 20 GHz-BW GFETs modulates the photoresponsivity, mixing optical and electrical signals. The performance far exceeds that in ref. 29 . The conversion efficiency (−67 dB) for a 67 GHz modulated optical signal (f opt ) is 21 dB higher than ref. 29 at f opt = 10 GHz, thanks to the use of an RF GFET with a strong coupling between the input RF signal and SLG (a 0.8 V signal induces E F~0 .2 eV). Our results pave the way for the use of graphene in CMOS-compatible OEMs.

Results
Graphene growth and characterization. SLG is grown via CVD on 35 μm-thick Cu foil, following ref. 37 . The temperature, T, is raised to 1000 ∘ C in an H 2 atmosphere (~200 mTorr), and kept constant for 30 mins. In all, 5 sccm CH 4 are then added to the 20 sccm H 2 flow to start growth, for additional 30 mins at 300 mTorr. The sample is then cooled at~1 mTorr to RT. We use Raman spectroscopy at 514nm to characterize the material. Figure 1a shows the Raman spectrum on Cu (red line), after Cu photoluminescence removal 38 . The D peak is absent, indicating negligible defects 39,40 . The 2D peak at~2705 cm −1 is a single Lorentzian with full width at half maximum (FWHM)~31 cm −1 , a fingerprint of SLG 41 . The position of the G peak, Pos(G), is 1593 cm −1 , with FWHM(G)~12 cm −1 . The 2D to G intensity and area ratios are I(2D)/I(G)~2.4, A(2D)/A(G)~6.3.
To prevent ohmic losses at microwave frequencies, a high resistivity Si wafer (> 8000Ωcm) covered with 285nm SiO 2 is used. SLG is wet transferred 42,43 on it as follows. A poly(methyl methacrylate) (PMMA) layer is spin-coated on the surface of SLG/Cu and then placed in a solution of ammonium persulfate (APS) and deionized (DI) water for Cu etching 42 . The PMMA membrane with attached SLG is then immersed into a beaker filled with DI water for cleaning APS residuals. After, the PMMA/ SLG stack is transferred onto the target substrate and the PMMA layer is removed. SLG is then ion etched to define the channel.
We then characterize via Raman spectroscopy the transferred SLG (blue curve, Fig. 1a). Both measurements on Cu and Si+SiO 2 are performed under the same conditions of laser power, objective, wavelength, and accumulation time. The Raman signal of SLG on Cu is more noisy than on Si+SiO 2 due to interference enhancement by the 300 nm SiO 2 layer on Si 44,45 . For SLG on 0.09 corresponds to a defect density~4 × 10 10 cm −240, 48 , consistent with what is commonly observed in CVD-SLG 49 . It is possible to improve the process to get a smaller D peak 50 .
Operational principle and device fabrication. Figure 1b is a sketch of our SLG OEM and illustrates its operational principle. It consists of a GFET with a symmetric dual-bottom gate finger. This layout is commonly used for RF applications 51 and GFETs 52 , and is well suited for GCPWs 53 . Dual-gate finger FETs have a more compact design and a reduced small-signal gate resistance compared with single-gate configurations, for a given equivalent channel width, resulting in a higher voltage gain 54 . A laser beam is modulated at f opt and focused on the GFET channel. As a result, a photocurrent that contains an AC component at f opt flows through the SLG channel. If a RF signal f RF is applied to the gate, the output current presents a term at f RF . When both optical and electric signals are applied, the device acts as an OEM: the output contains the product of the two signals, and two AC components at f opt + f RF and f opt − f RF appear.
A schematic cross-section of the bottom gate GFET is in Fig. 1c. The fabrication starts by patterning the dual-bottom gate finger by e-beam lithography (EBPG 5000 Plus). The gates are made of a 40 nm-thick Al layer deposited by evaporation. A 4 nm Al 2 O 3 layer is formed on top of the gates by exposing the substrate to pure oxygen for 30 mins 55 with an Oxford Plasmalab80Plus at~100 mTorr. This thin oxide acts as gate dielectric. The source and drain contacts are made in a two-steps process. First, Cr/Au (5/50 nm) pre-contacts are deposited on SLG. Then, ohmic contacts are obtained by placing 30 nm Au on the Cr/Au-SLG junction. Finally, a CPW is built with a Ni/Au film (50/300 nm). Figure 1d is a scanning electron microscopy (SEM) image of the bottom gates covered by SLG. The inset shows a GFET integrated into the CPW. The red square indicates the area occupied by the GFET. The bottom gate GFET design is suitable for OEMs since (1) the SLG channel is on the gate and can be directly illuminated; (2) the use of a thin (4 nm) Al 2 O 3 dielectric and short gate (<0.4 μm or less) ensures high-frequency operation 5,56,57 .
