Asymmetric dual-grating gates graphene FET for detection of terahertz radiations

Graphene shows unique electrical and optical properties such as high values of carrier mobility (∼10⁴ cm² V⁻¹ s⁻¹ on a SiO₂ substrate), high thermal conductivity, fast carrier relaxation, and light transparency (97.3%) among others.^1,2 These properties can be improved encapsulating the graphene sheet between two flakes of hexagonal boron nitride (h-BN) where the carrier mobility could exceed 10⁵ cm² V⁻¹ s⁻¹ at room temperature.³ In 2004, Novoselov et al.⁴ obtained and investigated the first monolayer graphene by mechanical exfoliation of bulk graphite. Since then, graphene-based devices have attracted great interest in Terahertz (THz) technology due to their potential use for different novel applications in the THz range⁵ and devices have started emerging such as THz sensors,^6,7 emitters,⁸ and modulators.^9,10 Graphene can have strong interaction with photons. Optical excitation of collective oscillations of carries, i.e., plasmons, has its response in the THz frequency range.^11,12 Furthermore, it is possible to create an inversion of the conical electronic band around the Dirac point with optical excitation.¹³ Recently, resonant plasmon response in bilayer graphene-based Field-Effect-Transistors (FETs) was demonstrated at low temperature and high THz frequencies.¹⁴ 

To couple the incoming THz radiation to a FET channel, different approaches such as using antennas,¹⁵ unequal metallization,¹⁶ asymmetrical boundary design,¹⁷ or even applying a dc current between the drain and source¹⁸ have been reported. In this work, the idea based on the use of periodic asymmetric grating gates¹⁹ is used to improve the responsivity of a graphene-based FET THz detector. FET detectors of THz radiation with asymmetric grating gates have previously proved to be highly efficient showing record values of responsivity in GaInAs/InP high-electron mobility transistors (HEMTs)^20,21 that were attributed to the spatial modulation of the plasmons under the grating fingers. Moreover, graphene-based grating structures have recently been studied as effective converters of incoming THz radiation to propagating plasmons where the asymmetric grating ensures the conservation of momentum²² and also as hybrid magneto-plasmonic structures to achieve Faraday rotation and optical transmission enhancement using a symmetric grating in the THz frequency range.²³ 

In the present paper, an asymmetric dual-grating gate graphene FET (ADGG-GFET) with a sheet of monolayer graphene encapsulated between two flakes of h-BN was fabricated. The dual aim of the vertical double heterostructure was to increase the mechanical stability and to reduce the interaction of the carriers in the graphene channel with the SiO₂/Si substrate and, hence, to enhance channel carrier mobility. The transistor was excited at different temperatures in the 4–300 K range by a two-tone THz radiation at frequencies of 0.15 THz and 0.3 THz, and a photocurrent up to 1.5 nA was measured at 4 K despite the fact that no antenna was implemented to couple the incoming THz beam. Detection of a 0.3 THz radiation at room temperature was demonstrated along with the ability of the new ADGG-GFET to be used as a THz sensor in security and imaging applications.

Both h-BN and monolayer graphene were obtained by mechanical exfoliation on a 290 nm thick SiO₂ thermally grown on a 4 in. Si wafer. A monolayer graphene flake was exfoliated from bulk graphite. Graphite flakes were first cleaved on a Scotch^TM tape and then folded into the latter several times. Since the ADGG-GFET concept requires a long channel, an additional step to the standard mechanical exfoliation method was introduced to achieve large graphene flakes.²⁴ Prior to exfoliation, SiO₂/Si substrates were exposed to oxygen plasma treatment. Finally, the graphene layer was brought into contact with the substrate and then annealed at 100 °C for 2 min before removing the tape. Relatively thick h-BN flakes were obtained from high-quality ultra-pure bulk h-BN crystals, which have been grown by the procedure described in Refs. 25 and 26. Large h-BN flakes (>40 μm length) were obtained without performing the plasma treatment of the substrate surface. Top and bottom h-BN flakes were selected to be larger than the graphene sheet to ensure that they completely encapsulate the graphene layer. Both h-BN and graphene flakes were identified first by optical contrast and then by Raman spectroscopy. The thickness of both h-BN flakes (top and bottom) was estimated to be ∼25 nm. The graphene-based heterostructure (h-BN/graphene/h-BN) was fabricated using a dry transfer technique similar to the one reported by Pizzocchero et al.²⁷ and detailed in Ref. 28, ensuring the highest quality of the graphene layer compared to other methods²⁹ since no polymers were in contact with the graphene during the assembly fabrication. Finally, the heterostructure was placed on top of a highly doped SiO₂/Si substrate. The h-BN/graphene/h-BN heterostructure was characterized by Raman spectroscopy, and an intensity ratio of around 8 between the 2D (I_2D) and G (I_G) bands in graphene was obtained showing the high quality of the encapsulated graphene sheet (see supplementary material 1).

