Article pubs.acs.org/journal/apchd5
Loading the Antenna Gap with Two-Dimensional Electron Gas Transistors: A Versatile Approach for the Rectification of Free-Space Radiation Valeria Giliberti,†,‡ Simone Panaro,§ Andrea Toma,§ and Michele Ortolani*,† †
Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy Center for Life NanoSciences, Istituto Italiano di Tecnologia (IIT), Viale Regine Elena 291, 00161 Roma, Italy § Nanostructures Department, Istituto Italiano di Tecnologia (IIT), 16163 Genova, Italy ‡
S Supporting Information *
ABSTRACT: Light conversion into dc current is of paramount interest for a wide range of upcoming energy applications. Here we integrated dipole antennas with field-effect transistors based on a two-dimensional electron gas, with the specific aim of rectifying freespace radiation exploiting both artificial and natural nonlinearities. In the present work, resonant conditions of antenna-coupled field-effect rectifiers have been identified in a terahertz experiment based on the well-established GaAs transistor technology. Rectification of free-space radiation has been observed in a broad 0.15−0.40 THz range by implementing quasi-optical coupling with a substrate lens to an AlGaAs/GaAs heterostructure transistor into the gap of a cross-dipole antenna. The short- and the opencircuit resonances have been clearly identified through a comparison between experimental photocurrent spectra, electromagnetic simulations, and antenna models. The former depends only on the dipole antenna geometry, while the latter is determined by the impedance matching between the antenna and the integrated device and, as such, can be even tuned to the desired frequency by applying a dc gate bias. In addition, the high-mobility two-dimensional electron gas supports plasma wave cavity resonances featuring natural hydrodynamic nonlinearity. The resonant peaks corresponding to the different rectification mechanisms have been identified and discussed in terms of simple lumped-element models. The demonstrated concepts are extrapolated toward infrared frequencies, where novel application demands and novel two-dimensional electron gas materials for antenna-coupled rectifiers are emerging. KEYWORDS: antenna loading, rectifier, two-dimensional electron gas, field-effect transistor, optoelectronics from both open-circuit resonances (where the field enhancement in the gap is maximum) and short-circuit resonances (at which maximum ac current flows in the loading device). The experimental verification of the aforementioned RF concepts extended to the optical regime, however, is not so straightforward,28−30 due to both the non-negligible kinetic inductance of the metals used for the antenna structures and the difficulties in the experimental determination of the load impedance at optical frequencies.31−33 Therefore, the interaction between an optical antenna and its loading device in a broad band of frequencies to identify open- and short-circuit resonances is something that deserves further joint experimental and numerical investigations. Within this context, field-effect devices based on emerging two-dimensional electron gas (2DEG) materials such as graphene and transition-metal dichalcogenides may open new avenues for realizing nanoscale rectifier/detector architectures in the optical regime.27,34−36 The field-effect transistors (FETs) possess by definition built-in artificial nonlinearity, which is especially useful for studying the coupling between antenna and loading devices, because the conductivity of the device can be
I
n the past decade, many experimental investigations of optical antennas appeared in the literature, at electromagnetic frequencies ranging from the ultraviolet1 down to the mid- and far-infrared.2−6 Huge field-enhancement factors have been demonstrated, especially in the antenna gaps,7 envisioning a clear-cut perspective in sensing,8−11 nonlinear spectroscopies,12−14 and radiative decay control.15,16 In a different class of optical antenna systems, the antenna gap contains an electronic device possessing free charge carriers that can conduct both ac and dc electrical currents. These systems include antenna-coupled radiation detectors,17−20 where dc signals proportional to the radiation power can be measured with large output bandwidth,21 and antenna-coupled rectifiers of optical fields for energy-harvesting applications,22 where ac (radiation) to dc power transfer takes place.23 When detectors and rectifiers are illuminated with a monochromatic free-space radiation beam, the free charge carriers in the device are accumulated preferentially at one side of the antenna gap due to nonlinear mechanisms (usually a junction diode), and therefore a dc current (or voltage) is extracted. The frequency positions of antenna resonances, which determine the conditions of optimal detector/rectifier performance, have seldom been discussed.24−27 In the RF regime, the dc signals extracted from antenna-coupled detectors/rectifiers can result © 2017 American Chemical Society
