Parallel-plate Actuators Research Articles

Frequency-dependent stability of parallel-plate electrostatic actuators in conductive fluids

We present an electromechanical stability analysis of passivated parallel-plate electrostatic actuators in conductive dielectric media and show that the pull-in instability can be eliminated by tuning the applied frequency below a design-dependent stability limit. A partial instability region is also obtained, where the actuator jumps from the pull-in displacement to another stable position within the gap. The results predict that the stability limit is always greater than the critical actuation frequency, and therefore any device that is feasible to actuate in a conductive fluid can be operated with stability over the full range of motion.

Design and Simulation of a MEMS Control Moment Gyroscope for the Sub-Kilogram Spacecraft

A novel design of a microelectromechanical systems (MEMS) control moment gyroscope (MCMG) was proposed in this paper in order to generate a torque output with a magnitude of 10−6 N·m. The MCMG consists of two orthogonal angular vibration systems, i.e., the rotor and gimbal; the coupling between which is based on the Coriolis effect and will cause a torque output in the direction perpendicular to the two vibrations. The angular rotor vibration was excited by the in-plane electrostatic rotary comb actuators, while the angular gimbal vibration was driven by an out-of-plane electrostatic parallel plate actuator. A possible process flow to fabricate the structure was proposed and discussed step by step. Furthermore, an array configuration using four MCMGs as an effective element, in which the torque was generated with a phase difference of 90 degrees between every two MCMGs, was proposed to smooth the inherent fluctuation of the torque output for a vibrational MCMG. The parasitic torque was cancelled by two opposite MCMGs with a phase difference of 180 degrees. The designed MCMG was about 1.1 cm × 1.1 cm × 0.04 cm in size and 0.1 g in weight. The simulation results showed that the maximum torque output of a MCMG, the resonant frequency of which was approximately 1,000 Hz, was about 2.5 × 10−8 N·m. The element with four MCMGs could generate a torque of 5 × 10−8 N·m. The torque output could reach a magnitude of 10−6 N·m when the frequency was improved from 1,000 Hz to 10,000 Hz. Using arrays of 4 × 4 effective elements on a 1 kg spacecraft with a standard form factor of 10 cm × 10 cm × 10 cm, a 10 degrees attitude change could be achieved in 26.96 s.

High isolation RF MEMS contact switch in V- and W-bands using two directional motions

Proposed is the concept of an RF MEMS contact switch with high isolation over 50 GHz, and experiment at work succeeds in showing its feasibility. High isolation was achieved using two directional motions, namely vertical and lateral movement of the contact part, contrary to typical MEMS switches that generally use one of two motions. Comb and parallel plate actuators enable the contact part to move in the lateral and vertical directions. The silicon on glass (SiOG) process is utilised to fabricate the silicon switch on a glass substrate. The RF characteristics are simulated and measured from 50-110 GHz to prove the high isolation capabilities in the V- and W-bands.

Electrostatically driven optical Z-axis scanner with thermally bonded glass microlens

This paper presents a design, fabrication and characterization results of an electrostatically-actuated microlens scanner capable of precise positioning of integrated glass ball microlens along Z-axis. The device can be used in a wide range of photonic applications, e.g. in MOEMS microscopes for active changing of focal plane during 3-D raster scanning. The scanner construction is based on parallel-plate electrostatic actuation scheme where suspended silicon platform with integrated microlens (movable electrode) is attracted to silicon cover (fixed electrode). Both parts, fabricated individually by bulk micromachining of standard silicon wafer, are vertically aligned and bonded in low-temperature process through SU-8 film. The glass microlens with diameter of 360 μm, effective focal length of about 260 μm, and numerical aperture of 0.57, is directly thermally bonded in the centre of platform. The device demonstrates vertical displacement up to 26 μm in semi-static mode and 38 μm at dynamic mode (fR=540Hz) with the max. 160 V of applied excitation voltage.

A Model for Electrostatic Actuation in Conducting Liquids

This paper presents a generalized model that describes the behavior of micromachined electrostatic actuators in conducting liquids and provides a guideline for designing electrostatic actuators to operate in aqueous electrolytes such as biological media. The model predicts static actuator displacement as a function of device parameters and applied frequency and potential for the typical case of negligible double-layer impedance and dynamic response. Model results are compared to the experimentally measured displacement of electrostatic comb-drive and parallel-plate actuators and exhibit good qualitative agreement with experimental observations. The model is applied to show that the pull-in instability of a parallel-plate actuator is frequency dependent near the critical frequency for actuation and can be eliminated for any actuator design by tuning the applied frequency. In addition, the model is applied to establish a frequency-dependent theoretical upper bound on the voltage that can be applied across passivated electrodes without electrolysis.

