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This work describes a novel micromechanical structure capable of producing out-of-plane motion from in-plane forces generated by electrostatic microelectromechanical system (MEMS) actuators. The MEMS actuator is fabricated in a commercial silicon-on-insulator (SOI) MEMS process and is anchored at two distinct locations through a pair of beams with a relatively low stiffness in the vertical direction. A comb-drive, whose fixed and moveable fingers are implemented in the same layer with a uniform thickness, is employed to create an attractive electrostatic force. This in-plane electrostatic force rotates the actuator along an axis defined by the anchors, which results in the vertical motion of a suspended platform. Due to the simple structure of the actuator, it can be readily manufactured with standard bulk micromachining processes. Experimental results demonstrate that the actuator can provide $1.02~\mu \text{m}$ of vertical displacement at a resonant frequency of 395 Hz when it is excited in air by a 10 V AC signal, while the displacement can be considerably increased in vacuum. It is further shown that the functionality of the actuator is not dependent on the type of excitation voltage; therefore, it can produce a $3.09~\mu \text{m}$ static out-of-plane motion when excited by a 40 V DC voltage. A comprehensive comparison to the published works in the literature indicates that the proposed actuator is the only SOI electrostatic MEMS actuator with a relatively thick structural layer, i.e., $10~\mu \text{m}$ , that can provide out-of-plane motion at low actuation voltage reported to date. [2022-0069] [ABSTRACT FROM AUTHOR]

Micromirrors with variable focal length are critical components of various optical systems. However, due to the limitations of microfabrication and actuation mechanisms, it is very difficult to control accurately the surface shape of a varifocal mirror. In this study, a novel surface-micromachined varifocal piston micromirror is presented. By simulating quasi-simply-supported boundary conditions, an accurate focusing of the mirror was achieved. The mirror is controlled by a parallel-plate electrostatic actuator. When the micromirror is actuated, as the driving voltage increases, the micromirror moves and deforms in two stages. In the first stage, four beams that support the mirror bend, which produces the micromirror vertical translation. When the translation reaches its limit, the micromirror enters the second stage, during which it bends to a concave shape and thus can focus light. A prototype based on the proposed concept was fabricated using a commercially available surface micromachining process. An analytical formulation, finite element model, and experimental measurements were adopted to study the electromechanical and optical performances of the micromirror. The focus length could be adjusted from 79.8 mm to 2.03 mm with a residual rms error less than 15 nm by changing the driving voltage. When the deformation reached its maximum, the first 21 Zernike aberration coefficients were all less than 3 nm. The proposed concept is also applicable to circular mirrors. [ABSTRACT FROM AUTHOR]

We present a microelectromechanical system (MEMS)-based closed-loop force sensor, capable of measuring bidirectional forces along one axis of motion. The device comprises an on-chip electrothermal displacement sensor and electrostatic actuators. It features a voltage-controlled stiffness-adjustment mechanism, providing the user with an additional means of tuning the sensor’s characteristics. This silicon-on-insulator device is an improvement on our previous design, offering a better dynamic range and a less complex calibration process. The sensor is fabricated based on a standard SOI MEMS process. It is then fully characterized and instrumented with a feedback controller. The closed-loop characterization reveals a ${1 {\sigma }}$ -resolution of 4.74 nN and a force sensing range of $- {211.7\, {\mu }\text {N}}$ to $\mathrm {211.5\, {\mu }N}$ , leading to a dynamic range of 92.9 dB. [2019-0248] [ABSTRACT FROM AUTHOR]

We propose a method to realize the kilogram through electrical units, namely, the volt. The device is based on a simple plane plate electrostatic actuator used to counterbalance the weight force. The geometry of the electric field is characterized by changing the distance between the plates while maintaining a constant force and measuring the capacitance. This approach leads to the realization of a simple and compact device for the absolute measurement of small masses. The preliminary results show a relative uncertainty of 10−3 for mass above 10 mg. A series of uncertainty sources has been pointed out. An improvement of one order of magnitude is expected by correcting these sources. [ABSTRACT FROM AUTHOR]

