Electrostatic repulsive out-of-plane actuator using conductive substrate

abstract: A pseudo-three-layer electrostatic repulsive out-of-plane actuator is proposed. It combines the advantages of two-layer and three-layer repulsive actuators, i.e., fabrication requirements and fill factor. A theoretical model for the proposed actuator is developed and solved through the numerical calculation of Schwarz-Christoffel mapping. Theoretical and simulated results show that the pseudo-three-layer actuator offers higher performance than the two-layer and three-layer actuators with regard to the two most important characteristics of actuators, namely, driving force and theoretical stroke. Given that the pseudo-three-layer actuator structure is compatible with both the parallel-plate actuators and these two types of repulsive actuators, a 19-element two-layer repulsive actuated deformable mirror is operated in pseudo-three-layer electrical connection mode. Theoretical and experimental results demonstrate that the pseudo-three-layer mode produces a larger displacement of 0–4.5 μm for a dc driving voltage of 0–100 V, when compared with that in two-layer mode.The final version of this article, as published in Scientific Reports, can be viewed online at: https://www.nature.com/articles/srep3511

Parametric Resonance of a Repulsive Force MEMS Electrostatic Mirror

We investigate the nonlinear dynamic behavior of an electrostatic MEMS mirror. The MEMS mirror is driven by repulsive force actuators, which avoid pull-in instability and enable large travel ranges. In parallel-plate actuators, the force on the structure is toward the substrate limiting the range of motion to the capacitor gap. Unlike parallel-plate, repulsive force actuators push the mirror away from the substrate not limiting the motion. The highly nonlinear nature of the repulsive force and the large motions create unique characteristics that dier from parallel-plate actuators. Repulsive force actuators show linear natural frequency hardening with increased DC voltages unlike parallel-plate ones that have frequency softening. A large parametric resonance is another attribute of repulsive force actuators as the limitations of a small gap and pull-in instability are eliminated. To simulate the system response, we use a lumped parameter model with linear and cubic stiness modulated by the excitation voltage that causes parametric resonances. Using the shooting technique, we obtained simulations that agree well with the nonlinear responses observed in our experiments. As the limitation of a small gap is overcome, the electrostatic force triggers large principal parametric resonances with amplitudes as large as the primary resonance. The parametric resonance is more pronounced at low DC excitation levels when geometric nonlinearities are not significant (axial stress is low). While the initial gap is only 2 microns, under parametric resonance, our one-millimeter diameter mirror reaches 43 m at 1.2 KHz when the excitation level is as low as VDC = 40 V; VAC = 1 V in a vacuum. The ability to achieve parametric resonances with repulsive force actuation can serve and improve the signal-to-noise ratio and speed in various applications such as confocal microscopy

Employing Boundary Element Approach With Genetic Algorithm to Increase Travel Range of Repulsive Actuators

The design of repulsive electrostatic actuators having enlarged travel range is achieved by combining the boundary element approach and a genetic algorithm. The boundary element method enables calculating the electrostatic forces without time consuming finite element simulations. Once a static equation that uses a model of effective lumped mass solves the travel ranges, the GA maximizes travel ranges by optimizing the dimensional parameters. The effectiveness of the scheme is demonstrated with extensive experimental results showing the travel ranges of a micro out-of-plane actuator are increased by up to 190%. The developed platform can improve the signal-to-noise ratios and the performance of general multi-electrode systems

