Parallel-plate Actuators Research Articles

An FEM Study on Minimizing Electrostatic Cross-Talk in a Comb Drive Micro Mirror Array.

We are developing a phase-modulating micro mirror-array spatial light modulator to be used for real holography within the EU-funded project REALHOLO, featuring millions of pixels that can be individually positioned in a piston mode at a large frame rate. We found earlier that an electrostatic comb-drive array offers the best performance for the actuators: sufficient yoke forces for fast switching even at low voltages compatible with the CMOS addressing backplane. In our first design, the well-known electrostatic cross-talk issue had already been much smaller than would have been possible for parallel-plate actuators, but it was still larger than the precision requirements for high-image-quality holography. In this paper, we report on our analysis of the crucial regions for the electrostatic cross-talk and ways to reduce it while observing manufacturing constraints as well as avoiding excessively high field strengths that might lead to electrical breakdown. Finally, we present a solution that, in FEM simulations, reduces the remaining cross-talk to well below the required specification limit. This solution can be manufactured without any additional processing steps and suffers only a very small reduction of the yoke forces.

Adaptive RBFNN‐based predictive control for the nanopositioning of an electrostatic MEMS actuator

AbstractElectrostatic micro electro mechanical system (MEMS) as an actuator is one of the most widely used actuators in micro dimension systems. Due to the high nonlinear characteristics in the micro actuator's model, nanopositioning has been a challenging problem for researchers. In addition, the system is subject to uncertainties associated with the system's unknown parameters and un‐modelled dynamics. Thus, to overcome these problems and achieve precise positioning a robust non‐linear control method is required. In this research, an optimal voltage control algorithm is initially designed utilizing the nonlinear predictive control approach. The Taylor expansion sequence is used to estimate the final position of the parallel plate actuator. To approximate unknown disturbances, a radial basis function neural network (RBFNN) has been designed. The estimations made were used in updating the control input in the previous step, and the obtained results showed an increase in the robustness of the designed controller. The stability of the closed‐loop system is also analyzed. Finally, a comparison is accomplished between the potential of the proposed controller and that of the feedback linearization and sliding mode controllers. The obtained results indicate better performance and robustness of the suggested controller.

Performance evaluation simulation of the optical splitters integrated with unidirectional fiber elements

Abstract This study has clarified the performance evaluation simulation of the optical splitters integrated with unidirectional fiber elements. The simulative performance evaluation of electrostatic, thermal, and piezoelectric actuation based micro electro mechanical systems. The force against the displacement based electrostatic and elastic forces for parallel plate actuator is simulated by MEMSover simulation software. The voltage with angular displacement for a torsion bar actuator is clarified. Besides the lateral displacement against voltage for a comb drive actuator is reported. The dependence of the film thickness on the deflection of a bimetallic cantilever, the dependence of passive beam length on deflection of a bimorph actuator and the transient response of a bent beam actuator are demonstrated. Moreover the piezoelectric actuator force against applied voltage and the piezoelectric actuator displacement against applied voltage variations are reported.

Non-Inchworm Electrostatic Cooperative Micro-Stepper-Actuator Systems with Long Stroke

In this paper, we present different microelectromechanical systems based on electrostatic actuators, and demonstrate their capacity to achieve large and stepwise displacements using a cooperative function of the actuators themselves. To explore this, we introduced micro-stepper actuators to our experimental systems, both with and without a guiding spring mechanism; mechanisms with such guiding springs can be applied to comb-drive and parallel-plate actuators. Our focus was on comparing various guiding spring designs, so as to increase the actuator displacement. In addition, we present systems based on cascaded actuators; these are converted to micromechanical digital-to-analog converters (DAC). With DACs, the number of actuators (and thus the complexity of the digital control) are significantly reduced in comparison to analog stepper-actuators. We also discuss systems that can achieve even larger displacements by using droplet-based bearings placed on an array of aluminum electrodes, rather than guiding springs. By commutating the voltages within these electrode arrays, the droplets follow the activated electrodes, carrying platforms atop themselves as they do so. This process thus introduces new applications for springless large displacement stepper-actuators.

Study and simulation of MEMS electrostatic actuators

The desire for cutting-edge technologies is at an all-time high as the world becomes more digital. To suit the unique requirements, numerous systems and their associated devices are on the market. One such developing technology for producing devices is Micro Electro Mechanical System (MEMS). The simplest description of MEMS technology is the combination of tiny mechanical and electromechanical components on a single chip using micromanufacturing techniques. Its benefits include low cost, lightweight, accurate measurement in small places, and low power usage. The main objective of this proposed work is to design, analyze and compare various electrostatic actuators. Analyses of the device's electrostatic actuation, capacitive sensing, displacement, Eigen frequency, resonant frequency, time domain response of parallel plate actuation electrodes with variable gap actuator, differential capacitive sensing, parallel plate capacitance, and balanced actuation are all done in-depth.

