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Abstract
We numerically and experimentally proposed a reconfigurable THz metamaterial (MM) by employing microelectromechanical cantilevers into a ladder-shaped MM (LS-MM). A fixed-free cantilever array with a dimpled tip behaved as Ohmic switches to reshape the LS-MM so as to actively regular the transmission response of THz waves. The cantilever tip was designed to be a concave dimple to improve the operational life without sacrificing the mechanical resonant frequency (fmr), and a fmr of 635 kHz was demonstrated. The device actively achieved a 115-GHz change in transmittance resonant frequency and a 1.82-rad difference in transmission phase shift, which can practically benefit advancing THz applications such as fast THz imaging and 6 G communications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves have drawn ever-increasing attention in recent years due to a wide potential in medicine identification [1], imaging [2], and wireless communications beyond 5 G [3–6]. Since most substances in nature react weakly with THz waves, there are few optical materials suitably operating in the THz region. Alternatively, metamaterials (MMs) as artificial materials, are of extensive attention due to the structure-dependent characteristics [7–12]. MMs are composited of periodic metallic unit cells, and they can desirably regulate THz waves by designing their structures, and thereby benefiting numerous appealing THz devices, such as optic complements [13], Fano-resonant sensors [14], and power attenuators [15].
With advance requirements for more diverse applications, active changes in the optical characteristics of THz waves are required [16]. Active THz MM has been flourishingly developing by employing various tuning approaches, such as electron injection, liquid crystal, and so on [17–20]. However, these approaches only achieve a small tuning contrast because the refractive-index-change of the substance and the environmental medium is limited. In contrast, microelectromechanical systems (MEMS) can convert electric energy to mechanical motion, and so obtain a big tuning contrast due to direct reshaping of MM structures [21]. Therefore, MEMS-driven MMs can advantageously actively tune THz waves [22,23], and be used as crucial components in filter [24,25], bolometer [26], polarization change [27], frequency-selective filter [28], slow-light device [29], optical activity controller [30], and detector [31].
The realization of THz devices with a short acquisition time is indispensable to develop advancing THz applications such as high-speed THz imaging. Since the maximum actuation speed of the MEMS actuator is bounded by its natural mechanical resonant frequency (fmr), increasing the fmr and hence extending the limitation in actuation speed is crucial to promoting fast MEMS devices [32]. In our prior work [33], we demonstrated a switchable ladder-shaped THz MM by employing an ultra-small MEMS cantilever array, the cantilever actuator reached a fmr of 585 kHz. However, the repeatability of the reported cantilever was poor because of lacking an anti-stiction structure.
One of the conventional methods to increase the life time of the cantilever is adding a stress compensation layer to provide a recover force during the vibration so as to avoid the permanent stiction. However, the fabricated cantilever may has an initially curved beam after the release process due to a mismatched residual stress between the bilayer [34,35]. The upwardly bending beam requires a higher drive energy while the downwardly bending beam sacrifices the tuning contrast. An alternative way is utilizing the RF MEMS switch technology, that is, employing a dimple stop as an anti-stiction structure into the cantilever [36]. RF MEMS switches require a smaller deformation of the root to reshape the MM, which prevent the cantilever from plastic deformation so as to improve the life time. Unlu et al. realized a THz modulator by employing MEMS cantilevers with a dimple stop into a mesh filter, and the transmission modulation depth was 70% [37]. However, the reported cantilever with dimples has a big mass, which results in a small fmr of 272 kHz. Additionally, the fabrication process of reported RF MEMS switches with a dimple is complicated, which is difficult to be implemented into MMs [38,39].
