Parallel-plate Actuators Research Articles

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.

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 differ 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 stiffness 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 2μm, under parametric resonance, our one-millimeter diameter mirror reaches ±43μm at 1.2kHz when the excitation level is as low as VDC=40V, VAC=1V 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.

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.

Active vibration isolator based on micromachined electrostatic actuators

Parallel plate actuators (PPAs) are widely used actuators in microelectromechanical systems. A PPA can be utilised as a passive/active vibration isolator. A novel active vibration isolator with a simple structure, which requires a constant voltage source and series capacitor, is proposed. The principle of the spring softening effect is analysed, which can avoid a specific external disturbance by changing its resonant frequency. A simulation study was performed to verify the feasibility of this type of isolator.

Electrostatic repulsive out-of-plane actuator using conductive substrate.

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.

Self‐sensing estimator for micromachined electrostatic actuators and parameters’ optimisation

Parallel plate actuators (PPAs) are widely used in micro-electro-mechanical systems. Control strategies for PPAs often require displacement and velocity feedback that may be measured with various sensing techniques, which may require additional structures or distort the steady-state behaviour. An alternative approach of designing an estimator using the measured voltage across the PPA without additional sensing structures and distortions is proposed in this work. This novel method can improve the performance and reduce the device's footprint with full-state (displacement and velocity) feedback information, using a series resistor. A system model using this configuration is investigated. The observability of this self-sensing technique is analysed using a small signal model. Then, a singular value decomposition is applied to examine how to further improve the observability by choosing appropriate parameters. Simulation and numerical studies were performed which validate this method.

Efficient primary and parametric resonance excitation of bistable resonators

We experimentally demonstrate an efficient approach to excite primary and parametric (up to the 4th) resonance of Microelectromechanical system MEMS arch resonators with large vibrational amplitudes. A single crystal silicon in-plane arch microbeam is fabricated such that it can be excited axially from one of its ends by a parallel-plate electrode. Its micro/nano scale vibrations are transduced using a high speed camera. Through the parallel-plate electrode, a time varying electrostatic force is applied, which is converted into a time varying axial force that modulates dynamically the stiffness of the arch resonator. Due to the initial curvature of the structure, not only parametric excitation is induced, but also primary resonance. Experimental investigation is conducted comparing the response of the arch near primary resonance using the axial excitation to that of a classical parallel-plate actuation where the arch itself forms an electrode. The results show that the axial excitation can be more efficient and requires less power for primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, the axial excitation technique can provide large amplitude motion while protecting the structure from pull-in. In addition to primary resonance, parametrical resonances are demonstrated at twice, one-half, and two-thirds the primary resonance frequency. The ability to actuate primary and/or parametric resonances can serve various applications, such as for resonator based logic and memory devices.

A 50–100 GHz ohmic contact SPDT RF MEMS silicon switch with dual axis movement

We firstly show the prototype of an ohmic contact Single-Pole Double-Throw Radio Frequency Micro-Electro-Mechanical Systems (SPDT RF MEMS) switch operating at 50–100GHz. The fabricated ohmic contact SPDT RF MEMS silicon switch moves both laterally and vertically, to improve the isolation at high frequencies by initially misaligning the contact part of the switch over a Coplanar Waveguide (CPW) transmission line. The lateral and vertical movement of the switch is operated by using comb and parallel plate actuators, respectively. The proposed switch was fabricated using Silicon-On-Glass (SiOG) bonding process. The insertion loss of the fabricated switch is measured according to the different operation states of the switch, in the range from 50 to 100GHz. The fabricated length of the transmission line is 4.6mm and the measured insertion loss and isolation are 9.13dB and 24.37dB at 70GHz, respectively.

