A flexible graphene terahertz detector

There is increasing interest for terahertz (THz) technology in various applications, such as information and communications, surveillance and security screening, biomedical and material diagnostics, and global environmental monitoring.^1,2 Over the past few decades, many breakthroughs in high-power sources,³ room-temperature detectors,^4,5 and real-time imaging^6,7 have pushed the THz research into future novel applications with significant potential, such as wearable smart electronics and multiple transmit and receive antenna systems (MIMO). However, many of these applications call for flexible, portable, and less expensive solutions compared to existing solid-state technologies.

The advancements in polymer technology have promoted flexible electronics and enabled the fabrication of high-frequency devices on flexible substrates for light-weight, low-cost, and shape-conforming applications. In the radio frequency range, flexible sensing/communication devices have been embedded into clothing or other fabrics.^8,9 Thus far, however, only one flexible THz device has been reported: a scanner based on carbon nanotubes.¹⁰ A flexible THz detector can be a key element for future niche applications, for instance, bendable THz electronics for high-speed indoor wireless communication and rf-energy harvesting and wearable THz sensors for medical applications. The quest for a material system and the device concept that allow flexible THz electronics is still a great challenge.

As the first real two-dimensional material, graphene possesses extreme thinness and the ability to reversibly undergo high strains and strain rates.^11,12 With respect to preparation, graphene can be grown over large areas by chemical vapor deposition (CVD) and subsequently transferred to any substrate. Moreover, graphene, which possesses a high intrinsic carrier mobility, high conductivity, and gapless spectrum, has potential for developing detectors,^13,14 sources,¹⁵ and modulators¹⁶ in the THz range.

Here, we report a flexible THz detector based on an antenna-coupled graphene field-effect transistor (GFET) and demonstrate room-temperature THz detection from 330 GHz to 500 GHz. Additionally, the effect of bending strain on the detector performance is also investigated and analyzed.

The detector was fabricated on a flexible and transparent polyethylene terephthalate (PET) substrate with a dielectric constant of 2.6 (see the supplementary material for detail fabrication processes). Figure 1(a) presents images of the detector with a gate length and channel width of 5.5 μm and 4 μm, respectively. The access area gaps between the gate and source/drain are 0.5 μm. The THz power is received by a split bow-tie antenna, which provides an asymmetric coupling condition between the source and drain.¹³ The gate capacitance per unit area (C_G) is 6.6 fF/μm², as extracted from the S-parameters.

The detector was characterized using the experimental setup shown in Fig. 1(c) (supplementary material). Since the layered structure of the detector is considerably thinner than that of the substrate, the following simple approximation can be used for the tensile strain in the graphene film:¹⁷ $ε=t/2r$⁠, where t is the thickness of the PET substrate and r is the radius of curvature. The detector was operated in the cold mode, i.e., V_ds = 0, to minimize 1/f noise and maximize sensitivity.¹⁸ The THz voltage responsivity was calculated as

where the factor 2 is due to the peak-to-peak amplitude and the factor $2$ originates from the lock-in amplifier rms amplitude. P and $ΔU$ are the total available THz beam power and the rectified THz voltage of the detector, respectively (see the supplementary material for detail measurements).

Figure 2(a) shows the conductance of the detector versus the gate-source voltage (V_GS) with different bending strains of $ε=0%$⁠, 0.875%, and 1.25%. The conductance is calculated as G = I_DS/V_DS, where I_DS and V_DS are the drain current and the drain-source voltage, respectively, from the transfer characteristics measured at V_DS = 0.5 mV. As shown in this figure, the Dirac voltages (V_Dir) of the detector are located at positive values of V_GS, indicating that the graphene channel is p-type. The asymmetric conductance curves are due to the additional resistance produced by the p-n junctions between the n-type gated channel and the p-type ungated regions at positive values of V_GS. For the analysis, we assume that graphene transport properties are dominated by Coulomb scattering and that the mobility does not depend on the concentration of the charge carriers.¹⁹ This assumption allows for extraction of the electron/hole mobility (⁠$μe/h$⁠) and residual carrier concentration (n₀) by fitting a commonly used semi-empirical model²⁰ to the measured conductance data in Fig. 2(a). The solid line in Fig. 2(a) represents the fitting results at $ε=0%$⁠. According to our calculations, the average values of μ and n₀ with different strains are 2700 cm²/Vs and 1.2 × 10¹² cm^–2, respectively, and do not reveal a clear dependence on the strain. The latter can be explained by the fact that the deviations of the mobility with strain in the studied range are less than the uncertainty produced by the fitting model.²¹ 