Received: November 14, 2016 Published: March 9, 2017 837
DOI: 10.1021/acsphotonics.6b00903 ACS Photonics 2017, 4, 837−845
ACS Photonics
Article
tuned by applying an external dc gate bias. Moreover, 2DEG materials possess natural plasma wave nonlinearities with very high-frequency cutoff,37 providing a third mechanism for obtaining dc signals (optical rectification), eventually amplified by nanoscale resonant plasma wave cavities in high-mobility 2DEGs.38 These artificial and natural nonlinearities are preserved even at frequencies well beyond the so-called transistor cutoff frequency; therefore operation of microwave FETs as rectifiers and detectors in the terahertz (THz) band has been widely reported.17−20,39−41 Traditionally, microwave FET fabrication technologies have been employed, mostly based on GaAs and GaN 2DEG heterostructures. The main technology challenge for having infrared and optical FET rectifiers is to scale down the FET dimensions to the optical antenna gap size, but the new 2DEG materials are very promising in this respect. Impedance matching of 2DEG FETs to antennas, and the consequent identification of open- and short-circuit resonances, has not been clearly demonstrated yet, not even in the THz band, where antenna impedances can be straightforwardly calculated, mostly due to the difficulty of modeling a nanoscale FET with few lumped elements.19 FET impedance modeling becomes even more complicated in the resonant plasma wave regime, which is reached at low temperatures for GaAs heterostructures and even at room temperature for ideal graphene sheets. In this work, we have numerically simulated the electromagnetic behavior of a terahertz cross-dipole antenna coupled to a generic 2DEG material, and a rectification experiment has been carried out by fabricating the cross-dipole antenna integrated with a 2DEG field-effect device, based on a highmobility 2DEG AlGaAs/GaAs heterostructure. The device works as rectifier in the sub-THz range (0.15−0.4 THz), at frequencies high enough that free-space radiation coupling is feasible on a small laboratory bench and low enough that load impedances can still be estimated with lumped-element models. The broad frequency range exceeding one octave has been reached by implementing quasi-optical coupling techniques, in which an integrated on-chip antenna is positioned in the focus of a substrate lens, hence making the microelectronic device behave like an optical detector/rectifier. The present work aims to identify resonant conditions of antenna-coupled 2DEG FETs in a sub-THz experiment by exploiting the well-established GaAs transistor technology, so as to extrapolate the demonstrated concepts toward infrared frequencies, where novel application demands and novel 2DEG materials for antenna-coupled rectifiers are emerging.17,21,22,34
Figure 1. Device concept. (a) A cross-dipole antenna, made of two orthogonal dipoles of length d, is coupled to the three terminals (source, drain, and gate) of a field-effect device based on a 2DEG (here indicated by the light blue square in the gap of the x-oriented dipole). The gap of the y-oriented dipole is connected to the source and gate terminals, with a gate electrode of length LG. The metal− semiconductor gate junction is of the Schottky type and rectifies both ac fields and currents. The gap of the x-oriented dipole is connected to the source and drain terminals and forms a microcavity of length LSD for 2D plasma waves displaying natural nonlinearity for optical rectification. (b) Electron microscope image of one of the devices fabricated with the GaAs field-effect transistor technology for operation in the 0.15−0.40 THz range (zoom-in panel e). Here, d = 180 μm, LSD = 10 μm, and LG = 500 nm. (c) Electric field distribution map in the gap of the cross-dipole antenna calculated for E//x at the short-circuit resonance frequency of the x-oriented two-arm dipole. (d) Same as (c) but for E//y and the y-oriented two-arm dipole: note the different maximum of the color scale. In the simulations, the 2DEG was modeled as a doped semiconductor layer with resistance per unit area equal to that of the 2DEG. (e) Electron microscope image of the cross-dipole antenna gap.
