Enhanced Coupling Efficiency in Geometric Terahertz Rectennas Based on Scalable CVD Graphene

Enhanced Coupling Efficiency in Geometric Terahertz Rectennas Based on Scalable CVD Graphene | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhanced Coupling Efficiency in Geometric Terahertz Rectennas Based on Scalable CVD Graphene Andreas Hemmetter, Jakob Holstein, Michael Möller, Jens Bolten, and 11 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9108655/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Ubiquitous electromagnetic radiation from wireless communication networks is an untapped energy source for low-power devices. Passive rectennas (a combination of a rectifier and an antenna) can harvest this energy to power devices and systems, such as autonomous sensors. Rectennas based on conventional rectifiers, however, lack the frequency response and zero-bias performance required to extend passive energy harvesting into the terahertz (THz) domain, which is crucial for Internet of Things (IoT) applications in the 6G era. In contrast, rectennas based on geometric rectifiers are ultrafast detectors that can operate without an external bias, making them ideally suited for zero-bias THz detection and energy harvesting. Geometric rectifiers require largely scatter-free, quasi-ballistic charge transport, which is typically achieved only in high-purity materials, which – as in the case of mechanically exfoliated graphene – may not be suitable for wafer-scale fabrication. In this work, we used commercially available graphene grown by chemical vapor deposition (CVD) to fabricate geometric rectennas and demonstrate operation up to 0.68 THz at zero bias. We employed a parallel arrangement of multiple rectifiers to increase the coupling efficiency between the rectifiers and the antennas, and thus the overall rectenna responsivity. Our results are a critical step towards large-scale fabrication of efficient geometric rectennas and enabling THz energy harvesting for low-power IoT devices. CVD graphene rectenna geometric rectifier terahertz detector 2D materials energy harvesting Figures Figure 1 Figure 2 Figure 3 INTRODUCTION Ubiquitous radio frequency (RF) communication networks, such as Wi-Fi, Bluetooth, cellular networks, and GPS, support numerous indispensable applications, including internet access, cellular voice communications, broadcasting, navigation, and remote control. As a result, urban environments exhibit high ambient RF power density, which can be used as an energy source for low-power devices 1 , a process known as RF energy harvesting. This can be achieved using antenna-coupled rectifiers ( rectennas) , which collect and utilize RF radiation. Here, the antenna captures ambient RF radiation, and the rectifier converts the induced oscillating voltage into a direct current (DC) output 2 . Rectenna-based energy harvesting could enable numerous applications in distributed networks of autonomous sensors 3 that collect environmental, biomedical, or location data for use in climate science, medical diagnostics, or logistics. In fact, rectennas operating up to Wi-Fi/Bluetooth frequencies (2.4 GHz) have achieved conversion efficiencies of up to 50% 4–6 . The growing number of wireless devices and their higher bandwidth increase both the power density and the frequency of ambient RF radiation, as exemplified by the development of 5G and 6G mobile networks 7 , with frequency allocations in the submillimeter and terahertz (THz) ranges 1 , 8 . However, conventional rectifiers (e.g., Schottky or metal-insulator-metal diodes) are limited in operating frequency and require voltage biasing, complicating rectenna-based energy harvesting in the THz range 2 , 9 , 10 . Efficient zero-bias rectennas 11 – 13 could, in contrast, enable wider adoption of THz-enabled applications 14 – 16 . Geometric rectifiers 17 can fill this gap. The geometric asymmetry in the conducting channel induces current asymmetry at the output. While this requires quasi-scatter-free (ballistic) charge carrier transport in the channel 18 , 19 , the absence of potential barriers or doping gradients means that no bias voltage is required for rectification, enabling zero-bias rectification 17 , 20 , 21 . However, typical geometric rectifier designs face two major obstacles to commercialization. First, among other options 17 , 22 – 25 , exfoliated graphene flakes 21 , 26 have been used for geometric rectifiers due to their high charge carrier mobility 27 and large mean free path 28 . However, this approach is not suitable for wafer-scale fabrication. Second, coupling geometric rectifiers to antennas results in a large impedance mismatch between the antenna and the rectifier, on the order of several orders of magnitude. This mismatch severely limits their overall efficiency because most of the captured THz radiation is reflected back to the antenna. Here, we address both major obstacles of geometric rectifiers. We fabricated geometric rectennas from commercially available graphene grown by chemical vapor deposition (CVD) 29 and coupled each antenna to multiple geometric rectifiers 30 . This configuration is uniquely possible with geometric rectifiers because of their inherent zero-threshold behavior. Connecting the rectifiers in parallel lowered the total rectifier input resistance and increased the coupling efficiency between rectifier and antenna. This increased the broadband THz responsivity in free-space measurements up to 0.68 THz, mainly limited by the available power of the THz source, a frequency not previously achieved with CVD graphene-based rectennas. Our approach enhances the scalability and efficiency of geometric THz rectennas for energy-harvesting applications, thereby enabling autonomous sensors, e.g., for Internet of Things (IoT) applications. DEVICE DESIGN We fabricated the geometric graphene rectennas on an oxidized 2 inch silicon (Si) wafer, as shown in Fig. 1 a. The center of the wafer contains multiple rectennas, with the rectifiers connected to bowtie antennas with a 60° flare angle and a total length of 150 µm (see Fig. 1 b). Additionally, some rectifiers are connected to large contact pads for DC characterization. There are two different four-terminal rectifier types: a funnel-type rectifier (“single funnel”) and a parallel connection of three rectifiers at the input (“triple funnel”). This triple-funnel arrangement reduces the overall input resistance of the rectifier combination and thus increases the coupling efficiency between the rectifier and the antenna. Colored scanning electron microscopy (SEM) images of both rectifier types are shown in Figs. 1 c and 1 d. The DC output can be probed at the upper (U) and lower (L) metallic contacts, located farther from the rectifier, to minimize influence on the antenna. The source (S) and drain (D) terminals on the left and right correspond to the rectifier inputs 19 , 20 . The input arms enter the central stem at an angle to inject charge carriers from S and D inputs preferentially toward the L terminal rather than the U output terminal. The graphene layer beneath the antennas and output metal contacts is patterned with densely packed triangular holes with a side length of 560 nm to form metal-graphene edge contacts (see the inset in Fig. 1 b). This pattern increases the total length of edge contacts and thus lowers the contact resistance between graphene and metal 31 . The graphene also extends beyond the metal area to ensure adequate adhesion between graphene and substrate during the fabrication process. Methods Methods Fabrication : Our geometric graphene rectennas were fabricated via the process outlined in Fig. 1 e. First, alignment markers were defined by electron-beam lithography (EBL, Raith EBPG 5200 system operated at 100 kV) on a 2-inch (50 mm) diameter, high-resistivity (> 10 kΩ·cm) Si wafer with 300 nm thermally grown SiO 2 . The alignment markers were then etched through the SiO 2 and into the underlying Si substrate with a fluorine-based inductively coupled plasma reactive ion etching (ICP-RIE) process (Oxford Plasmalab 100 ICP RIE). The resist residue, a major cause of graphene delamination, was removed by thorough cleaning the substrate before the graphene transfer in organic solvents and piranha solution (H 2 SO 4 :H 2 O 2 ), as verified by atomic force microscopy (AFM, see Supporting Information, S1). We transferred CVD-grown graphene grown obtained from General Graphene (Knoxville, USA) from a 150 x 150 mm² copper foil growth substrate to the sample surface using a wet transfer. 29 , 32 – 34 The transferred graphene layer (approximately 10 x 10 mm 2 ) was placed in the center of the 2-inch wafer, as shown in the inset in Fig. 1 e. The protective resist residue was removed from the graphene by dissolving it in acetone and by annealing at 300°C for 3 h under an argon atmosphere at 50 mTorr, thereby increasing adhesion to the substrate. We then defined the graphene channel via EBL using hydrogen silsesquioxane (HSQ) resist, as outlined by Passi et al . 35 The pattern was transferred to the graphene layer by RIE (Oxford Plasmalab 100 ICP RIE) with low-power oxygen-based plasma for 4 min. The developed resist remained on the graphene channel at this point to prevent delamination and organic contamination during the following lithography step. A final EBL step using a two-layer (poly)methyl methacrylate (MMA/PMMA) resist defined the liftoff mask for the metallic contacts and antennas. Prior to metal deposition, the remaining HSQ resist within the masked areas was removed using a diluted buffered oxide etchant (BOE; NH 4 F:HF in H 2 O). Thus, graphene was exposed and formed an ohmic contact with the 5/35 nm Ti/Au metal deposited by electron-beam evaporation (FHR Star 200 EVA) onto the graphene layer. The process was completed by lifting off the excess metal together with the resist mask in acetone. In addition to the geometric rectennas on high-resistivity Si/SiO 2 substrates, we fabricated two more samples using the same process. The first sample was fabricated on a 20 x 20 mm 2 lightly doped substrate ( n -Si with 90 nm thermally grown SiO 2 , resistivity 10–40 Ω·cm). This substrate allowed transfer-length and rectification measurements with a global back-gate to control the carrier density and type 36 . The second sample (a high-resistivity 2-inch Si wafer with 90 nm thermally grown SiO 2 ) contained rectennas with shorter antennas, each 92 µm long, to judge the influence of the antenna response on the rectified voltage. Electrical Characterization DC measurements on the four-terminal geometric rectifiers were performed in a Lakeshore probe station under vacuum at both room temperature (293 K) and at 20 K. A current \(\:{I}_{\text{S}\text{D}}\) was forced between the S and D input terminals, and the voltage difference between the L and U output terminals \(\:{(V}_{\text{L}\text{U}}={V}_{\text{L}}-{V}_{\text{U}})\) was measured. At each backgate voltage step (from − 20 V to 20 V in steps of 5 V), \(\:{I}_{\text{S}\text{D}}\) was swept from − 500 µA to 500 µA. THz measurements were performed in a free-space setup. An HP8341A synthesizer provided a signal between 13.8 and 18.8 GHz, which was then transformed into the range of 0.49–0.68 THz by a ×36 multiplier source (RPG-ZTX750). The synthesizer output was modulated with a 331 Hz square wave, which was further supplied to an AMETEK DSP 7265 lock-in amplifier as a reference. The available THz power was measured by a calibrated pyroelectric detector (THz 10 HS by SLT Sensor- und Lasertechnik GmbH, calibrated by Physikalisch-Technische Bundesanstalt, Braunschweig, Germany), positioned at the source’s waveguide flange. The output power spectrum (see the Supporting Information, S2) has an average beam power of 50 µW. A Teflon lens (50 mm focal length) and a 3-inch parabolic mirror were then used to prefocus the beam and direct it 90° upward to a hyperhemispherical Si lens (diameter 12 mm, height 6.8 mm) in contact with a 525 µm thick high-resistivity carrier wafer for system alignment with an x‒y stage. The lens optimized radiation coupling to an aplanatic condition and further focused the beam to a small spot directly at the device under test. The wafer height was adjusted to place the focal point exactly on the top surface, where the rectenna was located. The spot was estimated to have a diameter of 650 µm based on a ray optics simulation in ZEMAX, which we compared with the antenna’s effective area derived from its simulated directivity (see Supporting Information, S2). The attenuation in the beam path was estimated to be -1.5 dB for the intrinsic substrate and − 3.0 dB for the doped substrate. The voltage output from the rectenna was probed with DC needles and read out with a DSP 7265 lock-in amplifier. Notably, neither a source–drain DC bias nor a gate voltage was applied during measurements, thereby achieving a true zero-bias detection condition, which is particularly important in energy-harvesting applications. Fabrication : Our geometric graphene rectennas were fabricated via the process outlined in Fig. 1 e. First, alignment markers were defined by electron-beam lithography (EBL, Raith EBPG 5200 system operated at 100 kV) on a 2-inch (50 mm) diameter, high-resistivity (> 10 kΩ·cm) Si wafer with 300 nm thermally grown SiO 2 . The alignment markers were then etched through the SiO 2 and into the underlying Si substrate with a fluorine-based inductively coupled plasma reactive ion etching (ICP-RIE) process (Oxford Plasmalab 100 ICP RIE). The resist residue, a major cause of graphene delamination, was removed by thorough cleaning the substrate before the graphene transfer in organic solvents and piranha solution (H 2 SO 4 :H 2 O 2 ), as verified by atomic force microscopy (AFM, see Supporting Information, S1). We transferred CVD-grown graphene grown obtained from General Graphene (Knoxville, USA) from a 150 x 150 mm² copper foil growth substrate to the sample surface using a wet transfer. 