A theoretical response of the electrostatic parallel plate to constant and low-frequencyaccelerations

A theoretical response of an electrostatic gap-closing actuator based on parallel plates toconstant and low-frequency accelerations has been derived as a function of theapplied acceleration and voltage. The nonlinear equation of motion is obtainedin a dimensionless form from the fact that the inertial and damping forces areneglected at a frequency much less than the resonant frequency of the parallel plate,and thereafter the nonlinear equation is solved for the stable inter-plate gap atthe acceleration and voltage. From the derived solution, the pull-in accelerationis obtained as a function of the applied voltage, and the pull-in voltage is alsoexpressed as a function of the acceleration. The closed-form solution is validated bycomparison with a numerical solution. The theoretical solution is in excellentagreement with the numerical results when the actuator is exposed to a constantacceleration as well as a low-frequency acceleration. The theoretical solution andpull-in acceleration and voltage thus provide guidance to prescribe operationalconstraints for devices that use the parallel plate actuator and to predict theresponse of the electrostatic gap-closing parallel plates to constant and low-frequencyacceleration.

Design and Characterization of a Fourier Transform Micro-Spectrometer

In this paper, we present a Fourier Transform micro-spectrometer which works based on a lamellar grating interferometer. The spectrometer model is electrostatically driven by parallel plate actuators which change the optical path difference (OPD) between movable grating facets and fixed ones. With a 200V input voltage, a maximum OPD of 48.7μm is achieved. The spectrum of a combined light source of a diode-pumped solid-state (DPSS) laser (λ=532.0nm) and a laser diode (λ=637.2nm) is experimentally acquired to demonstrate the performance of the model. The reconstructed spectrum displays two separate spectral peaks at 530.5nm and 635.2nm and the corresponding full-width at half-maximum (FWHM) resolutions are 9.8nm and 12.8nm respectively, indicating good wavelength accuracy and optical resolution.

Vertical Mirror Fabrication Combining KOH Etch and DRIE of (110) Silicon

This paper presents fabrication of MEMS-actuated optical-quality vertical mirrors as the key active optical components in a silicon optical bench (SOB) technology. The fabrication process is based on a combination of potassium hydroxide (KOH) etch and deep reactive ion etching (DRIE) of (110) SOI wafers. The process starts by creating optical-quality vertical surfaces by KOH etch, followed by an oxidation step to protect them. The patterned wafer is then etched by DRIE to define actuators. The process is designed to allow the KOH etch and DRIE to be independently optimized without compromising either while at the same time meeting the challenge of lithography on high-aspect-ratio structures. Three variations of the fabrication process are demonstrated, two that use double masking layers and one that uses a silicon masking layer. We demonstrate in-plane scanners and fast translational vertical mirrors fabricated using these processes. In addition, we propose extensions of the fabrication process to account for DRIE aspect-ratio limitations. Mask layouts of key SOB building blocks, including vertical mirrors, beam splitters, and parallel-plate actuators, are also presented. [2008-0146]

Design methodology for variable capacitors

A theoretical and systematic methodology has been developed to design variable capacitors based on the parallel plate and two-degree-of-freedom (DOF) torsional actuator. For easy design of a variable capacitor without any time-consuming numerical analysis or simulation, closed-form expressions for the capacitance of parallel plate actuators and torsional microactuators are obtained as functions of applied voltage and geometry. A theoretical capacitance of the parallel plate capacitor is obtained in a closed-form. Model and formulation of the capacitance of two-DOF variable capacitors are presented and the capacitance, height and angle of the capacitor are numerically solved to give their pull-in value in simple expressions. The theoretically and numerically solved capacitances are in good agreement within an error of 4.3% with those from experiments using surface-micromachined variable capacitors. As such, the derived capacitance and suggested methodology can be used for design and analysis of the parallel plate and the two-DOF variable capacitor.

Influence of Damping on the Dynamical Behavior of the Electrostatic Parallel-plate and Torsional Actuators with Intermolecular Forces.

The influence of damping on the dynamical behavior of the electrostaticparallel-plate and torsional actuators with the van der Waals (vdW) or Casimir force(torque) is presented. The values of the pull-in parameters and the number of theequilibrium points do not change whether there is damping or not. The ability ofequilibrium points is varied with the appearance of damping. One equilibrium point is anunstable saddle with a different damping coefficient, the other equilibrium point is astable node when the damping coefficient is greater than some critical value, andotherwise it is a stable focus. Then there are two heteroclinic orbits passing from theunstable saddle point to the stable node or focus.

Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators

Electrostatic parallel-plate actuators are a common way of actuating microelectromechanical systems, both statically and dynamically. In the static case, the stable actuation voltages are limited by the static pull-in condition, which indicates that the travel range is approximately limited to 1/3 of the initial actuation gap. Under dynamic actuation conditions, however, the stable voltages are reduced, whereas the travel range can be much extended. This is the case with the dynamic pull-in and the resonant pull-in conditions (RPCs). Using energy analysis, this paper extends the study of pull-in instability to the resonant case and derives the analytical RPC. This condition predicts snapping or pull-in of the structure for a given domain of dc and ac actuation voltages versus quality factor, taking into account the nonlinearities due to large amplitudes of oscillation. Experimental results are presented to validate the analytically derived RPC.

A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators

Though the effect of fringing field in electrostatic parallel-plate actuators is a well-understood phenomenon, the existing formulations often result in complicated mathematical models from which it is difficult to determine the deflection of the moving plate for given voltages and hence, they are not suitable for accurate actuation control. This work presents a new formulation for tackling the fringing field, in which the effect of fringing field is modeled as a variable serial capacitor. Based on this model, a robust control scheme is constructed using the theory of input-to-state stabilization (ISS) and backstepping state feedback design. This method allows loosening the stringent requirements on modeling accuracy without compromising the performance. The stability and the performance of the system using this control scheme are demonstrated through both stability analysis and numerical simulation.

A two-beam method for extending the working range of electrostatic parallel-plate micro-actuators

Electrostatic actuation is widely used because of its rapid speed and low power consumption. The parallel-plate actuator is one of the most basic, but also most common electrostatic actuators for Micro Electro Mechanical System (MEMS) applications. The effective working range of parallel-plate actuator is limited to only one-third of the initial gap owing to the pull-in instability. Different strategies have been reported to extend the stable working range, but are mostly focused on improvement of the control circuit. In this paper, we aim to report some progress toward solution of the working range problem from the design of suspension beam. A suspension beam called “two-beam” is presented to achieve parallel-plate actuator with extended working range, but without penalties of complex control circuit and large actuation voltage. A bumper structure is employed in the design of two-beam to change the spring constant near the critical point of pull-in, and a two-layered polysilicon surface process is used to fabricate this two-beam structure. Theoretical calculation and numerical simulation indicate that the working range can be extended depending on the position and depth of the bumper. The fabrication of a 2×2 array of parallel-plate actuators suspended by four sets of two-beam is implemented, and a somewhat larger working range, i.e. about 50% of the initial gap is achieved in the experiment.

Flatness-Based Control of Electrostatically Actuated MEMS With Application to Adaptive Optics: A Simulation Study

Typical adaptive optics (AO) applications require continual measurement and correction of aberrated light and form closed-loop control systems. One of the key components in microelectromechanical system (MEMS) based AO systems is the parallel-plate microactuator. Being electrostatically actuated, this type of devices is inherently instable beyond the pull-in position when they are controlled by a constant voltage. Therefore extending the stable travelling range of such devices forms one of the central topics in the control of MEMS. In addition, though certain control schemes, such as charge control and capacitive feedback, can extend the travelling range to the full gap, the transient behavior of actuators is dominated by their mechanical dynamics. Thus, the performance may be poor if the natural damping of the devices is too low or too high. This paper presents an alternative for the control of parallel-plate electrostatic actuators, which is based on an essential property of nonlinear systems, namely differential flatness, and combines the techniques of trajectory planning and robust nonlinear control. It is, therefore, capable of stabilizing the system at any point in the gap while ensuring desired performances. The proposed control scheme is applied to an AO system and simulation results demonstrate its advantage over constant voltage control

Dynamic Pull-In of Parallel-Plate and Torsional Electrostatic MEMS Actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided

Cantilever beam electrostatic MEMS actuators beyond pull-in

The operational range of electrostatic MEMS parallel plate actuators can be extended beyond pull-in in the presence of an intermediate dielectric layer, which has a significant effect on the behavior of such actuators. Here, we study the behavior of cantilever beam electrostatic actuators beyond pull-in using a beam model along with a dielectric layer. The results from the simple beam model are validated with 3D simulations performed in CoventorWare™. Three possible static configurations of the beam are identified over the operational voltage range. We call them floating, pinned and flat; the latter two are also called arc-type and S-type in the literature. We compute the voltage ranges over which the three configurations can exist and the points where transitions occur between these configurations. Voltage ranges are identified where bi-stable and tri-stable states exist. A classification of all possible transitions (pull-in and pull-out as well as transitions we term pull-down and pull-up) is presented based on the dielectric layer parameters. Dynamic stability analyses are presented for the floating and pinned configurations. For high dielectric layer thickness, discontinuous transitions between configurations disappear and the actuator has smooth predictable behavior, but at the expense of lower overall tunability.

