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Leonardo Viti, Alisson R. Cadore, Xinxin Yang, Andrei Vorobiev, Jakob E. Muench, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jan Stake, Andrea C. Ferrari, Miriam S. Vitiello

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[Thermoelectric graphene photodetectors with sub-nanosecond response times at terahertz frequencies](https://mdr.nims.go.jp/datasets/3af30fcc-c746-4434-888b-eb863486fd72)

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NanophotonicsResearch articleLeonardo Viti, Alisson R. Cadore, Xinxin Yang, Andrei Vorobiev, Jakob E. Muench,Kenji Watanabe, Takashi Taniguchi, Jan Stake, Andrea C. Ferrari and Miriam S. Vitiello*Thermoelectric graphene photodetectors withsub-nanosecond response times at terahertzfrequencieshttps://doi.org/10.1515/nanoph-2020-0255Received April 26, 2020; accepted June 4, 2020; published onlineJuly 10, 2020Abstract: Ultrafast and sensitive (noise equivalent po-wer <1 nW Hz−1/2) light-detection in the terahertz (THz) fre-quency range (0.1–10 THz) and at room-temperature is keyfor applications such as time-resolved THz spectroscopy ofgases, complex molecules and cold samples, imaging,metrology, ultra-high-speed data communications,coherent control of quantum systems, quantum optics andfor capturing snapshots of ultrafast dynamics, in materialsand devices, at the nanoscale. Here, we report room-temperature THz nano-receivers exploiting antenna-coupled graphene field effect transistors integrated withlithographically-patterned high-bandwidth (∼100 GHz)chips, operating with a combination of high speed (hun-dreds ps response time) and high sensitivity (noise equiv-alent power ≤120 pW Hz−1/2) at 3.4 THz. Remarkably, this isachievedwith various antenna and transistor architectures(single-gate, dual-gate), whose operation frequency can beextended over the whole 0.1–10 THz range, thus paving theway for the design of ultrafast graphene arrays in the farinfrared, opening concrete perspective for targeting theaforementioned applications.Keywords: 2D materials; nano-detectors; terahertz frequencies.1 IntroductionHot-carrier assisted photodetection is an efficient andinherently broadband detection mechanism in single layergraphene (SLG) [1–4]. When a photon is absorbed by theelectronic population (either via interband or intrabandtransitions), the photoexcited carriers can relax energythrough electron–electron scattering or emission of opticalphonons [5, 6], which usually occurs on a time scale of 10–100s fs [5, 6]. However, the electron-to-lattice relaxation viaacoustic phonons is slower (1–2 ps) [6], leading to a quasi-equilibrium state where the thermal energy is distributedamongst electrons [5, 6] and not sharedwith the lattice. Thisproduces an intriguing scenario, where the energy isabsorbed by a system with an extremely low thermalcapacitance (ce ∼ 2000 kBμm−2, kB is the Boltzmann con-stant) [7–10], thus leading to the ultrafast (∼fs−ps) onsetof thermal gradients in SLG-based nanostructures. Atterahertz (THz) frequencies this effect is more relevant,since the emission of optical phonons is energeticallyforbidden [11], thus hindering this additional pathway forenergy relaxation. SLG is therefore a promising materialfor engineering high-speed (∼ps response time) opto-electronic THz devices that could benefit from the abovemechanism [12].*Corresponding author:MiriamS. Vitiello, NEST, IstitutoNanoscienze– CNR and Scuola Normale Superiore, Piazza San Silvestro 12, Pisa,56127, Italy, E-mail: miriam.vitiello@sns.it. https://orcid.org/0000-0002-4914-0421Leonardo Viti: NEST, Istituto Nanoscienze – CNR and Scuola NormaleSuperiore, Piazza San Silvestro 12, Pisa, 56127, Italy,E-mail: leonardo.viti@nano.cnr.it. https://orcid.org/0000-0002-4844-2081Alisson R. Cadore, Jakob E. Muench and Andrea C. Ferrari: CambridgeGraphene Centre, University of Cambridge, 9, JJ Thomson Avenue,Cambridge, CB3 0FA, UK, E-mail: arc87@eng.cam.ac.uk (A.R. Cadore),jem227@eng.cam.ac.uk (J.E. Muench), acf26@hermes.cam.ac.uk(A.C. Ferrari). https://orcid.org/0000-0003-1081-0915 (A.R. Cadore).https://orcid.org/0000-0002-3124-3385 (J.E. Muench). https://orcid.org/0000-0003-0907-9993 (A.C. Ferrari)Xinxin Yang, Andrei Vorobiev and Jan Stake: Department ofMicrotechnology and Nanoscience, Chalmers University ofTechnology, Gothenburg, SE-41296, Sweden,E-mail: xinxiny@chalmers.se (X. Yang),andrei.vorobiev@chalmers.se (A. Vorobiev), jan.stake@chalmers.se(J. Stake). https://orcid.org/0000-0003-4464-6922 (X. Yang).https://orcid.org/0000-0003-2882-3191 (A. Vorobiev). https://orcid.org/0000-0002-8204-7894 (J. Stake)Kenji Watanabe and Takashi Taniguchi: National Institute forMaterials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan,E-mail: WATANABE.Kenji.AML@nims.go.jp (K. Watanabe),TANIGUCHI.Takashi@nims.go.jp (T. Taniguchi). https://orcid.org/0000-0003-3701-8119 (K. Watanabe). https://orcid.org/0000-0002-1467-3105 (T. Taniguchi)Nanophotonics 2021; 10(1): 89–98Open Access. © 2020 Leonardo Viti et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0International License.https://doi.org/10.1515/nanoph-2020-0255mailto:miriam.vitiello@sns.ithttps://orcid.org/0000-0002-4914-0421https://orcid.org/0000-0002-4914-0421mailto:leonardo.viti@nano.cnr.ithttps://orcid.org/0000-0002-4844-2081https://orcid.org/0000-0002-4844-2081mailto:arc87@eng.cam.ac.ukmailto:jem227@eng.cam.ac.ukmailto:acf26@hermes.cam.ac.ukhttps://orcid.org/0000-0003-1081-0915https://orcid.org/0000-0003-0907-9993https://orcid.org/0000-0003-0907-9993mailto:xinxiny@chalmers.semailto:andrei.vorobiev@chalmers.semailto:jan.stake@chalmers.sehttps://orcid.org/0000-0003-4464-6922https://orcid.org/0000-0002-8204-7894https://orcid.org/0000-0002-8204-7894mailto:WATANABE.Kenji.AML@nims.go.jpmailto:TANIGUCHI.Takashi@nims.go.jphttps://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-1467-3105The detection of THz light is important for applicationsin imaging [13], tomography [14], security [15, 16], bio-medicine [17], and quantum optics [18]. An ideal THzphotodetector (PD) should have a low noise equivalentpower (NEP < nW Hz−1/2), a large dynamic range (ideally >3decades), have high detection speed (<ns), be broadband(0.1–10 THz), and operate at room temperature (RT).However, current RT THz PDs fail in targeting this combi-nation of sensitivity, speed, and spectral range [19].Graphene-based THz detectors relying on different phys-ical mechanisms [4] have been widely demonstrated in thelast few years [2, 12, 20–28] and include nanodevicesexploiting the photovoltaic (PV) [22], the bolometric [23],the photothermoelectric (PTE) [2, 12, 27] and the plasmawave (PW) or Dyakonov–Shur effects, the latter in either itsnon-resonant [20, 25] or resonant (at low temperatures) [26]configurations. At RT, PTE PDs have proven to be the mostsensitive and fast [2, 12, 27], due to the occurrence ofphotoinduced temperature gradients which alter the elec-tronic thermal distribution on a fast (∼100 fs) timescale [5,6] and to the absence of an applied dc current through theSLG channel, which usually increases the noise level (darkcurrent) in alternative physical configurations [23]. PTEdetectors are demonstrated to reach response times∼100 ps at 1 THz [12]. The best combination of performanceat frequency above 3 THz has been achieved in a thermo-electric RT graphene device [2], showing simultaneouslyNEP < 100 pWHz−1/2, response time τ∼40 ns (setup-limited),and a three orders of magnitude dynamic range. In thisdevice, an ad hoc dual-gated, H-shaped antenna, having astrongly sub-wavelength gap (100 nm), defines a p–njunction, to which the performance improvement isascribed. More recently, NEP ≤ 160 pW Hz−1/2 with responsetimes of 3.3 ns have been also reported in thermoelectricreceivers exploiting broadband bow-tie antennas [27].Here, we undertake the task of boosting the detectionperformances with respect to that benchmark. We exploittwo different architectures: a single-gated hBN/graphene/hBN field effect transistor (GFET) (Figure 1C) and a split-gate hBN/graphene/hBN p–n junction (Figure 1D). Bydeeply investigating the photodetection mechanism, weshow that, independently from the geometry, both the ar-chitectures operate mainly via the PTE effect. We thenevaluate and compare the detection performances, provingthat τ can be lowered at the hundreds ps level, withoutspoiling the detector sensitivity. This is achieved as fol-lows. First, we minimize the absorption area in the GFETchannel. This allows maximizing the temperature increasewithin the electronic thermal distribution, since a smallerabsorption area entails a smaller amount of carriers to beheated by the incoming electromagnetic field, and, in turn,a larger temperature increase [2]. Secondly, as a furtherrefinement, we use a novel electrodes design, which fea-tures on-chip transmission lineswith bandwidth >100GHz,and readout electronics having bandwidth >1 GHz.By embedding the hBN/SLG/hBN layered materialsheterostructures (LMH) [29, 30] in FET coupled to on-chipplanar THz antennas (Figure 1A and B), we demonstrateultrafast (τ < 1 ns) detection of >3 THz light at RT, with arecord combination of speed, NEP and sensitivity, inde-pendent on the specific architecture. This is possible owingto the fast (∼100 fs) onset of thermal gradients along theSLG channel and the subsequent generation of a PTEphotovoltage [1], not dependent on the selected architec-ture. Thus, encapsulated SLG-based devices coupled toantenna structures can be used for the characterization ofhigh (>10 MHz) repetition rate THz sources and high-speed(<1 ns) and low noise (NEP < 1 nW Hz−1/2) THz imaging.2 Results and discussionWe engineer two photodetector configurations as follows.Sample A is an hBN encapsulated GFET integrated with aplanar bow tie