Electrostatic Microelectromechanical Systems Research Articles

Accurately estimating the scanning angle of an electrostatic MEMS mirror with a novel damping model

A novel damping model to accurately analyze the scanning angle of electrostatic microelectromechanical system (MEMS) mirrors is proposed in this article. The computational fluid dynamic (CFD) simulations are used to calculate the aerodynamic moment of the MEMS mirror oscillating in air. The simulation results demonstrate the linear dependence of the equivalent damping coefficient of the MEMS mirror on the oscillation amplitude and frequency. Then the equivalent damping expression of the MEMS mirror is established. The damping model is applied to the dynamic equation of the MEMS mirror for numerical solution. The frequency responses of the electrostatic MEMS mirror under square wave excitation with different voltage amplitudes and duty cycles are obtained. The measurement results provide good accuracy verification for numerical results. This verifies the accuracy of the proposed damping model, which can be used to accurately estimate the scanning angle in the design and parameter optimization process of electrostatic MEMS mirrors.

Mathematical modeling of an electrostatic MEMS with tilted elastomeric micro-pillars

The aim of this study is to develop a comprehensive mathematical model for an electrostatic MEMS (Micro-Electro-Mechanical Systems) with gap-filling tilted micro-pillars. Elastomeric pillars are used due to their high dielectric constant, resulting in a higher equivalent permittivity of the gap medium. This leads to increased sensitivity and decreased required voltage. Although this system has gained popularity in recent years, a thorough understanding and accurate predictions of its behavior require a detailed mathematical model. Regrettably, the existing literature does not offer adequate information. The present model incorporates three coupled set of nonlinear differential equations that govern the longitudinal and transverse vibrations of the PDMS (Polydimethylsiloxane) pillars, as well as the transverse vibrations of the moving electrode. It demonstrates how the device's behavior is affected by varying tilt angles and numbers of micro-pillars. The viscoelastic properties of the PDMS pillars are also taken into account, following the Kelvin-Voigt model with non-linear strains. Numerical methods are used to solve the governing equations, enabling investigation of static deformation and vibrational responses under different DC (Direct Current) and DC+AC (Alternating Current) actuations. The nonlinear equations proposed in this study provide a valuable tool for accurately predicting the behavior of capacitive MEMS devices that use microstructured gaps with tilted micro-pillar arrays.

(Invited) SAE-MEMS Technology for Electrostatic Vibrational Energy Harvesters

Energy harvesting [1] is expected to be a self-powering technology for small wireless sensor nodes in the next generation Internet-of-Things (IoT). In particular, small vibrational energy harvesters (VEHs) based on micro-electro-mechanical systems (MEMS) technology, which are battery-free and can generate electricity even at night or in the dark, are being investigated worldwide for next-generation power sources for small wireless IoT nodes [2,3]. Electrostatic MEMS VEHs, which use semi-permanent charge-holding dielectrics called "electrets," are useful for power generation using environmental vibrations because they have a higher output power density at lower frequencies than other methods [4]. Further miniaturization, higher performance, and higher productivity will be required to use electret-type MEMS VEHs as power sources for compact wireless IoT nodes and other devices. Although the integration of MEMS VEHs with power management circuits enables miniaturization, higher performance, and improved productivity, the monolithic integration of electret-type MEMS VEHs and electronic circuits is an unexplored area in conventional technology. Conventional electrostatic MEMS VEHs involve corona discharge, electron beam irradiation, X-ray irradiation, or high-temperature treatment as electret charge processing, which imposes restrictions on the design and manufacturing of MEMS structures and the integration of MEMS and electronic circuits. Recently, self-assembled electrets (SAEs), which are electrets that do not require any charging process, have been developed using materials for organic electroluminescent devices [5]. The surface charge density of SAEs is equivalent to those of previously reported electrets for VEHs, and thus SAE is expected to improve the performance of VEH and simplify the manufacturing process. However, there have been no reports of MEMS devices using SAEs.Our proposed method is the first technology to form SAEs inside MEMS structures using only a vacuum evaporation process at room temperature, and we have succeeded in actual vibration power generation [6]. This technology can be integrated into existing semiconductor processes because the electret formation requires only room-temperature deposition, making it possible to monolithically integrate electret-type MEMS VEHs and electronic circuits on the same substrate. In addition, since the SAE surface potential is proportional to the film thickness, the amount of electricity generated can be further increased by increasing the thickness of the SAE film. Therefore, this technology is expected to accelerate the miniaturization, performance, and productivity improvement of MEMS environmental vibration power generation devices. Akinaga, “Recent advances and future prospects in energy harvesting technologies,” Jpn. J. Appl. Phys. 59 (2020) 110201.D. Mitcheson, E. M. Yeatman, G. K. Rao, A. S. Holmes, and T. C. Green, “Energy Harvesting from Human and Machine Motion for Wireless Electronic Devices” Proc. IEEE 96 (2008) 1457–1486.Suzuki, “Recent progress in MEMS electret generator for energy harvesting,” IEEJ Trans. Elec. Electron. Eng. 6 (2011) 101-111.Toshiyoshi, S. Ju, H. Honma, C.-H. Ji, and H. Fujita, “MEMS vibrational energy harvesters,” Sci. Technol. Adv. Mater. 20 (2019) 124-143.Tanaka, N. Matsuura, and H. Ishii, “Self-Assembled Electret for Vibration-Based Power Generator,” Sci. Rep. 10 (2020) 6648.Yamane, H. Kayaguchi, K. Kawashima, H. Ishii, and Y. Tanaka, “MEMS post-processed self-assembled electret for vibratory energy harvesters,” Appl. Phys. Lett. 119 (2021) 254102.

