Parallel-plate Electrostatic Actuators Research Articles

Varifocal-Piston Micromirror With Quasi-Simply Supported Piecewise Linear Flexure

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.

Tri-electrode MEMS electrostatic actuator with lower control voltage and higher stroke for actuator array implementations

Employing a tri-electrode actuator in place of a conventional parallel plate electrostatic actuator, can enable significantly lower control voltage operation for applications such as deformable mirrors or MEMS switches. The effect of the tri-electrode design parameters, including intermediate electrode spacings, background electrode voltage and gap spacing between the driving electrodes, are studied. It is shown possible to reduce the control voltage by approximately two times for a unipolar voltage supply, and four times for a bipolar supply. Extension of travel range before snap-down of 70% is shown.

A flexible model for studying fringe field effect on parallel plate actuators

Electrostatic parallel plate actuators are common in micro-electro-mechanical systems due to their compatibility with micro-fabrication technology. Parallel plate actuators suffer from an instability problem called the pull-in phenomenon that happens when the applied DC voltage exceeds a certain value called the static pull-in voltage. The value of this critical voltage is important in many applications that depend on parallel plate actuators such as switches and static gas sensors. The fringe field around the edges of the plates could severely affect the performance of the actuator. This paper introduces a new model for the parallel plate actuator to calculate the value of static pull-in voltage. The proposed model considers the fringe field between the two plates. The static pull-in voltage of some PolyMUMPs actuators is practically measured and compared to the simulation results that involve the fringe field effect. The model is simulated using MATLAB to show the influence of that field on the static pull-in voltage. The MATLAB results of the proposed model are validated with ANSYS.

Dynamics of a parallel-plate electrostatic actuator in viscous dielectric media

Understanding the dynamics of a parallel-plate electrostatic actuator, that is, the complex temporal interactions between the mechanical and electrostatic nonlinearities will help optimize the actuator performance for micromanipulation applications. In this paper, we analyze the response of the actuator in a clamped–clamped configuration immersed in viscous dielectric media. We model the actuator as a continuous system by deriving a reduced-order model, and solving it by employing the Galerkin method and linear undamped mode shapes for a clamped–clamped beam. Our model incorporates the inertial loading effect and squeeze film damping by the media, nonlinear mid-plane stretching forces in the beam electrode of the actuator, and nonlinear contact force during the physical contact of the beam electrode with the stationary electrode. The model is utilized to study the actuator dynamics over a broad range, three orders of magnitude of viscosity and two orders of magnitude of relative permittivity of the media. We report three main observations: (1) the actuator response near the vicinity of the pull-in instability region is sensitive to the external forces such as electrostatic force and viscous damping force; (2) the actuator at lower actuation voltages and/or higher actuation frequencies can be approximated to be a linear system; and (3) the high relative permittivity of a media amplifies the generated force, resulting in pull-in to occur at lower actuation voltage amplitudes, and the high dynamic viscosity of a media increases the pull-in time.

A Customized Nonlinear Micro-Flexure for Extending the Stable Travel Range of MEMS Electrostatic Actuator

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]

Surface micromachined MEMS deformable mirror based on hexagonal parallel-plate electrostatic actuator

Deformable mirrors (DM) based on microelectromechanical system (MEMS) technology are being applied in adaptive optics (AO) system for astronomical telescopes and human eyes more and more. In this paper a MEMS DM with hexagonal actuator is proposed and designed. The relationship between structural design and performance parameters, mainly actuator coupling, is analyzed carefully and calculated. The optimum value of actuator coupling is obtained. A 7-element DM prototype is fabricated using a commercial available standard three-layer polysilicon surface multi-user-MEMS-processes (PolyMUMPs). Some key performances, including surface figure and voltage-displacement curve, are measured through a 3D white light profiler. The measured performances are very consistent with the theoretical values. The proposed DM will benefit the miniaturization of AO systems and lower their cost.