The device has a cutoff frequency (not de-embedded) f t2 5 GHz, and a maximum oscillating frequency f max~1 4GHz, as deduced from the S-parameters measured with a Vector Network Analyzer (VNA, Agilent, E8361A). To calibrate the VNA, we use the Line-Reflect-Reflect-Match approach 58 . This allows us to eliminate errors in S-measurements introduced by the environment, such as cables and probe tips used to contact the device under test, and the VNA non-idealities.
Electrical and optoelectronic measurements. The setup in Fig. 2a is used to measure photocurrent and optoelectronic mixing. The output of a 1.55 μm distributed feedback laser is modulated by a Mach Zehnder modulator in the double sideband suppression carrier mode 59 , to obtain a modulated beam at f opt . This is then amplified with an Erbium-doped fiber amplifier. The maximum f opt that our setup can probe is 67 GHz. The diameter of the focused laser spot is~2 μm (inset of Fig. 2a). The maximum power impinging on the sample is~60 mW, which corresponds to~20 mW/μm 2 . The gate and drain are connected to a VNA with two high-frequency (67 GHz) air coplanar probes. Bias tees are used to add a DC bias to channel and gate electrodes, and to measure the DC currents and voltages with a Source-Measure-Unit (Keithley 2636B). After illuminating the device, we verify the stability of the signal before measuring the RF photocurrent, whereas monitoring the DC value of the channel resistance, to a Representative Raman spectra at 514 nm of SLG as-grown on Cu (red), and after transfer on SiO 2 /Si (blue). b Principle of operation of our OEM. The mixing of the electrical signal at f RF with the photodetected signal at f opt generates two signals at the output (drain): f opt + f RF and f opt − f RF . c Schematic GFET cross-section. The two Al gates (pale blue) are covered by a thin Al 2 O 3 oxide (pink). SLG (black) is placed on the two gates. The drain and source contacts are Au (yellow) and Cr (green). d SEM image of GFET with dualbottom gate finger covered by SLG. The metal in contact with SLG is Au. The inset shows the GFET (red rectangle) integrated into a coplanar waveguide (CPW) (scale bar: 100 μm). ensure that no damage nor significant modification is induced by the laser power or DC bias. We do not observe any degradation or time-dependent drift in the DC or RF currents over a period of at least 3 h, the typical measurement time.
We now present the results for a representative OEM with SLG channel width W = 24 μm, length L = 400 nm, and gate length L G = 200 nm. The blue curve in Fig. 2b is the source-drain current, I DS , as a function of gate voltage, V GS , at V DS = 200 mV, which shows the typical ambipolar conduction behavior of a GFET (i.e, electrical conductivity due to electrons/holes (e/h), depending on the position of E F with respect to the charge neutrality point, CNP) 60 . The minimum conductance is reached at V GS = 1.1 V, which corresponds to the CNP voltage (V CNP ). When V GS increases (decreases) with respect to V CNP , the e (h) density increases, leading to a reduction of channel resistivity, so an increase of the current flowing in the channel 60 . μ is calculated as μ = Lg m /(W ⋅ C G V DS ) 61 . The transconductance g m = dI DS /dV GS 13 is obtained from the transfer characteristic I DS (V GS ) at V DS = 10 mV. The gate capacitance is C ox is~5 fF/μm, obtained from S parameters measurements on 60 devices of the same kind 55 . We get μ~2500 cm 2 V −1 s −1 , consistent with that of non-encapsulated CVD-SLG 37 .