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.

THE GREEN-RVACHOV QUASI-FUNCTION METHOD IN THE NUMERICAL ANALYSIS OF MICROELECTROMECHANICAL SYSTEMS USING TWO-SIDED APPROXIMATIONS

The work is devoted to developing a bilateral iterative method of numerical analysis of one electrostatic microelectromechanical system based on the use of the Green – Rvachev quasi-function. Microelectromechanical systems are miniature devices that combine electronic and mechanical components of micron size. Electrostatically activated microelectromechanical systems have certain disadvantages that limit the range of their operation. One of these is the pull-in instability of the functional components of the system, which occurs if the applied voltage difference is above a particular critical value. The mathematical model of the system under consideration in the work is a semi-linear elliptic equation with the Laplace operator and the Dirichlet condition. To construct an approximate solution of the problem, it is proposed to use the methods of nonlinear analysis in semi-ordered spaces, particularly the results of V. I. Opoitsev on the solvability of nonlinear operator equations with a heterotonic operator. The boundary value problem simulating the most straightforward microelectromechanical system under the action of external pressure is reduced to the Urison integral equation using the Green – Rvachev quasi-function method, which makes it possible to expand the application of the method of two-sided approximations for problems in areas of somewhat arbitrary geometry. The paper substantiates the possibility of constructing iterative sequences with two-sided convergence to a positive solution of the problem: the computational scheme is given, the conditions for its convergence to the desired solution are obtained, and the a posteriori error estimate is derived. The method is illustrated by a computational experiment for a problem considered in a rectangular area. The computational experiment results are presented in the form of the surface and lines of the level of the approximate solution, and the two-sided nature of the convergence of the proposed method is also graphically illustrated.

Self-aligned single-electrode actuation of tangential and wineglass modes using PMN-PT

Considering the evolution of rotation sensing and timing applications realized in micro-electro-mechanical systems (MEMS), flexural mode resonant shapes are outperformed by bulk acoustic wave (BAW) counterparts by achieving higher frequencies with both electrostatic and piezoelectric transduction. Within the 1–30 MHz range, which hosts BAW gyroscopes and timing references, piezoelectric and electrostatic MEMS have similar transduction efficiency. Although, when designed intelligently, electrostatic transduction allows self-alignment between electrodes and the resonator for various BAW modes, misalignment is inevitable regarding piezoelectric transduction of BAW modes that require electrode patterning. In this paper transverse piezoelectric actuation of [011] oriented single crystal lead magnesium niobate–lead titanate (PMN–PT) thin film disks are shown to excite the tangential mode and family of elliptical compound resonant modes, utilizing a self-aligned and unpatterned electrode that spans the entire disk surface. The resonant mode coupling is achieved by employing a unique property of [011] PMN–PT, where the in-plane piezoelectric coefficients have opposite signs. Fabricating 1-port disk transducers, RF reflection measurements are performed that demonstrate the compound mode family shapes in the 1–30 MHz range. Independent verification of mode transduction is achieved using in-plane displacement measurements with Polytec’s laser Doppler vibrometer (LDV). While the tangential mode achieves a 40o/s dithering rate at 335 kHz resonant frequency, the n = 2 wine-glass mode achieves 11.46 nm tip displacement at 8.42 MHz resonant frequency on a radius of 60 μm disk resonator in air. A single electrode resonator that can excite both tangential and wine-glass modes with such metrics lays the foundation for a BAW MEMS gyroscope with a built-in primary calibration stage.

A Threshold Helium Leakage Detection Switch with Ultra Low Power Operation.