antenna, asymmetrically connected to thesource (s) and top-gate (gT) electrodes, Figure 1C. Sample Bis an hBN encapsulated GFET where two split-gates (gTL,left gate and gTR, right gate, Figure 1D), connected to thetwo branches of a linear dipole antenna, defining a p–njunction at its center [2]. Such antenna geometries arewidely used in THz optoelectronics [2, 4, 24, 31] and bothenable broadband operation [2, 32].The hBN encapsulated GFET devices are fabricated asfollows. hBNcrystals are grownby the temperature-gradientmethod under high pressures and temperatures [33]. Bulkgraphite is sourced from Graphenium. hBN and SLG areindividually exfoliated on SiO2/Si by micromechanicalcleavage [34]. Initially, optical contrast [35] is utilized toidentify SLG [29, 30]. The transfer technique employs astamp of polydimethylsiloxane (PDMS) and a film of poly-carbonate (PC) mounted on a transparent glass slide forpicking up the layered materials and transfer them to thefinal and undoped SiO2/Si substrate. The presence andquality of SLG is thenconfirmedbyRaman spectroscopy [36](see Section 4). The thickness of hBN is determined byatomic force microscope (AFM) and Raman spectroscopy[37, 38]. Combining the results from optical microscopy,Raman spectroscopy and AFM, blister-free areas with fullwidth at half maximum (FWHM) of the 2D peakFWHM(2D) < 18 cm−1 are selected for device fabrication.Following their assembly, we process the hetero-structures into antenna-coupled FETs. The GFET channel is90 L. Viti et al.: Graphene photodetectors with sub-nanosecond responsefirst shaped by electron beam lithography (EBL), followedby dry etching of hBN and SLG [39] in SF6. The SLG channelgeometry is schematically represented in Figure 1: thechannel is LC = 3 μm long and WC = 0.8 μm wide. Thecontact regions have lateral extensions. By simplegeometrical considerations, it can be demonstrated thatthese extensions increase the perimeter of the stack,i.e., the length of the edge-contacts, thus reducing thecontact resistance by 30%, with respect to more standardrectangular channel geometry. Edge Au/Cr electrodes aredefined by standard EBL [39, 40], followed bymetallization(40:5 nm) and lift-off.We use, for both samples A and B, bottom hBN flakesof almost identical thickness (h), in order to make thecomparison of the device performances consistent andreproducible. It is indeedworthmentioning that, due to thedecrease of the electron–hole charge fluctuations at thesubstrate [41], changes of the bottom hBN layer thicknesscan significantly affect the FET mobility [29, 42]. In thepresent case, the flakes thicknesses, retrieved by AFM are:bottom hBN h = 23 nm, top hBN h = 8 nm, for sample A, andbottom hBN h = 25 nm, top hBN h = 17 nm for sample B. Thelow thickness of the heterostructures (<45 nm) and of theedge-contacts (∼45 nm) allows us to use a thinner oxide(70 nm) as encapsulating layer before gT deposition(Figure 1C and D), thus increasing the effective gate-to-channel capacitance per unit area:Cg∼ 100 nF cm−2 for bothsamples. This parameter is important for THz FET detectors[25], since the responsivity (Rv), a figure of merit defined asthe ratio between photovoltage (Δu) and impinging opticalpower, is typically proportional to the sensitivity of the FETconductance to changes in the gate voltage (Vg) [25].In order to reduce parasitic capacitances, usuallydetrimental for high-speed (>1 GHz) detection, and simul-taneously minimize parasitic losses [43], we design andfabricate a microwave transmission line connected to the sand drain (d) edge-electrodes based on a coplanar strip-line (CPS) geometry [24], Figure 1B. We use this radio fre-quency (RF) on-chip component because of its simplicity.In contrast to the standard strip-line geometry [44], it doesnot require a ground plane, and, unlike the coplanarwaveguide architecture [44], it consists of only two parallelmetallic strips on the substrate top surface. In our devices,the strips are separated by a 2 μmgap,where one conductor(ground electrode, s) provides the electrical ground for theother (signal electrode, d). This architecture shows analmost perfect transmission below 30 GHz, with S21 = 0 dB,S11 < −40 dB, whereas at 3.4 THz the transmission isreduced, but not canceled, with S21 = −3.5 dB andS11 = −25 ÷ −35 dB (details about simulations are given inSupplementary material). The transmission of the THzsignal between the antenna-coupled GFET and the con-tacts can be detrimental for the overall detector perfor-mance. This is mainly due to the fact that the antennamodes lose energy (resulting in a decreased resonancequality factor), if the antenna is not isolated from the sur-rounding circuit. Therefore, our design also includes a low-pass hammer-head filter along the CPS (Figure 1B) [45],with a cutoff frequency fcut-off ∼ 300 GHz, which enhancesthe isolation between antenna and readout circuit. ItFigure 1: Detector