We now consider the photoresponse. The OEM is biased at V DS = 200 mV and illuminated with a laser modulated at f opt = 67 GHz. The electrical power P RF measured by the VNA is used to derive the photocurrent I ph . From Joule's law 13 , with Z VNA = 50 Ω the VNA input impedance. The use of bias tees allows us to simultaneously measure the DC component, i.e., the dark current (blue curve in Fig. 2b) and the AC component, i.e., the photocurrent (orange curve in Fig. 2b) as a function of V GS , for a 25 mW incident optical power. The photocurrent, I ph , sign depends on V GS . I ph is positive and has a local maximum close to the CNP. At low (equilibrium) E F (<130 meV), the laser power induces interband heating 32 , thus an increase of n (positive photoconductivity). Therefore, the photocurrent has the same sign as the DC current in the channel, owing to the DC bias. At high E F > 130 meV, the sign of the photocurrent is opposite to the DC current (negative photoconductivity). In this case, laser heating induces intraband transitions, which lead to a reduction of electronic screening of the long-range Coulomb interaction between SLG's carriers and charged impurities in the substrate 22,32 . The E F at which the transition between positive and negative photocurrent takes place is~0.1-0.2 eV 32,34 . The value depends on the charge transport scattering rate in SLG, i.e., the mean time interval between two collisions in the diffusive transport picture 62 , and on the charge neutrality region width 63 (see Methods). In our experiment, we observe this transition at 130 meV. The external photoresponsivity, R ext , is defined as 15,64 R ext = jI ph j P c w eff , with P c w eff = 31%P cw the fraction of the optical power coupled to the SLG channel. We get R ext~0 .22 mA/W. For V GS = 0V, the device reaches its maximum I ph~− 4.2 × 10 −4 mA and the photocurrent generated by a 67 GHz laser modulation is measured as a function of DC bias and optical power. Figures 3a, b plot the photocurrent as a function of DC bias at P opt = 40 mW and as a function of the optical power for V DS = 330 mV. The response is linear in both cases, as expected for a photoconductor 34 . The frequency response of the photodetected power is then measured as a function of f opt , Fig. 4a. We get a flat response over the whole band that can be investigated by our VNA, showing that the intrinsic photodetection BW is >67 GHz. The photocurrent can originate from the SLG channel located above the gate, or from the SLG-metal contacts that are not gated (see Fig. 1c). As the photoresponse strongly depends on V GS , as shown in Fig. 2b, we ascribe it to the illuminated part of the SLG channel located above the gate. If both contacts are illuminated, the photocurrents are opposite and cancel out. If the photocurrent originates mainly from one SLG-metal contact, the photocurrent at V DS = 0V should be significant. R ext~0 .8 mA/W was reported in ref. 65 for a detector exploiting the metal-SLG contacts, at V DS = 0V. As seen in Fig. 3, at V DS = 0V the photocurrent is negligible. We also rule out possible asymmetric heating effects on the channel, owing to beam location, by performing a photocurrent measurement as a function of laser spot position. We observe a very weak response at V DS = 0V, regardless of laser spot position, as shown in Methods, Fig. 10. Thus, the role of contacts can be neglected.
In order to operate the device as an OEM (instead of a PD), an RF signal f RF is added to the DC gate, Fig. 1b. f opt is maintained at 67 GHz, whereas f RF is swept between 2 and 65 GHz. A VNA is used to record P IF and the transistor power at the intermediate An important parameter for OEMs is the downconversion efficiency 5 : P IF /P RF , with P RF the power at the source and P IF that measured at the VNA. For our device, the maximum P IF /P RF is −67 dB at V GS = 0.6 V. For this V GS , Fig. 4b plots P IF /P RF as a function of f IF . The BW and P IF /P RF of our OEMs far exceed (+37 GHz in BW and 2 orders of magnitude in P IF /P RF ) those of ref. 29 , where the input RF signal modulates the SLG bias (resistive coupling), thus the photocurrent amplitude. In our OEMs, the input RF signal is coupled to SLG via the gate oxide (capacitive coupling), which results in a modulation of E F and, consequently, in a change of the photocurrent mechanism and sign. These high BW and P IF /P RF come from the strong coupling (i.e., strong electric field for a small applied voltage, 0.25 V/nm) between the input RF signal (applied to the Al back-gate) and the SLG channel, thanks to the use of a~4 nm oxide. As a consequence, an efficient field effect is achieved 60 . A signal with an amplitude~0.8 V induces a E F modulation~0.2 eV. Thus, a small signal (0.8 V) is needed to obtain optoelectronic mixing. The high-frequency operation of the GFET (~20 GHz, 3 dB BW, Fig. 4b) comes from the short channel length (400 nm) and the small gate capacitance C ox~6 0 fF 66 . Figure 5a is a color map of the 67 GHz photocurrent as a function of V GS , V DS . We then add to the DC gate bias an electrical signal at 10 GHz. The resulting downconverted photocurrent at f IF = 57 GHz is plotted as a function of V DS , V GS in Fig. 5b. By differentiating the map in Fig. 5a with respect to V GS , we obtain Fig. 5c, which resembles Fig. 5b. This is best seen in Fig. 6, which plots both values as a function of V GS for V DS = 200 mV. The curves of the downconverted photocurrent and of the derivative of the photocurrent can be superposed. This result is valid regardless of frequency, see Methods Fig. 9.

