Terahertz photodetection in scalable single-layer-graphene and hexagonal boron nitride heterostructures

Layered materials (LMs) and related heterostructures (LMHs) are a versatile platform for engineering optoelectronic and photonic devices.^1–3 They can be synthesized with wafer-scale methods^2,4,5 and stacked to form LMHs. Being compatible with Si and a wider range of III–V materials and substrates,^2,5–7 they open new prospects for emerging research domains, such as future high-density optical communications,⁶ high-speed datacom,⁸ quantum nanophotonics,⁹ and optoelectronics.^1,3 In particular, LMs are a versatile platform for photodetectors (PDs) operating across a broad range of frequencies from microwaves¹⁰ to telecom,⁸ visible,^1–3 and x rays.¹¹ 

Terahertz (THz) radiation (0.1–10 THz) finds application in biomedicine,¹² security,¹³ spectroscopy,¹⁴ cultural heritage,¹⁵ astronomy,¹⁶ real-time imaging,¹⁷ and high data-rate communications.¹⁸ In this frequency range, optoelectronic systems employing LMs realized in scalable processes have mostly been developed for light modulation^19,20 and nonlinear optics,^21,22 whereas similar processes for nanoscale receivers are still at an early stage and limited to few examples involving scalable large-area single layer graphene (SLG).^23–28 

The challenge is twofold. 1) The quest for technological maturity requires integration with established platforms, such as complementary metal oxide semiconductors (CMOSs). 2) Performance in SLG grown by chemical vapor deposition (CVD)^24–28 still does not match that obtained with exfoliated hexagonal boron nitride (hBN)/SLG/hBN heterostructures.^29–34 Above 1 THz, few ns response times (τ) and noise equivalent power (NEP) ∼1 nW Hz^−1/2 have been reported at room temperature (RT) on THz PDs based on large-area (∼cm²) CVD SLG,²⁸ but these are still inferior to those reported in high-quality hBN-encapsulated SLG (τ = 880 ps, NEP = 80 pW Hz^−1/2),^29,31 in Schottky diodes³⁵ (NEP ∼ 100 pW Hz^−1/2, electrical bandwidth ∼40 GHz, operation frequency <1.8 THz), in high-electron-mobility transistors³⁶ (HEMTs, NEP ∼ 100 pW Hz^−1/2, τ < 10 ps), or in portable THz cameras based on FETs or microbolometer arrays^37,38 (NEP ∼30 pW Hz^−1/2, τ > 10 μs). Table I summarizes the performance of RT THz detectors realized with scalable graphene-based structures.

As a step toward commercial development of THz PDs based on LMs and LMHs, we propose here the use of substrate treatment³⁹ or large-area encapsulation⁴⁰ to reach stable and repeatable state-of-the-art performances at RT. We develop RT PDs operating at 2.8 THz based on large-area (∼1 × 1 cm²) CVD SLG with and without large-area (∼1 × 1 cm²) CVD hBN capping, Fig. 1(a).

A  ∼10 nm thick layer of Al₂O₃ is deposited on a SiO₂/Si substrate (resistivity  ∼10 kΩ cm) by atomic layer deposition (ALD) (see the supplementary material). SLG is grown in a hot wall CVD system using a ∼30 μm thick Cu foil as a substrate. The foil, suspended on a quartz holder and loaded into the CVD system, is annealed at 1050 °C for 2 h under H₂ gas (100 sccm) at 760 Torr and cooled down to RT. For the growth, the foil is annealed at 1050 °C with 50 sccm hydrogen flow at 0.4 Torr for 2 h. 5 sccm CH₄ is introduced to start growth, which is completed in 30 min by stopping the CH₄ flow. The system is then naturally cooled down to RT under 50 sccm H₂. As-grown SLG/Cu is spin-coated with poly (methyl methacrylate) (PMMA) (A4-950) at 1000 rpm for 1 min and baked at 80 °C for 10 min. PMMA-coated SLG/Cu is kept in water overnight to oxidize the Cu foil. PMMA/SLG is then electrochemically delaminated by applying 2 V between the Pt anode and PMMA/SLG/Cu cathode in a NaOH aqueous electrolyte (∼1 M). The PMMA/SLG stack is cleaned in water and transferred on Al₂O₃/SiO₂/Si substrates, which are then baked at 80 °C for 10 min after ∼10 h natural drying. PMMA is removed by soaking in acetone and isopropyl alcohol (IPA).

hBN is grown on c-plane Al₂O₃ (0001) at 1400 °C, 500 mbar for 30 min in an AIXTRON CCS 2D reactor. 10 sccm N₂ is used to transport the single-source precursor, borazine, to the reactor. Before hBN growth, the sapphire substrates are annealed in H₂ for 5 min at 750 mbar and 1180 °C. As-grown hBN on c-plane sapphire is then spin-coated with PMMA (A4-950) at 1000 rpm for 1 min and baked at 80 °C for 10 min. PMMA-coated hBN on sapphire is kept in ∼8% H₃PO₄ for ∼10 h to delaminate PMMA/hBN. This is cleaned in water and transferred on SLG/Al₂O₃/SiO₂/Si. After natural drying, this is baked at 80 °C for 10 min. PMMA is removed by soaking it in acetone and IPA.

