Electrostatic MEMS Actuators Research Articles

Flexural–torsional modal interaction in MEMS actuators initiated by minuscule asymmetry

AbstractAn efficient actuation technique for electrostatic MEMS actuators exploiting electro-mechanical-mechanical modal interactions is proposed. The flexural–torsional equations of motion are established, and we manifest that the initiation of a 2:1 autoparametric modal interaction between in-plane bending and torsional modes of the actuator that is supposed to be symmetrical with respect to its axis of rotation is contingent upon the presence of a quadratic stiffness term, which arises from the existence of non-zero first moments of area of the actual cross-section in prismatic microbeams. In order to efficiently reduce the AC voltage value required to reach the activation of the 2:1 mechanical modal interaction, the electrical resonant frequency is syntonized to half of the natural frequency of the in-plane bending mode. The results indicate that the amplitude of the in-plane motion saturates upon the initiation of an energy exchange between the bending and torsional motions. Through suitable tuning of the AC frequency, the amplitude of the in-plane motion is minimized, while the amplitude of the torsional motion, the indirectly excited mode, is maximized. Our results demonstrate that the actuator's torsional motion, when subjected to a 1:2:1 electro-flexural–torsional modal interactions, is triggered by applying a maximum voltage of 10 V, resulting in about 20 degrees rotational angle. Furthermore, prolific frequency combs are generated as a result of secondary Hopf bifurcations along the large-amplitude response branches, inducing quasi-periodicity in the MEMS dynamics.

Impact of Solid Materials in the Gap Space between Driving Electrodes in a MEMS Tri-Electrode Electrostatic Actuator.

MEMS electrostatic actuators can suffer from a high control voltage and a limited displacement range, which are made more prevalent by the pull-in effect. This study explores a tri-electrode topology to enable a reduction in the control voltage and explores the effect of various solid materials forming the space between the two underlying stationary electrodes. Employing solid dielectric material simplifies fabrication and can reduce the bottom primary electrode's fixed voltage. Through numerical analysis, different materials were examined to assess their impact. The results indicate that the primary electrode's fixed voltage can be reduced with an increase in the dielectric constant, however, with the consequence of reduced benefit to control voltage reduction. Additionally, charge analysis was conducted to compare the actuator's performance using air as the gap-spacing material versus solid materials, from the perspective of energy conservation. It was found that solid materials result in a higher accumulated charge, reducing the need for a high fixed voltage.

Advancing simulation efficiency for MEMS electrostatic actuators

This paper presents an overview of the research progress on Multiphysics simulation of MEMS electrostatic actuators. MEMS electrostatic actuators have shown significant development potential in applications such as ADWSS and VOA. However, the increasing size and complexity of these devices have posed challenges to traditional Multiphysics simulation methods, leading to lengthy computational times that hinder the overall device development process. In order to enhance simulation efficiency and meet the demands of device development, the use of simplified single physics field models have been explored. The results have demonstrated that the simplified single physics filed simulation model yields comparable results to traditional Multiphysics simulations with an error tolerance of within 10%, while reducing simulation time by 80-90%.

An Ultrathin Internal Dielectric Actuator for Extended Range Deflection Pull-in Free Actuation

MEMS electrostatic actuators suffer from pull-in instability, making them highly nonlinear and limiting their useful range of motion. This report resolves the performance-limiting issues of the gap-closing transducer by using an ultrathin dielectric layer (UDL) for actuation. The device has an electromechanical coupling coefficient of 4.26% and an average deflection sensitivity of 119 nm/V over a range of 350 nm for upto 3.3 V dc bias. The UDL capacitance and deflection show a square law dependence on voltage. The device can thus be used as an actuator upto the full range of motion with better performance. Additionally, the UDL or gap capacitance can be used for feedback to maintain constant gap or strain. UDL actuation may also be combined with gap actuation to lower the pull-in voltage without changing the gap or the actuator thickness. 2022-0213

MEMS enabled suspended silicon waveguide platform for long-wave infrared modulation applications