29 , 32 – 34 The transferred graphene layer (approximately 10 x 10 mm 2 ) was placed in the center of the 2-inch wafer, as shown in the inset in Fig. 1 e. The protective resist residue was removed from the graphene by dissolving it in acetone and by annealing at 300°C for 3 h under an argon atmosphere at 50 mTorr, thereby increasing adhesion to the substrate. We then defined the graphene channel via EBL using hydrogen silsesquioxane (HSQ) resist, as outlined by Passi et al . 35 The pattern was transferred to the graphene layer by RIE (Oxford Plasmalab 100 ICP RIE) with low-power oxygen-based plasma for 4 min. The developed resist remained on the graphene channel at this point to prevent delamination and organic contamination during the following lithography step. A final EBL step using a two-layer (poly)methyl methacrylate (MMA/PMMA) resist defined the liftoff mask for the metallic contacts and antennas. Prior to metal deposition, the remaining HSQ resist within the masked areas was removed using a diluted buffered oxide etchant (BOE; NH 4 F:HF in H 2 O). Thus, graphene was exposed and formed an ohmic contact with the 5/35 nm Ti/Au metal deposited by electron-beam evaporation (FHR Star 200 EVA) onto the graphene layer. The process was completed by lifting off the excess metal together with the resist mask in acetone. In addition to the geometric rectennas on high-resistivity Si/SiO 2 substrates, we fabricated two more samples using the same process. The first sample was fabricated on a 20 x 20 mm 2 lightly doped substrate ( n -Si with 90 nm thermally grown SiO 2 , resistivity 10–40 Ω·cm). This substrate allowed transfer-length and rectification measurements with a global back-gate to control the carrier density and type 36 . The second sample (a high-resistivity 2-inch Si wafer with 90 nm thermally grown SiO 2 ) contained rectennas with shorter antennas, each 92 µm long, to judge the influence of the antenna response on the rectified voltage. Electrical Characterization DC measurements on the four-terminal geometric rectifiers were performed in a Lakeshore probe station under vacuum at both room temperature (293 K) and at 20 K. A current \(\:{I}_{\text{S}\text{D}}\) was forced between the S and D input terminals, and the voltage difference between the L and U output terminals \(\:{(V}_{\text{L}\text{U}}={V}_{\text{L}}-{V}_{\text{U}})\) was measured. At each backgate voltage step (from − 20 V to 20 V in steps of 5 V), \(\:{I}_{\text{S}\text{D}}\) was swept from − 500 µA to 500 µA. THz measurements were performed in a free-space setup. An HP8341A synthesizer provided a signal between 13.8 and 18.8 GHz, which was then transformed into the range of 0.49–0.68 THz by a ×36 multiplier source (RPG-ZTX750). The synthesizer output was modulated with a 331 Hz square wave, which was further supplied to an AMETEK DSP 7265 lock-in amplifier as a reference. The available THz power was measured by a calibrated pyroelectric detector (THz 10 HS by SLT Sensor- und Lasertechnik GmbH, calibrated by Physikalisch-Technische Bundesanstalt, Braunschweig, Germany), positioned at the source’s waveguide flange. The output power spectrum (see the Supporting Information, S2) has an average beam power of 50 µW. A Teflon lens (50 mm focal length) and a 3-inch parabolic mirror were then used to prefocus the beam and direct it 90° upward to a hyperhemispherical Si lens (diameter 12 mm, height 6.8 mm) in contact with a 525 µm thick high-resistivity carrier wafer for system alignment with an x‒y stage. The lens optimized radiation coupling to an aplanatic condition and further focused the beam to a small spot directly at the device under test. The wafer height was adjusted to place the focal point exactly on the top surface, where the rectenna was located. The spot was estimated to have a diameter of 650 µm based on a ray optics simulation in ZEMAX, which we compared with the antenna’s effective area derived from its simulated directivity (see Supporting Information, S2). The attenuation in the beam path was estimated to be -1.5 dB for the intrinsic substrate and − 3.0 dB for the doped substrate. The voltage output from the rectenna was probed with DC needles and read out with a DSP 7265 lock-in amplifier. Notably, neither a source–drain DC bias nor a gate voltage was applied during measurements, thereby achieving a true zero-bias detection condition, which is particularly important in energy-harvesting applications. DC RESULTS AND DISCUSSION First, we extracted key device properties such as mobility and the mean free path from gated transfer-length measurements (see SI S3). Our devices reach a hole mobility of 3464 cm 2 /Vs at zero gate bias, which was extracted from gated transfer-length measurements as outlined by Zhong et al . 37 While this value is significantly lower than that of high-quality 28 , hBN-encapsulated 38 – 40 or suspended 27 graphene, it matches mobility values typically achieved with large-scale CVD-grown graphene devices fabricated on a wafer scale 41 – 43 . The charge neutrality point is shifted to positive voltages, which we attribute to the effects of the remaining HSQ resist layer on top of the channel 44 . The extracted hole mobility is greater than the electron mobility (2218 cm 2 /Vs at a gate bias of 10 V), likely due to charge transfer at the graphene‒metal interface 45 . The mean free path length 26 , 46 , 47 was calculated with Eq. 1 $$\:\lambda\:=\:\frac{h}{2q}\mu\:\sqrt{\frac{n}{\pi\:}}$$ 1 where \(\:h\) is Planck’s constant, \(\:q\) is the electric charge, \(\:\mu\:\) is the charge carrier mobility, and \(\:n\) is the charge carrier density. Based on the TLM data, the maximum mean free path is l = 65 nm for holes at a charge density of \(\:n=1.3\times\:{10}^{13}\:c{m}^{-2}\) , which is comparable to the width of the rectifier input arms (< 100 nm). Similar mean free path values have been reported in ballistic rectifiers made from unencapsulated mechanically exfoliated 48 , 49 and CVD graphene 50 . The maximum electron mean free path is approximately 35 nm. Except close to the charge neutrality point (CNP), the mean free path remains relatively constant over a wide gate bias range; the increase in carrier density with gate bias ( \(\:n\:\propto\:V\) ) is offset by a proportional decrease in mobility ( \(\:\mu\:\propto\:{V}^{-1}\) ). Importantly, the hole mean free path without applied gate voltage, i.e., at a Dirac point \(\:{V}_{\text{C}\text{N}\text{P}}\) between 5 and 10 V, is approximately 60 nm. Due to the short mean free path length \(\:\lambda\:\) relative to the width of the input arms \(\:w\) , the device operates in a quasi-ballistic regime. Imperfect ballisticity in the channel therefore reduces the expected voltage output, which can be estimated 51 by \(\:{V}_{\text{L}\text{U}}\propto\:{\left(\frac{1}{2}\right)}^{2w/\lambda\:}\) . We then investigated the rectification behavior of a triple-funnel geometric rectifier (inset in Fig. 2 a) via four-point DC measurements with a stepped gate voltage. The measured V LU - I SD curves at room temperature (T = 293 K, Fig. 2 a) and at cryogenic temperature (T = 20 K, Fig. 2 b) exhibit parabolic behavior around \(\:{I}_{\text{S}\text{D}}\) = 0 µA, which is expected from the Landauer–Büttiker formalism for ballistic rectification 51 and can be expressed as $$\:{V}_{\text{L}\text{U}}\left({I}_{\text{S}\text{D}}\right)=\:\gamma\:\:{I}_{\text{S}\text{D}}^{2}+{R}_{\text{l}\text{i}\text{n}}{I}_{\text{S}\text{D}}+{V}_{\text{L}\text{U},\:0}$$ 2 Here, the \(\:\gamma\:\) is the quadratic component of the curvature, \(\:{R}_{\text{l}\text{i}\text{n}}\) is the linear component, and \(\:{V}_{\text{L}\text{U},0}\) is a voltage offset. The quadratic component of the output voltage difference is superimposed on a linear component \(\:{R}_{\text{l}\text{i}\text{n}}{I}_{\text{S}\text{D}}\) , arising from a lateral spatial shift of the graphene channel with respect to the S and D input terminals. We extracted the quadratic component of the curvature \(\:\gamma\:\) by calculating the second derivative of the measured curves at \(\:{I}_{\text{S}\text{D}}\) = 0 µA (Fig. 2 c), which revealed that the curvature changes sign in accordance with the dominant charge carrier type in the graphene channel. The curvature is positive at voltages below and negative at voltages above the CNP. Since the average value of the first-order contribution vanishes under a sinusoidal input current ( \(\:{I}_{\text{S}\text{D}}\left(t\right)={I}_{0}\text{sin}\left(2\pi\:ft\right)\) ), only the quadratic component, quantified by the zero-bias curvature \(\:{\gamma\:}_{0}\) in Fig. 2 c, plays a role in zero-bias rectification: $$\:⟨{V}_{\text{L}\text{U}}⟩=\:⟨({\gamma\:}_{0}\:{I}_{0}^{2}{\text{sin}}^{2}\left(2\pi\:ft\right)+{R}_{\text{l}\text{i}\text{n}}\:{I}_{0}\text{sin}\left(2\pi\:ft\right)+{V}_{\text{L}\text{U},0}⟩=\:\frac{{\gamma\:}_{0}}{2}{I}_{0}^{2}+{V}_{\text{L}\text{U},0}$$ 3 The combined observations of quadratic output characteristics at low DC input currents and the dependence of the zero-bias curvature on the applied gate voltage suggest that quasi-ballistic rectification is a significant contributing factor to the rectification in our devices (see SI S4 for an extended discussion). However, several other possible mechanisms could also be responsible for rectification in the devices. These include bolometric heating, photothermal effects, plasma-wave mixing 52 , 53 , modulation of the graphene resistivity with the source-drain voltage, and even the formation of a rectifying barrier at the graphene–metal interface. At 20 K, the measured voltage difference increases in magnitude for both electron and hole conduction in graphene. Furthermore, the characteristic becomes more quadratic, as evidenced by an increase in curvature relative to measurements at room temperature. Since thermal effects should be strongly suppressed at lower temperatures, we can rule them out as a dominant effect in our device. Additionally, rectification is evident even at small input currents in the µA range, which should result in only minimal channel heating. The thermoelectric effect in a four-terminal graphene rectifier has also been numerically studied, and it was shown that the voltage induced by the Seebeck effect is orders of magnitude smaller than the voltage expected from ballistic conduction 54 . Furthermore, as discussed by Auton et al 21 , the measured polarity of the output voltage opposes that of the thermally generated voltage but matches that expected from ballistic rectification. We compared the measured output voltage to that calculated from a drift‒diffusion model 55 – 57 of the same rectifier. While ballistic transport is more accurately modeled via Monte Carlo 58 , 59 or atomistic models 60 , the drift‒diffusion model has been shown to yield accurate results at a much lower computational cost 54 , 57 , 61 . We find qualitative agreement between the simulated and experimental quadratic voltage outputs of a triple-funnel rectifier at room temperature (see SI S5), further indicating that ballistic rectification dominates the operation of our devices. THZ RESULTS AND DISCUSSION We performed free-space measurements on the fabricated rectennas under ambient conditions at frequencies between 0.49 and 0.68 THz. These measurements allowed direct comparison with the work of Auton et al . 