The stability and pull-in voltage of electrostatic parallel-plate actuators in liquid solutions

This paper deals with parallel-plate electrostatic actuators in liquids. We study the stability conditions of such actuators and show that the pull-in effect can be shifted beyond one-third of the gap, and can even be suppressed. We demonstrate that the insulating layers of the actuator plates, which are originally designed to avoid any current leakages or short-circuits, play a major role in this phenomenon. Experiments are performed on fabricated devices; silicon nitride layers are used to completely encapsulate the actuator plates. The voltages required to close the actuator gap are measured in various liquids and compared to the values obtained by analytical calculations. This study gives guidelines for the design of parallel-plate actuators featuring in liquids either a binary-state operation when the pull-in effect occurs, or a continuous displacement within the full gap.

Using Dynamic Voltage Drive in a Parallel-Plate Electrostatic Actuator for Full-Gap Travel Range and Positioning

The nonlinear dynamics of the parallel-plate electrostatically driven microstructure have been investigated with the objective of finding a dynamic voltage drive suitable for full-gap operation. Nonlinear dynamic modeling with phase-portrait presentation of both position and velocity of a realistic microstructure demonstrate that instability is avoided by a timely and sufficient reduction of the drive voltage. The simulation results are confirmed by experiments on devices fabricated in an epi-poly process. A 5.5-V peak harmonic drive voltage with frequency higher than 300 Hz allows repetitive microstructure motion up to 70% of gap without position feedback. The results of the analysis have been applied to the design of a new concept for positioning beyond the static pull-in limitation that does include position feedback. The measured instantaneous actuator displacement is compared with the desired displacement setting and, unlike traditional feedback, the voltage applied to the actuator is changed according to the comparison result between two values. The low level is below the static pull-in voltage and opposes the motion, thus bringing the structure back into a stable regime, while the high level is larger than the static pull-in voltage and will push the structure beyond the static pull-in displacement. Operation is limited only by the position jitter due to the time delay introduced by the readout circuits. Measurements confirm flexible operation up to a mechanical stopper positioned at 2 /spl mu/m of the 2.25 /spl mu/m wide gap with a 30 nm ripple.

Suppression of the pull-in instability for parallel-plate electrostatic actuators operated in dielectric liquids

We study electrostatic parallel-plate actuators operated in dielectric liquids. The stable operation zone of the actuators in common liquids is extended far beyond one-third of the initial gap, which is the typical limit of stability for such actuators operated in air. The pull-in effect can even be totally suppressed. In spite of higher dielectric constants in liquids than in air, which is expected to magnify the electrostatic forces, the required voltages to actuate are not significantly reduced and may even be larger. These results are discussed with regard to the dielectric constant of the liquids and to the electrical insulating layers of the parallel plates which appear to play a major role. Finally, the analytical approach is compared to experiments performed on fabricated devices.

Simple models for piston-type micromirror behavior

Parallel-plate electrostatic actuators are a simple way to achieve piston motion for large numbers of mirrors in spatial light modulators. However, selection of design parameters is made difficult by their nonlinear behavior. This paper presents simple models for predicting static and dynamic behaviors of fixed–fixed parallel-plate electrostatic actuators. Static deflection equations are derived based on minimization of the total potential energy of the beam. Beam bending, residual stress, beam stretch and applied electrostatic force are included in the potential energy formulation. Computation time is reduced by working with assumed mode shapes. The problem of predicting midpoint beam deflection has been reduced to finding the roots of a third-order equation. Model results are compared to finite-element analysis results. In the dynamic analysis, Lagrange's method is used to derive the nonlinear equation of motion. An equation for predicting natural frequency, assuming small midpoint deflections about a dc setpoint, is presented. In addition, the effect of gas pressure on the damped natural frequency of a rigid actuator is analyzed. Experimental measurements of static deflection and frequency response are compared to model predictions. The actual micromirrors exhibit less strain stiffening than the model predicts.