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.

On the snap-through buckling analysis of electrostatic shallow arch micro-actuator via meshless Galerkin decomposition technique

Micromechanical systems (MEMS) based on electrostatic actuators are commonly involved in driving and actuating high-speed micro-structures. For this to be efficient, these micro-actuators must produce sufficient actuating force in order to achieve the required large strokes for such operations (usually in the order of tens of microns). However, this larger amount of displacement will require high actuation electrostatic voltages (typically in the order of hundreds of volts) or larger actuator dimensions, resulting in a bulky and inefficient design. To overcome these challenges, this paper examines the possible use of the snap-through instability in an electrostatically actuated and initially curved (shallow arch) clamped-clamped microbeam actuator arrangement. An extended version of the variational Hamilton principle is applied to derive nonlinear equations governing the steady-state behavior of the structure under step DC load. These equations are solved by effectiveness meshless numerical Galerkin decomposition technique. A convergence study is performed to show the effectiveness and advantages of the applied numerical approach to the formulated nonlinear problem. The investigation inspects different initial curvature profiles (first three symmetric buckled modes: first, third, and fifth modes) for the shallow arch. It was reported that the presence of the snap-through instability, for all investigated initial profiles, in the structural behavior of the micro-actuator produces a non-trivial order of magnitude increase in its resultant displacement as compared to the classical parallel-plate actuator with identical geometrical dimensions and operating conditions. In addition, out of the assumed first three symmetric buckled modes to outline the initial curvature of the shallow arch microbeam, only the first and fifth modes showed a strong impact on the micro-actuator performances.

Exploiting Pull-In/Pull-Out Hysteresis in Electrostatic MEMS Sensor Networks to Realize a Novel Sensing Continuous-Time Recurrent Neural Network

The goal of this paper is to provide a novel computing approach that can be used to reduce the power consumption, size, and cost of wearable electronics. To achieve this goal, the use of microelectromechanical systems (MEMS) sensors for simultaneous sensing and computing is introduced. Specifically, by enabling sensing and computing locally at the MEMS sensor node and utilizing the usually unwanted pull in/out hysteresis, we may eliminate the need for cloud computing and reduce the use of analog-to-digital converters, sampling circuits, and digital processors. As a proof of concept, we show that a simulation model of a network of three commercially available MEMS accelerometers can classify a train of square and triangular acceleration signals inherently using pull-in and release hysteresis. Furthermore, we develop and fabricate a network with finger arrays of parallel plate actuators to facilitate coupling between MEMS devices in the network using actuating assemblies and biasing assemblies, thus bypassing the previously reported coupling challenge in MEMS neural networks.

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.

Response Analysis of Nonlinear Free Vibration of Parallel-Plate MEMS Actuators: An Analytical Approximate Method

In this work, nonlinear free vibration of electrostatically actuated micromechanical system has been investigated. These nonlinear solutions are analytically derived. An undamped spring-mass model and dynamic equation of motion are employed for the parallel-plate microelectrostatic actuator. The first analytical approximate period and periodic solution of the mentioned problems are constructed with the help of Galerkin’s method and coupling of Galerkin’s with Newton’s method. In addition, the second and third analytical approximate solutions are also derived. The “exact” solutions are obtained from direct integration. In this work, the well-known static and dynamic pull-in parameters are discussed. Phase trajectory becomes non-periodic with the dynamic pull-in point. The approximate and “exact” solutions of period, phase trajectory, and time-dependent displacement of microelectrostatic actuators at various physical parameters are obtained and compared. It is found that the analytical approximate solutions are not only an explicit expression but also have excellent precision for a wide range of nonlinear vibration with different amplitudes.

Towards the Analogy of Electrostatic and Electromagnetic Transducers

Electromechanical, or mechatronic, transducers exchange energy between the mechanical and electrical domain via electrostatic and electromagnetic transduction principles, which are the basis for actuators and sensors. This paper reveals the simple analogy between electrostatic and electromagnetic transducers. Summarizing the well-known Gauß, Ampère’s, Ohm’s, Chua’s, Newton’s, Hook’s and the damping laws into a signal-flow diagram with linearized coefficients, the model shows the transducers reciprocity and physical behavior of damped spring-mass mechatronic systems. The presented modeling approach simplifies the derivation of transfer functions, the pull-in phenomenon, and the coupling factors for the design of feedback methods for mechatronic systems. The analogies are shown by comparing an electrostatic and an electromagnetic parallel-plate actuator, represented by a torsional MEMS scanning mirror and a hybrid reluctance fast steering mirror, respectively. The paper discusses the actuators performance and compares the transducer coefficients and the intrinsic stiffness regarding pull-in.

