Electrostatic Comb-drive Actuators Research Articles

Suppressing residual vibrations in comb-drive electrostatic actuators: A command shaping technique adapted to nomadic applications

Residual vibrations are a recurrent problem in MEMS actuators leading to a limitation of their dynamics and lifespan. This paper presents a voltage-controlled technique and its applicability to suppress residual vibrations in high voltage (about 100 V) electrostatic comb-drive actuators. The studied actuator is composed of a driving module and a clutch module devoted to the step by step driving of linear or circular gears.The proposed method is based on a command shaping technique well adapted to be integrated in an Application-Specific Integrated Circuit (ASIC), especially for nomadic applications. Firstly, an electrodynamic characterization is used to extract the key voltages of the optimized command signals. The key voltages correspond to the beginning and the end of the actual displacement. The command signals consist of two begin/end voltage jumps and a linear voltage rise/fall in an optimized time between the key voltages. Then, experimental validations investigated the influence of voltage fall time for a MEMS chip and the resulting dispersion for a set of 8 MEMS chips. The results show that residual vibrations are reduced by a factor higher than 20 in terms of the amplitude rate of bounces against back stop and the settling time of free oscillations. Finally, an analog circuit capable of building the optimized command signals is proposed and will be implemented in the next generation of the ASIC driving the electrostatic two-module actuator.

Design of electrostatically tunable terahertz metamaterial with polarization-dependent sensing characteristic

We present a design of MEMS-based tunable terahertz (THz) metamaterial (TTM) with polarization-dependent sensing characteristic. The MEMS-based TTM device is reconfiguration by using two electrostatic comb-drive actuators, which exhibits tunable dual-band resonances in both transverse electric (TE) mode and transverse magnetic (TM) modes. The tuning ranges of free spectra ranges are 42 GHz and 82 GHz for TE and TM modes, respectively by increasing the gap between the left and right semicircle-shaped ring resonators. The electromagnetic responses of the proposed MEMS-based TTM device can be switched between dual-resonance and triple-resonance by changing the distance between the left and right semicircle-shaped ring resonators along y-axis direction. These results indicate MEMS-based TTM device shows polarization-sensitive and switching characteristics. MEMS-based TTM device is particularly sensitive to the environmental refraction index, and there is a linear relationship between the shift of resonant frequency and the change of refraction index. The sensitivity is 0.186 THz/RIU while the maximum figure of merit and quality factor reach 208 and 248, respectively at the first TE resonance. These outstanding and unique results of MEMS-based TTM device provide an effective approach for the design of highly linear and sensitive gas and environmental applications.

Micromachined Subterahertz Waveguide-Integrated Phase Shifter Utilizing Supermode Propagation

In this work, we propose a new concept of phase shifting by tuning the coupling distance between two parallel silicon slabs that support the propagation of an in-phase supermode. A prototype device was implemented in the 220-330-GHz band by integrating the micro-electro-mechanical system (MEMS)-actuated phase-shifting mechanism, based on two moveable parallel-coupled high-resistivity silicon slabs, inside a metallized hollow rectangular waveguide in silicon-on-insulator (SOI) micromachining technology. The prototype device has been characterized to a maximum continuous phase tunability of 550° with a maximum insertion loss of 1.87 dB achieved at 330 GHz. A maximum figure-of-merit (FOM) of 375°/dB is achieved at around 320 GHz, which presently is the highest FOM value reported for any phase shifter in the subterahertz (sub-THz) frequency range. The bandwidth covers the whole waveguide band with an average and worst case insertion loss of 1.94 and 2.5 dB, respectively, a worst case insertion-loss variation of 0.7 dB and a phase error better than 4° for all phase states. A large displacement of MEMS electrostatic comb-drive actuators that are co-fabricated in the micromachined waveguide platform is achieved by a driving voltage of 50 V. The prototype footprint is 7.3 ×5.3 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Improvement of silicon microdisk resonators with movable waveguides by hydrogen annealing treatment

In silicon photonics, silicon microdisk resonators with movable waveguides driven by electrostatic comb-drive actuators have been used as wavelength-selective switches. However, the sidewall roughness of silicon waveguides formed by the etching process is the main cause of optical loss in such devices, which leads to the deterioration of the wavelength selectivity. In this study, we fabricated a silicon microdisk resonator with a movable waveguide and performed a hydrogen annealing treatment as a postprocessing step to remove the sidewall roughness. By using scanning electron microscopy, a reduction in sidewall roughness was confirmed following the hydrogen annealing treatment. Then, the extinction ratio at the through port was evaluated while changing the gap between the microdisk and the movable waveguide. A dip in the extinction ratio was observed at the resonant wavelength while decreasing the gap, which indicated that the fabricated device successfully functioned as a wavelength-selective switch. Due to the hydrogen annealing treatment, the quality factor of the dip increased from 7102 to 37 402. These results show that the hydrogen annealing treatment can be used as a postprocessing step and is helpful for improving the wavelength selectivity of silicon photonic wavelength-selective switches.