layout. (A) Photodetectorschematics: THz radiation is coupled to theGFET by a planar antenna and thephotoresponse is recorded as a dcphotovoltage (Δu) between the s andd electrodes. (B) On-chip RF components.The s and d electrodes are shaped in CPSgeometry. Inset (left): the shapeof the activeLMH channel (green area) guarantees alower contact resistance with respect to arectangular geometry. The s and d contactshave a thickness of 45 nm inproximity of theGFET channel (yellow areas) and a thicknessof 140 nm far from the GFET channel. Inset(right): planar low-pass filter, with cut-offfrequency 300 GHz. (C) Sample A. Top:schematics of the LMH and electrodeslayout, highlighting the different layerthicknesses. False color SEM image of thetop-gated GFET (center) and optical micro-scope overview (bottom), where the bow-tie antenna position is marked with a dashed box. (D) Sample B. Top: schematics of the LMH andcontacts design. False color SEM image of the GFET showing the split-top-gate geometry with the 90 nm gap (center) and optical microscopeoverview (bottom), where the position of the planar dipole antenna is marked with a dashed box. All scale bars are in units of micron.L. Viti et al.: Graphene photodetectors with sub-nanosecond response 91consists of a capacitive shunt with a lumped capacitanceCf = 500 aF. The dimensions of the structure are optimizedby time-domain simulations sim (CST Microwave Studio)(see Supplementary material).The presence of the filter leaves the S-parametersalmost unaltered for frequencies <30 GHz: S21 = 0 dB,S11 < −30 dB. On the other hand, it modifies the trans-mission line properties at 3.4 THz: S11 = −4 dB, S21 ∼ −24 dB.To further increase the signal extraction from the activeelement, the CPS has an adiabatically matched transition[46] between bonding pads and GFET electrodes, whichhinders the formation of spurious reflections and conse-quent losses.After this common protocol, samples A and B areprocessed following different architectures. For sample A,Figure 1C, the lobe of a THz planar bow-tie antenna (110 nmthick) is connected to the s electrode. Then, a thin top-gateoxide bi-layer is placed on the LMH, also covering the s andd contacts: 20 nm HfO2 deposited via atomic layer depo-sition (ALD) and 50 nm Al2O3 deposited via Ar sputtering.The photodetector is then finalized by the fabrication of gT,in the shape of the armof a bow-tie antenna, thus forming acomplete bow-tie together with the s electrode. The an-tenna radius is 21 μm and the gap between antenna arms is250 nm (Figure 1C). For sample B, Figure 1D, the same oxidebi-layer is deposited before the antenna fabrication. Theantenna is here shaped as a linear dipole, with 24 μm armsseparated by a gap of 90 nm (Figure 1D, further images arereported in the Supplementarymaterial). The two branchesof the antenna also serve as top split-gates for the GFET.The gate voltages (VgL, left gate bias and VgR, right gatebias) can be individually controlled in order to create, atthe center of the active channel, a p–n junction whose sizeis approximately corresponding to the gap between the twosplit-gates [2, 47]. The gate geometry is therefore nominallythe only difference between the two samples.The devices are then characterized electrically andoptically at RT. The two-probeGFET transfer curve,measuredfor sample A in Figure 2A, shows a channel resistance(R) peak at Vg = −4.6 V (charge neutrality point, CNP). Theextracted field-effect mobility (μFE) is 17,000 cm2 V−1 s−1 forholes and 19,000 cm2 V−1 s−1 for electrons, with a residualcarrier density n0 ∼ 9 × 1011 cm−2. This is fitted using the for-mula [48]R=R0+ (LC/WC)·(1/n2deμFE),whereR0 is the contactresistance and n2d is the gate-dependent charge density,given by [48] n2d = [n02 + (Cg/e (Vg − VCNP))2]1/2.We then test the RT sensitivity using a focused 3.4 THzbeam with an average power Pt = 100 μW (see Section 4).The intensity distribution on the focal plane (Figure 2D,sample A), displayed through the xy map of Δu, unveilsthe Airy pattern [49] of the focused beam, showing fourconcentric rings (maxima) with the central Airy disk. Thisdemonstrates the good signal-to-noise ratio (∼1000 atPt = 100 μW) of the proposed device. From the two-dimensional Gaussian fit of the intensity distribution inFigure 2D, we obtain standard deviations σx = 95 ± 1 μmand σy = 87 ± 1 μm along the x and y directions, respec-tively, from which we infer FWHM ∼ 303 ± 2 μmFigure 2: Electrical and opticalcharacteristics of single-gate GFET. (A) Elec-trical resistance R as a function of Vg at RT ina two-terminal configuration. (B) Rvmeasured at RT as a function of Vg (left ver-tical axis), compared with the normalizedexpected photothermoelectric and over-damped plasma wave photovoltages (rightvertical axis). (C) NEP calculated as a func-tion ofVg under the assumption of Johnson–Nyquist dominated noise spectral density[2]. A minimum NEP ∼ 