A reconfigurable ladder-shaped THz metamaterial integrated with a microelectromechanical cantilever array

Terahertz (THz) waves have recently attracted interest because of their unique spectral specificity and transmission properties^1,2 and have expanded potential in nondestructive inspection and wireless communications beyond 5G.^3–6 To develop fundamental components of THz applications, such as attenuators and phase shifters, superior manipulation of the transmission power and phase of THz waves is highly sought. Since most natural materials react weakly with THz waves due to an intrinsic limit, artificial materials, metamaterials (MMs), are of popular interest.

MMs consist of periodic metallic unit cells with a subwavelength size, and they can exhibit desired optical characteristics by designing unit cells.^7–13 The structure-dependent response enables MMs to regulate THz waves on demand.^14–16 To develop THz applications, such as high-speed 3D THz imaging based on time-of-flight, THz pulses used to scan an object should meet the following requirements: a large contrast to create a clear image and a fast acquisition to obtain a high time resolution.^17,18 Therefore, active manipulations of THz waves with high contrast and high speed are indispensable. Active THz MMs have extensively been developed by integration with various tuning methods.^19,20

The tunability of THz MMs has been realized using liquid crystals, electron injection, and so on.^21–24 However, these tuning methods only obtain a low tuning contrast due to a limited refractive index change in the material and the surrounding medium. In addition, difficulties exist in integrating their external actuating triggers into the system. In contrast, microelectromechanical systems (MEMS) can achieve a high tuning contrast owing to the direct reconfiguration in structures.²⁵ Additionally, MEMS are easy to integrate into integrated circuits (ICs) for future miniaturized applications. Thus, MEMS-driven MMs (MEMS-MMs) are good candidates for actively modulating THz waves.^26–32 

Conventional reported MEMS actuators were designed in large sizes to obtain sufficient reconfiguration for a high tuning contrast. However, the size and mass of a MEMS actuator are inversely proportional to its mechanical resonant frequency (f_mr) and hence the tuning speed.³³ In other words, devices with a large actuator sacrifice the tuning speed; thus, they cannot serve applications requiring a short acquisition time. Only ∼tens of kHz (∼tens of μs) in tuning speed has been reported, thus far.^34–36 Han et al.³⁷ reported a THz device implementing a reconfigurable MEMS capacitor within a split-ring resonator, and an 87% contrast in transmission amplitude was obtained. The cantilever-type MEMS actuator had a beam length of 39 μm, which limits its tuning speed by a f_mr of 40 kHz. Liu et al.³⁸ proposed a MEMS-MM achieving 80% contrast in THz absorption. A membrane actuator with a side length of 180 μm was used to deform the MM atoms. The device operated with an acquisition time of ∼27 μs. Since the operational speed of the MEMS actuator is limited by its f_mr, increasing f_mr and, thus, extending the maximum operational speed of the actuator are critical to developing high-speed MEMS-driven THz MMs.

In this study, we design and experimentally demonstrate a switchable THz MEMS-MM with a high f_mr. A ladder-shaped MM (LS-MM) was designed based on a strongly coupled I-shaped structure.³⁹ Unlike reported MEMS-MMs using a large actuator to sufficiently reconfigure MMs, a small reconfiguration of the unit cells of the LS-MM can change the resonance to obtain a 94.6% contrast in transmittance, which allows independent ultrasmall cantilever actuators (a beam length of 14 μm) to separately reshape each unit cell of the LS-MM. The measured f_mr of our device was ten times higher than that in the reported work and reached 585 kHz. Taking advantage of the compatibility, miniaturization, and flexibility of IC processes, this device offers a practical pathway for high-performance THz imaging, scanning spectrometry, and wireless communications.

Figure 1(a) schematically depicts the structure of the proposed MEMS-driven LS-MM (MEMS-LS-MM). A 500-μm-thick quartz glass substrate was used. A 6-μm-wide gold lead array for applying a drive voltage was embedded under a 0.4-μm-thick SiO₂ film to avoid electrical short-circuit. The period of leads associated with the y-directional period of the LS-MM was much smaller than the wavelength of the THz incidences. Therefore, the optical behavior of leads satisfies the condition of the working principle of a wire grid polarizer, and the lead array does not affect the transmittance of the device for E_y-polarized THz waves. A ladder-shaped 2D gold MM consisting of two arms and a split bar was formed on the surface layer to react with the normally incident THz waves. A MEMS cantilever array with initially suspended beams was aligned to the split bar of the LS-MM (detailed geometric dimensions are shown in Fig. 3 and listed in Table I). The design of the geometric parameters is discussed in Figs. S2–S4 in the supplementary material). Figure 1(b) shows the operation concept of the MEMS-LS-MM. By applying a potential difference between the leads and the LS-MM, the suspended cantilever tip pulls down to merge the split bar of the LS-MM into a connecting bar, correspondingly switching the device from the off- to on-state. The device at two states has different induced charge distributions, thus resulting in a switchable THz transmission response by the off-to-on reconfiguration.

