1. Introduction

The Terahertz (THz) frequency range has drawn an increasing interest over the last decade, owing to its potential in a number of key applications such as biomedical diagnostics and homeland security where the advantages arising from the non-ionizing nature of THz rays and their capability to penetrate some specific materials like paper, clothes, etc. can be fully exploited [1]. Moreover, THz radiation allows detecting substance-specific spectroscopy features with a sub-millimetric diffraction-limited resolution, therefore becoming very attractive for non-destructive quality and process control and for environmental monitoring implementations [2].

The lack of a sensitive, fast, low-cost and portable room-temperature (RT) detector technology is one of major constrain for the full exploitation of THz technology. Among the commercially available uncooled THz detectors, Golay cells and pyroelectric sensors although operating in a quite broad frequency range (0.1-5 THz) show slow response rates limited by their thermal-time-constant to frequencies in the 10-400 Hz range [3]. Schottky diodes can, on the contrary, easily reach response times ≈10⁻⁹ sec, but their responsivity performance shows a dramatic drop above 1 THz [3].

The huge effort for the realization of compact and sensitive RT THz detectors has recently led to the development of a novel class of fast electronic devices based on high-electron-mobility transistors (HEMT) or Field Effect Transistors (FETs) [4, 5]. These devices behave like THz detectors once exploiting the nonlinearity arising from the simultaneous modulation of carrier drift velocity and channel carrier density by the optical incoming beam induced oscillations of the gate and source (or drain) potentials. By employing III-V materials HEMT, or FET THz detectors showing fast response times (~2 µs [3,6,7]) and high detectivities (NEP ≈10⁻¹⁰ W/√Hz [8, 3]) across the sub-THz and THz spectral range have been realized. The same approach has also been employed for the realization of top-gated graphene FETs [9] and lateral-gate InAs nanowire (NW) one-dimensional FET detector [10,11], showing impressive detection performances in the 0.3 – 3 THz range with a responsivity R_ν larger than 50 V/W [12], NEP < 100 pW/√Hz, and response times ≤ 5 μs [11].

THz detection in the channel of a FET was first predicted in the early 1990's in the Dyakonov-Shur plasma-waves theory [13, 14], according to which a FET hosting a 2D electron gas can act as a cavity for plasma waves (collective density oscillations). With proper antenna architectures the THz field at frequency ν creates an ac potential between gate (G), source (S) and drain (D) electrodes. The simultaneous modulation of the carrier velocity and carrier density in the transistor channel is an essential requirement for the rectification. A correct asymmetrical arrangement of coupling leads to a net dc voltage between S and D electrodes and the subsequent THz radiation detection. The rectified dc signal is then converted in a continuous source-drain voltage (Δu) or current (Δi) with an amplitude proportional to the intensity of the THz beam: THz radiation excited plasma oscillations can either propagate in the channel (2πντ >1) (high frequency regime - plasma waves) or be damped (overdamped plasma waves) [13]. If THz radiation coupling to the transistor is frequency independent the rectification related to overdamped plasma excitations leads always to broadband THz detection.

In their present implementations NW-FETs operation has been experimentally proven to be essentially broadband at RT. However, the frequency behavior of the devices can be in principle controlled by means of a specific antenna design. A narrow-band antenna can indeed add resonances to the spectral response of an otherwise broadband detector, ideally filtering out the non-resonant components. THz detectors showing a resonant response can be extremely useful for detection applications involving spectral signatures of molecules or absorption by wet tissues. Despite this, antenna-integrated devices with highly resonant characteristics have not been explored so far for THz detection experiments using FETs.

Electrically resonant structures in the THz range have recently gained large interest for the possibility to tailor the response of conventional dielectric materials in order to “create” properties usually unachievable in nature [15]. Some peculiar characteristics of the metamaterials have then been employed in THz photomixing experiments [16].

In the present work, we demonstrate how the properties of resonant metamaterials can be imported in the detection scheme of a NW-based FET, making resonant its response to THz radiation.