The device geometry (i.e., channel length) was defined on the graphene heterostructure by electron beam lithography (EBL) using polymethylmethacrylate (PMMA) as a mask. Then, the heterostructure was dry-etched to define a pyramidal shape and fabricate the quasi-one-dimensional (1D) or edge contacts in an inductively coupled plasma with a SF6 atmosphere (40 SCCM, P = 6 mTorr, P = 75 W at 20 °C). Only source (S) and drain (D) accesses were opened by dry etching to ensure that the asymmetric top gates do not contact the graphene layer. A second EBL step was used to define the drain and source edge contacts,³⁰ as well as the top gates (TG₁ and TG₂), followed by electron beam evaporation of Cr/Au = 5/45 nm. Figures 1(a) and 1(b) show an optical image of the fabricated ADGG-GFET, where the two top gates were laid out to be asymmetrical between the source and drain contacts. Figure 1(c) shows the schematic 3D description of the ADGG-GFET with its geometrical parameters. The top h-BN flake was used as a dielectric for the two asymmetric top insulated-gates, and the highly doped silicon substrate was used as the back gate (BG) contact. The geometrical parameters of the grating are the following: L_G1 = 1 μm, L_G2 = 2 μm, d₁ = 1 μm, d₂ = 3 μm, s₁ = 1 μm, and s₂ = 1.5 μm, and the total source to drain distance is 25.5 μm. In ADGG structures, it is possible to excite the gated plasmons at frequencies $fp$ = ns/2L_G, where s is the plasma wave velocity in the graphene layer (with a typical value ∼10⁶ m/s), L_G is the gate finger width, and n = 1, 2, 3, etc. The geometrical parameters of the ADGG-GFET would give an effective excitation of plasmons at frequencies close to 0.3 THz (L_G2 = 2 μm) and 0.6 THz (L_G1 = 1 μm), leading to a plasmon-enhanced detection in our device and, therefore, increasing the efficiency of the detector at those frequencies.

Figure 1(d) shows the resistance between D and S contacts (R_DS) vs the BG bias voltage (V_BG) at different temperatures in the range of 300 K down to 4 K when both top gates were grounded. The charge neutrality point (CNP) was obtained for a value of the back gate bias of V_BG ≈ −5.8 V. This points toward an unintentionally n-type doping of the graphene layer. In the low temperature range (<70 K), R_DS becomes anomalous, and different small peaks emerge around the CNP. Their origin is attributed to the action of the asymmetric top gates generating different doping profiles along the channel under the gated and ungated portions of the channel. A similar behavior has been reported by Velasco et al.³¹ using an air bridge and creating different p–n–p junctions along the graphene sheet and showing two conductance minima. By fitting the measured data in Fig. 1(c) to the model presented by Kim et al.³² and reviewed by Gammelgaard et al., ³³ the carrier mobility (μ) was extracted (see supplementary material 2). Electron mobility was estimated over 60 000 cm² V⁻¹ s⁻¹ and 96 000 cm² V⁻¹ s⁻¹ at 300 K and 4 K, respectively.

