Graphene-based THz detectors

There are three crucial steps to consider in the design of resonant photodetectors. First, the incoming radiation needs to be efficiently compressed into plasmons propagating in the FET channel. Second, the channel should act as a high-quality plasmonic cavity, where constructive interference of propagating plasma waves leads to the enhancement of the field strength. Third, the high-frequency plasmon field needs to be rectified into a dc photovoltage. To meet these hard-to-satisfy5,6,7,8 requirements, we fabricated proof-of-concept detectors using high-mobility bilayer graphene (BLG) FETs. To this end, we first applied a standard dry transfer technique to encapsulate BLG between two relatively thin (d ≈ 80 nm) slabs of hBN30. The heterostructure had side contacts (Fig. 1a) which were extended to the millimeter scale and one of them served as a sleeve of the broadband antenna, Fig. 1c and Supplementary Fig. 3a, b (see Methods). Another antenna sleeve was connected to the top gate covering the FET channel (inset of Fig. 1d). In this coupling geometry, the incident radiation induces high-frequency modulation of the gate-to-channel voltage thereby launching plasma waves from the source terminal3. The detector was assembled on a THz–transparent Si wafer attached to a Si lens focusing the incident radiation onto the antenna (Fig. 1b).

Fig. 1 Graphene-based THz detectors. a Schematics of the encapsulated BLG FET used in this work. b 3D rendering of our resonant photodetector. THz radiation is focused to a broadband bow-tie antenna by a hemispherical silicon lens yielding modulation of the gate-to-source voltage, as indicated in a. c Optical photograph of one of our photodetectors. Scale bar is 200 μm. d Conductance of one of our BLG FETs as a function of the gate voltage V g , measured at a few selected temperatures. Inset: zoomed-in photograph of c showing a two-terminal FET with gate and source terminals connected to the antenna. Scale bar is 10 μm Full size image

We studied four BLG FETs, from 3 to 6 μm in length L and from 6 to 10 μm in width W, all exhibiting typical field-effect behavior as seen from measurements of the conductance G (Fig. 1d and Supplementary Fig. 3e). In particular, G is minimal at the charge neutrality point and rises with increasing V g . The mobility of our devices at the characteristic carrier density n = 1012 cm−2 exceeded 10 m2/Vs and remained above 2 m2/Vs at temperatures T = 10 K and 300 K, respectively, as determined from the characterization of a multiterminal Hall bar produced under identical protocol reported in Methods (Supplementary Note 1 and Supplementary Fig. 1).

Broadband operation

We intentionally start the photoresponse measurements at the low end of the sub-THz domain, where the plasma oscillations are overdamped (see below). This allows us to compare the performance of our detectors with previous reports5,6,7,8,23. Figure 2a shows an example of the responsivity R a = ΔU/P, where ΔU is the emerging source-to-drain photovoltage and P is the incident radiation power, as a function of the top gate voltage V g under irradiation with frequency f = 0.13 THz in one of our BLG detectors (see Methods). In good agreement with the previous studies, the R a (V g ) dependence follows the evolution of the FET-factor \(F = - {\textstyle{1 \over \sigma }}{\textstyle{{d\sigma } \over {dV_{\mathrm{g}}}}}\), shown in the inset of Fig. 2a. In particular, R a increases in magnitude upon approaching the charge neutrality point (NP) where it flips sign because of the change in charge carrier type.

Fig. 2 Plasmon-assisted THz photodetection. a Responsivity measured at f = 130 GHz and three representative temperatures. Orange rectangle highlights an offset stemming from the rectification of incident radiation at the p-n junction between the p-doped graphene channel and the n-doped area near the contact. Upper inset: FET-factor F as a function of V g at the same T. Lower inset: maximum R a as a function of T. b Gate dependence of responsivity recorded under 2 THz radiation. The upper inset shows a zoomed-in region of the photovoltage for electron doping. Resonances are indicated by black arrows. Lower inset: resonant responsivity at liquid-nitrogen temperature Full size image

We have studied the operation of our detectors at different temperatures and found that R a grows with decreasing T (bottom inset of Fig. 2a) and reaches its maximum R a ≈ 240 V/W at T = 10 K due to a steeper F(V g ) at this T (top inset of Fig. 2a). At large positive V g , R a approaches zero at all T, whereas at negative V g , a positive offset is observed (orange rectangle in Fig. 2a). This behavior is common for this type of devices and is related to additional rectification by p–n junctions at the boundaries between the p-doped graphene channel and the n-doped contact regions24,31,32.