break the source−drain symmetry that would have prevented the formation of a net rectified current flux for E//x.40 The cross-dipole antenna in Figure 1a was fabricated on a GaAs heterostructure chip choosing d = 180 μm and implementing a field-effect GaAs transistor in its gap (see Methods, scanning electron micrograph shown in Figure 1b and e). We performed electromagnetic simulations of the cross-dipole antenna in the 0.15−0.40 THz range, where the experiment was performed. The 2DEG was modeled as a doped semiconductor layer with resistance per unit area equal to that of the GaAs heterostructure material.43 In Figure 1c (1d) we report the electric field intensity map calculated for E//x (E//y) at the short-circuit resonance frequency of the x-oriented (y-oriented) two-arm dipole νsc1, i.e., the frequency when the linear antenna acts as a half-wave dipole and the current in the antenna gap is maximum. The expected value of νsc1 for our geometry is νsc1 = 0.32 THz (see the calculation below). The electric field distribution is almost identical for the two polarization directions, indicating that the two orthogonal dipoles can be considered as independent from each other and are selectively excited when the radiation polarization is parallel to the given dipole axis. It is also worth noticing that the field intensity in the cross-dipole gap weakly depends on the y-coordinate, even if the gate electrode is attached to only one of the dipole arms of the y-oriented antenna. This indicates that the electromagnetic problem in the cross-dipole gap is almost one-dimensional (x-dependent), allowing us to construct a lumped-element model in which the electromagnetic radiation operates as an ac voltage source for the parallel impedance of the dipole antenna and the conducting device. This procedure may seem obvious to do
■
RESULTS AND DISCUSSION The main feature of antenna-coupled field-effect devices is that they have three terminals (source, drain, and gate, or even more gate electrodes, see, e.g., ref 38); therefore a simple dipole antenna gap is not sufficient to selectively couple the radiation to all device terminals.19,20,39−41 The minimal antenna structure would be a trimer,41,42 i.e., a dipole connected to the source and drain terminals plus a third identical arm connected to the gate and orthogonal to the source−drain dipole. The design selected here instead is a cross-dipole antenna (Figure 1a), where a fourth arm is added in front of the third to obtain higher symmetry between the two orthogonal electric-field polarization directions E//x and E//y. To this aim, the total dipole length d is kept identical for the two antenna axes, while the two gaps are inevitably of different length. The gate electrode is asymmetrically positioned within the 2DEG channel in order to 838
DOI: 10.1021/acsphotonics.6b00903 ACS Photonics 2017, 4, 837−845
ACS Photonics
Article
probed just below the gate electrode, which is assumed to be proportional to the ac current through the gate junction (see Methods). For both E//x and E//y, there is clear resemblance between experiment and simulation concerning the main peak position at 0.18 and 0.30 THz, although the relative peak height does not perfectly match. The peak centered at 0.30 THz is present in the experimental data and in the simulations for both polarizations, and it can be safely identified as the f irst shortcircuit resonance of the two-arm dipole antenna. Indeed, the frequency of such resonance for an isolated dipole antenna of length d = 180 μm printed on GaAs is expected at νsc1 = c/ (2d[(ε1 + ε2)/2]1/2) = 0.320 THz, where one considers the effective dielectric constant generated by the two half-spaces made of GaAs (ε2 = 12.56) and vacuum (ε1 = 1.00).44 As already highlighted in the description of Figure 1c,d, the fact that the short-circuit resonance is found at the same frequency in the simulations for both E//y and E//x with an almost identical electric field distribution in the cross-dipole antenna gap confirms that the two orthogonal dipole structures can be approximately considered as two independent dipole antennas. The slight difference in the experimental values (0.297 THz for E//y and 0.305 THz for E//x) may be due to the different gap length. The simulated spectra in Figure 2a and b display a second maximum at 0.18 THz, which is also present in the experimental spectra. As confirmed by the near-field intensity maps calculated at 0.18 THz (see Supporting Information S1), this peak may be attributed to geometric resonances of the long dc bias lines (see Figure 1b) working as “unintentional antennas” with their own short-circuit resonance at vsc0 = 0.18 THz.45,46 The intensity mismatch between simulations and experiment in Figure 2b at vsc0 is probably due to unavoidable inhomogeneity of the THz illumination outside the diffractionlimited spot size in the experiment. The extra peak around 0.36 THz observed in the experiment for E//y is not present in the simulated ac current spectrum, and it will be discussed further on in this paper. The second type of resonances in our terahertz device is related to the natural 2D material nonlinearity. In Figure 3, the ΔqSD(ν) spectrum