20 , which, to the best of our knowledge, is the only other experimental four-terminal graphene geometric rectenna study at THz frequencies in the literature. Our measurement setup is shown schematically in Fig. 3 a. The input and output resistances for the single- and triple funnel devices were measured separately at DC (see Table 1 ). Table 1 Input and output resistance values for the two types of devices studied here. R SD refers to the resistance between the antenna terminals. The R LU refers to the resistance at the DC output terminals. Single funnel R SD [kΩ] R LU [kΩ] 26.0 31.5 Triple funnel 7.3 31.6 Care must be taken regarding what power normalization is used when comparing reported THz responsivities of rectennas. Here, we report the optical voltage responsivity ( \(\:{\gamma\:}_{\text{T}\text{H}\text{z}}=\:\frac{\pi\:{V}_{\text{L}\text{U}}}{\sqrt{2}{P}_{\text{T}\text{H}\text{z}}}\) ), where \(\:{P}_{THz}\) is the total available power (considering only the reflection and absorption losses at the wafer and lens interfaces) 62 , and the prefactor \(\:\pi\:/\sqrt{2}\) originates from the square-wave modulation of the input signal. The extrinsic responsivity reaches 0.21 V/W for the single-funnel rectenna and 0.77 V/W for the triple-funnel rectenna (see dark-colored points in Fig. 3 b). In general, the effective antenna area relative to the beam spot size affects the actual incident power and thus the responsivity. Following normalization to the isotropic radiator used by Auton et al ., 20 the triple (single) funnel device reaches an intrinsic peak responsivity of 11.8 V/W (3.3 V/W) between 0.49 and 0.68 THz (light-colored points in Fig. 3 b). The lack of significant frequency dependence indicates a broadband antenna response and device operation below its cutoff frequency, which has been estimated to reach far into the THz region 21 . In contrast, additional measurements on rectennas with a shorter antenna (92 µm total length) show an increase in responsivity with frequency, which is consistent with their simulated resonance frequency at 0.94 THz (see Supporting Information, S2). In addition to the open-circuit voltage, we measured the short-circuit current produced by the triple-funnel rectenna under illumination to calculate a current responsivity \(\:\beta\:\) analogously to the voltage responsivity reported above. The relative voltage and current responsivity (normalized to the value at the design frequency of 0.6 THz, γ c or β c ) are shown in Fig. 3 c. The ratio of the voltage and current responsivities (red circles in Fig. 3 d) agrees well with the output resistance measured at DC (31.6 kΩ). Regardless of incident power normalization 63 , the THz responsivity of the triple funnel structure is on average 4.7 ± 1.5 higher than that of the single funnel structure. The increase in responsivity from the single to triple funnel rectenna can be explained by a similar increase in the coupling efficiency \(\:{\eta\:}_{c}\) between the antenna and the rectifier from 2.1% to 7.4%, as calculated by Eq. 4 $$\:{\eta\:}_{\text{c}}=\frac{4{R}_{\text{A}}{R}_{\text{S}\text{D}}}{{\left({R}_{\text{A}}+{R}_{\text{S}\text{D}}\right)}^{2}}$$ 4 where \(\:{R}_{\text{A}}\) and \(\:{R}_{\text{S}\text{D}}\) are the real parts of the antenna and rectifier input impedances, respectively. The higher responsivity of the triple-funnel rectenna also reduces the optical noise-equivalent power (NEP) due to the thermal (Johnson‒Nyquist) noise ( \(\:NE{P}_{\text{J}\text{N}}=\:\frac{\sqrt{4\:{k}_{\text{B}}T{R}_{\text{L}\text{U}}}}{{\gamma\:}_{\text{T}\text{H}\text{z}}}\) ) of the rectenna. The minimum optimal NEP calculated without normalization decreases from 108.2 to 29.2 nW/√Hz from a single to a triple rectifier and from 6.8 to 1.9 nW/√Hz with isotropic normalization (Fig. 3 d). In these measurements, no source-drain or gate bias has been applied, and the dominant noise source is thermal noise because the output voltage is perpendicular to the input signal 20 . The NEP depends on the output resistance \(\:{R}_{\text{L}\text{U}}\) , which was nearly equal in our single- and triple-funnel devices because their graphene channels at the output have the same length. In principle, however, adding many more rectifiers would lead to a longer output channel, which would somewhat increase \(\:{R}_{\text{L}\text{U}}\) (which, however, tends to be dominated by the contact resistances) and thus increase the NEP accordingly. Considering the fabrication with CVD graphene, the results compare favorably with previously demonstrated geometric rectennas made from exfoliated graphene (shown in Table 2 ). Under comparable measurement and normalization conditions, our rectennas exhibit similar responsivity and NEP. Crucially, our work hence demonstrates the feasibility of achieving state-of-the-art rectenna performance using scalable materials. A significant output voltage was generated by a geometric rectenna fabricated using CVD graphene, whereas previous devices were based on non-scalable, exfoliated graphene flakes. 20 Relying solely on CVD-grown graphene enables the parallel fabrication of multiple devices on a wafer-scale substrate, rather than individual devices. A feature enabled by the use of CVD graphene is the parallel fabrication of multiple devices on a wafer-scale substrate, rather than individual devices to which one is usually limited with exfoliated graphene. We also point out another novel aspect of our work. The parallel arrangement of geometric rectifiers increases the coupling efficiency between the antenna and the rectifier. This arrangement is uniquely enabled by the zero-threshold behavior of a geometric rectifier. Other rectenna systems using rectifiers with a potential barrier (i.e., mostly heterojunction diodes) usually focus only on the connection of multiple antennas to a single rectifier 30 (to increase the voltage at the rectifier input and overcome the diode’s potential barrier) or of a single antenna and rectifier 64 (for simplicity), and would not benefit from the proposed rectenna architecture. A geometric rectifier, however, does not contain a built-in potential, and it can therefore rectify even the small voltages generated by a single antenna. Table 2 Comparable geometric rectennas in literature. The devices investigated in this work are highlighted in green. Values are normalized to the effective antenna area (calculated from a directivity D = 13 dBi) and the effective area of an isotropic radiator (D = 1). *Measured at a lower frequency of 110 GHz. The area-normalized responsivity between 0.64 and 0.69 THz reaches a maximum of ~ 11 V/W; thus, the calculated NEP is ~ 1.85 nW/√Hz. Thermal noise was used to calculate the NEP. Rectenna Material Bias Frequency [THz] THz responsivity [V/W] NEP [nW/√Hz] Ref. normalization D = 13 dBi D = 1 D = 13 dBi D = 1 Triple funnel + bowtie CVD graphene unbiased 0.49–0.68 0.77 11.8 29.2 1.9 This work Single funnel + bowtie CVD graphene unbiased 0.49–0.68 0.21 3.3 108.2 6.8 This work Single funnel + bowtie Exfoliated graphene + hBN gate bias 0.07–0.69 ~ 11 764* ~ 1.85 0.034* 20 Ballistic diode + bowtie Exfoliated graphene unbiased 28.3 ~ 0.6 43.0 68 We also want to emphasize the reproducibility of the fabrication process: Further measurements of single-funnel devices fabricated on another wafer show little variation in responsivity, indicating that the fabrication method, the doping level of graphene, and the detector alignment are consistent and reproducible (see Supporting Information, S6). Our prototype fabrication process relies on electron beam lithography. However, the critical dimensions are attainable using high-throughput nanoimprint lithography (NIL). Together with the scalable graphene material and fabrication flow demonstrated in this work, NIL could be used to fabricate entire arrays of geometric graphene rectennas with minimal per-device cost 65 – 67 . CONCLUSION In this work, we demonstrated the successful fabrication and operation of geometric THz rectennas using CVD graphene suitable for wafer-scale fabrication. We achieved high coupling efficiency and compensated for the lower mobility of the CVD material by implementing a parallel connection of multiple rectifiers to a single antenna. This enabled room-temperature zero-bias rectification up to 0.68 THz (limited by the radiation source) in free-space measurements, which we expect to be mainly limited by the available THz power and frequency range of the source. Our approach shows that geometric rectification in graphene can be harnessed without relying on unscalable exfoliated materials. Consequently, our work establishes a clear path for integrating efficient THz rectifiers with established semiconductor technology, unlocking the potential of THz energy harvesting for autonomous sensors in next-generation wireless IoT networks. Declarations Ethics approval consent to participate Consent for publication Not applicable. Competing interests The authors declare no competing interests. Supporting Information Supporting information includes the following: S1) AFM images before and after graphene transfer; SEM image of a larger transferred graphene layer; Raman spectrum of the transferred graphene; S2) CST Microwave Studio model of the bowtie antennas with complex feedpoint impedance; ZEMAX estimation of the spot size behind the hyperhemispherical Si lens; measured available THz power measured with a calibrated detector; S3) details on the gated transfer-length measurements and extraction of contact resistance, sheet resistance, mobility, and mean free path; S4) discussion of alternative rectification mechanisms; S5) simulated voltage output of a triple-funnel rectifier at dc using the drift‒diffusion model; S6) measured output voltage spectrum for single-funnel and triple-funnel devices with open and blocked THz beam path, measured responsivity of additional single-funnel rectennas (92 µm) on an additional substrate, measured voltage output at 653 GHz under a gate voltage sweep and frequency sweeps at different gate voltages on a separate sample fabricated on lightly doped Si. Funding This work was financially supported by the European Union’s Horizon 2020 research and innovation programme under the grant agreement No. 101006963 (GreEnergy) and from the European Union’s Horizon Europe Research and Innovation Program under the 2D Pilot Line (2D-PL, Grant No. 101189797). J. H. acknowledges funding from RO 770 49 − 1 of the INTEREST priority program (SPP 2314). A. L. acknowledges funding from the Lithuanian Science Foundation (project No. S-MIP22-83). Author Contribution A. H., Z. W., A. G., and M. L. conceived the experiments. A. H. designed the devices and performed the electrical characterization. A. H., M. M., J. B., and L. E. fabricated the devices. B. C. performed the AFM and Raman measurements. J. H., A. H., and A. L. performed the THz characterization and noise measurement. D. M. and L. P. provided the drift‒diffusion model. All the authors contributed to discussions and the analysis and interpretation of the results. A. H. wrote the initial manuscript and all the authors revised it. Acknowledgement The authors thank Dr. Andrey Generalov from VTT Finland for providing the 10 Ω·cm to 40 Ω·cm n-doped/90 nm-SiO2 wafer. The authors thank Dr. Christine Hendriks for her corrections and suggestions regarding the manuscript’s style and composition. Data Availability All data supporting this study are available from the corresponding author on reasonable request. References Pecunia V, et al. Roadmap on energy harvesting materials. J Phys Mater. 