Calculation of the optical characteristics of the MEMS-LS-MM was performed by the finite element method via COMSOL Multiphysics 6.0 (COMSOL, Inc.). E_y-polarized THz waves were normally incident on the surface of the MEMS-LS-MM. The simulation model was set with Floquet periodicity boundary conditions in both the x- and y-directions. The optical constants of the SiO₂ substrate were set with the measured value (see Fig. S1 in the supplementary material), while gold was set as a perfect electric conductor. Figures 2(a) and 2(b) show the transmittance and transmission phase shift normalized by a SiO₂ reference. As the MEMS-LS-MM was switched from off- to on-state, the resonant frequency of the transmittance dip was shifted from 1.52 to 0.69 THz. At the on-state resonance, a tuning contrast of 94.6% was accomplished by a high transmittance for the off-state and a low transmittance for the on-state, which indicates that the MEMS-LS-MM can work as an optical shutter for 0.69 THz wave. The transmission phase shift dropped at the off- and on-state-resonances, resulting in a phase delay. In particular, a 1.4-rad delay was obtained at 1.21 THz, where the transmittance of 59.5% remains the same for both the off and on states, suggesting that this device can serve as a phase shifter.

Near-field coupling behaviors of the device were calculated to elucidate the resonance mechanism. The electric field was confined within the split bar of the LS-MM underneath the cantilever in the off state [Fig. 2(c)], whereas it was confined around the arm edge in the on state [Fig. 2(d)]. The magnetic field separately concentrated around the upper and lower part of the split bar at the off-state [Fig. 2(e)] and smoothly concentrated alongside the merged connecting bar at the on-state [Fig. 2(f)]. These results can be explained by the LC resonance and the equivalent circuit model.^40–43 The optical resonant frequency is determined by $for∝1Leff · Ceff$⁠, where L_eff and C_eff are the total effective inductance and capacitance of a unit cell, respectively. The equivalent circuit of a unit cell is illustrated in Fig. 2(g). The cantilever behaved as a variable capacitor, which was inversely proportional to the adjustable tip gap δ by $Cδ∝1δ$⁠. At the off-state, a small C_δ of approximately 0 associated with the initial δ can be assumed to be an open wire. In the on-state, δ was 0, and C_δ approached infinity, which can be assumed to be a short-circuit wire. A different C_δ at off- and on-states led to a different C_eff, thus changing the f_or of off- and on-states. The comparison of equivalent circuits at off- and on-states is explained in the supplementary material [see Fig. S5]. By designing the geometric parameters to modify C_eff and L_eff, f_or can be accordingly obtained. For instance, the effect of the bar length on the f_or of an on-state LS-MM was discussed in our prior work.⁴⁴ 

We fabricated the MEMS-LS-MM on a quartz glass substrate using standard surface micromachining techniques (see Fig. S6 of the supplementary material for the fabrication flow). A MEMS-LS-MM pattern was formed within an area of 6 × 10 mm², larger than the THz incident beam spot of 5 mm in diameter. Figure 3 shows the SEM images of the fabricated MEMS-LS-MM. By well-managing the deposition and release process in fabrication, a cantilever array with a flat and suspended beam was obtained. The designed and fabricated dimensions are listed in Table I, where the fabrication values were obtained by averaging the measurements of 10 random units among the MEMS-LS-MM.

For the mechanical characterization, we calculated the f_mr and vibration mode of the cantilever using an eigenfrequency study via COMSOL Multiphysics 6.0. In the geometry of the simulation model, the beam root was built with a curvature to approximate the real fabricated structure. The edge of the beam vibrated with a maximum displacement at a f_mr of 579 kHz, as shown in the inset in Fig. 4. The measurement of f_mr was conducted using a Polytec MSA-400 microsystem analyzer (Polytec, Inc.) in the air. A chirp wave with a peak voltage of ±5 V_AC was input. Figure 4 presents the measured FFT magnitude of the vibration velocity as a function of the mechanical frequency. The fundamental resonance was found at 585 kHz, suggesting that one complete vibration cycle of the cantilever takes 1.71 μs. The quality factor Q of the mechanical resonance was computed as 67 from the measured values shown in Fig. 4, which was higher than the reported value of 5.2 in Ref. 45.