Discussion
This behavior can be explained by a small-signal analysis.
Let us consider the modulated optical power impinging on the PD, P opt = P cw + P mod sin(2πf opt t), with P mod the amplitude of the varying part of the optical power. The photocurrent is proportional to P opt through the factor R ext . This depends on V GS , as for Fig. 2b, and is almost independent on f opt , Fig. 4a. Therefore, the photocurrent can be written as: By applying to the gate a DC bias V GS and a small signal δ V GS sinð2πf RF tÞ, we get: where We include dependence on injected electrical frequency through a frequency-dependent proportionality constant β(f RF ). The total The first is the DC photocurrent. The second describes the DC photocurrent modulated by the electrical signal. The third represents the photocurrent modulated at f opt , Fig. 2b. The fourth describes the optoelectronic mixing and can be rewritten as: Equation (5) has two components at f opt + f RF and f IF = f opt − f RF . It shows that the mixed signal depends exclusively on Δ R ext , i.e., on the derivative of R ext with respect to V GS , not on R ext itself, in accordance with Fig. 5. Δ R ext is maximum for V GS~0 .6 V, Fig. 6, i.e., in a region where the photocurrent changes sign, indicated in Fig. 2b with a green dot. The sharper is the transition between the two competing phenomena (photoconductive and bolometric) generating the photocurrent, the higher is Δ R ext and the optoelectronicmixing efficiency.
Since R ext is proportional to the photoconductivity σ ph (V GS ) 30 , the optimization of the mixing efficiency (Δ R ext ) requires dσ ph dV GS to be maximized. σ ph (V GS ) depends on several factors, such as the residual charge carrier density, n 0 63 , and the dominating scattering mechanisms 63,67 . So, it depends on SLG quality and its dielectric environment. We compute σ ph (V GS ) from the Drude model for free carrier conductivity in SLG 63 : where T e is the electron temperature, Γ is the scattering rate, D is the Drude weight 63,67 , and μ c is the chemical potential. We calculate μ c (see Methods for details), and then the effect of e-h puddles by replacing μ c with μ c ! ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi μ 4 c þ Δμ puddles 4 4 q 63 , where Δ μ puddles is the energy width of the puddles region 63 . The photoconductivity due to illumination of the SLG channel at a given μ c is then given by 63 : where T light is the hot-electron temperature of the illuminated SLG and T dark is the electron temperature in dark, see Methods for details. Figure 7 plots the measured photoconductivity (blue) and the computed one (red) using Eq. (7). We calculate Δμ puddles from n 0 , extracted from the experimental DC measurement of the conductivity (see Methods). We calculate Γ from the measured μ (see Methods). We get Γ~50 meV, which corresponds to a scattering   ARTICLE time τ~80 fs at E F~2 00 meV, at the maximum V GS , in agreement with experiments. We then calculate dσ ph dV GS to find the maximum downconversion efficiency. This can be increased by~27 dB (power unit) for SLG with μ fe~3 0,000 cm 2 V −1 s −1 (τ = 1/Γ~0.6 ps) and n 0~1 0 11 cm −2 , see Methods. Thus, the control of the transition between the two different photocurrent mechanisms could lead to a maximization of Δ R ext and, in turn, a maximization of downconversion efficiency.