2023;6:042501. Donchev E, et al. The rectenna device: From theory to practice (a review). MRS Energy Sustain. 2014;1:1. Atzori L, Iera A, Morabito G. The Internet of Things: A survey. Comput Netw. 2010;54:2787–805. Sun H, Guo Y, He M, Zhong Z. Design of a High-Efficiency 2.45-GHz Rectenna for Low-Input-Power Energy Harvesting. IEEE Antennas Wirel Propag Lett. 2012;11:929–32. Assimonis SD, Bletsas A. 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Graphene geometric diodes for terahertz rectennas. J Phys Appl Phys. 2013;46:185101. Moddel G, Zhu Z, Grover S, Joshi S. Ultrahigh speed graphene diode with reversible polarity. Solid State Commun. 2012;152:1842–5. Singh AK, Auton G, Hill E, Song A. Graphene based ballistic rectifiers. Carbon. 2015;84:124–9. Song AM. Formalism of nonlinear transport in mesoscopic conductors. Phys Rev B. 1999;59:9806–9. Ludwig F, et al. Terahertz Detection with Graphene FETs: Photothermoelectric and Resistive Self-Mixing Contributions to the Detector Response. ACS Appl Electron Mater. 2024;6:2197–212. Holstein J. 2024 49th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) 1–2 (IEEE, Perth, Australia, 2024). 10.1109/IRMMW-THz60956.2024.10697713 Prakash K, et al. Thermoelectric rectification in a graphene-based triangular ballistic rectifier (G-TBR). J Comput Electron. 2021;20:2308–16. Garg A, Jain N, Kumar S, Kasjoo SR, Singh AK. Analysis of nonlinear characteristics of a graphene based four-terminal ballistic rectifier using a drift-diffusion model. Nanoscale Adv. 2019;1:4119–27. Garg A, Jain N, Singh AK. Drift-diffusion modeling and simulation of four terminal ballistic rectifier. in 2016 IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT) 1995–1998 (IEEE, Bangalore, India, 2016). 10.1109/RTEICT.2016.7808187 Prakash K et al. Drift diffusion modelling of three branch junction (TBR) based nano-rectifier. in. 2019 IEEE 14th Nanotechnology Materials and Devices Conference (NMDC) 1–4 (IEEE, Stockholm, Sweden, 2019). 10.1109/NMDC47361.2019.9083999 Truccolo D, Boscolo S, Esseni D, Midrio M, Palestri P. Modeling and optimization of graphene ballistic rectifiers. Solid-State Electron. 2022;194:108314. Truccolo D, Palestri P, Esseni D, Boscolo S, Midrio M. 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Science. 1996;272:85–7. Chou SY, Krauss PR. Imprint lithography with sub-10 nm feature size and high throughput. Microelectron Eng. 1997;35:237–40. Zhu Z, Joshi S, Moddel G. High Performance Room Temperature Rectenna IR Detectors Using Graphene Geometric Diodes. IEEE J Sel Top Quantum Electron. 2014;20:70–8. Additional Declarations No competing interests reported. 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Lemme","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBUlEQVRIiWNgGAWjYLCCByCCvYGBgbEBxOIBEcz4tSSAFR5gYDhImhaJBCK16LafMWBIqNgWzS/59pn0xx0M8vztZw8+LmCwlsOlxexMWgJDwpnbuTNnp5tJHDzDYDjjTF6y8QyGdGOcWg4kH2BIbLudu+F2GtuNg23/GRtu8JhJ8zAcTmzApeX8wwaGxH+3c/ffPAbSwmA//waP+W+glnqcWm6AbGkA2iLBBtaSuAFoCzNQSwJOh914lnAg4djt3Bln0th/nG1jSN54JsdYmscg3RC3w3IMH3youZ3b336M2aCyjcF23vEzhp95KqzlcdkCAgewiBng0zAKRsEoGAWjgBAAAO4JXk8dxd3XAAAAAElFTkSuQmCC","orcid":"","institution":"RWTH Aachen University","correspondingAuthor":true,"prefix":"","firstName":"Max","middleName":"Christian","lastName":"Lemme","suffix":""}],"badges":[],"createdAt":"2026-03-12 23:08:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9108655/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9108655/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105925312,"identity":"0ce2c49a-4660-4eb2-af8a-e00747ee9a4d","added_by":"auto","created_at":"2026-04-01 13:20:11","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":392255,"visible":true,"origin":"","legend":"\u003cp\u003eGraphene geometric rectennas and their fabrication. a) A photograph of an entire fabricated 2-inch wafer. The graphene rectennas are located in the central 10 x 10 mm2 area. b) Colorized SEM image of the bowtie antenna in the horizontal and DC terminals in the vertical direction (scale bar: 10 μm). The antenna has a total length of 150 μm and a flare angle of 60°. The inset in b) shows a close-up image of the structured graphene below the contact. The scale bar in the inset is 1 μm. c) SEM image (colorized to highlight the metal) of the device with a single funnel-type rectifier. d) Three funnel-type rectifiers connected in parallel with respect to the input terminals (colorized to highlight the metal). The electron beam lithography resist residue is visible only at the upper contact. In the ballistic regime, charge carriers predominantly move toward the lower terminal (scale bar: 300 nm). The four terminals are labeled as they are referred to in the text: upper (U), lower (L), source (S), and drain (D). e) Fabrication process. The white notches indicate the etched alignment markers, the red strips represent the resist mask used to structure the graphene below the metal contact.\u0026nbsp;\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9108655/v1/2d820ed7c20da58dabafd978.jpg"},{"id":106093379,"identity":"67f7ef9d-560b-4561-98a5-fad5d6e9ce9c","added_by":"auto","created_at":"2026-04-03 11:37:04","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":166145,"visible":true,"origin":"","legend":"\u003cp\u003eRectification measurements of a CVD graphene-based four-terminal geometric rectifier at DC. a) Output voltage difference V\u003csub\u003eLU\u003c/sub\u003e with respect to the input source–drain current I\u003csub\u003eSD\u003c/sub\u003e at various backgate voltages measured at room temperature. The inset shows the device characterized at DC (colorized SEM image). b) The measurement is repeated at T = 20 K. The parabolic behavior expected from the Landauer–Büttiker formalism is clearly visible. c) The zero-bias curvature is extracted from the second derivative of the measured V\u003csub\u003eLU\u003c/sub\u003e-I\u003csub\u003eSD\u003c/sub\u003e curves. The curvature changes sign across the charge neutrality point, showing dominant hole and electron contributions to the rectification. The measurements at cryogenic temperatures (black) reveal a greater curvature than the measurements at room temperature (red). Even without an applied gate (V\u003csub\u003eg\u003c/sub\u003e = 0 V), the curvature is measurable.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9108655/v1/6638e2ad4be0ce2052234a69.jpg"},{"id":105925314,"identity":"632e2a56-a5dd-457b-9085-8e2631527c31","added_by":"auto","created_at":"2026-04-01 13:20:11","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":291097,"visible":true,"origin":"","legend":"\u003cp\u003eTerahertz measurements in free space. a) Schematic THz measurement setup. The beam path consists of a frequency multiplier (×36, RPG ZTX750) THz source, a collimating PTFE lens (50 mm focal length), a 3-inch 90°-off-axis focal length parabolic mirror prefocusing the beam and directing it upward to the x-y stage, and a hyperhemispherical Si lens (12 mm diameter, 6.8 mm height) directly below the carrier wafer (525 µm). The rectenna sample is placed on the carrier wafer and contacted with needles from the top. b) Voltage responsivity versus source frequency for single funnel (blue) and triple funnel (green) devices. Two common normalizations with respect to the incident power have been used to calculate the responsivity: normalization to the total source power (opaque points) and normalization to the received power of an isotropic radiator (transparent points). c) Relative voltage (γ, green dots) and current responsivities (β, black dots) of the triple-funnel rectenna, normalized to their respective values at the design frequency of 0.6 THz (γc, βc). The ratio of the voltage and current responsivities (red circles) agrees with the output resistance of the device measured at dc. d) Assuming that thermal noise is dominant in the rectifier, the noise-equivalent power (NEP) can be calculated from the spectral noise voltage density and the responsivity. These values also depend on the chosen normalization.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9108655/v1/c26e68a1cac7af1ae6510511.jpg"},{"id":106405418,"identity":"c9ecc0dc-93f9-4b19-9c5f-be1f7e65c336","added_by":"auto","created_at":"2026-04-08 09:26:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1648070,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9108655/v1/25a268b5-34ca-4d52-8f37-f92ae4b2b08a.pdf"},{"id":106401724,"identity":"96bbdc5d-b34b-4067-b536-264578fd86c0","added_by":"auto","created_at":"2026-04-08 09:09:18","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2823028,"visible":true,"origin":"","legend":"","description":"","filename":"20260226HemmetterEnhancedCouplingSI.docx","url":"https://assets-eu.researchsquare.com/files/rs-9108655/v1/976ba4a836dbf8b9b4cd0756.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhanced Coupling Efficiency in Geometric Terahertz Rectennas Based on Scalable CVD Graphene","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eUbiquitous radio frequency (RF) communication networks, such as Wi-Fi, Bluetooth, cellular networks, and GPS, support numerous indispensable applications, including internet access, cellular voice communications, broadcasting, navigation, and remote control. As a result, urban environments exhibit high ambient RF power density, which can be used as an energy source for low-power devices\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, a process known as RF energy harvesting. This can be achieved using antenna-coupled rectifiers (\u003cem\u003erectennas)\u003c/em\u003e, which collect and utilize RF radiation. Here, the antenna captures ambient RF radiation, and the rectifier converts the induced oscillating voltage into a direct current (DC) output\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Rectenna-based energy harvesting could enable numerous applications in distributed networks of autonomous sensors\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e that collect environmental, biomedical, or location data for use in climate science, medical diagnostics, or logistics. In fact, rectennas operating up to Wi-Fi/Bluetooth frequencies (2.4 GHz) have achieved conversion efficiencies of up to 50%\u003csup\u003e4\u0026ndash;6\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe growing number of wireless devices and their higher bandwidth increase both the power density and the frequency of ambient RF radiation, as exemplified by the development of 5G and 6G mobile networks\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, with frequency allocations in the submillimeter and terahertz (THz) ranges\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. However, conventional rectifiers (e.g., Schottky or metal-insulator-metal diodes) are limited in operating frequency and require voltage biasing, complicating rectenna-based energy harvesting in the THz range\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Efficient zero-bias rectennas\u003csup\u003e\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e could, in contrast, enable wider adoption of THz-enabled applications\u003csup\u003e\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Geometric rectifiers\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e can fill this gap. The geometric asymmetry in the conducting channel induces current asymmetry at the output. While this requires quasi-scatter-free (ballistic) charge carrier transport in the channel\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, the absence of potential barriers or doping gradients means that no bias voltage is required for rectification, enabling zero-bias rectification\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eHowever, typical geometric rectifier designs face two major obstacles to commercialization. First, among other options\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan additionalcitationids=\"CR23 CR24\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, exfoliated graphene flakes\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e have been used for geometric rectifiers due to their high charge carrier mobility\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e and large mean free path\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. However, this approach is not suitable for wafer-scale fabrication. Second, coupling geometric rectifiers to antennas results in a large impedance mismatch between the antenna and the rectifier, on the order of several orders of magnitude. This mismatch severely limits their overall efficiency because most of the captured THz radiation is reflected back to the antenna.