Detecting helium leakage is important in many applications, such as in dry cask nuclear waste storage systems. This work develops a helium detection system based on the relative permittivity (dielectric constant) difference between air and helium. This difference changes the status of an electrostatic microelectromechanical system (MEMS) switch. The switch is a capacitive-based device and requires a very negligible amount of power. Exciting the switch's electrical resonance enhances the MEMS switch sensitivity to detect low helium concentration. This work simulates two different MEMS switch configurations: a cantilever-based MEMS modeled as a single-degree-freedom model and a clamped-clamped beam MEMS molded using the COMSOL Multiphysics finite-element software. While both configurations demonstrate the switch's simple operation concept, the clamped-clamped beam was selected for detailed parametric characterization due to its comprehensive modeling approach. The beam detects at least 5% helium concentration levels when excited at 3.8 MHz, near electrical resonance. The switch performance decreases at lower excitation frequencies or increases the circuit resistance. The MEMS sensor detection level was relatively immune to beam thickness and parasitic capacitance changes. However, higher parasitic capacitance increases the switch's susceptibility to errors, fluctuations, and uncertainties.

High-flexibility and high-accuracy phase delay calibration method for MEMS-based fringe projection systems.

Microelectromechanical system (MEMS) mirror based laser beam scanning (LBS) projectors for fringe projection profilometry (FPP) are becoming increasingly popular attributing to their small size and low cost. However, the initial phase of the scanning MEMS mirror employed in an LBS projector may vary over time, resulting in unstable and distorted fringe patterns. The distorted fringe patterns will largely decrease the accuracy of the three-dimensional (3D) topographic reconstruction. In this paper, an efficient phase delay calibration method based on a unique fringe projection sequence and a corresponding image processing algorithm is proposed. The proposed method can compensate the phase uncertainty and variation with no need to add any extra components. One LBS projector has been constructed using a uniaxial electrostatic MEMS mirror that has a mirror size of 2.5 mm × 2.5 mm and a scanning field of view of 60 ∘ at its resonance of 1523 Hz. 3D reconstruction experiments are conducted to study how the 3D reconstruction results are affected by the phase delay. The standard deviation of a sphere reconstruction is improved from 2.05 mm to 0.20 mm after the positive phase delay deviation of 5 μs is compensated using this new calibration method.

Capacitive Sensing for 2-D Electrostatic MEMS Scanner in a Clinical Endomicroscope.

A flexible fiber-coupled confocal laser endomicroscope has been developed using an electrostatic micro-electromechanical system (MEMS) scanner located in at distal optics to collect in vivo images in human subjects. Long transmission lines are required that deliver drive and sense signals with limited bandwidth. Phase shifts have been observed between orthogonal X and Y scanner axes from environmental perturbations, which impede image reconstruction. Image processing algorithms used for correction depend on image content and quality, while scanner calibration in the clinic can be limited by potential patient exposure to lasers. We demonstrate a capacitive sensing method to track the motion of the electrostatically driven two-dimensional MEMS scanner and to extract phase information needed for image reconstruction. This circuit uses an amplitude modulation envelope detection method on shared drive and sensing electrodes of the scanner. Circuit parameters were optimized for performance given high scan frequencies, transmission line effects, and substantial parasitic coupling of drive signal to circuit output. Extraction of phase information further leverages nonlinear dynamics of the MEMS scanner. The sensing circuit was verified by comparing with data from a position sensing detector measurement. The phase estimation showed an accuracy of 2.18° and 0.79° in X and Y axes for motion sensing, respectively. The results indicate that the sensing circuit can be implemented with feedback control for pre-calibration of the scanner in clinical MEMS-based imaging systems.

A SOI Out-of-Plane Electrostatic MEMS Actuator Based on In-Plane Motion

This work describes a novel micromechanical structure capable of producing out-of-plane motion from in-plane forces generated by electrostatic microelectromechanical system (MEMS) actuators. The MEMS actuator is fabricated in a commercial silicon-on-insulator (SOI) MEMS process and is anchored at two distinct locations through a pair of beams with a relatively low stiffness in the vertical direction. A comb-drive, whose fixed and moveable fingers are implemented in the same layer with a uniform thickness, is employed to create an attractive electrostatic force. This in-plane electrostatic force rotates the actuator along an axis defined by the anchors, which results in the vertical motion of a suspended platform. Due to the simple structure of the actuator, it can be readily manufactured with standard bulk micromachining processes. Experimental results demonstrate that the actuator can provide <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.02~\mu \text{m}$ </tex-math></inline-formula> of vertical displacement at a resonant frequency of 395 Hz when it is excited in air by a 10 V AC signal, while the displacement can be considerably increased in vacuum. It is further shown that the functionality of the actuator is not dependent on the type of excitation voltage; therefore, it can produce a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.09~\mu \text{m}$ </tex-math></inline-formula> static out-of-plane motion when excited by a 40 V DC voltage. A comprehensive comparison to the published works in the literature indicates that the proposed actuator is the only SOI electrostatic MEMS actuator with a relatively thick structural layer, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10~\mu \text{m}$ </tex-math></inline-formula> , that can provide out-of-plane motion at low actuation voltage reported to date. [2022-0069]