Robust Voltage Control for an Electrostatic Micro-Actuator

When a parallel-plate electrostatic actuator (ESA) is driven by a voltage source, pull-in instability limits the range of displacement to one-third of the gap between plates. In this paper, a nonlinear active disturbance rejection controller (NADRC) is originally developed on the ESA. Our control objectives are stabilizing and increasing the displacement of an ESA to 99.99% of its full gap. Most of the reported controllers in literature are based on linearized models of the ESAs and depend on detailed model information of them. However, the ESA is inherently nonlinear and has model uncertainties due to the imperfections of microfabrication and packaging. The NADRC consists of a nonlinear extended state observer (NESO) and a feedback controller. The NESO is used to estimate system states and unknown nonlinear dynamics for the ESA. Therefore, it does not require accurate model. We simulate the NADRC on a nonlinear ESA in the presences of external disturbance, system uncertainties, and noise. The simulation results verify the effectiveness of the controller by successfully extending the travel range of ESA beyond pull-in point. They also demonstrate that the controller is robust against both disturbance and parameter variations, and has low sensitivity to measurement noise. Furthermore, the stability for the control system with NADRC is theoretically proved.

Interdisciplinary considerations on the design of MEMS actuators from a perspective of their optimality

Various phenomena are emerging in existing micro-electro-mechanical systems (MEMS). In order to fully exploit the potential of such systems, a synergy of multiple engineering fields should be reached through a careful analysis of the designed system and its optimization. It is common practice that complex multi-physics finite element method (FEM)-based models are created to analyze the system. Nevertheless, without a clear understanding of the occurred phenomena, an optimal design will be hard to attain. In this paper, we demonstrate that only minimal design changes in existing MEMS actuators can potentially lead to noticeable improvements of the system. We present a case study considering an electrostatic rotational parallel-plate actuator under sliding mode control. This type of actuator is one of the most successful commercial examples of this actuator widely applied in MEMS-based optical switches. The results of this paper confirm that the control strategy of the actuator is a substantial part of the system and should be taken into account; specifically, it can affect the parameters of the designed actuator in order to modify the dynamics of the system in a desired way. In our case, this can reduce the amplitude of output chattering or reduce the switching time of the actuator. Moreover, this paper points out various design flaws, namely when synergy between various system requirements was not reached successfully and only a suboptimal solution was discovered.

Energy-efficient full-range oscillation analysis of parallel-plate electrostatically actuated MEMS resonators

Electrostatic parallel-plate actuators are a common way of actuating microelectromechanical systems, both statically and dynamically. Nevertheless, actuation voltages and oscillations are limited by the nonlinearity of the actuator that leads to the pull-in phenomena. This work presents a new approach to obtain the electrostatic parallel-plate actuation voltage, which allows to freely select the desired frequency and amplitude of oscillation. Harmonic Balance analysis is used to determine the needed actuation voltage and to choose the most energy-efficient actuation frequency. Moreover, a new two-sided actuation approach is presented that allows to actuate the device in all the stable range using the Harmonic Balance Voltage.

Ultra-Low Power Digitally Operated Tunable MEMS Accelerometer

This paper presents the concept as well as fabrication and measurement results for a new class of MEMS accelerometers that can be operated directly by a digital processor without the need for an analog front end. Elimination of the analog front end for such digitally operated accelerometers can significantly lower the sensor power consumption. The accelerometer consists of a proof mass and a number of parallel plate electrostatic actuators that can be turned ON and OFF in a sequential manner by a digital controller. Consequently, an ON or OFF output is provided for each input condition based on an output electrode making contact with the biased proof mass. Following a simple switching algorithm, a binary search can be performed by the digital controller to find the acceleration as a binary number. Furthermore, this paper also estimates the operating power consumption for such an accelerometer. A simple 2-b version of such accelerometers has been successfully fabricated and operated in the 0-1-g range. The same device concept and the configuration can be enhanced to higher number of bits.