\u003c/p\u003e \u003cp\u003eHere, we address both major obstacles of geometric rectifiers. We fabricated geometric rectennas from commercially available graphene grown by chemical vapor deposition (CVD)\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e and coupled each antenna to multiple geometric rectifiers\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. This configuration is uniquely possible with geometric rectifiers because of their inherent zero-threshold behavior. Connecting the rectifiers in parallel lowered the total rectifier input resistance and increased the coupling efficiency between rectifier and antenna. This increased the broadband THz responsivity in free-space measurements up to 0.68 THz, mainly limited by the available power of the THz source, a frequency not previously achieved with CVD graphene-based rectennas. Our approach enhances the scalability and efficiency of geometric THz rectennas for energy-harvesting applications, thereby enabling autonomous sensors, e.g., for Internet of Things (IoT) applications.\u003c/p\u003e"},{"header":"DEVICE DESIGN","content":"\u003cp\u003eWe fabricated the geometric graphene rectennas on an oxidized 2 inch silicon (Si) wafer, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea. The center of the wafer contains multiple rectennas, with the rectifiers connected to bowtie antennas with a 60° flare angle and a total length of 150 µm (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb). Additionally, some rectifiers are connected to large contact pads for DC characterization. There are two different four-terminal rectifier types: a funnel-type rectifier (“single funnel”) and a parallel connection of three rectifiers at the input (“triple funnel”). This triple-funnel arrangement reduces the overall input resistance of the rectifier combination and thus increases the coupling efficiency between the rectifier and the antenna. Colored scanning electron microscopy (SEM) images of both rectifier types are shown in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec and \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed. The DC output can be probed at the upper (U) and lower (L) metallic contacts, located farther from the rectifier, to minimize influence on the antenna. The source (S) and drain (D) terminals on the left and right correspond to the rectifier inputs\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. The input arms enter the central stem at an angle to inject charge carriers from S and D inputs preferentially toward the L terminal rather than the U output terminal. The graphene layer beneath the antennas and output metal contacts is patterned with densely packed triangular holes with a side length of 560 nm to form metal-graphene edge contacts (see the inset in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb). This pattern increases the total length of edge contacts and thus lowers the contact resistance between graphene and metal\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. The graphene also extends beyond the metal area to ensure adequate adhesion between graphene and substrate during the fabrication process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e "},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e\u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eMethods\u003c/span\u003e\u003c/h2\u003e \u003cp\u003e \u003cb\u003eFabrication\u003c/b\u003e: Our geometric graphene rectennas were fabricated via the process outlined in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee. First, alignment markers were defined by electron-beam lithography (EBL, Raith EBPG 5200 system operated at 100 kV) on a 2-inch (50 mm) diameter, high-resistivity (\u0026gt; 10 kΩ·cm) Si wafer with 300 nm thermally grown SiO\u003csub\u003e2\u003c/sub\u003e. The alignment markers were then etched through the SiO\u003csub\u003e2\u003c/sub\u003e and into the underlying Si substrate with a fluorine-based inductively coupled plasma reactive ion etching (ICP-RIE) process (Oxford Plasmalab 100 ICP RIE). The resist residue, a major cause of graphene delamination, was removed by thorough cleaning the substrate before the graphene transfer in organic solvents and piranha solution (H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e:H\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e), as verified by atomic force microscopy (AFM, see Supporting Information, S1).\u003c/p\u003e \u003cp\u003eWe transferred CVD-grown graphene grown obtained from General Graphene (Knoxville, USA) from a 150 x 150 mm² copper foil growth substrate to the sample surface using a wet transfer.\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e The transferred graphene layer (approximately 10 x 10 mm\u003csup\u003e2\u003c/sup\u003e) was placed in the center of the 2-inch wafer, as shown in the inset in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee. The protective resist residue was removed from the graphene by dissolving it in acetone and by annealing at 300°C for 3 h under an argon atmosphere at 50 mTorr, thereby increasing adhesion to the substrate.\u003c/p\u003e \u003cp\u003eWe then defined the graphene channel via EBL using hydrogen silsesquioxane (HSQ) resist, as outlined by Passi \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e35\u003c/sup\u003e The pattern was transferred to the graphene layer by RIE (Oxford Plasmalab 100 ICP RIE) with low-power oxygen-based plasma for 4 min. The developed resist remained on the graphene channel at this point to prevent delamination and organic contamination during the following lithography step.\u003c/p\u003e \u003cp\u003eA final EBL step using a two-layer (poly)methyl methacrylate (MMA/PMMA) resist defined the liftoff mask for the metallic contacts and antennas. Prior to metal deposition, the remaining HSQ resist within the masked areas was removed using a diluted buffered oxide etchant (BOE; NH\u003csub\u003e4\u003c/sub\u003eF:HF in H\u003csub\u003e2\u003c/sub\u003eO). Thus, graphene was exposed and formed an ohmic contact with the 5/35 nm Ti/Au metal deposited by electron-beam evaporation (FHR Star 200 EVA) onto the graphene layer. The process was completed by lifting off the excess metal together with the resist mask in acetone.\u003c/p\u003e \u003cp\u003eIn addition to the geometric rectennas on high-resistivity Si/SiO\u003csub\u003e2\u003c/sub\u003e substrates, we fabricated two more samples using the same process. The first sample was fabricated on a 20 x 20 mm\u003csup\u003e2\u003c/sup\u003e lightly doped substrate (\u003cem\u003en\u003c/em\u003e-Si with 90 nm thermally grown SiO\u003csub\u003e2\u003c/sub\u003e, resistivity 10–40 Ω·cm). This substrate allowed transfer-length and rectification measurements with a global back-gate to control the carrier density and type\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. The second sample (a high-resistivity 2-inch Si wafer with 90 nm thermally grown SiO\u003csub\u003e2\u003c/sub\u003e) contained rectennas with shorter antennas, each 92 µm long, to judge the influence of the antenna response on the rectified voltage.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eElectrical Characterization\u003c/strong\u003e \u003c/p\u003e\u003cp\u003eDC measurements on the four-terminal geometric rectifiers were performed in a Lakeshore probe station under vacuum at both room temperature (293 K) and at 20 K. A current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e was forced between the S and D input terminals, and the voltage difference between the L and U output terminals \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{(V}_{\\text{L}\\text{U}}={V}_{\\text{L}}-{V}_{\\text{U}})\\)\u003c/span\u003e\u003c/span\u003e was measured. At each backgate voltage step (from − 20 V to 20 V in steps of 5 V), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e was swept from − 500 µA to 500 µA.\u003c/p\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eTHz measurements were performed in a free-space setup. An HP8341A synthesizer provided a signal between 13.8 and 18.8 GHz, which was then transformed into the range of 0.49–0.68 THz by a ×36 multiplier source (RPG-ZTX750). The synthesizer output was modulated with a 331 Hz square wave, which was further supplied to an AMETEK DSP 7265 lock-in amplifier as a reference. The available THz power was measured by a calibrated pyroelectric detector (THz 10 HS by SLT Sensor- und Lasertechnik GmbH, calibrated by Physikalisch-Technische Bundesanstalt, Braunschweig, Germany), positioned at the source’s waveguide flange. The output power spectrum (see the Supporting Information, S2) has an average beam power of 50 µW. A Teflon lens (50 mm focal length) and a 3-inch parabolic mirror were then used to prefocus the beam and direct it 90° upward to a hyperhemispherical Si lens (diameter 12 mm, height 6.8 mm) in contact with a 525 µm thick high-resistivity carrier wafer for system alignment with an x‒y stage. The lens optimized radiation coupling to an aplanatic condition and further focused the beam to a small spot directly at the device under test. The wafer height was adjusted to place the focal point exactly on the top surface, where the rectenna was located. The spot was estimated to have a diameter of 650 µm based on a ray optics simulation in ZEMAX, which we compared with the antenna’s effective area derived from its simulated directivity (see Supporting Information, S2). The attenuation in the beam path was estimated to be -1.5 dB for the intrinsic substrate and − 3.0 dB for the doped substrate. The voltage output from the rectenna was probed with DC needles and read out with a DSP 7265 lock-in amplifier. Notably, neither a source–drain DC bias nor a gate voltage was applied during measurements, thereby achieving a true zero-bias detection condition, which is particularly important in energy-harvesting applications.\u003c/p\u003e \u003c/div\u003e\u003cp\u003e \u003cb\u003eFabrication\u003c/b\u003e: Our geometric graphene rectennas were fabricated via the process outlined in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee. First, alignment markers were defined by electron-beam lithography (EBL, Raith EBPG 5200 system operated at 100 kV) on a 2-inch (50 mm) diameter, high-resistivity (\u0026gt; 10 kΩ·cm) Si wafer with 300 nm thermally grown SiO\u003csub\u003e2\u003c/sub\u003e. The alignment markers were then etched through the SiO\u003csub\u003e2\u003c/sub\u003e and into the underlying Si substrate with a fluorine-based inductively coupled plasma reactive ion etching (ICP-RIE) process (Oxford Plasmalab 100 ICP RIE). The resist residue, a major cause of graphene delamination, was removed by thorough cleaning the substrate before the graphene transfer in organic solvents and piranha solution (H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e:H\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e), as verified by atomic force microscopy (AFM, see Supporting Information, S1).\u003c/p\u003e\u003cp\u003eWe transferred CVD-grown graphene grown obtained from General Graphene (Knoxville, USA) from a 150 x 150 mm² copper foil growth substrate to the sample surface using a wet transfer.\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e–\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e The transferred graphene layer (approximately 10 x 10 mm\u003csup\u003e2\u003c/sup\u003e) was placed in the center of the 2-inch wafer, as shown in the inset in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee. The protective resist residue was removed from the graphene by dissolving it in acetone and by annealing at 300°C for 3 h under an argon atmosphere at 50 mTorr, thereby increasing adhesion to the substrate.\u003c/p\u003e\u003cp\u003eWe then defined the graphene channel via EBL using hydrogen silsesquioxane (HSQ) resist, as outlined by Passi \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e35\u003c/sup\u003e The pattern was transferred to the graphene layer by RIE (Oxford Plasmalab 100 ICP RIE) with low-power oxygen-based plasma for 4 min. The developed resist remained on the graphene channel at this point to prevent delamination and organic contamination during the following lithography step.