taken with E//x and Vg such that the 2DEG density under the gate n2D,g = n2D,0 = 2.2 × 1011 cm−2 (where n2D,0 is the 2DEG density in the absence of a gate electrode) is plotted together with the simulated ac current spectrum of Figure 2a. The illumination condition and the experimental configuration are sketched in Figure 3b. Peaks at vsc0 = 0.18 THz and vsc1 = 0.30 THz in ΔqSD(ν) are generated by ac current rectification in the Schottky-gate junction (even in SD output coupling, as demonstrated by dc circuit analysis). The three extra peaks in ΔqSD(ν), marked in Figure 3a by gray arrows and partly overlapping with the short-circuit resonances, are instead due to distributed nonlinear down-conversion of THz radiation by three 2D resonant plasmon modes of the microcavity of length LSD = 10 μm, as described in ref 47. Briefly, at the microcavity resonant frequencies both the 2D electron density modulation and the nonlinear conversion efficiency related to hydrodynamic motion of electrons are maximum. The rectified signal is the result of integration along x over the entire 2DEG channel (distributed rectification, contrasted to local rectification by the junction). As in any nonlinear medium, a nonzero ac electric field intensity is required inside the 2DEG, while short-circuit antenna resonances ideally correspond to zero ac electric field in the antenna gap. Therefore, as observed, the positions of the natural nonlinearity peaks do not correspond to any pure
numerically for sub-THz antennas, but it is not trivial in the case of transistor loads;19,20 therefore we have performed a spectroscopic experiment on the fabricated device. In the experiment, we constructed a quasi-optical lens− antenna coupling fixture that allows illumination of the device of Figure 1b with free-space optical beams of frequency tunable in the broad 0.15−0.40 THz range and power level effectively coupled to the antenna around 1 μW in the entire frequency band, considering only the fundamental Gaussian mode propagation (see Methods). The integrated metal antenna transforms the incoming electromagnetic plane waves into ac field patterns and ac currents in the gap, and the different nonlinearities of the 2DEG field-effect device produce different types of dc charge displacement signals either at the source− gate port, ΔqG(ν), or at the source−drain port, ΔqSD(ν) (see Methods). We performed spectroscopy of these signals for the two orthogonal electric field polarization directions E//x (parallel to the channel direction) and E//y (orthogonal to the channel direction). In Figure 2a,b, the experimental
Figure 2. Short-circuit resonances. (a) Comparison between experimental source−gate ΔqG light-induced spectrum (continuous line) and simulated spectrum of the ac current below the gate electrode Iac (dashed line) for E//x. The ΔqG spectrum has been obtained for a 2DEG density under the gate n2D,g = n2D,0 = 2.2 × 1011 cm−2 (where n2D,0 is the 2DEG density in the absence of a gate electrode). The position where Iac has been calculated is indicated by the red dot in the sketches of the xy and yz cross sections reported on the left. (b) Same as (a) but for E//y. (c) Sketch showing the polarization directions (E//x, red arrow, and E//y, black arrow) and the experimental configuration corresponding to the spectra ΔqG in panels (a) and (b). (d) Trend of the z-component of the ac electric field Ez versus z across the gate−semiconductor junction for E//x (red curve) and E//y (black curve). The two curves have been obtained assuming that the electric field below the gate electrode is almost entirely directed along the z-direction (E ≈ Ez) and using the values provided by the electromagnetic simulations for the electric field E on the gate electrode (Figure 1c,d) and at the 2DEG level, i.e., just below the gate electrode (a, b).
spectrum ΔqG(ν) is reported respectively for E//x and for E//y (see Figure 1c for a sketch of the experimental conditions). The signal ΔqG(ν) is produced by the rectification of ac current flow through the Schottky-type gate junction provided by the z-component of the ac electric field below the gate electrode expected to be nonzero for both E//x and E//y (see the plot in Figure 2d). In Figure 2a,b, we also report the simulated spectrum (dashed curves) of the field intensity 839
DOI: 10.1021/acsphotonics.6b00903 ACS Photonics 2017, 4, 837−845
ACS Photonics
Article
Figure 3. Plasma wave cavity resonances. (a) Comparison between experimental spectrum of the source−drain dc signal ΔqSD obtained for E//x and n2D,g = 2.2 × 1011 cm−2 (yellow curve) and the simulated ac current Iac (red dashed curve, same as in Figure 2a). The gray arrows indicate the frequency position of the plasma wave cavity modes according to the finite element modeling simulations of the hydrodynamic motion of 2D electrons in the microcavity of length LSD = 10 μm.47 The plasma wave peaks are made more evident in the violet curve in the bottom panel, obtained by subtracting from the ΔqSD two Lorentzian peaks centered at νsc0 and νsc1. (b) Sketch showing the polarization direction and the experimental configuration corresponding to the ΔqSD spectrum curve in (a).