In this work, we numerically and experimentally proposed an active THz MM by integrating dimpled-tip MEMS cantilever with a ladder-shaped MM (LS-MM) based on our prior work [33]. Unlike reported MEMS cantilevers utilizing a solid-lump dimple, we designed a cantilever with a hollow and concave dimple. Owing to the light mass of this dimple structure, the cantilever with a high fmr over six hundred kHz was realized for the first time. The device achieved an active transmission response for THz waves with an electrostatic actuation, a 115-GHz change in transmittance resonant frequency and a 1.82-rad difference in transmission phase shift were demonstrated. This work fabricated the dimple structure in four steps, which was easier than that of the reported work in six steps. Taking advantage of the ease of integrating into integrated circuits for miniaturization, this device offers a potential in fast THz imaging and 6 G communications.
2. Design and calculation
Figure 1(a) illustrates schematics of the proposed MEMS-driven LS-MM (MEMS-LS-MM). The device consists of a 500-µm-thick SiO2 substrate, a 6-µm-wide Au lead array, a 0.4-µm-thick SiO2 isolation film, and a planar gold LS-MM with a MEMS cantilever array. The LS-MM was prepared on the top layer to couple with the income THz electromagnetic fields. The one-unit cell of the LS-MM was composed of two arms and a split bar. A MEMS cantilever array was aligned to the split bar of the LS-MM. They have one fixed end that anchors in the LS-MM, and another initially free end with a concave dimpled tip. The operation state of a one-unit cell was shown in Fig. 1(b). The cantilever moves towards the lead in a parallel-plate configuration manner. The free-end cantilever tip is suspended at the rest state, which is called off-state in this work; with a small electrical potential difference, lower than or equal to the pull-in voltage (Vpull-in), applied between the LS-MM and leads, the electrostatic force pulls the movable cantilever tip towards the lead as the intermedium-state; when the applied voltage is higher than the Vpull-in, the electrostatic force exceeds the spring force of the cantilever for all displacements, and the tip is snapped into the MM thereby merging the split bar into a connecting bar, corresponding to the on-state. The induced charge distributes differently on the LS-MM at different states, thus, the THz transmission response can be actively controlled by actuating the cantilevers. Owing to the concave dimple, the displacement of the cantilever tip required to reshape the LS-MM is smaller than that of a flat tip, therefore, the deformation of the cantilever root is small, and the cantilever can escape from the permanent stiction caused by a plastic deformation during the vibration. Moreover, since this dimple is a hollow structure but not a solid mass, the cantilever is light and hence can operate at a high speed.
Fig. 1. Schematics of the proposed MEMS-LS-MM. (a) Geometric structure of the array and a one-unit cell of the device. (b) Charge distribution (left-hand side) and the cross-sectional view (right-hand side) of the one-unit cell at different states.
Simulation of the optical responses of the MEMS-LS-MM was conducted by the finite element method based on Maxwell’s equations via COMSOL Multiphysics 6.0 (COMSOL, Inc.). In the calculation model, both the x- and y-directions side boundary were set with Floquet periodicity boundary conditions, and the top and bottom domains were set with perfectly matched layers and scattering boundary conditions to avoid extra reactions resulted by interference waveforms. Ey-polarized THz incomes were normally incident on the device. The material property of the SiO2 were set with the measured optical constants (see Supplement 1), while gold was set as a perfect electric conductor. Figures 2(a) and 2(b) plot the calculated transmittance and transmission phase shift normalized by a bare SiO2 reference. As the device was actuated from off- to on-state, the resonance of the transmittance valley was shifted from 1.26 to 0.67 THz. Two drops in the transmission phase shift were found at the off- and on-state-resonances, and leading to a phase delay. In particular, at 1.01 THz, the off- and on-state-device had the same transmittance but a 1.98-rad phase delay, indicating that the MEMS-LS-MM can be favorable for phase shifters. A higher phase shift is possible by replacing the design of the LS-MM with a high phase shift MM, for instance, the one reported in Ref. [20]., and using the same scheme as here.
Fig. 2. Calculated results of the device at the off- and on-states. (a) Transmittance. (b) Transmission phase shift. Real parts of the electric fields in y-component of the device at the (c) off- and (d) on-state both for an incidence of the on-state-resonance of 0.67 THz.