\u003c/p\u003e\u003cp\u003eA final EBL step using a two-layer (poly)methyl methacrylate (MMA/PMMA) resist defined the liftoff mask for the metallic contacts and antennas. Prior to metal deposition, the remaining HSQ resist within the masked areas was removed using a diluted buffered oxide etchant (BOE; NH\u003csub\u003e4\u003c/sub\u003eF:HF in H\u003csub\u003e2\u003c/sub\u003eO). Thus, graphene was exposed and formed an ohmic contact with the 5/35 nm Ti/Au metal deposited by electron-beam evaporation (FHR Star 200 EVA) onto the graphene layer. The process was completed by lifting off the excess metal together with the resist mask in acetone.\u003c/p\u003e\u003cp\u003eIn addition to the geometric rectennas on high-resistivity Si/SiO\u003csub\u003e2\u003c/sub\u003e substrates, we fabricated two more samples using the same process. The first sample was fabricated on a 20 x 20 mm\u003csup\u003e2\u003c/sup\u003e lightly doped substrate (\u003cem\u003en\u003c/em\u003e-Si with 90 nm thermally grown SiO\u003csub\u003e2\u003c/sub\u003e, resistivity 10–40 Ω·cm). This substrate allowed transfer-length and rectification measurements with a global back-gate to control the carrier density and type\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. The second sample (a high-resistivity 2-inch Si wafer with 90 nm thermally grown SiO\u003csub\u003e2\u003c/sub\u003e) contained rectennas with shorter antennas, each 92 µm long, to judge the influence of the antenna response on the rectified voltage.\u003c/p\u003e\u003cp\u003e \u003cstrong\u003eElectrical Characterization\u003c/strong\u003e \u003c/p\u003e\u003cp\u003eDC measurements on the four-terminal geometric rectifiers were performed in a Lakeshore probe station under vacuum at both room temperature (293 K) and at 20 K. A current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e was forced between the S and D input terminals, and the voltage difference between the L and U output terminals \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{(V}_{\\text{L}\\text{U}}={V}_{\\text{L}}-{V}_{\\text{U}})\\)\u003c/span\u003e\u003c/span\u003e was measured. At each backgate voltage step (from − 20 V to 20 V in steps of 5 V), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e was swept from − 500 µA to 500 µA.\u003c/p\u003e\u003cp\u003eTHz measurements were performed in a free-space setup. An HP8341A synthesizer provided a signal between 13.8 and 18.8 GHz, which was then transformed into the range of 0.49–0.68 THz by a ×36 multiplier source (RPG-ZTX750). The synthesizer output was modulated with a 331 Hz square wave, which was further supplied to an AMETEK DSP 7265 lock-in amplifier as a reference. The available THz power was measured by a calibrated pyroelectric detector (THz 10 HS by SLT Sensor- und Lasertechnik GmbH, calibrated by Physikalisch-Technische Bundesanstalt, Braunschweig, Germany), positioned at the source’s waveguide flange. The output power spectrum (see the Supporting Information, S2) has an average beam power of 50 µW. A Teflon lens (50 mm focal length) and a 3-inch parabolic mirror were then used to prefocus the beam and direct it 90° upward to a hyperhemispherical Si lens (diameter 12 mm, height 6.8 mm) in contact with a 525 µm thick high-resistivity carrier wafer for system alignment with an x‒y stage. The lens optimized radiation coupling to an aplanatic condition and further focused the beam to a small spot directly at the device under test. The wafer height was adjusted to place the focal point exactly on the top surface, where the rectenna was located. The spot was estimated to have a diameter of 650 µm based on a ray optics simulation in ZEMAX, which we compared with the antenna’s effective area derived from its simulated directivity (see Supporting Information, S2). The attenuation in the beam path was estimated to be -1.5 dB for the intrinsic substrate and − 3.0 dB for the doped substrate. The voltage output from the rectenna was probed with DC needles and read out with a DSP 7265 lock-in amplifier. Notably, neither a source–drain DC bias nor a gate voltage was applied during measurements, thereby achieving a true zero-bias detection condition, which is particularly important in energy-harvesting applications.\u003c/p\u003e"},{"header":"DC RESULTS AND DISCUSSION","content":"\u003cp\u003eFirst, we extracted key device properties such as mobility and the mean free path from gated transfer-length measurements (see SI S3). Our devices reach a hole mobility of 3464 cm\u003csup\u003e2\u003c/sup\u003e/Vs at zero gate bias, which was extracted from gated transfer-length measurements as outlined by Zhong \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e37\u003c/sup\u003e While this value is significantly lower than that of high-quality\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, hBN-encapsulated\u003csup\u003e\u003cspan additionalcitationids=\"CR39\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e or suspended\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e graphene, it matches mobility values typically achieved with large-scale CVD-grown graphene devices fabricated on a wafer scale\u003csup\u003e\u003cspan additionalcitationids=\"CR42\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. The charge neutrality point is shifted to positive voltages, which we attribute to the effects of the remaining HSQ resist layer on top of the channel\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. The extracted hole mobility is greater than the electron mobility (2218 cm\u003csup\u003e2\u003c/sup\u003e/Vs at a gate bias of 10 V), likely due to charge transfer at the graphene‒metal interface\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe mean free path length\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e was calculated with Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\lambda\\:=\\:\\frac{h}{2q}\\mu\\:\\sqrt{\\frac{n}{\\pi\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:h\\)\u003c/span\u003e\u003c/span\u003e is Planck\u0026rsquo;s constant, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e is the electric charge, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e is the charge carrier mobility, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e is the charge carrier density. Based on the TLM data, the maximum mean free path is l\u0026thinsp;=\u0026thinsp;65 nm for holes at a charge density of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n=1.3\\times\\:{10}^{13}\\:c{m}^{-2}\\)\u003c/span\u003e\u003c/span\u003e, which is comparable to the width of the rectifier input arms (\u0026lt;\u0026thinsp;100 nm). Similar mean free path values have been reported in ballistic rectifiers made from unencapsulated mechanically exfoliated\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e,\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e and CVD graphene\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. The maximum electron mean free path is approximately 35 nm. Except close to the charge neutrality point (CNP), the mean free path remains relatively constant over a wide gate bias range; the increase in carrier density with gate bias (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\:\\propto\\:V\\)\u003c/span\u003e\u003c/span\u003e) is offset by a proportional decrease in mobility (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\propto\\:{V}^{-1}\\)\u003c/span\u003e\u003c/span\u003e). Importantly, the hole mean free path without applied gate voltage, i.e., at a Dirac point \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{\\text{C}\\text{N}\\text{P}}\\)\u003c/span\u003e\u003c/span\u003e between 5 and 10 V, is approximately 60 nm. Due to the short mean free path length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:\\)\u003c/span\u003e\u003c/span\u003e relative to the width of the input arms \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:w\\)\u003c/span\u003e\u003c/span\u003e, the device operates in a quasi-ballistic regime. Imperfect ballisticity in the channel therefore reduces the expected voltage output, which can be estimated\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{\\text{L}\\text{U}}\\propto\\:{\\left(\\frac{1}{2}\\right)}^{2w/\\lambda\\:}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eWe then investigated the rectification behavior of a triple-funnel geometric rectifier (inset in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) via four-point DC measurements with a stepped gate voltage. The measured \u003cem\u003eV\u003c/em\u003e\u003csub\u003eLU\u003c/sub\u003e \u003cem\u003e- I\u003c/em\u003e\u003csub\u003eSD\u003c/sub\u003e curves at room temperature (T\u0026thinsp;=\u0026thinsp;293 K, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) and at cryogenic temperature (T\u0026thinsp;=\u0026thinsp;20 K, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb) exhibit parabolic behavior around \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e = 0 \u0026micro;A, which is expected from the Landauer\u0026ndash;B\u0026uuml;ttiker formalism for ballistic rectification\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e and can be expressed as\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{V}_{\\text{L}\\text{U}}\\left({I}_{\\text{S}\\text{D}}\\right)=\\:\\gamma\\:\\:{I}_{\\text{S}\\text{D}}^{2}+{R}_{\\text{l}\\text{i}\\text{n}}{I}_{\\text{S}\\text{D}}+{V}_{\\text{L}\\text{U},\\:0}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eHere, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\gamma\\:\\)\u003c/span\u003e\u003c/span\u003e is the quadratic component of the curvature, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{\\text{l}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e is the linear component, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{\\text{L}\\text{U},0}\\)\u003c/span\u003e\u003c/span\u003e is a voltage offset. The quadratic component of the output voltage difference is superimposed on a linear component \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{\\text{l}\\text{i}\\text{n}}{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e, arising from a lateral spatial shift of the graphene channel with respect to the S and D input terminals. We extracted the quadratic component of the curvature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\gamma\\:\\)\u003c/span\u003e\u003c/span\u003e by calculating the second derivative of the measured curves at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e = 0 \u0026micro;A (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec), which revealed that the curvature changes sign in accordance with the dominant charge carrier type in the graphene channel. The curvature is positive at voltages below and negative at voltages above the CNP.\u003c/p\u003e \u003cp\u003eSince the average value of the first-order contribution vanishes under a sinusoidal input current (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{S}\\text{D}}\\left(t\\right)={I}_{0}\\text{sin}\\left(2\\pi\\:ft\\right)\\)\u003c/span\u003e\u003c/span\u003e), only the quadratic component, quantified by the zero-bias curvature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\gamma\\:}_{0}\\)\u003c/span\u003e\u003c/span\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, plays a role in zero-bias rectification:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\u0026lang;{V}_{\\text{L}\\text{U}}\u0026rang;=\\:\u0026lang;({\\gamma\\:}_{0}\\:{I}_{0}^{2}{\\text{sin}}^{2}\\left(2\\pi\\:ft\\right)+{R}_{\\text{l}\\text{i}\\text{n}}\\:{I}_{0}\\text{sin}\\left(2\\pi\\:ft\\right)+{V}_{\\text{L}\\text{U},0}\u0026rang;=\\:\\frac{{\\gamma\\:}_{0}}{2}{I}_{0}^{2}+{V}_{\\text{L}\\text{U},0}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe combined observations of quadratic output characteristics at low DC input currents and the dependence of the zero-bias curvature on the applied gate voltage suggest that quasi-ballistic rectification is a significant contributing factor to the rectification in our devices (see SI S4 for an extended discussion).