Merging parallel-plate and levitation actuators to enable linearity and tunability in electrostatic MEMS

In this study, a linear electrostatic MEMS actuator is introduced. The system consists of a MEMS cantilever beam with combined parallel-plate and electrostatic levitation forces. By using these two forcing methods simultaneously, the static response and natural frequency can be made to vary linearly with the voltage. The static response shows a linear increase of 90 nm/V and is maintained for more than 12μm of the tip displacement. The natural frequency shows a linear increase of 16 Hz/V and is maintained throughout a 2.9 kHz shift in the natural frequency. This wide range of linear displacement and frequency tunability is extremely useful for MEMS sensors and actuators, which suffer from the inherent nonlinearity of electrostatic forces. A theoretical model of the system is derived and validated with experimental data. Static response, natural frequency, and frequency response calculations are performed. Merging these two mechanisms enables high oscillation branches for a wide range of frequencies with potential applications in MEMS filters, oscillators, and sensors.

Translational MEMS Platform for Planar Optical Switching Fabrics.

While 3-D microelectromechanical systems (MEMS) allow switching between a large number of ports in optical telecommunication networks, the development of such systems often suffers from design, fabrication and packaging constraints due to the complex structures, the wafer bonding processes involved, and the tight alignment tolerances between different components. In this work, we present a 2-D translational MEMS platform capable of highly efficient planar optical switching through integration with silicon nitride (SiN) based optical waveguides. The discrete lateral displacement provided by simple parallel plate actuators on opposite sides of the central platform enables switching between different input and output waveguides. The proposed structure can displace the central platform by 3.37 µm in two directions at an actuation voltage of 65 V. Additionally, the parallel plate actuator designed for closing completely the 4.26 µm air gap between the fixed and moving waveguides operates at just 50 V. Eigenmode expansion analysis shows over 99% butt-coupling efficiency the between the SiN waveguides when the gap is closed. Also, 2.5 finite-difference time-domain analysis demonstrates zero cross talk between two parallel SiN waveguides across the length of the platform for a 3.5 µm separation between adjacent waveguides enabling multiple waveguide configuration onto the platform. Different MEMS designs were simulated using static structural analysis in ANSYS. These designs were fabricated with a custom process by AEPONYX Inc. (Montreal, QC, Canada) and through the PiezoMUMPs process of MEMSCAP (Durham, NC, USA).

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.

H2S MEMS-based gas sensor

Background: Microelectromechanical systems are now one of the fastest growing engineering fields. We introduce a static gas sensor based on PolyMUMPs parallel plate actuators. The sensor exploits the pull-in phenomenon of the parallel plate actuators. The target gas is hydrogen sulfide (H2S), which is a toxic gas and popular in laboratories, factories, and petroleum industry. Aim: Reach a gas sensor in which the gas can easily be detected by a simple electronic circuit using new polymer combinations. Approach: Two concentrations of H2S (40 and 100 ppm) are used to test the ability of the sensor to capture the molecules of the gas. Gas injection process is done in a gas chamber and at ambient conditions (ambient temperature and pressure). Results: The two concentrations were successfully detected by the sensor and the electronic circuit verified the pull-in of the sensor. That was achieved using two different polymers (polypyrrole polymer and copper oxide–tin oxide/polypyrrole). Conclusions: The sensor successively detects H2S gas with 40 and 100 ppm concentrations. Verifying the pull-in of the sensor using a simple detection circuit could help in quickly moving those sensors from prototype to product.

PWM as a Low Cost Method for the Analog Control of MEMS Devices

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.

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.

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

This paper investigates efficient actuation methods of shunt MEMS switches and other parallel-plate actuators. We start by formulating a multi-physics model of the micro switch, coupling the nonlinear Euler–Bernoulli beam theory with the nonlinear Reynolds equation to describe the structural and fluidic domains, respectively. The model takes into account fringing field effects as well as mid-plane stretching and squeeze film damping nonlinearities. Static analysis is undertaken using the differential quadrature method (DQM) to obtain the pull-in voltage, which is verified by means of the finite element model and validated experimentally. We develop a reduced order model employing the Galerkin method for the structural domain and DQM for the fluidic domain. The proposed waveforms are intended to be more suitable for integrated circuit standards. The dynamic response of the micro switch to harmonic, square and triangular waveforms are evaluated and compared experimentally and analytically. Low voltage actuation is obtained using dynamic pull-in with the proposed waveforms. In addition, global stability analysis carried out for the three signals shows advantages of employing the square signal as the actuation method in enhancing the performance of the micro switch in terms of actuation voltage, switching time, and sensitivity to initial conditions.

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.