The 3 dB BW is~19.7 GHz when operated as OEM, Fig. 4. This behavior is modeled in Eq. (3) by including the factor β(f RF ). To understand the optoelectronic-mixing dependence on f RF and, thus, on f IF (f opt being fixed), we consider a typical figure of merit of high-frequency transistors: the transducer power gain 5 , defined as: G T = P load P avs , where P load is the power delivered to the load and P avs is the source power. G T coincides with the modulus of the S 21 parameter when source and load are matched 5 . This is the case in our measurements, where the power is delivered from the VNA 50Ω-source and measured on a 50Ω receiver. G T is close to the S 21 parameters. An external impedance matching could increase the downconversion efficiency by maximizing the power delivered by the GFET, other than increasing BW. We do not observe saturation in the photodetected signal at the highest optical power available in our setup (60 mW). Thus, illuminating a wider channel surface, while maintaining the same optical power density, should increase the downconversion efficiency. An enhancement of SLG-light interaction can also improve the downconversion efficiency. In all,~70% absorption could be achieved by integrating SLG on a waveguide 68 . This could enhance the downconversion efficiency by~30 dB, compared with the normal incidence case (~2.3% absorption 23 ).
In summary, we reported high-frequency graphene transistors operating as OEMs for frequencies up to at least 67 GHz. The photodetection BW exceeds 67 GHz. The BW of the devices operated as OEMs is 19.7 GHz. The conversion efficiency is at least two orders of magnitude higher than previous graphene OEMs 29 . It can be further increased using high-quality samples with μ~10,000-100,000 cm 2 V −1 s −1 and increasing light-matter interaction. This can increase the downconversion efficiency >50 dB, overcoming state-of the-art performances of OEMs based on any other technology 31 . Our frequency operation is already comparable with state-of-the-art performance of OEMs based on any other technology 31 . Thus, our work paves the way for the use of graphene-based transistors as OEMs in applications exploiting mm-waves, such as telecommunications and RADAR/LIDAR.

Methods
Photocurrent modeling. Equations 1-5 show that the optoelectronic-mixing efficiency is proportional to Δ R ext , which can be expressed as: Since R ext is proportional to σ ph (V GS ) 30 , the optimization of the mixing efficiency requires dσ ph dV GS to be maximized. The mixing efficiency can be related via Δ R ext to SLG's μ and n 63,67 . The Drude model for free carrier conductivity in SLG gives 63 : In the case of Dirac Fermions the Drude weight is 63 : with k B the Boltzmann constant. In the GHz range, ω~10 9 −10 10 rad/s. This value is negligible compared to our Γ, which lies in the range 10 12 −10 13 rad/s 32 . The photoconductivity owing to the illumination of the SLG channel is then 63 : This depends on T, as experimentally shown in ref. 34 . Increasing T decreases the photodetection efficiency 34 . This is consistent with the screening reduction of the scattering mechanism while increasing T e 32 , since a smaller T change between dark and illumination conditions takes place. μ c is T-dependent. It decreases while increasing T to keep the number of conduction band carriers constant 69 . So, it is lower in illumination conditions with respect to dark. To account for this, we compute μ c by numerical inversion of the following T-dependent formula 60,63 : In Eq. (12), C ox is the geometrical gate capacitance per unit area, v 0 is the Fermi velocity and Li 2 is the dilogarithm function. This is valid in low and high doping and also includes the effects of quantum capacitance. Γ is calculated from μ fe2 500 cm 2 /(Vs) using 16 : We get Γ~80 meV, i.e. τ~50 fs for μ c~0 .2 eV. Charge puddles are taken into account by replacing μ c with 63 : Δμ puddles is calculated as 60 : Here, n 0~5 ⋅ 10 11 cm −2 extracted from the measured DC minimum of conductivity σ min 60 : From the DC measurements, we get C ox~4 fF/μm 2 . The experimental curve in Fig. 7 uses T e as a fitting parameter, getting T e~3 20 K in the laser spot region.
Optoelectronic mixing efficiency. We now evaluate the effects of μ and n 0 on mixing efficiency. Since our SLG is substrate-supported and not encapsulated in hBN, long-range scattering limits conductivity 32 , more specifically Coulomb scattering 32,70,71 . In this regime, the typical τ is in the range of hundreds of fs 32 . Highquality SLG can have low n 0 (<10 12 cm −2 ) and high μ > 100,000 cm 2 V −1 s −1 ) 50 .