Near-field coupling characteristics of the MEMS-LS-MM were calculated to investigate the nature of the optical resonance shift at the off- and on-state. The y-component electric field mainly confined within the split bar of the LS-MM at the off-state (Fig. 2(c)), whereas concentrated along the arm edge at the on-state (Fig. 2(d)). These behaviors can be explained with the equivalent circuit model and LC resonance [40,41], which were discussed in Ref. [33]. The optical resonant frequency for of the device is determined by ${f_{\textrm{or}}}\; $= $\frac{1}{{2\mathrm{\pi }}}\cdot{({{L_{\textrm{eff}}}\cdot{C_{\textrm{eff}}}} )^{ - \frac{1}{2}}}$, where Leff and Ceff are the total effective inductance and capacitance, respectively. In a one-unit cell, a variable capacitance, Cδ, induced by the cantilever was inversely proportional to the adjustable air gap δ between the tip and the LS-MM by ${C_\delta } \propto \frac{1}{\delta }$. The different δ at off- and on-states led to a different Cδ and hence a different Ceff, thus shifting the for of the device.
Of note, in the design of the geometric structure of the dimpled-tip cantilever, there is a one-side wall structure connecting the anchor and beam as shown in Fig. 3(a), and this structure is designed to harden the fixed end and hence increase the fmr[42]. In the dimpled tip, the point at the wall-free-side edge was named wall-free tip, while the one at the inside edge of the wall was named wall-side tip, the locations of the points were marked with pink dots in Fig. 3 (a). The effect arising from the asymmetric wall on the mechanical deformation of the cantilever during vibration was calculated by using an eigenfrequency study of the MEMS module of COMSOL Multiphysics 6.0. The displacement field of the tip was uneven: the wall-free tip deforms larger than the wall-side tip (Fig. 3(b)). That means, the cantilever tip slightly twists when it vibrates. Specifically, the normalized displacement of the wall-side tip was 97% of that of the wall-free tip (Fig. 3(c)). In short, the wall-side tip provides the cantilever with a high fmr and the wall-free tip obtains a bigger displacement, thus, the cantilever is capable of simultaneously obtaining sufficient deformation and a high fmr, which is the advantage of this asymmetric structure.
Fig. 3. Calculated deformation of the cantilever during vibration. (a) The geometry of the cantilever at the initial state in the calculation model. (b) A snapshot of the displacement field of the cantilever, where the hollow black frame shows the initial position of the cantilever. (c) The normalized displacement of the edge of the dimpled tip, where d is the distance from the wall-free side tip as marked in (a).
3. Fabrication
The MEMS-LS-MM was fabricated on a quartz glass substrate by using standard surface micromachining techniques. Figure 4 shows the fabrication flow to prepare the MEMS-LS-MM. First, a piranha cleaning (H2SO4 : H2O2 = 2 : 1) was performed to a quartz glass substrate (Fig. 4(a)) [43]; then, Ti/Au/Ti films were deposited with a sputtering technique on the substrate, in which the 5-nm-thick Ti films were used as adhesive layers (Fig. 4(b)); next, films were patterned to be the lead array by photolithography and wet etching (Fig. 4(c)). Subsequently, SiO2/Ti/Au films were deposited (Fig. 4(d)), and the LS-MM was patterned with photolithography and wet etching (Fig. 4(e)). Next, a Cr film was deposited (Fig. 4(f)) followed by patterning (Fig. 4(g)) to serve as the sacrifice for the dimpled tip. Next, photolithography was conducted to form the anchor hole pattern (Fig. 4(h)), and an Au film was deposited with a sputtering technique as the cantilever beam layer (Fig. 4(i)); then, the final round of photolithography (Fig. 4(j)) and wet etching (Fig. 4(k)) were carried out to pattern the cantilever beam. Finally, the sample was soaked in piranha solution and Cr etchant to fully remove the sacrificial resist and Cr pattern, and then dried by a CO2 supercritical drier to prevent stiction by a capillary force (Fig. 4(l)). By employing a Cr sacrificial pattern through steps (f, g), patterning the resist shape for cantilever beam in step (h), and etching the Cr sacrificial pattern in step (l), a cantilever with a dimpled tip can be fabricated finally. The fabrication process for the dimple in this work (4 steps) is easier than reported work (6 steps) [37].