As-grown and transferred SLG and hBN are characterized by Raman spectroscopy with a Renishaw InVia spectrometer equipped with 100× objective at 514.5 nm. A statistical analysis of seven spectra on as-grown SLG on Cu, 27 spectra on SLG on Al₂O₃/SiO₂/Si, 36 spectra on hBN/Al₂O₃/SiO₂/Si, and 26 spectra on hBN/SLG/Al₂O₃/SiO₂/Si is performed to estimate the defect density and doping. Errors are calculated from the standard deviation across different spectra, the spectrometer resolution (∼1 cm⁻¹), and the uncertainty associated with different methods to estimate doping from the position of G peak Pos(G), its full-width-half-maximum [FWHM(G)], the intensity and area ratios I(2D)/I(G), A(2D)/A(G), and the position of 2D peak Pos(2D).^41–43 The Raman spectrum of as-grown SLG on Cu is in Fig. 1(b), after Cu photoluminescence removal.⁴⁴ The 2D peak is a single Lorentzian with FWHM(2D) = 30 ± 5 cm⁻¹, which is a signature of SLG.⁴⁵ Pos(G) = 1584 ± 2 cm⁻¹, FWHM(G) = 16 ± 4 cm⁻¹, Pos(2D) = 2698 ± 2 cm⁻¹, and I(2D)/I(G) = 3.8 ± 1.0 A(2D)/A(G) = 7.2 ± 1.8. No D peak is observed, indicating negligible density of Raman active defects.^46,47 A typical Raman spectrum of SLG/Al₂O₃/SiO₂/Si is in Fig. 1(b). The 2D peak retains its single-Lorentzian line shape with FWHM(2D) = 36 ± 2 cm⁻¹. Pos(G) = 1597 ± 3 cm⁻¹, FWHM(G) = 14 ± 2 cm⁻¹, Pos(2D) = 2692 ± 2 cm⁻¹, I(2D)/I(G) = 1.9 ± 0.5, and A(2D)/A(G) = 4.9 ± 0.5, indicating a p-doping with Fermi level E_F = 290 ± 90 meV,^41,42 which corresponds to a carrier concentration n = 6.5 ± 3.3 × 10¹² cm⁻².^41,42 I(D)/I(G) = 0.03 ± 0.04 corresponds to a defect density n_D = 1.7 ± 0.7 × 10¹⁰ cm⁻² for excitation energy 2.41 eV and E_F = 290 ± 90 meV.⁴³ A Raman spectrum of the transferred hBN on Al₂O₃/SiO₂/Si is in Fig. 1(b). The position of E_2g peak is Pos(E_2g) = 1371 ± 1 cm⁻¹, with FWHM(E_2g) = 26 ± 1 cm⁻¹.⁴⁸ A Raman spectrum of SLG capped by hBN is in Fig. 1(b). The single-Lorentzian 2D peak has FWHM(2D) = 37 ± 2 cm⁻¹. Pos(G) = 1598 ± 3 cm⁻¹, FWHM(G) = 13 ± 1 cm⁻¹, Pos(2D) = 2692 ± 2 cm⁻¹, I(2D)/I(G)= 1.8 ± 0.3, and A(2D)/A(G)= 5.1 ± 0.6, indicating a p-doping with E_F = 300 ± 100 meV,^41,42 which corresponds to n = 7.2 ± 4.1 × 10¹² cm⁻².^41,42