350 pW Hz−1/2 is ob-tained for Vg = −7 V. (D) Logarithmic plot ofthe normalized photovoltage on the focalplane, for an average impinging THz powerof 100 μW. The four Airy maxima are indi-cated by blue arrows on the left of the cen-tral Airy disk. The red arrow indicates theportion of the focal plane where the beam isblocked by the output window of the cryo-stat inwhich theQCL ismounted. The FWHMof the beam is 303 μm. (E) Rv plotted as afunction of T measured at Vg = −5 V (bluedots) and Vg = −9 V (magenta dots).92 L. Viti et al.: Graphene photodetectors with sub-nanosecond response(see Supplementary material for further details). This isused to estimate the fraction of total power that im-pinges on the detector Pa = Pt · (Aλ/Aspot) = 2.7 μW, whereAλ = λ2/4 = 1.9 × 10−3 mm2 is the diffraction limited area (seeSupplementary material) and Aspot = π · (FWHM/2)2 = 72 ×10−3 mm2 is the beam spot area. Then, by measuring Δu(see Section 4) as a function of Vg and dividing the as-obtained values by Pa, we retrieve the plot of Rv as afunction of Vg (Figure 2B). The maximum Rv = 30 VW−1 isobtained for Vg = −7 V and the trend is compatible with adominant PTE response (see Supplementary material).This is corroborated by the following argument. AtVsd = 0 V, in a single-gated GFET, connected by identicalmetallic layers at the s and d contacts, both the PTE and thenon-resonant PW detection mechanisms can in principlebe activated [25, 27]. In the geometry of sample A, the PTEphotovoltage reads ΔuPTE = ΔTe · (Sg − Su) [25, 27, 31], whereΔTe is the THz-induced electronic temperature differencebetween the (hot) source side of the channel, correspond-ing to the gap at the center of the bow-tie antenna, and the(cold) drain side (Figure 1C), Su is the Seebeck coefficient ofthe ungated region between the s and g electrodes and Sg isthe Seebeck coefficient of the gated LMH channel. Byimposing Su = Sg for Vg = 0 V and assuming ΔTe weaklydependent on Vg [2, 25], we can analytically compute thegate voltage dependence of ΔuPTE ∝ Sg − Su (see Supple-mentary material for further details). The same argumentapplies to the overdamped PW photovoltage [20, 25],ΔuPW ∝ −σ−1(∂σ/∂Vg). The comparison between ΔuPTE(Vg),ΔuPW(Vg) and the experimental Rv(Vg) curves (Figure 2B)unveils that the PTE effect well matches with our experi-mental observation and better reproduces our data withrespect to the PWmodel, which predicts that themaximumresponse (in absolute value) occurs at Vg = −3.5 V and Rv isfinite and negative at Vg = 0 V, in stark contrast with ourmeasurements, where Rv ≈ 0 VW−1 at Vg = 0 V. Thisconclusion is further supported by the temperature (T )dependent analysis of the responsivity, which unambigu-ously shed light on the core detection dynamics.To this purpose we mount the detector in a He fluxcryostat and we vary the heat sink T in the 6–260 K range.The measured responsivity (Figure 2E) shows a non-monotonic behavior as a function of T, with a maximumaround a crossover temperature T * = 60 K, in agreementwithwhat observed in other spectral ranges [50]. The originof such a behavior can be retrieved by the analysis of theelectron cooling dynamics in SLG. ΔuPTE is proportional toΔTe, which, in turn, is proportional to the cooling lengthξ = (k/γce)1/2 [1, 2, 50] (the proportionality holds as long asξ < LC), where k is the thermal conductivity and γ is thecooling rate. Since both k and ce scale linearly with T, thefunctional dependency of the cooling length ξ (and ΔuPTE),with respect to T, is the same as γ−1/2. For T < T *, γ(T ) isdominated by acoustic phonon emission and scales as∼T −1, whereas at higher T, the disorder-assisted scattering(supercollision) gives rise to a competing cooling channelwhich follows the power law γ ∼ T [50]. The two effects giverise to a crossover temperature (T *) forwhich γ isminimumand, consequently, ΔuPTE is maximum. We then comparethe temperature dependence of Rv at two distinctive gatevoltages, Vg = −5 V (close to CNP, low carrier density,n2d ∼ 1012 cm−2) and at Vg = −9 V (away from CNP, holesdensity up to n2d ∼ 4 × 1012 cm−2). The non-monotonicbehavior is more evident at lower n2d, in qualitativeagreementwith previous findings on PTE detection [25, 50].In a non-degenerate electron system, ΔuPTE(T ) iscompletely determined by ΔTe, being the Seebeck coeffi-cient weakly dependent from T [25]; conversely, in thedegenerate case, S is proportional to T [51] and compen-sates the decrease of ΔTe at higher T, resulting in an almostT-independent ΔuPTE. For sample A, under the assumptionof a noise spectral density (NSD, i.e., noise power per unitbandwidth) dominated by thermal fluctuations [31] (seeSupplementarymaterial), we estimateNEP= 1/Rv · (4kBRT)1/2.The NEP curve as a function of Vg (Figure 2C) shows a min-imum NEP ∼ 350 pW Hz−1/2 at Vg = −7 V.We use a similar approach for the optical and electricalcharacterization of sample B. Figure 