A torsional thrust stand for measuring the thrust response time of micro-Newton thrusters

Drag-free technology functions as the keystone for space-based gravitational wave detection satellites moving along a geodesic path, like the Laser Interferometer Space Antenna (LISA) Pathfinder, to achieve ultra-high microgravity level. Several prerequisites for micro-thrusters operated under the drag-free technique include constantly adjustable thrust, high resolution, low noise and fast response time. Accordingly, a torsional thrust measurement system was methodically devised to measure the thrust response time of such micro-thrusters on the ground. The characteristics of the dynamic thrust change with time are inverted by the angular displacement of the torsional pendulum, established by the dynamic equation of the same, thus, measuring the rise/fall time of the thrust applied to the torsional pendulum. Calibration of the torsional pendulum thrust measurement system is carried out by the standard electrostatic force generated by the electrostatic comb-drive or microelectromechanical actuator, facilitating the suitable identification of the pendulum parameters. Afterwards, the electrostatic and electromagnetic forces generated by the actuator are applied to validate the measurable thrust response time of the torsional thrust stand. The experimental results show that the above-mentioned thrust stand can effectively measure the thrust response time up to 10 ms for a thrust step in 10 s of micronewtons, which qualifies as the thrust response time required by micro-thrusters for space-based gravitational wave detection.

Temperature stability study of resonant angular scanning micromirrors with electrostatic comb-drive actuators

Resonant rotational scanning micromirrors with electrostatic comb-drive actuators are widely used in generating structured lights for 3D sensing, but their resonant scanning stability is affected considerably by the working temperature, which in turn compromises the sensing accuracy. The resonant scanning instability is mainly exhibited as the temperature drifts of the quality factor (Q) and the resonance frequency. In this paper, we focus on the Q variation due to the temperature dependence of air damping. The temperature dependence of the air damping in a comb-drive micromirror is investigated using both simplified analytical damping models and computational fluidic dynamic (CFD) models. The modeling results show that the temperature dependence of the viscous damping of the comb drive is opposite to that of the drag damping of the mirror plate, providing a means of minimizing the temperature dependence of Q by adjusting the structural parameters of the comb drive and the mirror plate. It has also been found from the modeling that the lengths of the comb-drive fingers and the mirror plate play the most significant role while the cavity height under the mirror plate has little effect if it is more than 10 % of the mirror plate length. Meanwhile, four micromirrors with different comb-finger or mirror-plate lengths are designed and fabricated. The testing results from these four fabricated mirrors have confirmed that the temperature coefficient of the Q value of an angular scanning comb-drive micromirror can be altered and ultimately compensated by changing the mirror-plate and/or comb-finger lengths.

A Two-Step Fabrication Method for 3D Printed Microactuators: Characterization and Actuated Mechanisms

The fabrication and integration of microactuators with 3D micromechanisms are necessary to develop microrobots with higher capability and complexity. In this work, a two-step fabrication method combining 3D printing with two-photon polymerization (TPP) and aluminum sputtering is demonstrated. Actuators using two different transduction mechanisms (thermal and electrostatic) were fabricated in this process, and a thermal actuator was printed with a mechanism in three-dimensional space without additional assembly steps. This work also provides parameterized characterizations which can be used as design guidelines for building actuators and mechanisms. A design approach to electrically isolate the actuators from the substrate is introduced so that the device can be functional after two fabrication steps without patterning the metal layer. Metal coverage on the sidewalls of trenches are characterized, which provides a design space for deciding electrode gaps and heights in electrostatic actuators. Using these guidelines, 500 $\mu \text{m}$ long thermal actuators showed a maximum displacement of 18.0 $\mu \text{m}$ at 8.31mW and reliably actuated up to 8,500 cycles. An interdigitated electrostatic comb-drive actuator was also successfully demonstrated, displacing 12.7 $\mu \text{m}$ when 160V was applied. Finally, a 3D actuated mechanism was designed by incorporating a thermal actuator with 3D compliant mechanisms to flap 250 $\mu \text{m}$ long wings. Flapping motion was successfully demonstrated. [2020-0010]