The stable travel range of parallel-plate electrostatic actuator with a linear suspension flexure is limited to a third of the nominal gap due to the pull-in instability resulting from the inherent nonlinear behavior of electrostatic force. To overcome this problem, the nonlinear suspension flexure that can counteract the nonlinearity of electrostatic force is widely adopted. Based on this concept, we present a novel method for designing a customized nonlinear micro-flexure with monotonically increasing stiffness. The mechanism is characterized that an ejector rod consisting of the double clamped-guided beams slides along a geometrically customized trajectory patterned on the slider, and thus, a prescribed force-displacement relationship in horizontal direction is generated. To validate this design concept, two specific flexures, a mimic-electrostatic-nonlinearity flexure, whose restoring force varies with the electrostatic force, and a seventh-order nonlinear flexure, whose flexure force is proportional to the eighth power of the deflection, were designed and fabricated on the silicon-on-insulator wafer. The experimental results show that the measured force-displacement curves for two nonlinear flexures are in good agreement with the theoretical predictions. In addition, the proposed method can be also introduced to other systems, in which the prescribed nonlinearity is needed. [2018-0240] [ABSTRACT FROM AUTHOR]

In this paper, we discuss the use of pulse width modulation (PWM) to control analog MEMS devices. We achieve a precise linear analog control of MEMS by applying PWM signal with a frequency well above the system’s mechanical natural frequency. We first demonstrate this using a parallel plate actuator and comb-drive, and then extend the technique to control a commercial deformable mirror. Such an approach allows the system designer to replace expensive drive electronics such as the high precision DACs and high voltage, linear amplifiers with a simple on-off switch. The advancements in the electronics industry tend to make precise timing cheaper and faster; our approach exploits these long-term trends to create low-cost control circuits. We also show how PWM control can linearize the positional response of the devices, where typically the position would depend quadratically on the applied analog voltage. [ABSTRACT FROM AUTHOR]

Planar and flexible climbing robots suffer from buckling while climbing on a vertical surface. This paper analyzes two different modes: one-end free buckling and two-ends fixed buckling. As an example for buckling analyses, the paper focuses on an electrostatic climbing robot that features thin body. As the body of the robot has only 2.5 mm of thickness, it is more prone to buckling than any other flexible robots, making it the best example for the buckling problem. Based on the analyses, the paper proposes a buckling-free control strategy for the electrostatic robots. The proposed strategy guarantees the force balance between adhesive force and weight force, as well as the elastic stability of the robot. To implement the strategy, the paper investigates the available region of the proper forces and optimal parameters on the prototype robot. A prototype of climbing robot was developed to verify the analyses and solutions, weighing merely 29 g (excluding battery and control circuits). It successfully climbed up a vertical wall without buckling, carrying the payload of 0.4 N. [ABSTRACT FROM PUBLISHER]

We present simulations of the failure of radio-frequency micro-electro-mechanical systems switches due to diffusional creep that include the quantification of uncertainty in the geometry, material parameters, and residual stress. The switch is modeled as an Euler–Bernoulli beam that is actuated electrostatically in a fluid medium. The fluid damping is modeled by a squeeze-film model and the beam model incorporates stretching nonlinearity in addition to Coble creep. The resulting nonlinear dynamic model is solved using a Ritz–Galerkin-based modal expansion and explicit time integration. The focus of this paper is on the effect of creep as a failure mechanism and the implications of uncertainty in the device geometry, material parameters, and boundary conditions. The degradation of the device performance is evidenced by decreases in the pull-in voltage, the pull-out voltage, and the impact velocity. We find that the variability in the experimentally measured pull-in voltage is accounted for by the inclusion of uncertainty in the material and geometric properties. [2015-0191] [ABSTRACT FROM PUBLISHER]