Long-wave infrared (LWIR, 6–14 µm) is an important wavelength range as it covers abundant vibrational molecular fingerprints that can be used for gas/liquid sensing and absorption spectroscopy. Silicon waveguide-based passive photonic devices that offer advantages toward chip-scale miniaturization of photonic integrated circuits (PIC) and photonic sensors in LWIR have been explored. However, the modulation of Si-based guided-wave propagation in LWIR remains less reported. Here, we demonstrate a MEMS tunable directional coupler operating at a long-wave infrared wavelength range (6.4–7 µm) using suspended Si waveguides with subwavelength gratings. Leveraging the membrane transfer technology, the whole photonic waveguide device membrane is transferred onto a receiver substrate with a cavity that allows sufficient displacement for MEMS electrostatic actuation. The proposed device experimentally achieved an optical attenuation of −14.25 dB with 90 V DC bias voltage, while having a response time of 177 µs. In addition, the demonstration of using such a device for computational spectroscopy has been validated.

Micro-triboelectric generator for zero-power shock detection

This work shows zero-power shock sensing for the combination of a micro-triboelectric generator and MEMS electrostatic actuator system where the mechanical shock to the generator causes it to produce voltage, this voltage is used to actuate a Micro-Electro-Mechanical-system (MEMS) switch. For the first time, we present the fabrication process of a Triboelectric-Nano-Generator (TENG) with MEMS technology. The MEMS-TENG has a suspended 1.5 mm × 1.5 mm plate separated by 2 μm from the substrate. The generator is a triboelectric transducer made of a suspended Al micro-plate above a polyimide (PI) thin layer that is covered by another Al layer in the back. In case the shock is sufficiently strong, the micro-plate hits its substrate. As a result of the impact, electrification happens and PI gets negatively charged, while the Al gets positively charged. Connecting the generator to a MEMS switch, we use the generated voltage to actuate a MEMS switch. The TENG was able to supply voltage difference up to 0.4 V at 2.3g. We use the MEMS-TENG to actuate a cantilevered MEMS switch (500 × 20 × 2 μm) separated by a 2 μm gap from a fixed bottom electrode. Triboelectric generators are known for high voltages and low currents, which makes them ideal for integration with MEMS electrostatic devices that require ultra-low power to operate. Our feasibility study opens doors to billions of innovative devices that can be created from this synergistic combination.

Stable Deflection in Ferroelectric Negative-Capacitance Hybrid MEMS Actuator With Cubic Nonlinear Spring

Electrostaticmicroelectromechanicalsystems (MEMS) actuators suffer from an instability called pull-in, wherein the movable electrode snaps onto the fixed electrode beyond a certain applied voltage. Thus, the entire allowed range is not utilized for stable operation. We propose pull-in free, low-voltage operation by using a cubic nonlinear spring with a ferroelectric negative-capacitance hybrid MEMS actuator. We use a physics-based framework based on the energy landscape to illustrate stability improvement. This framework uses energy–displacement and voltage–displacement plots for analysis. We predict that the actuator can operate in three distinct modes: 1) monostable; 2) bistable; and 3) always-stable, based on the value of the cubic spring constant. We also estimate the threshold values of the cubic spring constant that demarcate the three modes of operation. By proper choice of the cubic spring constant, we predict pull-in free, low-voltage operation of the hybrid actuator, when compared to the standalone MEMS actuator. The results obtained are in agreement with the numerical simulations. This work will aid in the design of electrostatic MEMS actuators for low-voltage applications without pull-in instability.

Cellular shape micromachined actuator ribbons

This work presents a new class of micromachined electrostatic actuators capable of producing output force and displacement unprecedented for MEMS electrostatic actuators. The actuators feature submicron high aspect ratio transduction gaps lined up in two-dimensional arrays. Such an arrangement of microscale actuator cells allows the addition of force and displacements of a large number of cells (up to 7600 in one demonstrated array), leading to displacements ranging in the hundreds of microns and several gram forces of axial force. For 50 µm thick actuators with horizontal dimensions in the 1–4 millimeter range, an out-of-plane displacement of up to 678 µm at 46 V, a bending moment of up to 2.0 µNm, i.e., 0.08 N (~8 gram-force) of axial force over a 50 µm by 2 mm cross-sectional area of the actuator (800 kPa of electrostatically generated stress), and an energy density (mechanical work output per stroke per volume) up to 1.42 mJ/cm3 was demonstrated for the actuators.