As shown in Fig. 2(a), the V_Dir of the detector increases with the strain, which is in qualitative agreement with the results presented in Ref. 22 and 23. The shift of the V_Dir can be explained by changes in device electrostatics caused by changes in mobile trapped charges in the gate dielectric and at the graphene-dielectric interface as the substrate is bending.²³ In particular, it was shown that the stress is responsible for the change in the trap activation energy level.²⁴ 

Figure 2(b) shows the voltage responsivity versus frequency in the entire available frequency range measured at V_GS = 1.4 V and without bending (the data with strains are shown in the supplementary material). As shown, the voltage responsivity generally increases with the frequency up to approximately 2 V/W. According to our experiments, the deviations around the average value are very reproducible; hence, they can be associated with the standing waves in the optical setup.²⁵ The increase in the responsivity with frequency can be explained by the increase in the transmitting and detector antenna gains and possibly by better conjugate impedance matching at the higher frequencies.^25–28 

Figure 2(c) shows the measured voltage responsivity as a function of the gate voltage at 487 GHz with different strains. As shown in this figure, the maximum value of the responsivity decreases with the strain. An empirical nonlinear equivalent circuit model predicts a second-order nonlinear response in the GFET-based THz detectors when an oscillating THz field is applied between the gate and source such that²⁸ 

where σ is the channel conductivity. It can be shown that the both overdamped plasma model and thermoelectric model arrive at a similar $VGS$ dependence.^14,29 The second derivative of the channel conductivity in the form of $σ=n02+(VGSCG/e)2eμe/h$ provides the maximum of the responsivity as

As shown in Eq. (3), a decrease in the dielectric constants due to the out-of-plane compressive strain caused by bending should result in a decrease in the responsivity. Additionally, in accordance with the model of screening of the charged impurity potential, one can expect an increase in n₀ with a decrease in the dielectric constant because of the reduced screening effect. Indeed, the model provides the following relationship:³⁰ 

where C₀ is the voltage fluctuation, $rs=e2/(kℏνF)$ is the effective fine structure constant, $νF$ is the Fermi velocity, and k is the dielectric constant. Therefore, the bending strain should result in an increase in n₀ due to the lower dielectric constant and hence a decrease in the voltage response. Thus, the reduction in the voltage response with bending strain observed in our experiments [see Fig. 2(c)] is consistent with the empirical nonlinear model. The solid line in Fig. 2(c) represents the simulation results at $ε=0%$ based on the model. As the gate voltage increases, the measured responsivity varies from negative to positive, which is consistent with the modelled responsivity. However, the amplitude of the modelled responsivity is 10 times larger than that from the measurements since the voltage responsivity calculated using Eq. (1) is underestimated, which does not take into account several other power reduction factors, including the power losses in the experimental setup, limited detector antenna gain, and impedance mismatch between the antenna and transistor.^25–27,31

The noise equivalent power (NEP) of the detector with zero bias is dominated by thermal Johnson-Nyquist noise and can be calculated as

where k_B is the Boltzmann constant and T = 300 K is the room temperature. Figure 2(d) shows the estimated NEP of the detector as a function of V_GS with different strains. The minimum NEP value without bending is less than 3 nW/$Hz$ at V_GS = 1.45 V in the n-type gated channel. As the strain increases from 0% to 1.25%, the minimum NEP increases from 2.4 nW/$Hz$ to 4 nW/$Hz$⁠, which reflects the excellent mechanical properties of graphene.

Figure 2(e) shows that the measured THz voltage response of the detector at the given V_GS = 1.4 V is linear with the incident THz power. The available output power from the rf-source was not able to drive the detector into saturation.

In summary, we have presented a flexible THz detector based on an antenna-coupled GFET for the development of novel THz devices. The THz responses of the detector with different strains and different frequencies were measured. The detector without bending offers THz voltage responsivity above 2 V/W and an NEP below 3 nW/$Hz$ at 487 GHz for room-temperature operation. Based on the bending tests, the responsivity only has a small reduction with increasing strain, which demonstrates the robustness of the detector. Furthermore, this work provides an important route towards high-performance and low-cost THz flexible technology.

See supplementary material for device fabrication and the experimental setup.

This work was supported in part by the EU Graphene Flagship, in part by the Swedish Foundation of Strategic Research (SSF) under Grant No. SE13‐0061, and in part by the Knut and Alice Wallenberg Foundation (KAW). The authors thank Maris Bauer of Johann Wolfgang Goethe-Universität for his help with THz power calibration.