The overall broadband responsivity of our BLG detectors is further improved in transistors with stronger nonlinearity, which can be conveniently parametrized by the FET-factor introduced above. To this end, we took advantage of the gate-tunable band structure of BLG and fabricated a dual-gated photodetector. Simultaneous action of the two gates results in a band gap opening and a steep F(V g ) dependence that, in turn, causes a drastic enhancement of R a (Supplementary Note 2). The latter exceeded 3 kV/W for a weak displacement field D of 0.1 V/nm (Supplementary Fig. 2b). This translates to the noise equivalent power (NEP) of about 0.2 pW/Hz1/2, estimated using the Johnson-Nyquist noise spectral density obtained for the same D. The observed performance of our detectors makes them competitive not only with other graphene-based THz detectors operating in the broadband regime23, but also with some commercial superconducting and semiconductor bolometers operating at the same f and T (Supplementary Table 1).

Resonant operation

The response of our photodetectors changes drastically as the frequency of incident radiation is increased. Figure 2b shows the gate voltage dependence of R a recorded in response to 2 THz radiation. In stark contrast to Fig. 2a, R a exhibits prominent oscillations, despite the fact that F as a function of V g is featureless (black curve in Fig. 2b). The oscillations are clearly visible for both electron and hole doping and display better contrast on the hole side, likely because of the aforementioned p–n junction rectification. Resonances are well discerned at 10 K, although they persist up to liquid-nitrogen T, especially for V g < 0. A further example of resonant operation of another BLG device is shown in Supplementary Note 3.

We have also studied the performance of our detectors at intermediate frequencies and found that the resonant operation of our devices onsets in the middle of the sub-THz domain (Supplementary Note 4). In particular, we have found that at f = 460 GHz, the resonances are already well-developed (Supplementary Fig. 4). At such low f, only two peaks in the photoresponse (one for electrons and one for holes) are observed for the same gate voltage span as in Fig. 2b along with an apparent increase of their full width at half-height. These observations are in full agreement with the plasmon-assisted photodetection model discussed below.

Plasmon resonances in graphene FETs

We argue that the observed peaks in the photoresponse emerge as a result of plasmon resonance in the FET channel. To this end, we model our FET as a plasmonic Fabry-Perot cavity endowed with a rectifying element. This results in responsivity given by

$$R_{\mathrm{a}} = \frac{{R_0}}{{\left| {1 - r_{\mathrm{s}}r_{\mathrm{d}}e^{2iqL}} \right|^2}},$$ (1)

where R 0 is a smooth function of carrier density n and frequency f that depends on the microscopic rectification mechanism, r s and r d are the wave reflection coefficients from the source and drain terminals, respectively, and q is the complex wave vector governing the wave propagation in the channel (Supplementary Note 5). In gated 2D electron systems, the relation between the frequency ω and the real part of the wave vector q′ is linear, ω = sq′, where the plasmon phase velocity is

$$s = v_{\mathrm{F}}\sqrt {4\alpha _ck_{\mathrm{F}}d} = \sqrt {\frac{e}{m}\left| {V_{\mathrm{g}}} \right|} .$$ (2)

Here m and e are the effective mass of carriers and the elementary charge respectively, v F and \(k_{\mathrm{F}} = \sqrt {\pi n}\) are the Fermi velocity and the Fermi wave vector, d is the distance to the gate, α c = e2/(4πε z ε 0 ħv F ) is the dimensionless coupling constant and ε z is the out-of-plane dielectric permittivity33,34. We further note that Eq. (2) is valid for monolayer graphene upon replacement of the effective mass m with the cyclotron mass, m → ħk F /v F (see Supplementary Note 6). The latter increases with gate-induced carrier density n, thereby limiting the tuning range of s for a given voltage span. In contrast, in the case of BLG, m is nearly constant (≈0.036m e ) for experimentally accessible values of V g , a feature that allows us to vary s over a wider range and thus switch the detector between multiple modes, as we now proceed to show.