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.

Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System

The mechanism of the inchworm motor, which overcomes the intrinsic displacement and force limitations of MEMS electrostatic actuators, has undergone constant development in the past few decades. In this work, the electrostatic actuation unit cell (AUC) that is designed to cooperate with many other counterparts in a novel concept of a modular-like cooperative actuator system is examined. First, the cooperative system is briefly discussed. A simplified analytical model of the AUC, which is a 2-Degree-of-Freedom (2-DoF) gap-closing actuator (GCA), is presented, taking into account the major source of dissipation in the system, the squeeze-film damping (SQFD). Then, the results of a series of coupled-field numerical simulation studies by the Finite Element Method (FEM) on parameterized models of the AUC are shown, whereby sensible comparisons with available analytical models from the literature are made. The numerical simulations that focused on the dynamic behavior of the AUC highlighted the substantial influence of the SQFD on the pull-in and pull-out times, and revealed how these performance characteristics are considerably determined by the structure’s height. It was found that the pull-out time is the critical parameter for the dynamic behavior of the AUC, and that a larger damping profile significantly shortens the actuator cycle time as a consequence.

Electrostatically Tuned Optical Filters Based on Hybrid Plasmonic-Dielectric Thin Films for Hyperspectral Imaging.

Hyperspectral imaging has a wide range of uses, from medical diagnostics to crop monitoring; however, conventional hyperspectral imaging systems are relatively slow, bulky, and rather costly. In this paper, we present an inexpensive, compact tunable optical filter for hyperspectral applications. The filter is based on a Fabry-Pérot interferometer utilizing hybrid metallic-dielectric mirrors and actuated using a MEMS electrostatic actuator. The optical filter is designed using the transfer matrix method; then, the results were verified by an electromagnetic wave simulator. The actuator is based on a ring-shaped parallel plate capacitor and is designed using COMSOL Multiphysics. An actuation displacement of 170 nm was used, which is the required distance to tune the filter over the whole visible range (400–700 nm). There are two designs proposed for the optical filter: the first was optimized to provide maximum transmission and the other is optimized to have minimum full-width-half-maximum (FWHM) value. The first design has a maximum transmission percentage of 94.45% and a minimum transmission of 86.34%; while the minimum FWHM design had an average FWHM value of 7.267 nm. The results showed improvements over the current commercial filters both in transmission and in bandwidth.

Measurement of gap distance dependence on thermal transfer between nanogap created by single crystal silicon cleavage using MEMS electrostatic actuator

Measurement of gap distance dependence on thermal transfer between nanogap created by single crystal silicon cleavage using MEMS electrostatic actuator

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.

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]

Impact of excitation waveform on the frequency stability of electrostatically-actuated micro-electromechanical oscillators

In this paper, the frequency stability of high-Q electrostatically-actuated MEMS oscillators with cubic restoring forces, and its relation with the amplitude, the phase and the shape of the excitation waveform, is studied. The influence on close-to-the carrier frequency noise of additive processes (such as thermomechanical noise) or parametric processes (bias voltage fluctuations, feedback phase fluctuations, feedback level fluctuations) is taken into account. It is shown that the optimal operating conditions of electrostatically-actuated MEMS oscillators are highly waveform-dependent, a factor that is largely overlooked in the existing literature. This simulation-based study covers the cases of harmonic and pulsed excitation of a parallel-plate capacitive MEMS resonator.