Full-gap tracking system for parallel plate electrostatic actuators using closed-loop control

Bi-directional full-gap tracking on parallel-plate electrostatic actuators using closed-loop control is demonstrated in this paper. On-Off control is explored, where the actuator position is controlled by actuating or releasing the actuator based on the actual position (weather it is above or below the desired position). Noise and delays introduced by the readout circuit compromise the performance of this control law working at 5MHz sampling frequency. A Proportional-Integral-Derivative control law with feedback linearization is also implemented. This second control law is more complex than the on-off control and requires extensive data processing. In addition, in order to effectively control the actuator, the structure characteristics need to be available as well as the response of the readout circuit (voltage/distance converter). In order to decrease the steady-state error and the overshoot of the structure position, various proportional-integral-derivative (PID) gains are tested. Both controllers are implemented using a FPGA (Field-programmable gate array), which increases the performance of the controller. The experimental results, for both the controllers, show bi-directional tracking of several wave forms at frequencies up to 1kHz (limited by the dynamics of the actuators). The extension of the travel range is about 88.9% of the full-gap available (due to the mechanical stoppers present in the structure). This corresponds to a displacement range extension of 267%.

A single-layer micromachined tunable capacitor with an electrically floating plate

This paper reports a novel micromachined tunable capacitor with an electrically floating movable plate. The device has been fabricated from a single metal layer based on a low-cost standard process. Tunable capacitors with electrically floating and non-floating plates have been characterized and compared with each other by using the same fabricated device with different configurations. The floating tunable capacitor exhibits a higher quality factor (Q-factor) compared to a non-floating capacitor by eliminating the spring’s resistance loss in radio frequency signal path. The device is actuated by an electro-thermal actuator to achieve high capacitance tuning range without the pull-in effect issue of parallel-plate electrostatic actuators. Experimental results show that the tunable capacitor has a wide capacitance tuning range of 631% with a low actuation voltage of 0.72 V. The floating tunable capacitor has a Q-factor at 1 GHz of 24.4, which is 5.5 times higher than that of a non-floating traditional tunable capacitor fabricated on the same chip.

Nonlinear Observability Analysis of Micro-machined Electrostatic Actuators Using Self-Sensing

Micro-machined electrostatic actuators (MEA) like parallel plate actuators (PPAs) and comb drive actuators (GCAs) are commonly used in many applications, including gyroscopes, resonators and RF switches. The detection of an actuators' mechanical motion is desired when they are combined with feedback control techniques, especially when the application requires high performance or is affected by disturbances. The motion can be detected by a variety of sensing techniques, including capacitive, piezoresistive and optical. Electrostatic parallel plate actuators can be modeled as a type of variable capacitor, which depends on the gap between a fixed electrode and a movable electrode. Thus, the displacement of the actuator can be obtained by measuring the capacitance. However, this practical method often requires high frequency excitation signal sources or additional sensing structures. The excitation power source not only affects the performance in the actuator's steady state, but it may also generate harmonics that distort the measurement signals due to the nonlinear characteristics of the actuator. In addition, the information about velocity may not be obtained without specific sensing structures. The additional structures occupy more space in each die, which could increase the cost and size, or decrease the performance. In this study, an estimator with a series resistor configuration is proposed. The estimator can estimate the displacement and velocity by measuring the voltage of the power supply and the voltage across the actuator itself. To evaluate the feasibility, a nonlinear observability analysis is applied. The analysis shows the observability index among different system states. A simulation study verified the proposed theories.

Analysis of Pull-in Voltage with Respect to Changes in Dielectric Material and their Thickness

Micro Electromechanical Systems (MEMS) actuators experience pull-in effect in their actuation range. MEMS actuating elements are thin parallel plate capacitor electrodes separated with air gap. Parallel plate electrostatic micro actuators are known to have the pull-in effect, where electrostatic attractive force exceeds the mechanical restoring force of the suspending spring, and that the movable plate spontaneously pulled into physical contact with the opposite electrode. In our model the effect of dielectric layer thickness is taken into account for predicting the pull-in voltage. The critical role of different dielectric layer materials in bringing down the static pull-in voltage is verified by using COMSOL.

Angled microfiber arrays as low-modulus, low Poisson's ratio compliant substrates

This paper presents a novel fabrication method for producing high-aspect-ratio, angled polymer microfiber arrays by directional pulling of polyethylene from low-aspect-ratio, microporous polycarbonate templates. These arrays represent a novel substrate for electrostatic sensors and actuators because they are characterized by low stiffness (<24 kPa effective elastic modulus), low Poisson's ratio (effectively zero at low strains), and very low density (<1% of solid polyethylene). Validation of these properties is presented by developing a model based on elastica theory, and by performing experiments using a parallel-plate electrostatic actuator fabricated with a fiber array as the dielectric and return spring.