Fabrication of an RF-MEMS-Switch on a hybrid Si-Ceramic substrate

Abstract The integration of MEMS sensors, microelectronics and RF circuits including RF-MEMS is still a challenging task but becomes crucial for the Internet of Things. A wafer-level silicon-ceramic composite substrate (called SiCer, Silicon-on-Ceramics) allows new options in smart system integration. SiCer substrates combine the benefits of two different worlds of materials. The silicon substrate is a suitable material to build active MEMS devices such as switches and resonators. The ceramic substrate, a Low Temperature Cofired Ceramic (LTCC), is well-known for RF circuit integration including resistors, capacitors and coils. Both materials are co-sintered into a monolithically composite substrate. Chemical and physical modification of the silicon interface allows a low-pressure sintering and therefore new techniques for generating buried cavities at the bond interface. A carbon paste is applied on the LTCC via screen printing. After sintering, this results in a defined cavity. To demonstrate the advantages of the buried cavities within SiCer substrates the fabrication process of a RF-MEMS switch is shown. The switch is intended for a switching matrix to select frequency bands in a mobile LTE receiver. A parallel-plate electrostatic actuation with in-plane movement has been selected. This type of switch allows a large displacement range and a low actuation voltage can be achieved.

FPCB Micromirror-Based Laser Projection Availability Indicator

This paper presents a flexible printed circuit board (FPCB) actuator-driven micromirror (referred to as FPCB micromirror hereafter)-based laser projection indicator. The device integrates two FPCB micromirrors, one red laser, one green laser, a dichroic laser combiner, and driving/control circuit. It generates and projects red or green static or rotating laser pattern on a remote translucent film to indicate availability, which well solves the wiring problem associated with traditional availability indicators. The FPCB micromirror consists of an FPCB electrostatic rotation parallel plate actuator with a silicon mirror plate bonded on its top. The FPCB micromirror is of much lower cost with much higher surface quality and larger aperture than conventional microelectromechanical systems (MEMS) micromirrors. The model of controlling the FPCB micromirrors to generate a rotating ellipse is derived and the prototype is fabricated and tested.

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%.

Analysis and dynamic simulation of the synthetic voltage division controller for extending the parallel plate actuator stable range of motion

Parallel-plate actuators (PPAs) are useful in micro-electro-mechanical systems (MEMS) devices. The main drawback of a PPA is that it has limited stable motion range. The series capacitor method (SCM) is a common way to solve this issue. However, the SCM requires a much higher voltage input to drive the PPA and series capacitor, and it is deleteriously affected by parasitic capacitance in parallel with the PPA. Additionally, it is usually difficult to obtain a sufficiently small series capacitor, which has to be no greater than half of the minimum capacitance of the PPA. In this work, a synthetic voltage division (SVD) controller is proposed to solve these problems. Firstly, this paper reviews the system dynamics of PPAs and the SCM. The effects of parasitic capacitance are also explored. Then, the SVD controller is presented in detail. It is demonstrated through simulation that the SVD controller can increase the stable range of motion while reducing the required input voltage and cancelling the effect of the parasitic capacitance.

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.

A MEMS PPA Based Active Vibration Isolator - STUDENT AWARD 3RD PLACE $500

Several types of micro-devices are adversely affected by high frequency mechanical vibrations present in the operating environment. Examples include MEMS vibratory gyroscopes and resonators, and micro-optics. Various types of MEMS vibration isolators have been developed for use in the packaging of these vibration sensitive devices. Passive isolators consist of a spring-mass-damper MEMS device and usually have a very high mechanical quality factor, which makes them susceptible to ringing at the isolator's resonant frequency. Active isolators have been realized by using state sensing of the proof mass motion and feeding one or more of these states back through an actuator to adjust the frequency response of the isolator. For example, the technique known as skyhook damping uses velocity feedback to adjust, and typically increase, the damping of the isolator. Although these technique are doable, they require state sensing or state estimation, with feedback electronics to drive the actuator. A simpler MEMS active vibration isolator architecture employs only a parallel plate actuator (PPA) with the MEMS spring-mass-damper structure. The PPA driven with a DC voltage, in its stable operating range, displaces the proof mass, which results in a change in the effective system spring constant due to the electrostatic spring softening effect. This results in a change in the resonant frequency and the quality factor of the isolator. However, due to the nonlinearities inherent in this type of device, the stable operating range is reduced as the PPA voltage is increased. Furthermore, even when the isolator is stable in steady-state, a sufficiently large transient response can also drive it into the unstable regime, resulting in the electrodes snapping into contact. In this study, the PPA based active vibrator isolator is developed and its performance is evaluated. The characteristics of the transient instability are investigated and its stable range of operation is specified, for booth external disturbances and rapid application of the control voltage. This MEMS PPA based active vibration isolator can improve performance compared to passive isolators, while being much simpler than state feedback active isolators.