\u003c/p\u003e \u003cp\u003eHowever, several other possible mechanisms could also be responsible for rectification in the devices. These include bolometric heating, photothermal effects, plasma-wave mixing\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e, modulation of the graphene resistivity with the source-drain voltage, and even the formation of a rectifying barrier at the graphene\u0026ndash;metal interface. At 20 K, the measured voltage difference increases in magnitude for both electron and hole conduction in graphene. Furthermore, the characteristic becomes more quadratic, as evidenced by an increase in curvature relative to measurements at room temperature. Since thermal effects should be strongly suppressed at lower temperatures, we can rule them out as a dominant effect in our device. Additionally, rectification is evident even at small input currents in the \u0026micro;A range, which should result in only minimal channel heating. The thermoelectric effect in a four-terminal graphene rectifier has also been numerically studied, and it was shown that the voltage induced by the Seebeck effect is orders of magnitude smaller than the voltage expected from ballistic conduction\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. Furthermore, as discussed by Auton \u003cem\u003eet al\u003c/em\u003e\u003csup\u003e21\u003c/sup\u003e, the measured polarity of the output voltage opposes that of the thermally generated voltage but matches that expected from ballistic rectification.\u003c/p\u003e \u003cp\u003eWe compared the measured output voltage to that calculated from a drift‒diffusion model\u003csup\u003e\u003cspan additionalcitationids=\"CR56\" citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e of the same rectifier. While ballistic transport is more accurately modeled via Monte Carlo\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e,\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e or atomistic models\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e, the drift‒diffusion model has been shown to yield accurate results at a much lower computational cost\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e,\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e. We find qualitative agreement between the simulated and experimental quadratic voltage outputs of a triple-funnel rectifier at room temperature (see SI S5), further indicating that ballistic rectification dominates the operation of our devices.\u003c/p\u003e"},{"header":"THZ RESULTS AND DISCUSSION","content":"\u003cp\u003eWe performed free-space measurements on the fabricated rectennas under ambient conditions at frequencies between 0.49 and 0.68 THz. These measurements allowed direct comparison with the work of Auton \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e20\u003c/sup\u003e, which, to the best of our knowledge, is the only other experimental four-terminal graphene geometric rectenna study at THz frequencies in the literature. Our measurement setup is shown schematically in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea. The input and output resistances for the single- and triple funnel devices were measured separately at DC (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eInput and output resistance values for the two types of devices studied here.\u003c/b\u003e \u003cem\u003eR\u003c/em\u003e\u003csub\u003eSD\u003c/sub\u003e refers to the resistance between the antenna terminals. The \u003cem\u003eR\u003c/em\u003e\u003csub\u003eLU\u003c/sub\u003e refers to the resistance at the DC output terminals.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSingle funnel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003csub\u003eSD\u003c/sub\u003e [kΩ]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csub\u003eLU\u003c/sub\u003e [kΩ]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e26.0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e31.5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTriple funnel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e31.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eCare must be taken regarding what power normalization is used when comparing reported THz responsivities of rectennas. Here, we report the optical voltage responsivity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\gamma\\:}_{\\text{T}\\text{H}\\text{z}}=\\:\\frac{\\pi\\:{V}_{\\text{L}\\text{U}}}{\\sqrt{2}{P}_{\\text{T}\\text{H}\\text{z}}}\\)\u003c/span\u003e\u003c/span\u003e), where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{THz}\\)\u003c/span\u003e\u003c/span\u003e is the total available power (considering only the reflection and absorption losses at the wafer and lens interfaces)\u003csup\u003e\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e, and the prefactor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\pi\\:/\\sqrt{2}\\)\u003c/span\u003e\u003c/span\u003e originates from the square-wave modulation of the input signal. The extrinsic responsivity reaches 0.21 V/W for the single-funnel rectenna and 0.77 V/W for the triple-funnel rectenna (see dark-colored points in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). In general, the effective antenna area relative to the beam spot size affects the actual incident power and thus the responsivity. Following normalization to the isotropic radiator used by Auton \u003cem\u003eet al\u003c/em\u003e.,\u003csup\u003e20\u003c/sup\u003e the triple (single) funnel device reaches an intrinsic peak responsivity of 11.8 V/W (3.3 V/W) between 0.49 and 0.68 THz (light-colored points in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The lack of significant frequency dependence indicates a broadband antenna response and device operation below its cutoff frequency, which has been estimated to reach far into the THz region\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. In contrast, additional measurements on rectennas with a shorter antenna (92 \u0026micro;m total length) show an increase in responsivity with frequency, which is consistent with their simulated resonance frequency at 0.94 THz (see Supporting Information, S2).\u003c/p\u003e \u003cp\u003eIn addition to the open-circuit voltage, we measured the short-circuit current produced by the triple-funnel rectenna under illumination to calculate a current responsivity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e analogously to the voltage responsivity reported above. The relative voltage and current responsivity (normalized to the value at the design frequency of 0.6 THz, \u003cem\u003eγ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e or \u003cem\u003eβ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. The ratio of the voltage and current responsivities (red circles in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed) agrees well with the output resistance measured at DC (31.6 kΩ).\u003c/p\u003e \u003cp\u003eRegardless of incident power normalization\u003csup\u003e\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e, the THz responsivity of the triple funnel structure is on average 4.7\u0026thinsp;\u0026plusmn;\u0026thinsp;1.5 higher than that of the single funnel structure. The increase in responsivity from the single to triple funnel rectenna can be explained by a similar increase in the coupling efficiency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\eta\\:}_{c}\\)\u003c/span\u003e\u003c/span\u003e between the antenna and the rectifier from 2.1% to 7.4%, as calculated by Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\eta\\:}_{\\text{c}}=\\frac{4{R}_{\\text{A}}{R}_{\\text{S}\\text{D}}}{{\\left({R}_{\\text{A}}+{R}_{\\text{S}\\text{D}}\\right)}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{\\text{S}\\text{D}}\\)\u003c/span\u003e\u003c/span\u003e are the real parts of the antenna and rectifier input impedances, respectively.\u003c/p\u003e \u003cp\u003eThe higher responsivity of the triple-funnel rectenna also reduces the optical noise-equivalent power (NEP) due to the thermal (Johnson‒Nyquist) noise (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:NE{P}_{\\text{J}\\text{N}}=\\:\\frac{\\sqrt{4\\:{k}_{\\text{B}}T{R}_{\\text{L}\\text{U}}}}{{\\gamma\\:}_{\\text{T}\\text{H}\\text{z}}}\\)\u003c/span\u003e\u003c/span\u003e) of the rectenna. The minimum optimal NEP calculated without normalization decreases from 108.2 to 29.2 nW/\u0026radic;Hz from a single to a triple rectifier and from 6.8 to 1.9 nW/\u0026radic;Hz with isotropic normalization (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). In these measurements, no source-drain or gate bias has been applied, and the dominant noise source is thermal noise because the output voltage is perpendicular to the input signal\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. The NEP depends on the output resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{\\text{L}\\text{U}}\\)\u003c/span\u003e\u003c/span\u003e, which was nearly equal in our single- and triple-funnel devices because their graphene channels at the output have the same length. In principle, however, adding many more rectifiers would lead to a longer output channel, which would somewhat increase \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{\\text{L}\\text{U}}\\)\u003c/span\u003e\u003c/span\u003e (which, however, tends to be dominated by the contact resistances) and thus increase the NEP accordingly.\u003c/p\u003e \u003cp\u003eConsidering the fabrication with CVD graphene, the results compare favorably with previously demonstrated geometric rectennas made from exfoliated graphene (shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Under comparable measurement and normalization conditions, our rectennas exhibit similar responsivity and NEP. Crucially, our work hence demonstrates the feasibility of achieving state-of-the-art rectenna performance using scalable materials. A significant output voltage was generated by a geometric rectenna fabricated using CVD graphene, whereas previous devices were based on non-scalable, exfoliated graphene flakes.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e Relying solely on CVD-grown graphene enables the parallel fabrication of multiple devices on a wafer-scale substrate, rather than individual devices. A feature enabled by the use of CVD graphene is the parallel fabrication of multiple devices on a wafer-scale substrate, rather than individual devices to which one is usually limited with exfoliated graphene. We also point out another novel aspect of our work. The parallel arrangement of geometric rectifiers increases the coupling efficiency between the antenna and the rectifier. This arrangement is uniquely enabled by the zero-threshold behavior of a geometric rectifier. Other rectenna systems using rectifiers with a potential barrier (i.e., mostly heterojunction diodes) usually focus only on the connection of multiple antennas to a single rectifier\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e (to increase the voltage at the rectifier input and overcome the diode\u0026rsquo;s potential barrier) or of a single antenna and rectifier\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e (for simplicity), and would not benefit from the proposed rectenna architecture. A geometric rectifier, however, does not contain a built-in potential, and it can therefore rectify even the small voltages generated by a single antenna.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eComparable geometric rectennas in literature.\u003c/b\u003e The devices investigated in this work are highlighted in green. Values are normalized to the effective antenna area (calculated from a directivity D\u0026thinsp;=\u0026thinsp;13 dBi) and the effective area of an isotropic radiator (D\u0026thinsp;=\u0026thinsp;1). *Measured at a lower frequency of 110 GHz. The area-normalized responsivity between 0.64 and 0.69 THz reaches a maximum of ~\u0026thinsp;11 V/W; thus, the calculated NEP is ~\u0026thinsp;1.85 nW/\u0026radic;Hz. Thermal noise was used to calculate the NEP.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRectenna\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBias\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFrequency [THz]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eTHz responsivity [V/W]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eNEP [nW/\u0026radic;Hz]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eRef.