Fabrication of a MEMS Micromirror Based on Bulk Silicon Micromachining Combined With Grayscale Lithography

A 1D MEMS (Micro-Electro-Mechanical Systems) mirror for LiDAR applications, based on vertically asymmetric comb-drive electrostatic actuators, is presented in this work employing a novel fabrication process. This novel micromachining process combines typical SOI-based bulk micromachining and grayscale lithography, enabling the fabrication of combs actuators with asymmetric heights using a single lithography step in the active layer. With this technique, the fabrication process is simplified, and the overall costs are reduced since the number of required lithography steps decrease. The fabricated mirrors present self-aligned electrodes with a $2.8~\mu \text{m}$ gap and asymmetric heights of the movable and the fixed electrodes of 20 $\mu \text{m}$ and 50 $\mu \text{m}$ , respectively. These asymmetric actuators are an essential feature for the operation mode of this device, enabling both in resonant and static mode operation. A mirror field of view (FOV) of 54° at 838 Hz was achieved under low-pressure, when resonantly operated, and a FOV of 0.8° in the static mode.

An On-Chip Micromachined Test Structure to Study the Tribological Behavior of Deep-RIE MEMS Sidewall Surfaces

An on-chip micro-mechanical test structure is presented to investigate the tribological behavior of deep reactive ion etching (DRIE) sidewall surfaces of microelectromechanical systems (MEMS) devices. The proposed test structure is fabricated on silicon on insulator (SOI) wafer using a standard surface micromachine process. Test structure consists of two orthogonally placed electrostatic comb-drive actuators, one is used to align a contact with the friction surfaces under a certain normal load, and another one is used to generate the tangential motion on contacted sidewall surfaces. To assess the frictional behavior of DRIE sidewall surfaces, both static and dynamic friction coefficients were studied for different DRIE process parameters. Wear analysis was carried out to extract the performance and reliability of MEMS sidewall surfaces during their operation. From the experiment results, it is found that with the increment of normal load, the static friction coefficient exhibits a nonlinear dependence, and however, it has less effect on the dynamic friction coefficient. DRIE process parameters have a significant influence on static and dynamic friction coefficients, i.e., variation in asperity size changes the real contact area between the contact pairs during their operation. From the wear analysis, it is found that the friction coefficient was very high initial value, then it drops with each subsequent cycle for a few cycles and finally reaches steady-state value.

Real-time tunable phase response and group delay in broadside coupled split-ring resonators

Manipulating the phase of electromagnetic radiation is of importance for applications ranging from communication to imaging. Here, real-time reconfigurable phase response and group delay of a tunable terahertz metamaterial consisting of dual-layer broadside coupled split-ring resonators is demonstrated. Utilizing electrostatic comb-drive actuators, the metamaterial resonant frequency is tuned by changing the lateral distance between the two layers which modifies the transmission amplitude and phase spectrum. The phase modulation is approximately 180\ifmmode \mathring{}\else \r{}\fi{} in the vicinity of the resonant frequency. In addition, remarkable modulation in the group delay of transmitted pulses (from \ensuremath{-}7 to 3 ps) is evaluated based on the measured frequency response using the convolution method when the lateral distance is changed from 0 to $24\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. A two-port resonator model, derived from coupled-mode theory and supported by finite-element full-wave simulations, reveals the underlying physics of the modulation. Specifically, the coupling factor between the two layers plays a critical role, the tuning of which provides a route for structure design and optimization. The capability of tuning the phase response and group delay enables applications, such as phase compensation and group-delay equalization at terahertz frequencies.

Trapezoidal-shaped electrostatic comb-drive actuator with large displacement and high driving force density

This paper presents a design of a comb finger shape and calculation of a trapezoidal-shaped electrostatic comb-drive actuator (TECA) in order to aim a higher electrostatic force density and larger displacement in comparison with the typical rectangular-shaped electrostatic comb-drive actuator (RECA). Relation between a beam's stiffness and a driving voltage has been examined to predict a pull-in effect occurring in TECA. Micro fabrication and characterization of TECA and RECA systems are performed by using a standard SOI-MEMS technology. Theoretical and experimental results confirm the strong points of TECA's structure (similar to the dimensions of RECA) such as a larger number of movable comb finger arrayed at the same length and larger displacement. At driving voltages of 47.9 and 50 (V), the calculation and measurement displacement of TECA are approximately 2.2 and 1.78 times larger than that of RECA, respectively.