3 plots the deviceperformance as a function of bias applied at the split-gates.By independently varying the two gate voltages, we controlthe Fermi level (EF) and, consequently, n2d on each side ofthe dual-gated SLG junction [2, 47]. The color plot of Rwith respect to VgR (right gate, horizontal axis) and VgL(left gate, vertical axis) in Figure 3A allows us to extracta hole and electron μFE ∼ 19,000 cm2 V−1 s−1 and15,000 cm2 V−1 s−1, respectively, with a residual carrierdensity n0 ∼ 1 × 1012 cm−2.The independent control of the EF on each side of thejunction allows individual control of the two Seebeck co-efficients SL and SR [2, 47], which can be used to maximizethe photoresponse. THz detection in a graphene p–njunction is expected to be dominated by the PTE effect [2].ΔuPTE, measured between the drain and source electrodes,can be written as [52]:ΔuPTE � ∫sd∂Te∂x⋅ S(x)dx � ΔTe ⋅ (SL − SR) (1)where ΔTe is the electronic temperature increase as aconsequence of the absorption of THz radiation at thejunction.Figure 3B is a colormap ofRv obtained by continuouslychanging VgR and VgL in the same ranges of Figure 3A. TheL. Viti et al.: Graphene photodetectors with sub-nanosecond response 93maxima of Rv (∼50 V W−1) are obtained when the two localgates have opposite polarity with respect to the CNP, i.e., inp–n or n–p junction configurations. The resulting six-foldpattern in the measured photovoltage is ascribed to thenon-monotonic gate voltage dependence of SL and SR oneach side of the junction, and is a unique fingerprint of adominant hot-carrier assisted PTE effect in SLG [1, 2, 53].Therefore, for the p–n junction, the room-temperature Rvcharacterization alone is sufficient to unambiguously un-veil the dominant PTE THz detection.From R and Rv, we can estimate the NEP of sample B,assuming a thermal-noise limited operation. The contourplot of NEP as a function of the two gate voltages(Figure 3C) shows a minimum NEP ∼120 pW Hz−1/2 atVgL = −8 V and VgR = −4 V. Sample B is therefore ∼3 timesmore sensitive than sample A. This can be attributed to thelarger field enhancement provided by the dual-gateconfiguration, in particular to the narrow (90 nm) gap be-tween the antenna arms, in agreement with Ref. [2].To extract the response time and the bandwidthBW = (2πτ)−1, we shine light from a pulsed THz quantumcascade laser (QCL, pulse width ∼150 ns and repetition rate333Hz) and record the signalwith a fast oscilloscope (5GS/s)after a pre-amplification stage (low noise voltage preampli-fier, model Femto-DUPVA, bandwidth 1.2 GHz, inputimpedance 50 Ω).Figure 4A and B shows the time traces of samples Aand B, recorded at zero gate bias with an oscilloscopehaving a temporal resolution 200 ps. We extract the rise-time τON and fall-time τOFF by using the fitting functionsVout = c0 + VON · [1−exp(−(t−c1)/τON)] and Vout = c2 + VOFF ·exp(−(t − c3)/τOFF), where c0, c1, c2, c3 are fitting parame-ters, and VON and VOFF are the voltage jumps in the wave-forms corresponding to the rising-edge and falling-edge.We find similar results for both devices, with rise-timesslightly shorter with respect to fall-times. Sample A showsτON = 1.3 ± 0.4 ns and τOFF = 1.5 ± 0.6 ns at Vg = 0 V, sampleB shows τON = 890 ± 150 ps and τOFF = 1.4 ns ± 0.25 ns atVgL = VgR = 0 V. These response times are, to the best of ourknowledge, the lowest in GFETdeviceswithNEP <1 nWHz−1/2.In terms of BW, considering the lower values of τ as limitresponse time,weobtainBW= 125± 35MHz for sampleAandBW = 180 ± 30 MHz for sample B, i.e., 50 times better than inRef. [2]. The small discrepancy between the latter values canbe ascribed tofluctuations in theQCL output power, possiblycaused by time jitter (±100 ps [54]) in the electrical circuitemployed to drive the laser.To further validate this assessment, we measure thedetector rise-time under different configuration of gatevoltages, i.e., at different charge densities and SLG re-sistances. The response time of a PD is ultimately limited bythe RC time constant of the circuit [2]. Therefore, if the PD isthe key element limiting the detection speed, a change in Rshould directly and proportionally reflect into a change inτ, via τ = R · C. We thus select and investigate three gatevoltage configurations, for both devices. The results areshown in the insets of Figure 4A and B.For sample A, we obtain τON = 1.3 ± 0.4 ns at Vg = 0 V(R = 4.2 kΩ), τON = 1.5 ± 0.6 ns at Vg = −5 V (R = 6.4 kΩ) andτON = 1.4 ± 0.3 ns atVg = −8 V (R = 5.7 kΩ), showing the lackof a direct proportionality relation between R and τON. Thesame conclusion can be drawn for sample B at VgR = 0 V,where τON = 890 ± 150 ns for VgL = 0 V (R = 3.7 kΩ),Figure 3: Electrical and optical characteristics of double-gatedgraphene p–n junction. (A) Analysis of electrical transport of GFET:two-terminal RT resistance as a function of split-gate biases. Thedashed lines indicate the CNP positions for VgL and VgR. (B) Colormap of Rv as a function of VgL and VgR. Rv undergoes many signchanges, corresponding to transitions between the different con-figurations of the p–n junction, attainable by polarizing the gates.