It follows from Eq. (1), that the responsivity of our Fabry–Perot rectifier is expected to peak whenever the denominator in Eq. (1) approaches zero. In our devices, the source potential is clamped to antenna voltage, and no ac current flows into the drain, therefore r s r d ≈ −1 (refs. 3,32). The resonances should therefore occur whenever the real part of the wave number is quantized according to

$$q\prime = \frac{\pi }{{2L}}(2k + 1),\quad k = 0,1,2 \ldots$$ (3)

The quantization rule (3) combined with Eq. (2) predicts a linear dependence of the mode number k on \(| {V_{\mathrm{g}}} |^{ - 1/2}\) which may serve as a benchmark for plasmon resonances in the FET channel. This is indeed the case of our photodetector, as shown in Fig. 3a, e and Supplementary Fig. 3c. The slope of the experimental \(k( {| {V_{\mathrm{g}}} |^{ - 1/2}} )\) dependence in Fig. 3a matches well the theoretical expectation for a BLG Fabry-Perot cavity of length L = 6 μm. At large \(| {V_{\mathrm{g}}} |^{ - 1/2}\), we find a slight upward trend in the experimental data with respect to the linear dependence. We attribute this trend to deviations of the plasmon dispersion from the linear law at short wavelengths which stem from the non-local relation between electric potential and carrier density33. Note that the known non-parabolicity of the BLG spectrum35 resulting in an increase of m at large density n would bend the dependence in Fig. 3a in the opposite direction.

Fig. 3 Plasmon resonances in encapsulated graphene FET. a Mode number k as a function of \(V_{\mathrm{g}}^{ - 1/2}\) (symbols). Solid line: theoretical dependence for L = 6 μm, m = 0.036m e , and f = 2 THz. The first mode supported by our Fabry-Pérot plasmonic cavity corresponds to k min = 3; the fundamental mode with k = 0 is beyond the accessible gate voltages. b Examples of high-frequency potential distribution in the plasmon mode (real part) under resonant conditions for given k. Brown and blue colors represent positive and negative values of electrical potential, respectively. S, G, and D stand for source, gate, and drain terminals, respectively. c Experimental (symbols) and calculated (solid line) plasmon wavelengths λ p as a function of carrier density, as obtained from a. The corresponding value of the inverse compression ratio, λ 0 /λ p , for f = 2 THz is given on the right axis. d Plasmon lifetime τ p and quality factor Q as obtained from the width of the resonances shown in e. Error bars stem from the fitting procedure. e Experimental and calculated responsivities as functions of \(V_{\mathrm{g}}^{ - 1/2}\), normalized to the effective antenna impedance \(Z = V_{\mathrm{a}}^2{\mathrm{/}}P\) relating the incident power to the resulting gate-to-channel voltage V a . The theoretical Dyakonov-Shur dependence (Supplementary Note 9) was obtained by using characteristic τ p = 0.6 ps from d. Inset: normalized responsivity R a /Z after the subtraction of a smooth non-oscillating background. The solid blue line is the best Lorentzian fit to the data, with δ = 0.1 V−1/2, which translates to τ p = 0.5 ps Full size image

Photovoltage-based spectroscopy of 2D plasmons

The resonant gate-tunable response of our detectors offers a convenient tool to characterize plasmon modes in graphene channels. From Eq. (3) it follows that resonances occur if L = (2k + 1)λ p /4, where λ p = 2π/q′ is the plasmon wavelength (Fig. 3b). Using the experimentally observed peak positions, we have determined the density dependence of λ p , shown in Fig. 3c, which flaunts excellent agreement with theory (Supplementary Note 5). The compression ratio λ p /λ 0 between the plasmon and free-space wavelength (λ 0 = c/f and c the speed of light in vacuum) ranges between 1/50 and 1/150, highlighting the ultra-strong confinement of THz fields enabled by graphene plasmons, matching the record value known in the literature20.