The switchable transmission response of the device was verified using a THz time-domain spectrometer (TeraProspector, Nippo Precision Co., Ltd.). The samples were settled in a chamber purged with dry air to remove the water vapor absorption peak. The y-polarized incoming THz waves are normally incident on the sample under test. First, a SiO₂ bare substrate and the unactuated device (off-state) were measured. Then, a bipolar square voltage of 150 V with a frequency of 40 kHz was applied across electrodes of the device for the on-state measurement. The alternating positive and negative voltages reduce the mobile free charge accumulation in the dielectric isolation layer, which may cause an electrical breakdown. Measured transmission data of the device at both the off- and on-states were normalized by the SiO₂ reference and plotted in solid curves in Fig. 5, alongside the SEM image insets of a cantilever operating at two states. By applying the drive voltage, the transmittance dip at 1.53 THz of the off-state clearly shifted to 0.78 THz of the on-state as predicted by calculations [dot curves in Fig. 5(a)]. As a result, a 60.1% change at 0.78 THz was experimentally achieved. The frequency band of interest is around the on-state resonance in contrast to the off-state resonance at approximately 1.53 THz, because the SiO₂ substrate has a relatively larger absorption in the higher frequency range (see Fig. S1 in the supplementary material for the extinction coefficient of the SiO₂ substrate). The fluctuation in the measured off-state transmittance spectrum at frequencies below 1 THz, such as a peak at approximately 0.4 THz, may originate from the data processing when cutting the Fabry–Pérot interference of the SiO₂ substrate. For this point, we plotted the raw data without cutting as well as the measured transmittance normalized by an air background in the supplementary material for a discussion (see Figs. S7 and S8). Figure 5(c) shows the transmittance normalized by the air reference. Although the influence of the interference of the SiO₂ substrate can be seen, the resonance frequency clearly shifted, as shown in Fig. 5(a). This interference signal can be eliminated by forming an antireflection layer on the backside of the SiO₂ substrate. Compared to the calculated transmittance of the MEMS-LS-MM in the on-state, the experimentally observed resonance slightly shifts to a higher frequency of 0.78 THz, and a small dip appeared around the off-state resonance of 1.53 THz. Some of these differences may be attributed to an actual hybridized state between fully on- and off-states caused by the imperfect actuation of cantilevers due to the variance in the cantilever structure and the uncertain defects in the lead array (see Fig. S9 for additional information about the hybridized state). Figure 5(b) shows the transmission phase shift of the MEMS-LS-MM. A sharp jump in the phase shift was found around the resonant frequencies of the two states, as expected, contributing to a clear phase delay. Specifically, a 0.9-rad delay was observed at 1.35 THz, where the transmittance of 37.6% for both the on- and off-states was the same.

The f_mr of the MEMS actuator can be further increased by thickening the cantilever beam,³³ although the required drive voltage is correspondingly increased. Optimizing the structure of the cantilever to provide an extra supporting stress to the beam, for instance, adding a wall structure around the beam root, is another possible approach. The limitation of this study is a high drive voltage (∼150 V) compared to that in another work (e.g., ∼60 V in Ref. 46); this limitation occurs due to the high stiffness of the cantilever beam, which may be improved by aligning the leads closer to the cantilever edge. During the optical measurement, the cantilever array was permanently stuck after being driven to snap down due to the lack of an anti-stiction structure. The repeatability can be improved by changing the cantilever structure, such as adding a dimple stop around the tip. As the first prototype device, further optimization, including the reduction in the operation voltage and the improvement of the repeatability, is required before practical applications.

In summary, we designed, fabricated, and evaluated a MEMS-LS-MM serving as an optical switch for THz waves. Compared to a conventional study with a mechanical resonance of ∼tens kHz, the cantilever actuator experimentally exhibited a resonance at 585 kHz. A Q-factor of 67 was obtained, which was higher than the reported Q-factors, indicating a lower energy loss. A 60.1% contrast in transmittance at 0.78 THz and a 0.9-rad delay in the transmission phase shift at 1.35 THz were experimentally achieved by applying a voltage of 150 V. The MEMS-LS-MM can advantageously develop applications, such as high-performance THz imaging.

See the supplementary material for the measured optical constants of the SiO₂ substrate, details of the fabrication processes, and a discussion of the effect of the SiO₂ substrate on the measured transmittance data.

This work was partially supported by MEXT KAKENHI 21H04659, JST, CREST Grant No. JPMJCR2102, Japan, and JSPS KAKENHI Grant No. JP22J11158. The authors thank Dr. Satoshi Tomita, Dr. Nobuaki Kikuchi, Dr. Seigo Ohno, and Dr. Toshiyuki Kodama for valuable discussions.