(C) Two-dimensional plot of the NEP (logarithmic scale) as a functionof VgL and VgR. A minimum NEP of 120 pW Hz−1/2 is obtained forVgL = −8 V and VgR = −4 V.94 L. Viti et al.: Graphene photodetectors with sub-nanosecond responseτON = 1.2 ± 0.2 ns for VgL = −5 V (R = 4.7 kΩ), andτON = 1.6 ± 0.3 ns for VgL = −8 V (R = 4.0 kΩ). This dem-onstrates that τ is not affected by the SLG resistance in thetested range. This illustrates that the PD itself is not limitingthe measured maximum speed, which is instead affectedby the switching time of the QCL. A higher intrinsic speedbeyond the set-up limited value is in good agreement withreports of high-speed, PTE-based SLG detectors for inte-grated photonics, with reported 3 dB BW in the tens of GHz[47]. In this work, high-speed performance is enabled bythe on-chip architecture, featuring RF electronic compo-nents, which mitigates the presence of parasitic capaci-tances and the undesirable crosstalk between sensingelement and outer on-chip components.Our results show that, up to a bandwidth of 150 MHz,the two proposed architectures are substantially equivalent.Both configurations lead to τ ∼ ns, even though the twogeometries are different: in sample A the THz field isdistributed along the un-gated portion of the channel(250 nm), whereas in sample B the two symmetric splitgates, defining a narrow gap (90 nm), provide a morelocalized enhancement of the THz field at the center of theSLG channel. The speed limit is, in both cases, lower thanthat reported inRef. [2], the switching speedbeing limitedbythe onset speed and jitter noise of the employedQCL system.This equivalence is not surprising. As revealed by the lowtemperature characterization of sample A (Figure 2E), botharchitectures mainly operate through the same detectionmechanism: the PTE effect. This is known to be the domi-nantmechanism for devices operating throughp–n junctionrectification [1, 2], however it has also been observed inantenna-coupled single-gated architectures [20, 25, 26],where the antenna provided asymmetric THz excitation,essential for the activationof thePTEmechanism.Moreover,our data show that the speed of the two devices does noteven depend on the existence of a p–n junction, but it onlyrequires that the gates create an imbalance in the Seebeckcoefficient along the graphene channel.3 ConclusionsIn summary, the performance achieved at RT on both devicesdemonstrates that PTE THz detectors, coupled with high-bandwidth on-chip (∼100 GHz) and external electronics,detect pulses with sub-ns temporal extension, openingFigure 4: Electrical bandwidth and responsetime. (A) Photovoltage time-trace underillumination with a 150 ns THz pulse havinga peak power of 10 mW, recorded withsample A at Vg = 0 V. The time constantsτON = 1.3 ± 0.4 ns and τOFF = 1.5 ± 0.6 ns areobtained by fitting the data. Inset: variationof τON as a function of Vg. The rise-time doesnot depend on the device resistance.(B) Time trace recorded with sample B atVgL = VgR = 0 V, giving τON = 890 ± 150 psand τOFF = 1400 ± 250 ps. Inset: variation ofτON as a function of Vg. The rise-time doesnot depend on the device resistance.Figure 5: Sample characterization andselection of the device area. (A) Ramanspectra before and after LMH assemblymeasured at 514 nm. The bottom hBN (b-hBN) is shown in blue, the top one (t-hBN)in green, the SLG in purple, and theassembled LMH in black, while the SiO2/Sisubstrate in red. The hBN E2g, G, and 2Dpeaks are highlighted by the dashed graylines. (B) False color optical image of theLMH. SLG is indicated by a black dashedline. Scale bar is 10 μm. (C) Spatial map ofFWHM(2D), indicating the area where theGFET is designed.L. Viti et al.: Graphene photodetectors with sub-nanosecond response 95unique perspectives for ultrafast applications in a plethora ofresearch field as ultrafast nano-spectroscopy, quantum sci-ence, coherent control of quantum nanosystems and highspeed communications. Further improvements on thedetection performances can be achieved via the on-chipintegration of coplanar waveguides and pre-amplificationstages. It is worth mentioning that, measuring the intrinsicspeed limit of the PTE mechanism in SLG devices, which isexpected to be τ ∼ 10 ps [2], would require completelyavoiding the limitations set by the readout electronics. Thiscould be obtained, for example, by exploiting interferometrictechniques, suchaspulseautocorrelationmeasurements [55].Our results open a route for characterization of highrepetition rate THz sources, transient effects in nonlinearoptoelectronic devices (e.g., saturable absorbers), time-resolved intracavity-mode dynamics of THz QCL frequencycombs and ultimately for high-speed and low