The single mirror interferometric MEMS display is a full-color, daylight-visible, video-rate reflective display with high brightness that consumes power only during content updates. It consists of an array of identical pixels each of which can produce a continuous range of colors through precise analog positioning of one moving element, a mirror. Electrostatic actuation is driven with an integrated active-matrix backplane of indium-gallium–zinc oxide thin-film transistors. Displays of $384\times384$ pixels built on a surface micromachining process on glass substrates have been demonstrated on both 6-in wafers and Gen 4.5 panels (730 mm $\times920$ mm) showing good yield and uniformity. [2016-0206] [ABSTRACT FROM PUBLISHER]

This paper presents two capacitive comb drive designs for electrostatic actuation of MEMS with the aim to eliminate the levitation effect often observed in such systems. By placing a shield over the comb drive fingers, it is possible to balance the electric field and suppress vertical forces while maintaining the desired lateral motion. By optimizing the comb geometry, we demonstrate that our approach is able to reduce the levitation by an order of magnitude and unwanted coupling of motion from out-of-plane to in-plane by a factor of 7 compared with standard comb architectures fabricated using PolyMUMPs technology, without the need of alternating comb finger polarities or additional control electrodes. Levitation was reduced to 160 nm, for 3.6- \mu \textm lateral displacement at a driving voltage of 80 $V$ . [2016-0156] [ABSTRACT FROM PUBLISHER]

The electrostatic actuation method has not been used widely in bimorph cantilevers despite its advantage of large displacement and low power consumption, mostly owing to the fact that it is limited to just two stable positions: 1) initial curled; and 2) final flat positions. In this paper, we first demonstrate a bimorph cantilever actuator having multiple steady-state positions in between those two boundary positions, accomplished by simply dividing the bottom electrode. We found that the number of steady-state positions and the steady-state tip heights can be controlled by the design of the bottom electrode. In our test experiment, the steady-state bimorph cantilever tip heights were 48 \mu \textm at 0 V, 28 \mu \textm at 21 V, 7 \mu \textm at 25 V, and 0 \mu \textm (flat) at 29 V, respectively. In order to relieve low reliability of the electrostatic bimorph cantilever, we devised non-contact actuation method and demonstrated that the lifetime of the electrostatic bimorph actuator greatly increased. This paper will pave the way to utilize bimorph cantilever actuators with greater versatility. [2016-0081] [ABSTRACT FROM AUTHOR]

A new bistable micro-electro-mechanical systems actuator functioned by the potassium ion electret technique is presented. We utilize a three-terminal comb-drive actuator with a built-in electret potential. We first describe the operation principle of the bistable device that is driven by a pulse and/or step-function voltage. We next explain the fabrication results and the procedure of the electret polarization. Device operation is demonstrated to determine the switching characteristics from one stable state to another with a 12 V pulse voltage of 300~\mu \texts duration. We also establish bistable switching operation with a step voltage of 5 V or less, which is manageable by a battery for portable equipment. Discrepancy of switching characteristics between the theory and the experiments is discussed from a point of view on the fringe electrical fields between the comb electrodes. [2016-0079] [ABSTRACT FROM AUTHOR]

Recently interest towards electrostatic actuators and machinery has increased for use in MEMS, mechatronics and renewable energy applications. Effective electromechanical power conversion using electrostatics requires dielectric liquids whose permittivity and breakdown field strength can facilitate adequate electric shear stress and pressure beyond the capabilities of media such as air or vacuum. This paper discusses design points for practical electrostatic force production and evaluates available off-the-shelf dielectric liquids in terms of electric pressure capability. Key dielectric properties including pressure, breakdown field strength, relative permittivity, and conductivity are measured. A custom test stand measures the attractive force between two electrodes mounted on load cells inside a tank filled with the liquid under test. Measurements demonstrate liquids capable of reaching several psi of electric pressure while correlating with analytical and finite element (FE) models, ultimately forming a basis for electrostatic actuator/machine design. The best liquid candidate, Vertrel XF, was poured into a proof of concept macro scale electrostatic machine demonstrating 0.9 N-m torque and 0.126 N-m/kg. Torque measurements verify the capability of Vertrel XF and the correlation between the electric pressure and shear stress in a rotating machine. [ABSTRACT FROM AUTHOR]