Dynamic Response of a Tunable MEMS Accelerometer Based on Repulsive Force

This paper describes a tunable MEMS electrostatic accelerometer that uses repulsive electrode configuration so that the design is not hampered by capacitive pull-in instability. The repulsive force configuration enables the increase of DC bias voltage without suffering from the pull-in failure mode. This flexibility in increasing voltage can be employed as a tuning parameter to widen the working frequency range and to improve the robustness of the accelerometer. A lumped parameter model is developed to simulate the response of the microstructure under a combination of electrostatic and dynamic mechanical loading. The electrostatic force is estimated using a finite element simulation. The nonlinear equations of motion are solved for harmonic base excitations and halfsineshockloadsusingtheshootingandthelong-timeintegrationmethods,respectively. Tovalidatethemodel,asensorisfabricated and characterized under harmonic base excitation and mechanical shocks. A mechanical sensitivity of 0.1µm g is achieved when the bias voltage is 40(V). The experimental data are in good agreement with the simulation results. The comprehensive dynamical characterization presented in this study contributes to the development of functional accelerometers with tunable capabilities to harmonic and shock accelerations

Experimental characterization of the electrostatic levitation force in MEMS transducers

In this study, a two-step experimental procedure is described to determine the electrostatic levitation force in MEMS transducers. In these two steps, the microstructure is excited quasi-statically and dynamically and its response is used to derive the electrostatic force. The experimental results are obtained for a 1 by 1 plate that employs 112 levitation units. The experimentally obtained force is used in a lumped parameter model to find the microstructure response when it is subjected to different dynamical loads. The natural frequency and the damping ratios in the model are identified from the experimental results. The results show this procedure can be used as a method to extract the electrostatic force as a function of the microstructure’s degrees of freedom. The procedure can be easily used for any microstructure with a wide variety of electrode configurations to predict the response of the system to any input excitation

A parametric electrostatic resonator using repulsive force

In this paper, parametric excitation of a repulsive force electrostatic resonator is studied. A theoretical model is developed and validated by experimental data. A correspondence of the model to Mathieu\u27s Equation is made to prove the existence and location of parametric resonance. The repulsive force creates a combined response that shows parametric and subharmonic resonance when driven at twice its natural frequency. The resonator can achieve large amplitudes of almost 24 μm and can remain dynamically stable while tapping on the electrode. Because the pull-in instability is eliminated, the beam bounces off after impact instead of sticking to the electrode. This creates larger, stable trajectories that would not be possible with traditional electrostatic actuation. A large dynamic range is attractive for MEMS resonators that require a large signal-to-noise ratio

A tunable Electrostatic MEMS Pressure Switch

We demonstrate a tunable air pressure switch. The switch detects when the ambient pressure drops below a threshold value and automatically triggers without the need for any computational overhead to read the pressure or trigger the switch. The switch exploits the significant fluid interaction of a MEMS beam undergoing a large oscillation from electrostatic levitation to detect changes in ambient pressure. If the oscillation amplitude near the resonant frequency is above a threshold level, dynamic pullin is triggered and the switch is closed. The pressure at which the switch closes can be tuned by adjusting the voltage applied to the switch. The use of electrostatic levitation allows the device to be released from their pulledin position and reused many times without mechanical failure. A theoretical model is derived and validated with experimental data. It is experimentally demonstrated that the pressure switching mechanism is feasible