In high-quality SLG encapsulated with hBN, as in ref. 50 , transport is dominated by random-strain fluctuations 33,72 . For such SLG, a change in μ < 20% was measured as a function of n 50 . In order to estimate the performance in such SLG, we assume no dependence of μ o n. Within this assumption, τ ∝ μ for μ >> K B T 60 , so Eq. (13) is still valid. For μ~100,000 cm 2 V −1 s −1 , τ can be up to 2ps for E F~0 .2 eV 16 . We thus calculate σ ph for μ up to 100,000 cm 2 V −1 s −1 and n 0~5 ⋅ 10 11 cm −2 , Fig. 8a. By comparing the green and the blue curves, which show the photoconductivity for μ~100,000 and 2.500 cm 2 V −1 s −1 , we predict an increase~40 times at both low (i.e. V GS = 0) and high electrostatic doping (i.e., for V GS = 1 V). We then differentiate the curves in Fig. 8a. Figure 8b shows an increase in dσ ph /dV GS , (i.e. an increase of Δ R ext ) of a factor~40. Another parameter that can be improved by employing high-quality SLG is n 0 . Fig. 8c plots the photoconductivity for n 0 between 10 11 cm −2 (corresponding to highquality SLG 50 ) and 5 × 10 11 cm −2 (our case), while keeping μ fe = 2500 cm 2 V −1 s −1 . In this case, the photoconductivity increases by a factor~1.4 near the CNP, as well as at high doping (V GS = 1 V), with dσ ph /dV GS almost doubled, Fig. 8d. This means that the voltage operating point of the device can be decreased.
Our prediction is based on the model presented in ref. 32 , which indicates the screening reduction of the Coulomb impurity scattering mechanism while increasing T 32 . For Coulomb scattering in samples with μ fe up to 1000 cm 2 V −1 s −171 , this is supported by several experimental and theoretical works 32,63,67 . For samples with ultrahigh μ fe up to 100,000 cm 2 V −1 s −150 ), the dominant mechanism limiting μ fe is strain disorder 33 , with two contributions: (i) random scalar potential and (ii) random gauge potential 33 . The first is sensitive to T increase owing to screening reduction 33 , similar to what happens for Coulomb scattering 32 , while the second is not 33 . Thus, for ultra-highquality μ fe samples, the "screening reduction" picture may not be accurate. Therefore, we use an intermediate value μ fe = 30,000 cm 2 V −1 s −1 , between 10,000 cm 2 V −1 s −1 (i.e., Coulomb scattering regime 71 ) and 100,000 cm 2 V −1 s −1 (i.e., random-strain fluctuations-induced scattering regime 33 ) to infer the performance boost of OEMs based on SLG FET owing to μ fe increase. In this case, for n 0 = 10 11 cm −2 , we predict an increase of dσ ph /dV GS by a factor~23 dB. Thus, the downcoversion efficiency in power units can increase~27dB, overcoming the OEMs state-of-the-art performance 12,31 .    9 plots the downconverted photocurrent at three frequencies as a function of V GS . This shows Fig. 6 is valid regardless of operating frequency.
Dependence of the laser spot position on photoresponse. Figure 10 shows the photoresponse as a function of laser spot position over the device, along the dashed black line. The photocurrent is measured with the VNA used for the RF measurements in Fig. 2a. The optical beam intensity is modulated at 10 GHz and the optical power impinging the sample is~10 mW. The beam scan step is~300 nm, smaller than the spot size of the laser~2 μm, as defined by the FWHM of the intensity of the Gaussian laser profile. The red dots represent the measured photocurrent at V DS = 0.2 V, whereas the blue ones are for V DS = 0 V. The maximum photocurrent is registered when V DS = 0.2 V and the laser spot is over the GFET channel. We observe very low photocurrent, comparable with the instrument noise floor (~−90 dBm electrical power detected over the internal 50Ω impedance of the instrument) at V DS = 0. At V DS = 0.2 V, we do not observe a change of the photocurrent sign (due to, e.g., asymmetrical heating effect 73 ) when the laser spot is scanned from the source to the drain contact. Thus, the role of contacts in the photocurrent generation can be neglected.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.