This paper demonstrates experimentally, theoretically, and numerically for the first time, a wide-range tunability of an in-plane clamped–clamped microbeam, bridge, and resonator actuated electrothermally and electrostatically. Using both actuation methods, we demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally by passing a dc current through it, and electrostatically by applying a dc polarization voltage between the microbeam and the stationary electrode. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Adding a dc bias changes the qualitative nature of the tunability both before and after buckling, which adds another independent way of tuning. This reduces the dip before buckling, and can eliminate it if desired, and further increases the fundamental frequency after buckling. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared with the experimental data and simulation results of a multi-physics finite-element model. A good agreement is found among all the results. [2015-0341] [ABSTRACT FROM PUBLISHER]

This paper presents a novel two-row interdigitating-finger repulsive-torque electrostatic actuator and its application to the micromirror vector display. The actuator consists of upper and lower rotation units and an output beam. Each unit has one row of rotation fingers, i.e., the lower and upper rotation fingers, which interdigitate with each other. The lower and upper rotation fingers are subject to different electric potentials. Each rotation finger and its underneath aligned fixed finger are subject to the same electric potential. The actuator generates repulsive torques to rotate the lower and upper fingers out-of-plane with the maximum rotation not limited either by the gap between fingers and the substrate nor by the pull-in effect. The output beam is connected to the lower row of rotation fingers, and therefore, the actuator has the same rotation as the lower unit. The actuator requires only two thin films and is suitable for surface micromachining. The model is established to verify the actuator and calculate its performance. Prototypes are fabricated and tested. The experimental results show that the actuator achieved a mechanical rotation of 11.5° at the static driving voltage of 150 V and a resonant frequency of 380 Hz with a sinusoidal driving voltage varying from 20 to 70 V. This paper demonstrates the application of the actuator in micromirror vector display. Four actuators are connected to the peripheries of a micromirror plate and independently controlled to drive the mirror plate to achieve quasi-static 2-D rotation. A laser beam is reflected and steered by the mirror plate to any desired direction to realize vector display. The prototype of the vector display micromirror is fabricated and tested. A vector display module integrating the micromirror, a laser, and a concave lens is built. Based on this module, an automotive head-up display system is developed, which is able to display the navigation map, speed, turning sign, and vehicle location on a translucent screen. [2015-0098] [ABSTRACT FROM AUTHOR]

This paper presents the design and fabrication of a new microelectromechanical systems microgripper with integrated electrostatic actuator and capacitive force sensor. One uniqueness of the proposed microgripper is that it possesses a single force sensor which can measure the gripping force and environmental interaction force in two axes in an alternate manner. The gripper structure is devised based on compliant rotary bearing and linear guiding flexure mechanisms, which enable the generation of a compact size. Analytical models are established to facilitate the parametric design of the gripper, which are verified by performing finite-element analysis simulation study. The microgripper is fabricated by the silicon-on-insulator-based process. Experimental calibrations are conducted to demonstrate the gripping and sensing performances. The feasibility and effectiveness of the developed gripper device are validated through the experimental investigations on gripping a human hair. [ABSTRACT FROM PUBLISHER]