Apart from λ p , the resonant responsivity carries information about another valuable characteristic of plasmons, namely, their lifetime, τ p . The latter is related to the peak width at half-height δ via (Supplementary Note 7)

$$V_{\mathrm{g}}^{ - 1/2}{\mathrm{/}}\delta = \omega \tau _{\mathrm{p}}.$$ (4)

Using Lorentzian fits to the photoresponse curves (inset of Fig. 3e), we have extracted τ p as a function of n, shown in Fig. 3d. The lifetime was found to range between ≈0.3 and ≈0.9 ps, which is slightly shorter than the transport time τ tr ≈ 2 ps as extracted from the mobility, τ tr = mμ/e (Supplementary Note 1). The corresponding quality factor, Q = 2πfτ p , was found to vary between 4 and 11 for f = 2 THz, and between 0.2 and 0.7 for f = 0.13 THz, see Fig. 3d. The latter implies that it is unreasonable to expect resonant photoresponse of such detectors in the GHz range, and they can only operate in the broadband (non-resonant) regime, in accordance with the data in Fig. 2a. On the contrary, the resonant responsivity should become more profound at higher frequencies of the THz window and can be further enhanced in graphene FETs of higher quality, such as those using graphite gates to screen remote charge impurities36.

Miniband plasmons in graphene/hBN superlattices

The approach demonstrated above is universal and can be applied to studies of plasmons in arbitrary high-mobility 2D systems embedded in FET channels, as we now proceed to show for the case of devices made of BLG/hBN moiré superlattices37.

Figure 4b and Supplementary Fig. 3c show examples of R a as a function of V g recorded in our superlattice devices in response to 2 THz radiation. As in the case of plain BLG, the overall evolution of the superlattice responsivity R a (V g ) follows that of the FET-factor (black curve) modulated by the plasmon resonances. Note the total number of resonances is smaller due to the shorter FET channel (cf. Supplementary Fig. 3c) and they are visible only for V g < 0, presumably due to a stronger nonlinearity in this detector for negative doping (in another superlattice FET, the resonances were well-observed for both V g polarities as shown in Supplementary Fig. 3c). Importantly, the FET-factor in these devices is, in turn, a more complex function of V g (cf. inset of Fig. 2a) due the presence of secondary neutrality points (sNP) stemming from a peculiar band structure of the BLG/hBN superlattice. The latter is characterized by narrow minibands emerging in the vicinity of the \(\tilde K{\mathrm{/}}\tilde K\prime\)-points of the superlattice Brillouin zone37 (Fig. 4c). The sNPs are clearly visible as peaks in the FET resistance which appear around V g = ±10 V (Fig. 4a).

Fig. 4 Miniband plasmons in BLG/hBN moiré superlattices. a Two-terminal resistance of one of our BLG/hBN superlattice devices as a function of V g measured at given T. Inset: illustration of the BLG/hBN superlattice demonstrating a mismatch between graphene and hBN lattice constants. For simplicity, only one graphene layer is shown. b Normalized responsivity (red) and the FET-factor (black) as a function of V g measured in the same device as in a. Dashed lines trace V g where the FET-factor reaches extreme values in the vicinity of the sNP. Pink (blue) arrows point to the resonant peaks near the secondary (main) NP. L = 3 μm. c Schematic representation of the BLG/hBN superlattice band structure. In the vicinity of the \({\tilde{\mathrm \Gamma }}\)-point (blue), BLG supports propagation of the ordinary plasma waves. Miniband THz plasmons emerge when the chemical potential approaches the sNP (pink) Full size image

A striking feature of the superlattice photoresponse is the resonances appearing when the Fermi level is brought close to the sNP (pink arrows in Fig. 4b). The resonances are of opposite sign with respect to those observed near the main NP (blue arrows), which indicates that they originate from the plasmons supported by the charge carriers of the opposite type (cf. Fig. 2b). Since the latter are hosted by the minibands near the \(\tilde K{\mathrm{/}}\tilde K{\prime}\)-points of the superlattice Brillouin zone (Fig. 4c), our measurements provide evidence for miniband plasmons that were long identified theoretically38 but remained elusive in experiment. To date, the experimental studies of superlattice plasmons have been only performed at room temperature using scattering-type scanning near field microscopy operating in the mid-IR domain39. The mid-IR excitation energy (10 μm ≈ 120 meV) is high enough to induce interband absorption close to the sNP, which hampers the observation of plasmons in superlattice minibands39. In contrast, our approach relies on the low-energy excitations (2 THz ≈ 8 meV), is applicable at cryogenic temperatures, and, therefore, paves a convenient way for further studies of miniband plasmonics.