Graphene field-effect transistors (GFETs) are fabricated by electron beam lithography (EBL) (Zeiss UltraPlus), ALD (Oxford, OpAL), and metal evaporation. We define U-shaped channels with length L_c = 2400 nm and width W_c = 1500 nm through reactive ion etching (O₂ for uncapped, CF₄/O₂ mixture for hBN-capped samples). We pattern source (s) and drain (d) contacts via EBL, and fabrication is finalized by depositing a 40 nm thick Pd layer by thermal evaporation and liftoff. For hBN-capped devices, this results in edge-contacts to the SLG channel, showing contact resistance R₀ ∼ 1 kΩ similar to the case of uncapped samples. We then define the top-gate oxide (∼40 nm HfO₂, grown by ALD) above the channel and finalize the fabrication by depositing 5/90 nm Cr/Au to establish the top-gate (g) electrodes. To reduce the detector shunt capacitance, s and d electrodes are connected to a coplanar strip line.³¹ A schematic cross section of the fabricated devices is in Fig. 1(a). For each material combination, Al₂O₃/SLG/HfO₂ and Al₂O₃/SLG/hBN/HfO₂, two distinct architectures are conceived, devised, and investigated. The first is based on single-top-gated GFETs integrated with a planar bow-tie antenna with radius 24 μm and flare angle 90° [Figs. 1(c) and 1(d)]. The antenna arms are connected to the s and g electrodes. The second design features two top-gates, connected to the left and right arms of a 24 μm radius bow-tie antenna. The antenna dimensions are chosen to be resonant with a radiation frequency of 2.8 THz.²⁸ 

These geometries are selected to activate the photo-thermoelectric (PTE) effect as a dominant detection mechanism.^31,32,49 This requires a spatial asymmetry along the source-drain (s-d) channel.³ In single-gated systems, the asymmetry is established by the spatial gradient of the electronic temperature (T_e) in the SLG channel, induced by the absorption of THz light in the antenna gap, which is located close to the s electrode.³¹ Instead, in p–n junctions, the electronic distribution is symmetrically heated at the center of the s-d channel, where the antenna gap is located.²⁹ Here, the asymmetry is determined by the longitudinal variation of the SLG Seebeck coefficient (S_b), whose profile along the s-d direction can be electrostatically defined by applying distinct gate voltages (V_g) on the left and right sides of the junction.

We activate a dominant PTE by design, since SLG displays unique thermoelectric properties, due to its low electronic specific heat (∼2000 k_B μm⁻² at RT,⁵⁰ where k_B is the Boltzmann constant), ultrafast (∼30 fs) carrier thermalization dynamics,⁵¹ and slower (∼4 ps) electron–phonon cooling.^52,53 Thus, it offers an outstanding route for performance optimization by means of, e.g., carrier lifetime engineering⁴⁹ or coupling to plasmonic-polaritonic quasi-particles.⁵⁴ PTE also allows for broadband,⁴⁹ RT, zero-bias operation.⁸ 

We first characterize the devices electrically by measuring the source–drain current (I_sd) as a function of V_g. The resistance (R) curve for a single-gated device is in Fig. 2(a). Instead, Fig. 2(b) shows the resistance map of a p–n junction device, measured as a function of the left- and right-gate voltages (V_gL and V_gR). We extract the field-effect mobility (μ_FE) for electrons and holes and the residual carrier density (n₀) by using the fitting function⁵⁵ R = R₀ + (L_c/W_c)·(1/n_2deμ_FE), where n_2d = {n₀² + [C_g/e·(V_g−V_CNP)]²}^−1/2 is the carrier density,⁵⁵ C_g is the gate-capacitance per unit area, and V_CNP is the charge neutrality point. We get μ_FE = 300–2000 cm²V⁻¹s⁻¹ for Al₂O₃/SLG-based GFETs and μ_FE = 3000–9000 cm²V⁻¹s⁻¹ for hBN-capped ones.

Figure 2(c) plots n₀ as a function of μ for the complete batch of devices, where μ is the average field-effect mobility of electrons and holes: each GFET is represented by a colored dot. From this comparison, hBN-capped samples show lower n₀ and higher μ with respect to Al₂O₃/SLG/HfO₂ devices. The field-effect measurements [Figs. 2(a) and 2(b)] can be used to evaluate S_b, which determines the PTE response of SLG-based PDs. This can be done starting from the experimental conductivity (σ) and using the Mott equation,³⁰ which, however, is not accurate at low carrier densities,⁵⁶ i.e., close to V_CNP. Thus, we theoretically calculate S_b using an effective medium theory (EMT)⁵⁶ in the framework of the linear Boltzmann equation^53,57 (see the supplementary material). Figure 2(d) shows the results of the EMT model applied to the device of Fig. 2(a), for which we get a maximum thermopower of S_max ∼ 70 μV K⁻¹.