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003enormalization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u0026nbsp;=\u0026nbsp;13\u0026nbsp;dBi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u0026nbsp;=\u0026nbsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u0026nbsp;=\u0026nbsp;13\u0026nbsp;dBi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u0026nbsp;=\u0026nbsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTriple funnel\u0026thinsp;+\u0026thinsp;bowtie\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCVD graphene\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eunbiased\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.49\u0026ndash;0.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e11.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e29.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle funnel\u0026thinsp;+\u0026thinsp;bowtie\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCVD graphene\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eunbiased\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.49\u0026ndash;0.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e108.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle funnel\u0026thinsp;+\u0026thinsp;bowtie\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExfoliated graphene\u0026thinsp;+\u0026thinsp;hBN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003egate bias\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.07\u0026ndash;0.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e~\u0026thinsp;11\u003c/p\u003e \u003cp\u003e764*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e~\u0026thinsp;1.85\u003c/p\u003e \u003cp\u003e0.034*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003csup\u003e20\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBallistic diode\u0026thinsp;+\u0026thinsp;bowtie\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExfoliated graphene\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eunbiased\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e~\u0026thinsp;0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e43.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003csup\u003e68\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWe also want to emphasize the reproducibility of the fabrication process: Further measurements of single-funnel devices fabricated on another wafer show little variation in responsivity, indicating that the fabrication method, the doping level of graphene, and the detector alignment are consistent and reproducible (see Supporting Information, S6). Our prototype fabrication process relies on electron beam lithography. However, the critical dimensions are attainable using high-throughput nanoimprint lithography (NIL). Together with the scalable graphene material and fabrication flow demonstrated in this work, NIL could be used to fabricate entire arrays of geometric graphene rectennas with minimal per-device cost\u003csup\u003e\u003cspan additionalcitationids=\"CR66\" citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eIn this work, we demonstrated the successful fabrication and operation of geometric THz rectennas using CVD graphene suitable for wafer-scale fabrication. We achieved high coupling efficiency and compensated for the lower mobility of the CVD material by implementing a parallel connection of multiple rectifiers to a single antenna. This enabled room-temperature zero-bias rectification up to 0.68 THz (limited by the radiation source) in free-space measurements, which we expect to be mainly limited by the available THz power and frequency range of the source. Our approach shows that geometric rectification in graphene can be harnessed without relying on unscalable exfoliated materials. Consequently, our work establishes a clear path for integrating efficient THz rectifiers with established semiconductor technology, unlocking the potential of THz energy harvesting for autonomous sensors in next-generation wireless IoT networks.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003e \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eEthics approval\u003c/span\u003e \u003c/strong\u003e \u003cp\u003e \u003cspan type=\"BoldSmallCaps\" class=\"BoldSmallCaps\" name=\"Emphasis\"\u003econsent to participate\u003c/span\u003e \u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003e \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eConsent for publication\u003c/span\u003e \u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003e \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eCompeting interests\u003c/span\u003e \u003c/strong\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003e \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eSupporting Information\u003c/span\u003e \u003c/h2\u003e \u003cp\u003eSupporting information includes the following: S1) AFM images before and after graphene transfer; SEM image of a larger transferred graphene layer; Raman spectrum of the transferred graphene; S2) CST Microwave Studio model of the bowtie antennas with complex feedpoint impedance; ZEMAX estimation of the spot size behind the hyperhemispherical Si lens; measured available THz power measured with a calibrated detector; S3) details on the gated transfer-length measurements and extraction of contact resistance, sheet resistance, mobility, and mean free path; S4) discussion of alternative rectification mechanisms; S5) simulated voltage output of a triple-funnel rectifier at dc using the drift‒diffusion model; S6) measured output voltage spectrum for single-funnel and triple-funnel devices with open and blocked THz beam path, measured responsivity of additional single-funnel rectennas (92 \u0026micro;m) on an additional substrate, measured voltage output at 653 GHz under a gate voltage sweep and frequency sweeps at different gate voltages on a separate sample fabricated on lightly doped Si.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was financially supported by the European Union\u0026rsquo;s Horizon 2020 research and innovation programme under the grant agreement No. 101006963 (GreEnergy) and from the European Union\u0026rsquo;s Horizon Europe Research and Innovation Program under the 2D Pilot Line (2D-PL, Grant No. 101189797). J. H. acknowledges funding from RO 770 49\u0026thinsp;\u0026minus;\u0026thinsp;1 of the INTEREST priority program (SPP 2314). A. L. acknowledges funding from the Lithuanian Science Foundation (project No. S-MIP22-83).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA. H., Z. W., A. G., and M. L. conceived the experiments. A. H. designed the devices and performed the electrical characterization. A. H., M. M., J. B., and L. E. fabricated the devices. B. C. performed the AFM and Raman measurements. J. H., A. H., and A. L. performed the THz characterization and noise measurement. D. M. and L. P. provided the drift‒diffusion model. All the authors contributed to discussions and the analysis and interpretation of the results. A. H. wrote the initial manuscript and all the authors revised it.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors thank Dr. Andrey Generalov from VTT Finland for providing the 10 Ω\u0026middot;cm to 40 Ω\u0026middot;cm n-doped/90 nm-SiO2 wafer. The authors thank Dr. Christine Hendriks for her corrections and suggestions regarding the manuscript\u0026rsquo;s style and composition.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data supporting this study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003ePecunia V, et al. Roadmap on energy harvesting materials. J Phys Mater. 2023;6:042501.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDonchev E, et al. The rectenna device: From theory to practice (a review). 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IEEE J Sel Top Quantum Electron. 2014;20:70\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Electronics](https://www.springer.com/journal/44291)","snPcode":"44291","submissionUrl":"https://submission.nature.com/new-submission/44291","title":"Discover Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"CVD graphene, rectenna, geometric rectifier, terahertz detector, 2D materials, energy harvesting","lastPublishedDoi":"10.21203/rs.3.rs-9108655/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9108655/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUbiquitous electromagnetic radiation from wireless communication networks is an untapped energy source for low-power devices. Passive \u003cem\u003erectennas\u003c/em\u003e (a combination of a rectifier and an antenna) can harvest this energy to power devices and systems, such as autonomous sensors. Rectennas based on conventional rectifiers, however, lack the frequency response and zero-bias performance required to extend passive energy harvesting into the terahertz (THz) domain, which is crucial for Internet of Things (IoT) applications in the 6G era. In contrast, rectennas based on geometric rectifiers are ultrafast detectors that can operate without an external bias, making them ideally suited for zero-bias THz detection and energy harvesting. Geometric rectifiers require largely scatter-free, quasi-ballistic charge transport, which is typically achieved only in high-purity materials, which \u0026ndash; as in the case of mechanically exfoliated graphene \u0026ndash; may not be suitable for wafer-scale fabrication. In this work, we used commercially available graphene grown by chemical vapor deposition (CVD) to fabricate geometric rectennas and demonstrate operation up to 0.68 THz at zero bias. We employed a parallel arrangement of multiple rectifiers to increase the coupling efficiency between the rectifiers and the antennas, and thus the overall rectenna responsivity. Our results are a critical step towards large-scale fabrication of efficient geometric rectennas and enabling THz energy harvesting for low-power IoT devices.\u003c/p\u003e","manuscriptTitle":"Enhanced Coupling Efficiency in Geometric Terahertz Rectennas Based on Scalable CVD Graphene","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-01 13:20:01","doi":"10.21203/rs.3.rs-9108655/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-12T16:54:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-12T05:54:34+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-09T13:22:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"178258072394095109323590712879894150936","date":"2026-05-07T19:51:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T03:43:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"258719859908926485337172801996562430358","date":"2026-04-29T00:56:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"95595822246974059686473302973918593759","date":"2026-04-27T16:44:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"279756323916598667591868834364164302097","date":"2026-04-27T10:24:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-30T10:49:20+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-24T11:57:52+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-19T17:57:08+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Electronics","date":"2026-03-19T17:13:58+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Electronics](https://www.springer.com/journal/44291)","snPcode":"44291","submissionUrl":"https://submission.nature.com/new-submission/44291","title":"Discover Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a8dc250a-8ebd-48a4-b64e-5645be014399","owner":[],"postedDate":"April 1st, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-12T16:54:42+00:00","index":63,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-12T05:54:34+00:00","index":62,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-09T13:22:49+00:00","index":61,"fulltext":""},{"type":"reviewerAgreed","content":"178258072394095109323590712879894150936","date":"2026-05-07T19:51:11+00:00","index":58,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T03:43:07+00:00","index":36,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-01T13:20:01+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-01 13:20:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9108655","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9108655","identity":"rs-9108655","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}