Application of multiplicative dimensional reduction method for uncertainty quantification and sensitivity analysis of MEMS electrostatic actuators

The effect of electrostatic actuation allows MEMS devices to have specific physical movements. They have several advantages including low power, low cost, and small size and are used widely in variable capacitors, micro-accelerometers, etc. In this study, we consider a MEMS actuator consisting of a moveable plate and a fixed plate in the presence of an applied electric field. The gap between the two plates can normally be changed by voltage control. It is known that as the gap reduces to two thirds of the original gap, the so-called “pull-in effect” tends to occur, causing the plates to collide (resulting in dielectric breakdown and actuator failure). It is therefore important to predict the onset of the “pull-in effect”. As it is practically impossible to obtain the model parameters precisely, this prediction should account for the presence of uncertainties. Sampling methods such as Monte Carlo and Quasi Monte Carlo are easy to use with the caveat of low accuracy and high computational cost. The other popular method is polynomial chaos. It has high accuracy and low computational cost under smoothness assumption for problems with small number of uncertain parameters. In this study, we consider a two-stage approach to quantify the parametric uncertainty of MEMS electrostatic actuators with a moderate number of causal stochastic factors. In the first stage, a multiplicative dimensional reduction method is used to approximate the variance-based global sensitivity measures in order to simplify the model for the uncertainty quantification stage. The second stage involves the use of the generalized polynomial chaos (gPC) approach to quantify uncertainty of the simplified model from the first stage.

Nonlinear Parameter Identification of a Resonant Electrostatic MEMS Actuator.

We experimentally investigate the primary superharmonic of order two and subharmonic of order one-half resonances of an electrostatic MEMS actuator under direct excitation. We identify the parameters of a one degree of freedom (1-DOF) generalized Duffing oscillator model representing it. The experiments were conducted in soft vacuum to reduce squeeze-film damping, and the actuator response was measured optically using a laser vibrometer. The predictions of the identified model were found to be in close agreement with the experimental results. We also identified the noise spectral density of process (actuation voltage) and measurement noise.

Critical pull-in curves of MEMS actuators in presence of Casimir force

We present analytic and computational studies of the dynamical behavior of an undamped electrostatic MEMS actuator with one-degree of freedom subject to a Casimir force. In such a situation, the well-known mathematical difficulty associated with an inverse quadratic term due to a Coulomb force is supplemented with an inverse quartic term due to the joint application of a Casimir force. We show that the small Coulomb and Casimir force situations, described by sufficiently low values of two positive parameters, λ and μ, respectively, are characterized by one-stagnation-point periodic motions and there exists a unique critical pull-in curve in the coordinate quadrant beyond which a finite-time touch down or collapse of the actuator takes place. We demonstrate how to locate and approximate the pull-in curve. When mechanical nonlinearity such as that due to the presence of a cubic elastic force term is considered in the equation of motion, we show that a similar three-phase oscillation-pull-in-finite-time-touchdown phenomenon occurs and that pull-in curves are actually enhanced or elevated by nonlinear elasticity. Furthermore, we compute solutions of the MEMS wave equations and show that the same characteristic phenomena of subcritical periodic motions and loss of periodicity of motion and onset of a critical pull-in curve occur as one increases the levels of the Coulomb and Casimir forces as in the one-degree-of-freedom case.

Discharging-phototransistor-integrated high-voltage Si photovoltaic cells for fast driving demonstration of an electrostatic MEMS actuator by wavelength modulation

In this article, the authors propose a high-voltage photovoltaic (PV) cell array integrating discharging phototransistors for the fast driving of an electrostatic MEMS actuator by light with wavelength modulation. A PV cell array and phototransistors are connected in parallel and colored with green and red lacquer, respectively. This circuit repeats the charge and discharge of a MEMS actuator by being illuminated with light whose color periodically changes between red and green. This method requires only a small additional area and can discharge the actuator at an arbitrary timing. The authors extract the parameters of the circuit and also demonstrate the dynamic driving of a MEMS comb-drive actuator.

Influence of Excitation Waveform on the Frequency Stability of an Electrostatic MEMS Oscillator

In this paper, we investigate the optimal operating conditions of electrostatically-actuated MEMS oscillators in terms of frequency stability. Through a simple model, the influence of the fluctuation of several design parameters (e.g. feedback phase, feedback amplitude, bias voltage) on oscillator performance is studied. It is shown that, in the nonlinear regime, the excitation waveform (e.g. square, sinusoid, impulsive, etc.) plays a critical role on the long-term frequency stability of electrostatic MEMS oscillators, as opposed to the well-known but idealized case of a Duffing oscillator.