We then evaluate the PDs' optical figures of merit: voltage responsivity (R_v), NEP, and τ. The detectors are illuminated by a 2.8 THz quantum cascade laser (QCL), driven in a pulsed mode (repetition rate 40 kHz, duty cycle 4%) delivering a peak power ∼25 mW, corresponding to an average power ∼1 mW. The antenna axis is oriented parallel to the linearly polarized electric field. The beam is focused by two TPX lenses onto a ∼200 μm radius circular spot. We select intermediate average power P₀ = 0.4 mW to characterize the PDs to avoid QCL overheating. The corresponding average intensity in the focal point is I₀ = 0.32 W cm⁻².

We measure the photovoltage (Δu) at the d electrode, while keeping s grounded. Δu is amplified by a voltage preamplifier (DL Instruments, M1201, gain γ = 1000) and sent to a lock-in (Stanford Research, 5210). We use a square-wave envelope with frequency f_mod = 1.333 kHz as a lock-in reference and as a triggering signal for the QCL pulse trains. Δu can be inferred from the demodulated lock-in signal (V_LI) as³⁰ Δu = (π$2/2$⁠)V_LI/γ, where the pre-factor π$2/2$ takes into account that the lock-in measures the root mean square of the fundamental Fourier component of the square wave produced by the QCL modulation. R_v is calculated from the ratio between Δu and the power P_a = I₀A_eff impinging on the detector, with A_eff the detector effective area, assumed equal to the diffraction limited area³⁰ A_eff = λ²/4 = 2800 μm², where λ is the free-space wavelength. We calculate the curve of R_v vs V_g for each single-gated GFET and the map of R_v vs V_gL and V_gR for each p–n junction. Typical examples of R_v vs V_g plots are in Figs. 3(a) and 3(b) for a single-gated GFET and a p–n junction, respectively. The photoresponse in single-gated GFETs follows the profile of S_b with an offset of S_bu ∼ S_b (V_g = 0 V) and with PTE voltage³⁰ V_PTE = ΔT_e·(S_b − S_bu), where ΔT_e is the T_e gradient between s (hot) and d (cold) sides of the SLG channel and S_bu is the Seebeck coefficient of the ungated region between the s and g electrodes. Figure 3(a) compares the measured R_v vs V_g and the theoretical PTE responsivity, R_PTE, vs V_g, with R_PTE inferred from V_PTE by considering ΔT_e/P₀ ∼ 1.5 K/mW, showing good qualitative agreement between the two curves. The discrepancy between theoretical and experimental responsivities at large positive V_g is ascribed to the fact that the adopted theoretical model (see the supplementary material) only includes electron scattering with charged Coulomb impurities as dominant effect limiting the conductivity, possibly neglecting additional contributions, e.g., phonon scattering or carrier inhomogeneities at the contacts. A dominant PTE detection mechanism is also observed in p–n junctions. E_F in SLG can be tuned across the Dirac point by the electrostatic gating applied to the left and right sides of the junction. The nonmonotonic dependence of S_b on E_F leads to multiple sign changes in R_v, resulting in a sixfold pattern²⁹ in the R_v map [Fig. 3(b)], a distinctive feature of PTE.^26,29

The sensitivity of THz detectors is evaluated through the NEP,²⁹ defined as the ratio between noise figure and responsivity. In order to calculate NEP, it is important to give a rigorous evaluation of the noise spectral density (NSD).^26,29–31 Thus, we measure the GFET NSD with a lock-in amplifier (Zurich Inst., UHFLI). The s electrode is grounded and the signal, demodulated by the lock-in, is collected at the d electrode, while a sweep of the modulation frequency is performed. The results are in Fig. 4(c) for a 50 Ω test resistor and for a prototypical SLG-based device. The white noise floor for the 50 Ω resistor is dominated by the lock-in noise figure. The Johnson–Nyquist NSD formula gives³⁰ N_J = (4k_BTR)^−1/2 = 0.91 nV Hz^−1/2 for a 50 Ω resistor operated at RT, whereas our instrumental noise floor is ∼8 nV Hz^−1/2, as expected for the noise level of the employed lock-in.⁵⁸ The NSD of one of the GFETs [R = 9 kΩ in Fig. 4(c)] is dominated by the 1/f component⁵⁹ for modulation frequency <1 kHz and flattens at NSD < 14 nV Hz^−1/2 at higher frequencies in agreement with the theoretically expected N_J = 12.3 nV Hz^−1/2. The GFET N_J is, thus, the main contribution to the overall noise figure in our setup (with pre-amplifier NSD ∼7 nV Hz^−1/2). The measured NSD at 1.333 kHz is then used to calculate NEP [Figs. 3(d) and 3(e)] as a function of the voltages applied to the gate electrodes.