Figure 5 shows SEM images of the fabricated device. A MEMS-LS-MM pattern was formed within 5.5 × 5.3 mm2 in area, larger than the THz incidence spot of 5 mm in diameter. There were 6000 cantilever units in one pattern area. A one side wall was formed around the cantilever anchor as designed. By well-managing the deposition condition and cantilever release process, a cantilever array with a straight and suspended beam was fabricated, and the tip of the beam was a concave shape. The designed and fabricated dimensions were listed in Table 1. To ensure sufficient contact between the tip and the LS-MM, the length of the dimple, l2, was designed to be 5 µm. The design of other geometric parameters of the LS-MM and the cantilever was discussed in prior works [12,33].
Fig. 5. SEM images of the fabricated device. Zoom-in view of (a) the array structure and (b) one-unit cantilever.
Table 1. Designed and fabricated dimensions of the device.
4. Mechanical characteristics
4.1 Switching cycle
The switching cycle with respect to the voltage ramp of the cantilever was measured in the air and plotted in Fig. 6. A sinusoidal input at 5 kHz with an amplitude of 180 V that is larger than the Vpull-in of 154 V was applied. An alternating positive and negative voltages were used to decrease the risk of electric breakdown of the dielectric isolation layer caused by the mobile free charge accumulation. The velocity of the cantilever tip with respect to the voltage ramp was measured via Polytec MSA-400 microsystem analyzer (Polytec, Inc.), and the signal was recorded with an oscilloscope (Fig. 6(above)). Then, the vibration distance of the tip was computed by an integral of the recorded velocity signal over measurement time via OriginPro (OriginLab Corporation), which is the transient displacement of the cantilever tip (Fig. 6(below)). The sign of the velocity indicated the direction of the cantilever motion by negative for a downward and positive for an upward motion. Periodic rapid drop and rise in the displacement data were observed, suggesting that a pull-in and release motion repeatedly occurred in the cantilever. The lifetime of the fabricated cantilever is estimated by applying the drive voltage at frequencies in the 5-500 kHz range, indicating that the cantilever still works after accumulating more than 100 million vibration cycles. The dynamic vibration of cantilevers was filmed in a video in Visualization 1. In the video, the applied voltage was manually turned on and off to show a visible vibration.
Fig. 6. Measured velocity (above) and the computed displacement (below) of the cantilever with respect to the voltage ramp.
4.2 Natural mechanical resonance
The mechanical frequency response of the cantilever was measured with a chirp input wave with a peak voltage of ±5 V in the air. Figure 7 plots the measured FFT signal of the vibration velocity versus the mechanical frequency. The laser spot was positioned at the edge of a wall-free side cantilever tip as shown in the inset of Fig. 7. The first mechanical resonance was found at 635 kHz, indicating that the cantilever takes 1.57 µs to complete one natural vibration cycle. A quality factor Q of 20 was computed from the measured frequency response, which was higher than the reported value of 5.2 in Ref. [37]. These results indicate that the cantilever with a dimpled tip remains a high fmr while improving the lifetime.
Fig. 7. Measured mechanic response of the cantilever actuator. The pink dots show the measured FFT signal of the magnitude of the vibration velocity. △fm is a −3 dB bandwidth. Inset shows the laser spot position in the cantilever.