2. Sample design and implementation

Following the approach described in [10] we have developed lateral gate InAs nanowire FETs which are now coupled to the free space THz radiation via the planar split-ring like four-leaf-clover-shaped (FLCS) antennas schematically sketched in Fig. 1(a). The antenna dimensions have been tailored to make the detector resonant with an incoming air-propagating beam having wavelength λ = 1mm, so that [16]: λ = 2[(D_x + D_y)-(G_x + G_y)-1.5w] where D_x and D_y are the lateral dimensions of the antenna in the direction perpendicular and parallel to the polarization of the incoming beam, respectively, G_x is the gap between the antenna axis and the lateral arms, G_y the distance between the two lobes (namely between S and G contacts) and w is the physical width of the metal line constituting the antenna [15]. The proposed FLCS antenna has impedance (Z) at resonance ~5 times larger than the corresponding full-wavelength single- and double- dipole (1800 Ω for the FLCS, 200 - 300 Ω for a full-wavelength dipole) [17], therefore potentially helping to improve the matching with the transistor. Moreover, this novel antenna has a higher quality (Q) factor and an extremely narrower bandwidth. Figure 1(b) shows the optical microscope image of the FLCS FET device.

 

Fig. 1 (a) Schematic of a four-leaf-clover-shaped antenna. The employed geometrical parameters are: D_x = D_y = 330 μm, G_x = G_y = 44 μm, w = 11 μm; they set the resonant frequency at ≈0.3 THz. (b) Optical image of the detector layout.

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In order to determine the expected resonance of the implemented THz FET we performed frequency domain finite element method (FEM) simulations using a commercial software (COMSOL Multiphysics). In the model, as in our experiment, the detector is placed on a silicon substrate with a 300 nm thin top layer of SiO₂ and the THz beam impinges from the free space onto the antenna. An electromagnetic plane wave with electric field amplitude 1 V/m, polarized along the y-axis (Fig. 1(a)) is assumed here to correspond to the background electric field E, which induces currents over the whole metallic surface. This latter current produces, in turn, an electric field whose y-component is in the region between the two antenna lobes. The electric field can be assumed to be equal to the ac THz voltage between G and S responsible for the generation of the photoresponse. Our simulations predict that (i) in order to obtain resonance at a frequency ν₀ = 0.3 THz the geometric parameters of the FLCS antenna have to be set at D_x = D_y = 330 μm, G_x = G_y = 44 μm and w = 11 μm; (ii) the FWHM (Full Width at Half Maximum) of the resonance is about 15 GHz, corresponding to ≈5% of the resonant frequency ν₀. Fig. 2(a) shows the antenna absorption cross section (σ_abs) plotted as a function of the THz frequency; σ_abs is calculated from the surface integral over the antenna lobes of the electromagnetic power loss (surface) density, divided by the intensity of the incoming wave, namely I = |E|²/ Z₀ = (1V/m)²/377Ω = 2.6 mW/m². The simulated electromagnetic power density scattered by the antenna is shown in the inset of Fig. 2(a).

 

Fig. 2 (a) FEM simulation of the absorption cross-section σ_abs of the four-leaf-clover-shaped antenna. Inset: scattered electromagnetic power on the plane of the antenna, a maximum of intensity is recognizable in the central zone where the NW FET is placed; (b) SEM image of the lateral-gated NW FET, the S-D distance l_SD is 1 μm.

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The fabricated devices are based on self-assembled InAs NWs, having a length of ≈1.5 μm and a diameter of 80 ± 26 nm [12], grown bottom-up on InAs (111)B substrates by chemical beam epitaxy in a Riber Compact-21 system using gold particles as a growth catalyst [18]. Trimethylindium (TMIn) and tertiarybutylarsine (TBAs) were used as metal-organic (MO) precursors and during the growth a selenium source of ditertiarybutylselenide (DTBSe) for n-type doping was used to achieve a carrier density n₀ ~10¹⁷ cm⁻³ [19]. Se-doping has been proven to be a successful way to both control the NW charge density and to optimize S-D and contact resistances in a NW FET, while ensuring a sharp pinch-off in the transistor transconductance [20].

The NWs were then mechanically transferred to a 350 μm thick high-resistivity Si substrate, with a 300 nm SiO₂ insulating oxide surface layer and a grid of metallic markers for the alignment of lateral gated NW-FETs in the subsequent lithographic steps. The sample was spin-coated with e-beam sensitive resist and S and D contact patterns, lateral gate and four-leaf-clover-shaped resonant antennas were exposed by electron beam lithography, defining a l_SD = 1 μm long transistor channel (Fig. 2(b)). The NW-FET was placed between the two lobes of the antenna (see green area in Fig. 1(a)). To achieve good ohmic contacts a passivation step was performed using a highly diluted ammonium polysulfide (NH₄)₂S_x solution in order to remove surface oxides and prevent reoxidation. Ohmic contacts were then realized by thermal evaporation of a Ti/Au (10/100 nm) layer. The devices were then glued on a Standard Dual-in-line chip via an electrically insulating adhesive, and wire bonded. A Scanning Electron Micrograph (SEM) image of the investigated NW-FET is shown in Fig. 2(b). The w_G = 80 nm wide lateral gate is here placed at a distance ≈80 nm from the NW.