We then characterize the detection speed by recording the time trace of Δu with an oscilloscope (Tektronix DPO520–4B, bandwidth 2 GHz). We use a THz pulse duration ∼1.6 μs, and we amplify the PD output with a high-bandwidth (1.1 GHz) voltage preamplifier (Femto, DUPVA-1–70) before the oscilloscope. We drive the QCL into the negative differential resistance regime,³⁰ which results in electronic instabilities that correspond to an intermittent output power: the QCL undergoes intensity fluctuations with characteristic time constants τ_qcl ∼0.9 ns. This strategy allows us to test the bandwidth of our PDs up to a maximum (2πτ_qcl)⁻¹ = 180 MHz. Figure 3(f) shows the waveform recorded by a single-gated GFET during an intensity fluctuation of the pulsed QCL. We evaluate τ from exponential fits to the waveform (see the supplementary material). We get τ = 7–20 ns for the investigated devices, with a mean value ∼12 ns, corresponding to a bandwidth ∼15 MHz.

Statistical analysis is applied to 28 devices to evaluate performance variability and identify correlations between electrical and optical properties. We first consider NEP variability. For Al₂O₃/SLG/HfO₂ devices, we get a mean value ∼7.6 nW Hz^−1/2 and an interquartile range²⁸ (IQR) ∼4.0 nW Hz^−1/2. For hBN-capped PDs, we have mean NEP ∼ 3.0 nW Hz^−1/2 with IQR ∼ 1.4 nW Hz^−1/2, which represents a variability improvement of factor >2 with respect to SiO₂/SLG²⁴ and Al₂O₃/SLG PDs. We then evaluate correlations among NEP, S_b, and n₀ using the Pearson coefficient⁶⁰ (ρ) as a metric. ρ(v₁,v₂) represents the measure of linear correlation between two discrete variables v₁ and v₂: |ρ| = 1 indicates an exact linear dependence and ρ = 0 indicates no linear correlation. We get ρ(S_max,n₀) = −0.95 for both hBN-capped and uncapped architectures, where S_max is the maximum |S_b| in the investigated V_g range, calculated with the EMT model. The scatterplot of S_max vs n₀ in Fig. 4(a) shows that hBN/SLG/Al₂O₃ LMHs have slightly larger S_max, even though they have significantly smaller n₀. This is due to the different dielectric environment: the larger ε_r of HfO₂ (with respect to hBN) on top of SLG is beneficial in terms of thermopower.⁵⁶ This similarity in S_max is reflected in the detectors NEP, where the difference between the two material architectures is not as pronounced as the difference in n₀ [Fig. 4(b)]. However, in agreement with results obtained on SiO₂/SLG/HfO₂ heterostructures,²⁸ NEP increases for larger n₀: ρ[log(NEP), log(n₀)] = 0.4. These correlations confirm that the physical mechanism underpinning THz detection is, as expected, PTE.

Thus, the Al₂O₃ termination alone does not show a significant performance improvement over SiO₂/Si substrates,²⁸ whereas large-area HfO₂/hBN/SLG/Al₂O₃ LMHs present advantages both in terms of absolute optical performance (average NEP ∼ 3.0 nW Hz^−1/2) and performance variability (IQR ∼ 1.40 nW Hz^−1/2). Large area hBN-top-encapsulation significantly reduces the device performance variability by over a factor 2 with respect to Ref. 28.

In summary, we reported THz PDs realized with large-area graphene and large-area hBN in wafer-scale compliant processes, capable of mitigating material degradation with respect to the quality benchmark of hBN-encapsulated SLG.^29–31 We demonstrate THz detection in a layered material heterostructure obtained by consecutive transfer of CVD graphene and CVD hexagonal boron nitride, a fabrication technique compatible with CMOS processing. This makes our PDs suitable for real-time imaging and short-range (∼10 m) THz communication applications, enabling multi-pixel architectures. A further benefit can come from the full large-area encapsulation of SLG in CVD-based hBN/SLG/hBN heterostructures.

See the supplementary material for the description of Al₂O₃ ALD, thermopower calculation, and detection speed analysis.

We acknowledge funding from ERC Projects via No. 681379 (SPRINT), Hetero2D, GSYNCOR, the EU Graphene and Quantum Flagships, the Marie Curie H2020-MSCA-ITN2017 TeraApps (No. 765426) grant, the CNR project (TEROCODE), EPSRC Grant Nos. EP/L016087/1, EP/K01711X/1, EP/K017144/1, EP/N010345/1, EP/V000055/1, and DSTL, University of Pisa under the “PRA-Progetti di Ricerca di Ateneo” (Institutional Research Grants)—Project No. PRA 2020-2021 92. For the purpose of open access, the authors applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.