Fabrication and operation of an electrostatic actuator for controlling nanometer-scale gaps in collapsed cantilever heterostructures

Vertical electrostatic wedge actuators are described that control nanometer-scale gaps between surfaces. Standard parallel-plate electrostatic actuators become difficult to stabilize across extremely small gaps because the nature of the forces and the force laws that describe them often deviate from a Coulomb's law dependence. In this work, a nanometer-scale air gap between a collapsed cantilever structure formed by two facing In0.53Ga0.47As surfaces, with areas of tens of microns, was controlled by a wedge electrostatic actuator. Upon actuation, the gap spacing between the surfaces was tuned over a maximum range of 55 nm with an applied voltage of 60 V.

MEMS Resonator With Displacement Sensor Based On Electro-Thermal Principles

This paper examines the feasibility of using displacement sensors based on electro-thermal principles in the design of resonators using MEMS technology. The use of this type of displacement sensor provides a new technology for low frequency resonator design. The theory and design of the displacement sensors are based on an existing body of work and show the displacement sensors have excellent resolution, small die footprint and a low operating voltage but have a high power consumption and low bandwidth. Two resonator designs, with a natural frequency of approximately 10 kHz, have been modeled and fabricated for experimentation. One is based on a microcantilever with parallel plate electrostatic actuators, while the other is based on fixed-guided micro-beams with comb electrostatic actuators. The electrical interface for the sensor output is a Wheatstone bridge. Both resonators are operated in air. The displacement sensors were able to capture the resonant motion of both resonators. The microcantilever based resonator had a quality factor of 195 and a resonance gain of –27 dB. The comb-drive based resonator had a quality factor of 440 and a resonance gain of –20 dB.

Varifocal Micromirror Integrated With Comb-Drive Scanner on Silicon-on-Insulator Wafer

We present a varifocal scanning micromirror fabricated from a silicon-on-insulator wafer. The varifocal scanning micromirror consists of a varifocal mirror with a rotational scanning function. The scanner and varifocal mirror are driven by comb and parallel-plate electrostatic actuators, respectively. The mirror rotates 5.5° at 45 V in static mode. The curvature of the varifocal mirror is changed from -4 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> (-128-mm focal length) to +5 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> (+93-mm focal length) by applying a voltage from 0 to 50 V. It is confirmed that the lateral position and spot size of the reflected laser beam from the varifocal scanning micromirror are changed simultaneously. Moreover, confocal sensing is demonstrated using a fiber-optic system with the proposed mirror.

Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking

This study addresses an output-error-constrained tracking problem for the one degree of freedom parallel-plate electrostatic actuator. The authors first formulate the control problem as a robust output regulation problem for an output feedback system. Then they show that it can be further converted into a robust regulation problem with output constraint by internal model design. Finally, a regulation controller for this regulation problem by using a barrier Lyapunov function technique is designed. By an appropriate selection of some controller parameter and an appropriate initial displacement of the movable plate, the final designed output-error-constrained tracking control law ensures that, in the presence of large parameter variations, the harmonic displacement of the parallel-plate electrostatic actuator can be beyond the pull-in position and up to the full gap without contacts between the movable and fixed plates during the transient period.

Capillary force actuators: Modeling, dynamics, and equilibria

Capillary force actuators provide forces via the alteration of the capillary pressure within a conducting liquid bridge through the application of electrical potential. A dynamic model of a capillary force actuator is developed. Separate models of the fluid/flexured platen and electrodynamics are constructed and linked together via the Young–Lippmann relation. Since the bridge height is small in comparison to the diameter, the liquid slug is shown to have a parabolic velocity profile. The radial pressure variation is then readily determined. Integration of the pressure and summation of the contact line tension term yields the actuation force. Combining this model with the electrodynamics and mechanical components yields a nonlinear model relating applied voltage to platen movement. The equilibria of this equation are determined as a function of voltage and their stability are analyzed. We show that the equilibrium will be stable for displacements exceeding one-third of the nominal bridge height, a greater range than that obtained with parallel plate electrostatic actuators. Depending on actuator design this range may be as large as 7/9th of the nominal bridge height but no larger.