3. Electrical and optical characterization

The electrical characterization of the fabricated devices was performed at RT by independently driving the source-to-drain (V_SD) and the gate-to-source (V_G) voltages in the range −25 to 25 mV and −8 to 8 V, respectively. To evaluate the resulting smaller channel current, the D contact was connected to a current amplifier, also acting as virtual ground, converting the current flowing through the NW into a voltage signal with a gain factor of 10⁶ V/A. The latter signal was recorded with a voltmeter. The S-D current (I_SD) measured as a function of V_G, while keeping V_SD = 0.025 V, is plotted on the right vertical axis of Fig. 3(a). The NW resistance varies from 2.5 MΩ to 10 kΩ while V_G is swept from −8 V to 8 V. From the analysis of the transfer characteristic (I_SD vs. V_G) we extracted the electron mobility and density within the nanowire following the experimental procedure described in [21] and [22]: μ = g_mw_G²/(C_wG·V_DS) ≈500 cm²/Vs, n = C_wGV_th/(2πr²w_G) ≈3·10¹⁷ cm⁻³, where g_m = 0.45 μA/V is the FET transconductance, C_wG ≈4 aF is the simulated [19] wire-to-gate capacitance and V_th = −2 V is the threshold voltage estimated from the average of the upward and downward gate sweep. From the mobility value μ we can derive an electron momentum relaxation time [23] τ = μm*/e = 6.5 fs meaning that the detector is operating in the low frequency regime (2πντ = 0.012 < 1), in which plasma waves are overdamped in the transistor channel.

 

Fig. 3 (a) Responsivity R_ν (left axis) and current I_SD (right axis) plotted as a function of V_G; R_ν is calculated from the photoresponse Δu at 0.292 THz; I_SD is measured at a source-drain bias V_SD = 0.025 V. (b) Red line: R_ν measured with the tunable source as a function of the incoming frequency (ν) in the 0.265 THz −0.375 THz range while V_G is kept at 8 V and the radiation is polarized along the y-axis of the FLCS antenna (θ = 0° or in the direction orthogonal to it (θ = 90°); The estimated FWHM is ~15 GHz, in good agreement with the result predicted by the FEM simulations.

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The optical characterization of the devices was performed employing two different sources: an electronic source based on frequency multipliers which radiates a monochromatic 0.292 THz beam and a tunable electronic source covering the 0.265-0.375 THz range. The THz beam was collected and focused by means of two off-axis parabolic mirrors on the detector antenna, i.e. between S and G contacts of the FET detector, in a beam spot of diameter d = 4 mm (see Fig. 5) and the intensity was mechanically chopped at a frequency of 530 Hz.

The optical power was P_t = 1.8 mW and P_t = 0.34 mW for the fixed frequency source and tunable source, respectively and the polarization of the incident plane wave was in both cases parallel to the antenna axis (y-axis in Fig. 1(a)). From geometrical consideration one can infer the total electromagnetic THz power P_a impinging on the antenna. Taking into account that the total detector area (roughly defined as the antenna area) is smaller than the diffraction limited one, the active area is taken equal to S_λ = λ²/4; beside this the beam spot area is given by S_t = πd²/4 and P_a can be calculated as P_a = P_t·(S_λ/S_t), meaning that P_a = 37.4 μW for the 0.292 THz source and P_a = 7.1 μW for the tunable one, respectively [9–11]. To evaluate the detector performance we measure the photoinduced source-drain voltage Δu at the D contact, while keeping V_SD = 0 and S grounded, with a lock-in amplifier connected to a low-noise voltage preamplifier having an input impedance of 10 MΩ and an amplification factor G_n = 25. Δu can be therefore estimated from the signal measured by the lock-in amplifier (LIA) via the relation: Δu = 2.2 · (LIA)/G_n, where the factor 2.2 takes into account that the lock-in gives the rms of the fundamental sine wave Fourier component of the square wave produced by the chopper. Loading effects due to the finite input impedance of the lock-in-amplifier were neglected [10].