In this brief, a robust control design is presented for an electrostatic microbridge actuator. For this system, a spatially distributed electrostatic force serves as control input. Moreover, a spatially distributed measurement of the bridge displacement is assumed to be available. For an accurate tracking of a reference trajectory—repeated periodically during the operation of the microbridge—an iterative learning control (ILC) approach is proposed based on so-called wave repetitive processes. The design procedure represents an efficient combination of linear matrix inequalities and an appropriate parameter optimization. By explicitly considering polytopic parameter uncertainty, the ILC becomes robust against uncertain parameters such as the squeeze film damping coefficient, the mass density, and the time constant of the electrostatic actuator. Convincing simulation results provide a numerical validation of the proposed ILC scheme as a prestage for a future experimental implementation. [ABSTRACT FROM PUBLISHER]

A three-degrees-of-freedom microelectromechanical systems (MEMS) electrostatic actuator was developed, fabricated, and tested. The actuator utilizes a piston-tube configuration that enables the use of electrodes with a wide area. Therefore, a large output force can be generated. The actuator also utilizes a flexure mechanism in which the in-plane ( $x$ - $y)$ stiffness is high compared with the out-of-plane ( $z$ -axis) stiffness. This flexure mechanism enables a large translation stroke along the $z$ -axis before experiencing lateral pull-in instability. A prototype of the actuator was able to achieve a pure translation (piston-style motion) of $28~\mu $ m at 80 V and an angle of rotation of 0.78° at 70 V. A mass of 1 mg was translated $24~\mu $ m at 80 V, indicating the ability of the actuator to provide high output force. The actuator was fabricated using the Micralyne MicraGEM-Si MEMS fabrication process, in which the pistons and tubes are fabricated in the device layers of two bonded Silicon on insulator (SOI) wafers. The misalignment between the pistons and the tubes using this process was $\sim 0.005$ of the gap between adjacent pistons and tubes. This amount of misalignment leads to a negligible lateral instability effect. [2014-0277] [ABSTRACT FROM AUTHOR]

To further decrease feature sizes, the semiconductor industry heavily improved the photolithography. Photoresist layers are exposed through photomasks and structured accordingly. The underlying substrate is then selectively altered by adding or subtracting material. The unrivaled precision, resolution, and accuracy allow an unmatched level of miniaturization, and several thousand electrical components can be processed simultaneously. This technology was expanded to the fabrication of sensors and actuators, creating microelectromechanical systems. With silicon, the possibilities of further expanding this technology to new dimensions and applications are limited. Reasons are the stiffness, 2.5-D fabrication, and lack of optical transparency. To enable new applications, we present the successful translation of wafer-level fabrication to millimeter-scale actuators. This was achieved by changing the material to ultraviolet (UV)-curable polymers. Based on the electrostatic zipper actuator, avoiding the common pull-in-effect is essential for the successful realization of an acceptable microactuator. Therefore, the bottom electrodes are split and shaped to adjust the generated electrostatic forces, balancing the mechanical restoring forces. Besides the theoretical design, the fabrication technology based on classic photolithography is explained. Experimental results include voltage-dependent deflection measurements, achieving 110- $\mu $ m deflection with 70 V driving voltage. The dynamic response measurements show resonance frequencies of 1.89 kHz. [2014-0181] [ABSTRACT FROM PUBLISHER]

To achieve higher hard disk drive areal density, the head–disk clearance had been reduced to <2 nm recently. Head–disk interaction monitoring with high sensitivity and resolution is desired to monitor the intense interactions at near-contact and to prevent head–disk contact. In this paper, head–disk interaction monitoring based on the electrostatic force manipulation (EFM) principle is discussed. The mechanisms of the two setups to apply alternating electrostatic force ( F\mathrm {es} ) across the head–disk interface were investigated. It was shown that the distribution of the applied F\mathrm {es} was different for the two setups. This led to further studies of the effects of the F\mathrm {es} distribution on interactions monitoring. The results showed that when an alternating F\mathrm {es} was distributed at the pole region, the magnitude of the electrodynamically excited first-harmonic vibration increased significantly as the gap fly height was reduced. It was very sensitive to spacing change and useful for the head–disk interactions monitoring at the near-contact regime. The second harmonic was found sensitive to head–disk contact. When the alternating F\mathrm {es} was distributed at the slider body, the magnitudes of the first and second harmonics were larger due to larger effective surface area. However, the fly height of the slider body was mainly affected by the protrusion push-up effect, and hence the first and second harmonics showed a reverse trend as compared with the case where F\mathrm {es} was distributed at the pole region. In addition, slider pitch motion was also significantly affected. The effective EFM setup was constructed to demonstrate its effectiveness in head–disk interactions monitoring and contact detection. [ABSTRACT FROM AUTHOR]