Figure 4. Open-circuit resonance. (a) Image plot of the experimental source−gate dc signal ΔqG for E//y as a function of the frequency and of the carrier density below the gate electrode n2D,g. The gray curves superimposed in the plot are selected ΔqG spectra obtained for n2D,g < 0.5 × 1011 cm−2 and n2D,g = n2D,0 = 2.2 × 1011 cm−2. (b) Sketch showing the polarization direction and the experimental configuration corresponding to the ΔqG spectra in (a) obtained by varying the dc gate bias Vg. (c) Dependence on n2D,g of the frequency of the peaks in ΔqG related to the short-circuit resonances νsc0 (light blue curve) and νsc1 (violet curve) and to the open-circuit resonance (yellow curve). There is a vertical offset of the curves in order to compare the frequency shift for the three peaks.
antenna resonance (indeed, they do not match νsc0 = 0.18 THz and νsc1 = 0.30 THz); rather they depend on the device geometry (through LSD) and dispersion relations (through n2D,0 and n2D,g), thus providing an extra degree of tunability (via Vg) as described in ref 47. Hereafter, we are investigating the open-circuit resonance, which results from the opposite imaginary impedance condition between the dipole antenna and the loading device (antenna reactance equal in value and opposite in sign with respect to the load reactance).28 At odds with classical conjugate impedance match, where real parts of antenna and load impedance are equal and power transfer from the radiation is maximized, in the open-circuit resonance as defined in refs 28 and 29 only the (necessary but not sufficient) condition of opposite imaginary impedance of antenna and load is met. In the open-circuit resonance, an ac electric potential difference is applied to the Schottky junction in the gap48−50 and a rectification peak is expected in the experimental spectrum. Indeed, the peak at 0.36 THz (Figure 2b, E//y) can be safely attributed to the opencircuit resonance of the y-oriented dipole. This resonance does not appear in the simulated spectra of Figure 2b, because the 2DEG reactance was not implemented in the device model, due to complexity of the existing 2DEG material models at optical frequencies.51,52 The peaks in the simulated spectra of Figure 2a and b indeed represent short-circuit antenna resonances only, defined as the frequency of zero reactance of the antenna.28 A further corroboration of the interpretation in terms of shortcircuit and open-circuit resonances in the experimental spectra of Figure 2a and b has been obtained by varying the load impedance in our antenna-coupled device by changing Vg and, consequently, n2D,g. In Figure 4 we report the normalized intensity of ΔqG for E//y in a color plot as a function of ν and n2D,g. Therein, the frequency of the peaks at 0.18 and 0.30 THz is almost constant, as expected for short-circuit resonances
since ideally they do not depend on the antenna load impedance. On the contrary, the peak around 0.36 THz redshifts with decreasing n2D,g, in accordance with an open-circuit resonance behavior. A simplified lumped-element model can be introduced in order to interpret the observed open- and short-circuit antenna resonances, including the gate-bias tuning of the open-circuit resonance frequency. The frequency-dependent input impedance Zin of an antenna is defined as the ratio between the driving voltage difference and the total (conduction and displacement) current flowing in the antenna and load.28,29 We consider an ideal gapless dipole impedance Zdip = Rdip − iXdip and a complex load impedance Zload = Rload − iXload. The short-circuit resonance is where Xdip(ν) = 0, while the opencircuit resonance is where Zin is maximum, i.e., at νoc defined as the frequency position of the open-circuit resonance where Xload = −Xdip. In our model, Xdip(ν) plotted in Figure 5 (thick black line) was obtained with the standard half-wave dipole formula by imposing the short-circuit resonance condition Xdip(νsc1) = 0 at the experimental value obtained for E//y. For calculating Xload, we used an equivalent RLC model where the gate-channel capacitance C is independent on gate bias (hence on n2D,g), while the resistance R and inductance L are both given by the sum of a constant term and a term that decreases with increasing n2D,g, according to the relations
R = R 0 + R1(n2D,g ) L = L0 + L1(n2D,g )
(1)
The carrier-dependent terms R1(n2D,g) and L1(n2D,g) can be assumed as the electron resistance and kinetic inductance of the 2DEG channel below the gate electrode that are defined by the 840
DOI: 10.1021/acsphotonics.6b00903 ACS Photonics 2017, 4, 837−845