A solid-state harmonic generator sub-THz source based on a dielectric resonator oscillator (DRO) with an output power of 6 mW at 0.3 THz and 3 mW at 0.15 THz was used to excite the ADGG-GFET. The source emitted power was measured close to the output of the source using a calibrated pyroelectric detector. The incoming THz radiation was modulated by using a mechanical chopper operating at 298 Hz, collimated by an off-axis parabolic mirror and focused by using a polished Tsurupika^TM lens. The device was placed inside an optical cryostat with a polyethylene window that is transparent to THz radiation. Under THz radiation excitation, a photocurrent was generated in the channel of the transistor that was measured at the drain contact using the lock-in technique while the source was kept grounded. The channel was kept unbiased throughout the THz detection measurements. Figure 2(a) shows the measured photocurrent under an excitation of 0.3 THz and 0.15 THz as a function of V_BG at 4 K. Both signals exhibit a similar behavior with an absolute maximum of photocurrent at V_BG ∼ −5.35 V. However, the photocurrent generated under a 0.3 THz radiation was considerably more intense than that generated under 0.15 THz excitation (∼20 times higher with a peak value close to 1.4 nA), exhibiting a higher signal-to-noise ratio. The higher values of the photocurrent generated for 0.3 THz excitation were attributed to a better coupling of the electromagnetic radiation to the ADGG-GFET at higher frequencies in the sub-THz range. It was theoretically and experimentally demonstrated^34,35 that the coupling of the radiation to the detector at frequencies close to 100 GHz is performed by the bonding wires, whereas at higher frequencies (>200 GHz), the contact pads and/or the gate fingers would be more efficient to couple the incoming THz radiations. Similar results were found while biasing the top gate [Fig. 2(b)] where the maximum photocurrent was found at V_TG ∼ −0.68 and V_TG ∼ −0.75 V for the excitation of 0.15 THz and 0.3 THz, respectively. The origin of the photoresponse in asymmetric grating gate based-FETs under THz radiation has been well-studied both theoretically^19,22 and experimentally,^20,21 and it is commonly attributed to plasmonic nonlinearities in the channel of the FET since these asymmetric structures ensure an efficient coupling between the incident THz radiation and the transistor’s channel plasmons.

Figure 2(c) shows the measured photocurrent generated by the incident 0.3 THz radiation as a function of V_BG in the 4–300 K temperature range. When the temperature increases, the maximum value of the photocurrent shifts toward more negative values of V_BG, its magnitude decreases, and the secondary peaks flatten out considerably. A similar behavior of the photocurrent was obtained when the experiment was carried out varying the top gate bias [Fig. 2(d)]. Nevertheless, since V_BG was kept at 0 V and only the top gate bias was modified, two maximum values of the photocurrent around ±0.7 nA were obtained at V_TG = −0.75 V and V_TG = −0.68 V. At low temperatures (4 K and 50 K), secondary peaks appear for V_TG ≈ −0.6 V and −0.9 V (see supplementary material 3). These observed peaks are predicted by theory from DC measurements and are related to the asymmetric design of the top gates. Moreover, the shape of the measured signal at 100 K is similar to the one reported on measurements of single gate graphene-based FETs^11,12 (see supplementary material 4).

Figure 3(a) gives the intensity of the photocurrent when the THz beam was switched on and off. The back-gate of the device was biased at V_BG ≈ −5.35 V, i.e., at which the photocurrent is found to be maximum at 4 K. This is a clear demonstration that the measured photocurrent is created by the THz beam as when it is switched off, the photocurrent (i.e., the dark-photocurrent) decreases to zero. This behavior was systematically observed at different temperatures from 4 K up to room temperature. Figures 3(b) and 3(c) give the room temperature photocurrent generated by THz illumination at 0.3 THz. A maximum of the intensity of approximately 30 pA (100 pA) was obtained when varying the back gate (top gate) bias. To the authors’ knowledge, this is the first clear observation of THz detection using an ADGG encapsulated-graphene FET in the low THz range without biasing the channel (neither in voltage nor in current).