Design and Analysis of a Novel MOEMS Gyroscope Using an Electrostatic Comb-Drive Actuator and an Optical Sensing System

In this paper, a novel vibratory optical MEMS gyroscope is proposed, which is composed of an optical sensing system, an electrostatic comb-drive actuator, and a mass-spring system with 2 degrees of freedom and a decoupling frame. The optical sensing system consists of a laser diode light source, a tunable photonic crystal, a photodetector, and integrated waveguides. The sensitive element of the proposed gyroscope has been designed with separated primary and secondary resonance frequencies to increase the operating bandwidth. Simulation results show that the functional characteristics of the proposed gyroscope are as follows: an operating frequency of 1830 Hz, a sense mode resonance frequency of 2330 Hz, an operating bandwidth of 200 Hz, a mechanical sensitivity of 0.14 nm/(°/s), an optical sensitivity of 0.051 nm/(°/s), and a measurement range of ±500 °/s.

Hierarchy of models for electrostatic comb-drive actuators in electrolytes

Electrostatic comb-drive actuators in electrolytes have many potential applications, the most popular of which is characterizing the mechanical properties of biological structures at small scales. Maximizing the utility of these devices for such applications requires a model capable of accurately predicting their behavior. The current state of the art model of these actuators assumes (i) that the native oxide is a pure dielectric, (ii) that the ion concentration of the bulk electrolyte is constant, and (iii) that the Stern layer can be neglected compared to the oxide layer. This model captures the general behavior of the electrostatic actuator in electrolytes, but has limited accuracy. We propose a hierarchy of models that addresses the suitability of these assumptions separately and in concert. We find that the model which removes assumptions (i) and (ii) is sufficient to accurately predict the displacement of a comb-drive actuator in electrolytes.

Design of a Novel MEMS Microgripper with Rotatory Electrostatic Comb-Drive Actuators for Biomedical Applications.

Primary tumors of patients can release circulating tumor cells (CTCs) to flow inside of their blood. The CTCs have different mechanical properties in comparison with red and white blood cells, and their detection may be employed to study the efficiency of medical treatments against cancer. We present the design of a novel MEMS microgripper with rotatory electrostatic comb-drive actuators for mechanical properties characterization of cells. The microgripper has a compact structural configuration of four polysilicon layers and a simple performance that control the opening and closing displacements of the microgripper tips. The microgripper has a mobile arm, a fixed arm, two different actuators and two serpentine springs, which are designed based on the SUMMiT V surface micromachining process from Sandia National Laboratories. The proposed microgripper operates at its first rotational resonant frequency and its mobile arm has a controlled displacement of 40 µm at both opening and closing directions using dc and ac bias voltages. Analytical models are developed to predict the stiffness, damping forces and first torsional resonant frequency of the microgripper. In addition, finite element method (FEM) models are obtained to estimate the mechanical behavior of the microgripper. The results of the analytical models agree very well respect to FEM simulations. The microgripper has a first rotational resonant frequency of 463.8 Hz without gripped cell and it can operate up to with maximum dc and ac voltages of 23.4 V and 129.2 V, respectively. Based on the results of the analytical and FEM models about the performance of the proposed microgripper, it could be used as a dispositive for mechanical properties characterization of circulating tumor cells (CTCs).

Influence of the side etching effect in DRIE on performance of electrostatic linear comb-drive actuators

Side etching and scalloping are unwanted but unavoidable phenomenon occurring during fabrication process of micro electro-mechanical system devices with the deep reactive ion etching technology. This paper reports the influence of deep reactive ion etching fabrication errors on the geometrical dimension (as a comb finger shape, width of the suspension beam), electrostatic force and displacement of electrostatic linear comb-drive actuators. A number of deep reactive ion etching experiments were carried out in order to find out the optimal etching and passivation time, which allows to achieve vertical and smooth sidewall, as well as acceptable side etching value. Discussion and evaluation of deviation between the theoretically calculated and measured displacements of the electrostatic linear comb-drive actuator were also reported.