ACS Photonics
Article
radiation and/or the electric field in the 2DEG channel for exploitation of natural nonlinearity. Indeed, the geometrical design of the 2DEG FET channel (values of LG, LSD in Figure 1e, channel width, gate electrode position) may be varied to change the equivalent circuit parameters. Clearly, the FET architecture provides a versatile approach to efficient rectifiers of free-space radiation. The usefulness of impedance matching between antenna and load can be appreciated by performing a quantitative comparison of the responsivity values of the present device with those of the state-of-the-art of microelectronic detectors in the 0.3−0.4 THz band, currently represented by Schottky barrier diodes (SBDs) fabricated on n-type GaAs epitaxial layers. This comparison is a very fair one, as both the material availability and the cost of the fabrication technology of our GaAs transistor detector are comparable to that of GaAs SBDs. For the comparison, we choose the quasi-optical zero-bias detectors from Virginia Diodes Inc.,63 which are mounted with a silicon lens in a package similar to ours; therefore we can assume that optical coupling losses and chip-to-lens alignment errors are similar. Also, we compare our devices to a graphene FET tested as rectifier at 0.6 THz.19 The voltage responsivity, as defined in ref 19, is reported in Table 1 for SBDs and for the
Figure 5. Tuning of the open-circuit resonance. Calculated reactance spectrum in the range of interest of the ideal gapless dipole (black) and of the equivalent RLC antenna load for two different values of n2D,g (dark blue and light blue). The curve indicated by gray markers superimposed on the plot is the experimental ΔqG spectra obtained for n2D,g = n2D,0 = 2.2 × 1011 cm−2. The orange vertical lines indicate the frequency of the open-circuit resonance where the dipole and the load reactance are equal in absolute value but of opposite sign for the two different values of n2D,g.
relations R1(n2D,g) = b/n2D,g and L1(n2D,g) = c/n2D,g where b and c depend on the geometric parameters of the channel and on the heterostructure material.53 Within this model, Zload is that of an RLC parallel circuit, where Xload(ν) crosses zero at ν0 = 1/ (2π(LC)1/2). Therefore, the value of ν0 as well as the value of Xload(ν) at any ν can be adjusted by changing Vg and hence n2D,g. In Figure 5 we plot Xload for two different values of n2D,g where we used C = 0.16 fF and effective values of R and L that reproduce the lowest (light blue curve: R = 2.5 kΩ, L = 1.4 nH) and highest (dark blue curve: R = 2.4 kΩ, L = 1.3 nH) peak position of the open-circuit resonance seen in Figure 4. As can be seen in Figure 5, the open-circuit position νoc (vertical orange lines) blue-shifts with increasing n2D,g. We note that, while rectification by antenna-coupled devices is currently achieved in terahertz Schottky diodes50 and overdamped plasma-wave detectors based on 2DEGs,54 their equivalent circuit is an RC circuit, not a RLC one. Adjustment of the open-circuit resonance frequency is possible only by physically adding an inductive metal element in the antenna gap.31,55 For example, the fact that the open-circuit resonance is seen in Figure 2b for E//y and not in Figure 2a for E//x is due to the large series inductance of the thin, long gate electrode contributing to L0 for E//y, which is instead absent for E//x. The open-circuit resonance for E//x is then probably at much higher frequency outside the measurement range. Field-effect devices with inductance L1 depending on n2D,g instead display dc tunability of the resonance frequency, as already observed in the RF range.56 The 2DEG inductance at terahertz frequencies was fully considered in ref 38 beyond the simple kinetic inductance formula used here for L1(n2D,g), and it could be implemented in advanced simulations. In summary, the terahertz experiment demonstrates the full validity of the optical antenna theory of refs 28 and 29 in describing the shortcircuit and the open-circuit resonances of an antenna-coupled field-effect rectifier. It is therefore worth considering 2DEGbased antenna-coupled rectifiers with some degree of frequency tunability and exploring the high-frequency physical limits of this strategy. The lumped element model developed above and the device tunability with Vg may prove very useful for future optimization studies aiming at maximizing the power transfer from free-space
Table 1. Performance Comparison of Quasi-Optical SubTHz Rectifying Detectors quasi-optical detectors