noise THzimaging, never pioneered so far.4 Methods4.1 Sample characterizationRaman measurements are performed using a Renishaw InVia spec-trometer equipped with a 100× objective, 2400mm−1 grating at 514 nm.The power on the sample is <1 mW to avoid any heating and damage.AFM is performed in tapping mode to characterize the topography andthickness of the LMHs using a Bruker Dimension Icon system.Figure 5Aplots the spectra of a typical LMH,with 8 and 23nm thicknesstop and bottom hBN flakes, while Figure 5B is a false color opticalimageof theLMH,highlighting the SLGedges. Figure 5A shows that theE2g peak for both bottom and top hBN are ∼1366 cm−1, with FWHM(E2g)∼9.3 and9.7 cm−1, consistentwith bulk hBN [37]. Figure 5Aplots theSLGG and 2D peaks before and after stacking. Before encapsulation, the 2Dand G peaks have FWHM(2D) ∼ 27 cm−1, Pos(2D) ∼ 2682 cm−1,Pos(G) ∼ 1589 cm−1, FWHM(G) ∼ 8 cm−1, and the intensity and areas ratioof 2D andG peaks are I(2D)/I(G) ∼ 1.4, A(2D)/A(G) ∼ 4.6, as expected forSLG with EF ≥ 250 meV [56, 57]. No D peak is observed, indicatingnegligible defects [58]. After LMH assembling, the combined hBN E2gpeak is at Pos(E2g) ∼ 1366 cm−1, with FWHM(E2g) ∼ 9.5 cm−1. For theencapsulated SLG we have Pos(2D) ∼ 2697 cm−1, FWHM(2D) ∼ 17 cm−1,Pos(G) ∼ 1584 cm−1, FWHM(G) ∼ 14 cm−1, I(2D)/I(G) ∼ 13, and A(2D)/A(G) ∼ 12, indicating EF≪ 100meV [56, 57]. The changes in FWHM(2D)after encapsulation indicates a reduction in the nanometer-scale strainvariations within the sample [29, 59]. Figure 5C shows an FHWM(2D)map across a bubble-free LMH sample, exhibiting homogeneous(spread < 1 cm−1) and narrow (∼17 cm−1) FWHM(2D), which is selected forthe GFET fabrication.4.2 Optical measurementsIn order to test the PD sensitivity, we use a 3.4 THz QCL, operating inpulse mode with a repetition rate of 40 kHz and a pulse width of 1 μsand refrigerated at 30 K by means of a Stirling cryocooler (estimatedlattice temperature of the active region 170 K [60]). The divergentbeam (divergence angle ∼ 30°) is collimated and then focused usingtwo picarin (tsupurica) lenses with focal lengths 50 mm and 30 mm,respectively. The average output power can be continuously variedup to ∼1 mW at the PD position. The measurements are performed bykeeping the s electrode grounded and by extracting the photovoltagesignal Δu at the d contact. The latter signal is then pre-amplified witha voltage pre-amplifier (FEMTO, input impedance 1 MΩ, gain 40 dB,BW 200 MHz) and recorded with a lock-in technique, referenced by a1333 kHz square wave. Δu is estimated as 2.2 VLI/η [31], where VLI isthe lock-in signal and η is the voltage preamplifier gain coefficient.The detectors are mounted on a xyz stage, allowing automatedspatial positioning.Acknowledgments:Weacknowledge funding from the ERCConsolidator Grant SPRINT (681379) and the EU Horizon2020 research and innovation programme Graphene Flag-ship under grant agreement No 785219 (GrapheneCore2),ERC grants Hetero2D, GSYNCOR, EPSRC grants EP/L016087/1, EP/K01711X/1, EP/K017144/1. M.S.V. acknowl-edges partial support from the second half of the BalzanPrize 2016 in applied photonics delivered to FedericoCapasso.Author contribution: L.V and M.S.V. conceived the coreidea. A.R.C and A.C.F. prepared the hBN/graphene/hBNheterostrcutures and characterized the quality of thegraphene; K.W. and T.T. provided high quality hBN; X.Y.,A.V. and J. S. contributed to the design of the microstripline; L.V. fabricated the sample and performed electricaland optical measurements; L.V. and M.S.V analyzed thedata and wrote the manuscript. All authors discussed theresults and contributed to the writing of the manuscript.M.S.V. supervised the study.Research funding: This research was funded by ERCConsolidator Grant SPRINT (681379) and the EU Horizon2020 research programme Graphene Flagship (785219),ERC grants Hetero2D, GSYNCOR, EPSRC grants EP/L016087/1, EP/K01711X/1, EP/K017144/1.Data availability: The data that support the plots withinthis paper and other findings of this study are availablefrom the corresponding authors upon reasonable request.Conflict of interest statement: The authors declare nocompeting financial interests.References[1] N. M. Gabor, J. C. W. Song, Q. 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Lett., vol. 86, 2005, Art no.111115.Supplementary Material: The online version of this article offers sup-plementary material (https://doi.org/10.1515/nanoph-2020-0255).98 L. Viti et al.: Graphene photodetectors with sub-nanosecond responsehttp://www.Avtechpulse.Com/Catalog/Avr-1-2-3-4_rev17.Pdfhttp://www.Avtechpulse.Com/Catalog/Avr-1-2-3-4_rev17.Pdfhttps://doi.org/10.1515/nanoph-2020-0255 Thermoelectric graphene photodetectors with sub-nanosecond response times at terahertz frequencies 1 Introduction 2 Results and discussion 3 Conclusions 4 Methods 4.1 Sample characterization 4.2 Optical measurements Acknowledgments References