Compliant Torsional Micromirrors with Electrostatic Actuation

Due to the existence of fabrication tolerance, property drift and structural stiction in MEMS (Micro Electro Mechanical Systems), characterization of their performances through modeling, simulation and testing is essential in research and development. Due to the microscale dimensions, MEMS are more susceptible and sensitive to even minor external or internal variations. Moreover, due to the current limited capability in micro-assembly, most MEMS devices are fabricated as a single integrated micro-mechanical structure composed of two essential parts, namely, mass and spring, even if it may consist of more than one relatively movable part. And in such a scale of dimensions, low resonant micro-structures or compliant MEMS structures are hard to achieve and difficult to survive. Another problem arises from the limited visibility and accessibility necessary for characterization. Both of these issues are thus attempted in this research work. An investigation on micromirrors with various actuations and suspensions is carried out, with more attention on the micromirrors with compliant suspensions, electrostatic actuation and capable of torsional out-of-plane motion due to their distinct advantages such as the low resonance and the low drive voltage. This investigation presents many feasible modeling methods for prediction and analysis, aiming to avoid the costly microfabrication. Furthermore, both linear and nonlinear methods for structure and electrostatics are all included. Thus, static and dynamic performances of the proposed models are formularized and compared with those from FEA (Finite Element Analysis) simulation. The nonlinear modeling methods included in the thesis are Pseudo Rigid Body Model (PRBM) and hybrid PRBM methods for complex framed microstructures consisting of compliant beam members. The micromachining technologies available for the desired micromirrors are reviewed and an SOI wafer based micromachining process is selected for their fabrication. Though the fabrication was executed outside of the institution at that time, the layout designs of the micro-chips for manufacture have included all related rules or factors, and the results have also demonstrated the successful fabrication. Then investigation on non-contact test methods is presented. Laser Doppler Vibrometer (LDV) is utilized for the measurement of dynamic performances of proposed micromirrors. Two kinds of photo-sensing devices (PSDs), namely, the digitized PSD formed by CCD arrays and the analog PSD composed of a monolithic photosensing cell, are used for static test set-ups. An interferometric method using Mirau objective along with microscope is also employed to perform static tests of the selected micromirrors. Comparison of the tested results and their related theoretical results are presented and discussed, leading to a conclusion that the proposed hybrid PRBM model are appropriate for prediction or analysis of compliantly suspended micromirrors including issues arising from fabrication tolerance, structural or other parametric variations

Master of Science

thesisContact surfaces in micromechanical pin joints, hinges, and sliders introduce stiction and friction that disrupt motion in micro-electromechanical systems (MEMS). This thesis presents compliant design alternatives that move both in-plane and out-of-plane without introducing contact interference. This document correlates experimental results from fabricated devices to numeric models developed to predict key mechanical responses. The microsystems include the following: • A spiral cantilever spring (shaped like a watch spring) deflects out-of-plane 70% of its largest in-plane dimension. The deflection occurs because of force imparted by injected charge from a scanning electron microscope. • Compliant beams in torsion enable motion that is similar to that of a bushing-style substrate or scissor hinge. • A manual torsion load turns an elastic hoop inside-out as an example of a compliant bistable threshold hinge. • A compliant linkage symmetrically translates in-plane rotary motion to radial motion, similar to a blade aperture mechanism in a camera. These devices exemplify microsystems that avoid failure-inducing surface contact by exploiting an increase in component compliance that occurs as a result of lower bending and torsion stress response in beams with microscale cross-sections

Electrostatically Driven Large Aperture Micro-Mirror Actuator Assemblies for High Fill-Factor, Agile Optical Phase Arrays

Aircraft laser beamsteering is accomplished using a single gimbaled mirror housed inside a turret, which protrudes from the fuselage and causes unwanted turbulence, vibrations, and weight. The Air Force is currently investigating the use of microelectromechanical systems (MEMS) micro-mirror arrays to replace aircraft beamsteering technology. MEMS micro-mirror arrays provide a unique solution to address these issues. Unfortunately, current MEMS micro-mirror technology cannot meet all the beamsteering requirements in a single assembly. These include high fill-factor, large aperture, 25 degrees of out-of-plane deflection, 4-axis tilt, and actuation speeds below 1 ms. In this research, a novel MEMS actuation scheme to address all these requirements using electrostatically driven bimorph cantilever beams was designed, modeled, fabricated, and characterized. Modeling results show a linear relationship between the number of cantilever beams and maximum deflection. Characterization of fabricated micro-mirror assemblies supports the modeling for individual actuators as well as for micro-mirror platform assemblies. Fabricated devices reached vertical deflections greater than 170 micrometer with pull-in voltages of 20 V and an optical range of 16 degrees. These large deflections, low pull-in voltage, and reasonable optical range shown in this research demonstrate the feasibility of using MEMS micro-mirror arrays to address aircraft beamsteering issues