A Monolithic Approach to Downscaling Silicon Piezoresistive Sensors

Multi-scale integration remains the primary challenge in the fabrication of miniature piezoresistive sensors, as the co-fabrication of a silicon nanowire along with a microscale shuttle is the main architecture facilitating high-sensitivity transduction. The efforts in this field are marred by the lack of batch techniques compatible with semiconductor manufacturing. A technology is introduced here that leads to the fabrication of a piezoresistive silicon nanowire sharing the same single-crystalline device layer of a thick silicon-on-insulator wafer as the microscale component. The approach is based on a combination of high-resolution lithography with a two-stage etching process. The demonstration is carried out by spanning an electrostatic comb-drive actuator and a micromechanical amplifier by a single nanowire. A gage factor range of 135-145 is obtained, corresponding to an almost 20% resistance change for a nanowire strain of 1.26 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The technique is shown to generate a two-order-of-magnitude scale difference within the same silicon crystal. It also provides ease of electrical access to the nanowire, as the nanowire does not remain buried underneath the thick micromechanical system. With the associated lack of high-temperature processes and its CMOS-compatibility, the technique is a promising enabler for future miniaturized piezoresistive sensors.

The stabilization system of primary oscillation for a micromechanical gyroscope

The mode of primary oscillations of a micromechanical gyroscope (MMG) sensor is provided by an electrostatic comb-drive actuator in which the interaction between the micromechanical structures and electronics occurs by means of a single or differential capacitive sensor. Two pairs of capacitive sensors are traditionally used for frequency stabilization of MMG primary oscillations. The first pair of capacitive sensors excites primary oscillations, while the second measures the amplitude of primary oscillations. The stabilization system provides a continuous frequency tuning of primary oscillations that increases the duration of transition processes, the time of operational readiness, and the instability of the output signal from the secondary oscillation channel of the MMGs. This paper presents a new approach to the primary oscillation control system of the two-component MMG. The method of calculating the natural resonant frequency is based on measurements of the total current passing through the comb-driver actuator capacitances, and a lock-in detection is suggested. This paper consists of the results of the numerical analysis, the description of the proposed approach to the frequency control of the primary MMG oscillations, and the Simulink model of the behaviour of the MMG stabilization system, depending on its mechanical-and-physical properties with regard to a 2% shift of the natural resonant frequency. The frequency control of the primary oscillations at 2% frequency detuning is performed within 0.11 s.

Development of new electrostatic micro cam system driven by elastic wings

In this paper, we improve and develop a micro cam system, in which reciprocating linear movement of two electrostatic linear comb-drive actuators (ELCA) is transformed into the unilateral rotation of a cam rim through six elastic wings of motion-transmission mechanisms. The system was fabricated by using SOI-MEMS technology and only one photo mask. Our experimental results show that the new micro cam system runs stably while the driving frequency ranging from 1 to 30 Hz with the driving voltage Vpp = 100 V. In addition, the average angular velocities of the cam rim matched with the theoretical results better than the velocities measured in the previous micro cam system.

SOIMUMPs micromirror scanner and its application in laser line generator

A SOIMUMPs 1-D rotation micromirror is presented. The micromirror is driven by electrostatic vertical comb-drive actuators to work at resonant mode to scan a laser beam. The residual stress in the metal film coated on the SOI device layer is used to generate vertical offset in the comb-drive actuators with the combs located far from the rotation axis to increase the torque. A concave lens is designed to put after the micromirror to amplify the laser beam scanning angle, as well as to compensate for the curvature of the micromirror. A micromirror-based scanning system is used to build a laser line generator with a continuously adjustable fan angle, which solves the limitation of a fixed fan angle in conventional laser line generators. Prototypes of the micromirror and the laser line generator are fabricated and measured. A driving circuit that can generate a high-voltage square wave driving signal with adjustable amplitude and frequency is designed. All the parts are integrated in a 44 mm×88 mm×44 mm box and powered with a single 5-V power supply. The optical scanning angle under 100 V with or without the concave lens is 27 deg and 12 deg, respectively, at a resonant frequency of 900 Hz.

Nano-optomechanical characterization of surface-plasmon-based tunable filter integrated with comb-drive actuator

We report a tunable plasmonic color filter consisting of a metamaterial periodic grating and microelectromechanical systems (MEMS) actuator. An aluminum subwavelength grating is integrated with electrostatic comb-drive actuators to expand the metal subwavelength period, which allows continuous control of the excitation wavelength of surface plasmons (SPs). We develop a batch fabrication process by employing a liftoff technique using an electron beam resist altered by the electron dose depending on different aspect ratios (length/width) for various components such as the subwavelength grating, nanohinge flexural suspensions, and comb fingers. We successfully demonstrate a continuous shift in the excitation wavelength over the 514–635 nm range by nanopitch expansion. The design margin of the grating period for SP excitation is evaluated by comparing the experimental pitch variation and theoretically calculated values. The resonance frequency of the tunable filter is optically measured to be approximately 10 kHz. The optically and mechanically obtained values agree well with the theory of electrostatic actuation and finite-difference time-domain simulation.