4. Results and discussion

The responsivity R_ν of the detector, defined as the ratio between the photoresponse (Δu) and the radiation power (P_a) impinging on the active area of the device, is reported on the left vertical axis of Fig. 3(a) as a function of V_G for the 0.292 THz source. R_ν increases with V_G following a trend similar to the NW conductance, and reaches a maximum value of ≈105 V/W for V_G = 8 V; the dark signal level was more than 2 order of magnitude lower in agreement with previous experimental reports [10]. It is worth noticing that the R_ν dependence from V_G is strongly affected by the load impedance of the readout circuit [24]. Figure 3(b) shows the responsivity measured at V_G = 8 V while varying the frequency of the tunable source from 0.265 THz to 0.375 THz and while varying the antenna orientation with respect to the polarization of the incoming beam. A sharp resonance is clearly visible at 0.292 THz, i.e. at a frequency 8 GHz lower than that predicted by the FEM model, with a FWHM bandwidth of 15 GHz, i.e. in perfect agreement with simulations (Fig. 2(a)). Furthermore the antenna response is strongly polarization sensitive, showing a clear increase when the incoming beam is polarized along the y-axis (see Fig. 1(a)) with an 85% sensitivity reduction in the orthogonal polarization.

Figure 4(a) shows the NEP extracted from Johnson-Nyquist noise N_th, calculated from the data of Fig. 3(a), as a function of V_G.. If one assumes that the thermal noise is the dominant mechanism a minimum NEP value of ~120 pW/√Hz can be reached [11]. To investigate the frequency noise spectral density we measured the signal to noise ratio (SNR) directly using a dynamic spectrum analyzer. Figure 4(b) shows the spectral density for the detected signal at V_SD = 0 and V_G = 8V. The dashed line shows the thermal noise value N_th = √(4k_BTR) extrapolated from Fig. 3(a) at V_G = 8V.

 

Fig. 4 (a) NEP calculated from the ration between the Johnson-Nyquist noise spectral density (N), and the responsivity of Fig. 3(a) plotted as a function of V_G. The minimum NEP level is ~120 pW/√Hz. (b) Noise spectral density measured with a dynamic spectrum analyser while the THz radiation, modulated at 530 Hz, was impinging on the device. The noise shows a 1/f dependence at low modulation frequencies: at 530 Hz N ~300 nV/√Hz. For ν > 100 kHz the thermal contribution becomes dominant.

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The detected signal is seen as a peak at the sampling frequency of 530 Hz. From its intensity, including the 3Hz resolution bandwidth (RBW) of the employed spectrum analyzer, we can extract a NEP value ~2 nW/√Hz and a SNR of ~60 dB. It is clearly visible that a 1/f-type flicker noise prevails on the low-frequency side over the thermal noise up to 100 kHz, in agreement with previous reports [25,26]. At larger frequencies the noise flattens to the white noise (thermal) level, leading to a NEP ~150 pW/√Hz including the small responsivity reduction measured at 100 kHz for NW FETs [11].

From the NEP value the specific detectivity (D*), defined as the inverse of the NEP normalized to the detector area, can be calculated: D* = √A/NEP ~2.5·10⁸ cm√Hz/W. From R_ν we have extracted the detector external quantum efficiency (η) as the ratio between the number of carriers reaching D electrode and the number of photons impinging on the antenna: η = (hν/e)·(R_ν/R_nw) = 1.2·10⁻⁵. Such a small value mostly arises from small photon energy (1 meV) in the sub-THz frequency range.

Our detector performance makes it already exploitable for large-area fast imaging [12] or to scan the emission profile of resonant light sources. Figure 5 shows the image of the optical beam impinging on the NW FET collected while mounting the detector on a X-Y translational stage scanned with a spatial step of 300 µm and 200 µm in the horizontal and vertical directions, respectively. The dimension of the optical spot is consistent with the 4 mm diameter Gaussian beam focused by the two f/3 parabolic mirrors.

 

Fig. 5 Image of the 4 mm-diameter optical beam collected with the NW FET while mounting the detector on a X-Y translational stage scanned with a spatial step of 300 µm and 200 µm in the horizontal and vertical directions, respectively.

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5. Conclusions and perspectives

We have demonstrated that an intrinsically broadband detector can be converted in a resonant one via antenna engineering. The FLCS antenna geometry indeed not only introduces sensitivity to the polarization, but also a narrow selectivity on frequency. The described approach allowed a significant improvement of the detector performance allowing to reach responsivities of ~105 V/W at 0.3THz, with noise equivalent power levels ≈10⁻¹⁰W/√Hz at room-temperature, extremely promising for ultra-sensitive metrology, high-resolution spectroscopy and biomedicine.

Further optimizations include the matching of the beam waist to the effective antenna cross section by employing an integrated Si lens [10] and the shrinking of antenna dimensions in order to push its operation to higher frequencies.