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.

Dynamic behavior of perforated parallel-plate actuator under squeeze film damping effect

Dynamic performance is one of the most critical factors in many MEMS products, such as micro accelerometers, vibratory gyroscopes, micro deformable mirror, etc. Essentially, the dynamic behavior is totally determined by two factors: the internal factor, the stiffness of structure and the external factor, the damping of environment. In this paper both factors are analyzed accurately and a theoretical dynamic model of parallel-plate actuators is presented. The stiffness of the structure, i.e. the spring constant k of the suspension beam that supports the moving plate of the actuator, is achieved by many accurate experimental tests. The damping of environment, referring to the squeeze film damping coefficient c in parallel-plate actuators, is analyzed by calculation and FEA simulation. Further, we consider c a linear function of the actuator displacement, but not a constant value. This treatment greatly improves the accuracy of the dynamic model and could be applied in parallel-plate actuators with large displacement. Dynamic behaviors of the actuators under squeeze film damping, such as natural frequency, response time and bandwidth, are predicted based on the model. Three kinds of parallel-plate actuators are designed and fabricated using a surface micromachining process to verify the estimation of the presented theoretical model and experimental test results have showed good consistency with the theoretical analysis. The dynamic model proposed in this paper could be broadly applied in the MEMS/NEMS systems.

Low-power microelectromechanically tunable silicon photonic ring resonator add-drop filter.

We experimentally demonstrate a microelectromechanically (MEMS) tunable photonic ring resonator add-drop filter, fabricated in a simple silicon-on-insulator (SOI) based process. The device uses electrostatic parallel plate actuation to perturb the evanescent field of a silicon waveguide, and achieves a 530 pm resonance wavelength tuning, i.e., more than a fourfold improvement compared to previous MEMS tunable ring resonator add-drop filters. Moreover, our device has a static power consumption below 100 nW, and a tuning rate of -62 pm/V, i.e., the highest reported rate for electrostatic tuning of ring resonator add-drop filters.

Linearized control of an uniaxial micromirror with electrostatic parallel-plate actuation

Electrostatic parallel-plate actuation is a common method for driving micromirrors with analog deflection control. This actuation enables high dynamics, low power consumption, compact design, large mirror deflection and a fabrication with MEMS-technology. The drawback is the highly nonlinear behavior of the angle vs. voltage curve by using the common single-ended or differential control. This paper presents an advanced control method. A four-electrode arrangement is used to drive the mirror. An "actuating electrode" which is placed close to the rotation axis and an "outer electrode" on each side are used. For the actuation, the electrodes from only one side are used. The outer electrode voltage is in dependence on the driving voltage which is applied at the actuating electrode. This dependence is described by a control function. This one allows realizing a nearly linear angle vs. driving voltage curve, by increasing or decreasing the additional actuating torque caused by the outer electrode. To show the suitability of this method, a laser beam is deflected by a micromirror and is detected by a position-sensitive device (PSD) which is mounted on a moving stage. The PSD is used as feedback sensor and the mirror is actuated using a linear PID-controller. Stage movements with a speed of up to 80 mm/s have been tracked over an angular range between 0.8° and 12.3° for tilting the mirror with an angular velocity of about 14.7°/s.

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.

Nonlinear Feedback Control to Enhance Stable Performance of Micromachined Electrostatic Parallel Plate Actuators

MEMS parallel plate actuators on elastic suspensions are open loop stable over one third of their rest gap distance. To increase the range of stable motion, a nonlinear feedback controller is proposed in this paper. Verification and error analysis are performed using MATLAB Simulink.