The non-resonant (broadband) detection is observed for overdamped plasma oscillation inside the channel when the quality factor ωτ ≪ 1, ω is the angular frequency, and τ is the carrier scattering time given by τ ∼ μm^*/e, where e is the absolute value of the electron charge and μ is the carrier mobility. The effective cyclotron mass (m^*) of charge carriers is given by m^* = ℏk_F/v_F, where v_F is the Fermi velocity (with a typical value ∼10⁶ m/s) and k_F is the Fermi momentum (⁠$kF=πn$⁠). The charge carrier concentration is given by¹⁸ n = C_ox(V_BG − V_CNP)/e (see supplementary material 2), where C_ox is the gate oxide capacitance per unit area. The estimated value of the scattering time is 0.16 ps (4 K) and 0.09 ps (300 K). At the frequency of interest, 0.3 THz, the value of ωτ was found to be 0.37 at 4 K and 0.23 at room temperature, respectively. Under such conditions, only non-resonant detection can be observed. In the overdamped plasma-wave regime, plasmonic rectification yields to a broadband photoresponse, given by^11,20

where U_a is the induced gate-to-source ac voltage and σ is the channel conductivity. The theoretical value of the photocurrent generated by the incoming THz radiation can be obtained using Eq. (1). Although the photocurrent generated as a function of the back-gate bias cannot be fully reproduced using Eq. (1), the behavior of the photocurrent predicted by Eq. (1) as a function of the top gate bias is in good agreement with the measurements (see supplementary material 4). This could be explained by the non-homogeneous conductivity inside the channel due to both top gates (G1 and G2), back gate, and the ungated part of the channel. Even though, in this work, only overdamped regime conditions are full-filled, the quality factor, ωτ, will increase both with channel carrier mobility and with the THz excitation frequency;¹⁴ therefore, measurements under excitation at frequencies in the range 1–5 THz may reveal a resonant behavior of the response of the ADGG-GFET.

To quantify the sensitivity of our detector, the current responsivity (⁠$Ri$⁠) was extracted from the measured data using

where P is the THz power incident on the transistor (∼1 mW at the device position, measured, as mentioned above, using a calibrated pyroelectric detector). The factor $π/2$ comes from the Fourier transform of the square-wave modulated THz signal detected as its rms value by the lock-in amplifier. S_t denotes the THz beam area given by S_t = πr², where r = 1.5 mm is the radius of the beam spot at 0.3 THz (measured by using a single pixel detector), and S_a is the active area of the ADGG-GFET (≈30 × 15 μm²). The factor S_t/S_a in Eq. (2) is the inverse coupling efficiency of the THz radiation to the active device area. Thus, this definition is the so-called “internal” responsivity that is obtained under the perfect lossless coupling condition. Even if no specific antenna was used to couple the incoming THz radiation, the bonding wires and the gates/source/drain metallic pads could play an antenna role, and therefore, to avoid an overestimation on the current responsivity, let us introduce the “effective” responsivity, $Rλ$⁠, in which the active area of the device was taken as the diffraction limit area^11,36 given by S_λ = λ²/4, where λ is the wavelength of the incoming THz radiation instead of S_a in Eq. (2). The new expression of $Rλ$ has the advantage of introducing also a frequency dependence. A maximum responsivity of $Rλ$ and $Ri$ are 85 μA/W and 55.6 mA/W, respectively, obtained at 4 K [Fig. 4(b)]. Another figure of merit that characterizes the device as a THz sensor is the Noise Equivalent Power (NEP), extracted from the measured data using the following formula:

where N is the noise spectral density of the transistor in V/$Hz$⁠. Since no V_DS bias (nor a drain-to-source bias current) was applied to the channel, we assumed that thermal noise (N_th) is the only source of noise in measurements. Hence, $N=Nth=4kBTRDS$⁠, where T is the temperature and R_DS is the channel resistance. A NEP minimum value of 1.3 nW/$Hz$ was obtained at 4 K [Fig. 4(a)]. At room temperature, the values obtained for the responsivity and NEP were 1.96 μA/W (⁠$Ri≈$ 1.28 mA/W) and 0.9 μW/$Hz$⁠, respectively. Those values, as stated above, were obtained using the diffraction limit area S_λ instead of the active area of the GFET detector, needless to say that both will be better if the active area, instead of S_λ, is used in calculations. Finally, we compared the performance of our device to the ones of other “plasma-waves” graphene-based THz sensors. The first graphene-FET, with a log-periodic circular-toothed antenna, was reported by Vicarelli et al.¹¹ with a maximum responsivity of ≈2 μA/W (0.05 V/W) at 0.3 THz. Later, bilayer graphene-FETs with bow-tie and log-periodic circular-toothed antennas³⁷ were used as broadband THz detectors, achieving a maximum responsivity of 1.3 mA/W at 0.358 THz. Degl’Innocenti et al.³⁸ and Zak et al.¹² reported maximum current responsivities of 34 μA/W at 2 THz and 5 mA/W at 0.6 THz, respectively, using CVD graphene-FETs with bow-tie antennas. Therefore, the “internal” responsivity of our device shows very competitive values without the implementation of an antenna with respect to other “plasma-waves” graphene-based THz detectors and even other THz detector technologies.²¹ Even the “effective” responsivity (i.e., worst case scenario) and NEP of our device are comparable with other equivalent room temperature graphene-FET THz detectors.^11,38 These parameters could be significantly improved introducing an antenna for efficient coupling of the THz radiations, by reducing the access resistance and by increasing the active area of the device with additional fingers. Moreover, the use of external elements integrated with the antenna such as aspheric focusing silicon lenses³⁹ or mesoscale dielectric particle lenses⁴⁰ would help to collect the THz radiation into the detector and, therefore, increase the performance of the device without the use of an on-chip antenna.

Finally, to demonstrate the ability of the ADGG-GFET in a real application, the transistor was used as the sensor of a room temperature imaging system at 0.3 THz. More information about the THz imaging system can be found in Ref. 34. A cutting blade [Fig. 5(a)] was placed inside a packaging material (in our case, a simple paper envelope) and irradiated by a 0.3 THz beam. A pixel-by-pixel THz image was obtained using a XY moving stage [Fig. 5(b)]. The THz radiation passes through the envelope containing the hidden blade, and its transmitted power is measured by the ADGG-FET that was gate voltage biased as V_BG = 0 V and V_TG = −0.8 V where a maximum intensity of the photocurrent was obtained. Using higher THz frequencies would improve the resolution of the THz images. The small footprint of the ADGG-GFET, unlike the one of FETs with an integrated antenna, would allow the integration of several ADDG-GFETs in multipixel array cameras.

A graphene-based field-effect-transistor with asymmetric dual-grating gates was fabricated and characterized under terahertz radiation at 0.15 THz and 0.3 THz. The graphene sheet was encapsulated between two flakes of h-BN and placed on a highly doped SiO₂/Si substrate, providing extremely high electron/hole mobilities around 60 000 cm²/V s and 100 000 cm²/V s at 300 K and 4 K, respectively. The area of the asymmetric dual-grating gate is 30 × 15 μm², far smaller than the diffraction-limited area, which was implemented on the h-BN top flake to efficiently excite the graphene Dirac plasmons and the resultant radiation rectification effect. Even though no antenna was used to couple the incoming radiation, a clear gate-bias-dependent photocurrent was measured under excitation at 0.3 THz and from 4 K up to room temperature, demonstrating high internal responsivities of up to 55.6 mA/W at 4 K. By using the fabricated detector, we successfully demonstrated high-contrast and high-spatially resolved terahertz sensing, promising inspection and security applications even at room temperature.

See the supplementary material for additional information on graphene characterization by Raman spectroscopy, ADGG-GFET electrical characterization, and estimated holes and electrons mobilities along with theoretical and experimental temperature dependent studies of the THz response at 0.3 THz.

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

This research was supported by the Agencia Estatal de Investigación of Spain (Grant Nos. MAT2016-75955, TEC2015-65477-R, and RTI2018-097180-B-100), the Junta de Castilla y León (Grant No. SA256P18), including funding by ERDF/FEDER and the JSPS KAKENHI (Grant No. 16H06361). J.A.D.N. thanks the Japan Society for the Promotion of Science (JSPS) for supporting him as an International Research Fellow. Growth of hexagonal boron nitride crystals was supported by the MEXT Element Strategy Initiative to Form Core Research Center, Grant No. JPMXP0112101001, and the CREST (Grant No. JPMJCR15F3), JST.