This paper reports a development of a transparent planar electrostatic actuator, which is useful for constructing interactive human–computer interfaces on flat panel displays. The actuator is a pair of transparent plastic films with strip electrodes in three-phase connections. Half of the electrodes in each film are X electrodes, and the rest are Y electrodes; electrostatic forces excited by applying three-phase voltage to these electrodes drive the actuator at speeds proportional to the excitation frequency. The stator film of the actuator has its X and Y electrodes alternately arranged in a four-by-four checkerboard pattern. The slider is a square film with its side twice that of a single square in the stator, with its electrodes separated by diagonal lines. A geometric analysis shows that this electrode arrangement brings position independence of overlapping areas of electrodes. The position independence gives the actuator a uniform thrust force characteristic required for long-stroke planar motion. Based on this concept, we fabricated a prototype by screen-printing. The prototype could exert approximately 100-mN thrust force with an excitation by a pair of 500-V three-phase voltages, and could travel along straight and curved paths within a 132 mm by 132 mm movable range. [ABSTRACT FROM PUBLISHER]

A microelectromechanical systems (MEMS) deformable mirror is described that uses a novel actuation scheme to increase the optical focus range. In this method, electrostatic-pneumatic actuation is used to achieve a convex surface curvature of the mirror with negative focus, while direct electrostatic actuation creates a concave surface with positive focus. Mirrors have demonstrated 20- $\mu $ m total stroke with more than 2-kHz bandwidth. The fabricated device consists of two membranes made of the photoset epoxy SU-8. One membrane serves as the deformable mirror and the other one as the pneumatic actuator. The pneumatic membrane also provides a built-in valve for pressure equalization. The principle of operation, fabrication process, and results are presented. [2014-0135] [ABSTRACT FROM AUTHOR]

We report the design, characterization, and control of a high-bandwidth microelectromechanical systems (MEMS) nanopositioner for on-chip atomic force microscopy (AFM). For the fabrication, a commercially available process based on silicon-on-insulator is used. The device consists of a scan table, moved in the $x$ – y$ plane by two sets of electrostatic comb actuators, capable of generating strokes in excess of \pm 5~ {\mu } m. The first resonance frequencies of the nanopositioner are approximately 4.4 and 5.3 kHz in lateral directions. Electrothermal sensors are used to measure the displacement of the scan table. To enable fast scans, a dynamic model of the system is identified and used to design a feedback controller that damps the oscillatory behavior of the device. The nanopositioner is tested as the scanning stage of an AFM to perform high-speed scans. [ABSTRACT FROM AUTHOR]

Capacitive comb actuators are widely used as MEMS motors due to their long range of linear motion, low power consumption, and ease of fabrication. Here, we present data from a thin comb capacitive actuator where fringe fields contribute significantly to the device performance. We characterize the observed levitation effect and discuss two methods to control the out-of-plane forces: 1) by means of alternating the comb polarity; and 2) by using an additional electrode below the comb. Considering two alternative designs, it is shown how the levitation force can be mitigated. One design decreases the out-of-plane motion by a factor of two, but also reduces the lateral range. An alternative design proved successful in decreasing out-of-plane motion by 75%, while enhancing the in-plane displacement of the linear comb actuator by over 35%. [ABSTRACT FROM AUTHOR]