5. Transmission characteristics
The active transmission characteristics of the MEMS-LS-MM was measured via THz time-domain spectrometer (THz-TDS) (TeraProspector, Nippo Precision Co., Ltd.). Figure 8 schematically shows the measurement setup. The sample under test was fixed with a holder in the chamber of the THz-TDS, the THz light was illuminated from the emitter and normally incident on the sample, and then detected by the detector. For applying drive voltage, a wave generator was connected to the device through the contact pad for the lead and LS-MM. The actuated and rest state of the device was controlled by powering the generator on and off. To measure the transmission response of the device at an actuated state, a bipolar square input wave that reduces the mobile free charge accumulation in the dielectric isolation layer was applied. The input square wave with an amplitude of 165 V and a frequency of 40 kHz that well below the mechanical resonance (635 kHz) was used to provide a constant actuation, so the cantilever remains the actuated state during the measurement. To measure the device at a rest state, the generator was powered off and no drive voltage was applied, the cantilever beam released back to the suspended position. Figure 9 shows the measured transmission results of the device at the rest and actuated states, both data were normalized by a bare SiO2 reference. With an electrical actuation, the optical resonant frequency shifts from 1.196 THz to 1.081 THz, resulting in a frequency change Δfor of 115 GHz. At 1.14 THz, a phase delay of 1.82 rad were experimentally achieved.
Fig. 9. Measured active transmittance (above) and transmission phase shift (below) of the device at the rest (0 V) and actuated (165 V) states.
6. Discussion
The measured Δfor (115 GHz) was smaller than the calculated value (590 GHz). One possible reason for the difference in the Δfor is the actuation imperfections and measurements errors. Additionally, the non-uniform vibration of the dimpled-tip cantilever is supposed to be responsible for the smaller Δfor in experiment. The optical resonant frequency is determined by for $ \propto $ (Leff · Ceff)-1. Since the basic shape of the LS-MM does not change at off- and on-states, Leff does not change. Therefore, the Δfor is dominantly affected by the change in Ceff at the off- and on-states. The cantilever introduces a variable capacitance Cδ and changes its value at the off- and on-states by varying the δ, and hence affect the Ceff. In experiment, the change in Cδ is smaller than that in calculation, which lead to a smaller Δfor. The reason why Cδ changes less in the experiment is that the non-uniform motion of the cantilever is averaged out. It can be seen from Figs. 3(b) and 3(c), the cantilever tip slightly twists when it vibrates, thus, the effective displacement, i.e., the change in δ of the whole dimpled tip, is averaged out and less than that of the wall-free tip. Consequently, the Cδ changes less in practical experiment.
It is worth noting that the proposed device is possible to analogously modulate the optical properties under operating conditions below the pull-in voltage, which is another potential advantage of this study. The for as a function of the δ was calculated and plotted in Fig. 10. As the δ decreases, the for gradually shifts. In particular, the for gradually varies with δ even for small values less than 200 nm. That means, by designing an initial δ to be smaller than the pull-in displacement, namely, smaller than one-third of the beam height h, the cantilever tip would be capable of stabilized at any position (at a range of 0 to δ) by controlling the magnitude of the applied voltage. Thus, any corresponding for could be obtained, which allows the device to achieve analog tuning for THz waves. The fabricated initial δ depends on the thickness of the sacrifice Cr, which can be controlled by changing the deposition time in the fabrication.
7. Conclusions
In summary, a MEMS-driven THz MM with a high fmr of 635 kHz and good repeatability was proposed and demonstrated for the first time. A fixed-free cantilever array behaved as Ohmic switches to reshape a ladder-shaped MM so as to control the transmission response for THz waves. In comparison of reported work, we improved the operational life of the cantilever switches without sacrificing the fmr owing to the design of a light dimpled tip. The MEMS device achieved a 115-GHz change in transmittance resonant frequency and a 1.82-rad difference in transmission phase shift with an electrostatic actuation, which can facilitate the development of THz waves in fast imaging and 6 G communications.
Funding
Japan Society for the Promotion of Science (JP22J11158); Japan Science and Technology Agency (JPMJCR2102); Ministry of Education, Culture, Sports, Science and Technology (21H04659).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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