Adiabatic CMOS-Based Electrostatic MEMS Actuation for Reduced Dynamic Power and Switching Activity

The basic purpose of MEMS actuation is to miniaturize the actuators and sensors for applications in nanoelectronics. The transistor switching current and power supply noises due to voltage drops across the metal lines can impair circuit timing and performance, posing a continuing problem for high-performance chip designers. This work presents an empirical concept of a reconfigurable charge pump based on FPGA for electrostatic actuation of the Microelectromechanical System (MEMS). The goal of the design is to produce enough on-chip voltages for actuating the MEMS that are continuously adaptive and reconfigurable. In this proposed method, pumping capacitors lying in the range of 1-pF have been deployed to decrease the area of design concerned. The various voltages are programmable digitally and created by dynamically altering the number of phases as well as the clock drive levels. The dynamic model is designed by adjusting the number of stages to produce on-chip voltages including clock drive speeds, assuming a purely capacitive load. The proposed model’s power consumption can be lowered in the steady state by lowering its clock frequency and electrostatic MEMS actuators with capacitive load. An average of 0.62 W is dissipated by the circuit when the eight stages are triggered. Consequently, with adiabatic and without adiabatic architecture, 0.0186 mW of minimum power difference is obtained.

MEMS-tunable dielectric metasurface lens using thin-film PZT for large displacements at low voltages.

Tunable focusing is a desired property in a wide range of optical imaging and sensing technologies but has tended to require bulky components that cannot be integrated on-chip and have slow actuation speeds. Recently, integration of metasurfaces into electrostatic micro-electromechanical system (MEMS) architectures has shown potential to overcome these challenges but has offered limited out-of-plane displacement range while requiring large voltages. We demonstrate for the first time, to the best of our knowledge, a movable metasurface lens actuated by integrated thin-film PZT MEMS, which has the advantage of offering large displacements at low voltages. An out-of-plane displacement of a metasurface in the range of 7.2 μm is demonstrated under a voltage application of 23 V. This is roughly twice the displacement at a quarter of the voltage of state of the art electrostatic out-of-plane actuation of metasurfaces. Using this tunability, we demonstrate a varifocal lens doublet with a focal shift of the order of 250 μm at the wavelength 1.55μm. The thin-film PZT MEMS-metasurface is a promising platform for miniaturized varifocal components.

Development of an Electrostatic Comb-Driven MEMS Scanning Mirror for Two-Dimensional Raster Scanning.

Microelectromechanical System (MEMS)-based scanning mirrors are important optical devices that have been employed in many fields as a low-cost and miniaturized solution. In recent years, the rapid development of Light Detection and Ranging (LiDAR) has led to opportunities and challenges for MEMS scanners. In this work, we propose a 2D electrostatically actuated micro raster scanner with relatively large aperture. The 2D scanner combines a resonant scanning axis driven by an in-plane comb and a quasistatic scanning axis driven by a vertical comb, which is achieved by raising the moving comb finger above the fixed comb finger through the residual stress gradient. The analytic formula for the resonant axis frequency, based on the mechanical coupling of two oscillation modes, is derived and compared with finite element simulation. A prototype is designed, fabricated, and tested, and an overall optical Field-of-View (FoV) of about 60° × 4° is achieved. Finally, some possibilities for further improvement or optimization are discussed.

Electrostatic Circular Membrane MEMS: An Approach to the Optimal Control

The recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) is an important issue, because, when an external electrical voltage is applied, the membrane deforms with the risk of touching the upper plate of the device producing an unwanted electrostatic effect. Therefore, it is important to know whether the movement admits stable equilibrium configurations especially when the membrane is closed to the upper plate. In this framework, this work analyzes the behavior of a two-dimensional (2D) electrostatic circular membrane MEMS device subjected to an external voltage. Specifically, starting from a well-known 2D non-linear second-order differential model in which the electrostatic field in the device is proportional to the mean curvature of the membrane, the stability of the only possible equilibrium configuration is studied. Furthermore, when considering that the membrane is equipped with mechanical inertia and that it must not touch the upper plate of the device, a useful range of possible values has been obtained for the applied voltage. Finally, the paper concludes with some computations regarding the variation of potential energy, identifying some optimal control conditions.

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 Dual-Mass Resonant MEMS Gyroscope Design with Electrostatic Tuning for Frequency Mismatch Compensation

The micro-electro-mechanical systems (MEMS)-based sensor technologies are considered to be the enabling factor for the future development of smart sensing applications, mainly due to their small size, low power consumption and relatively low cost. This paper presents a new structurally and thermally stable design of a resonant mode-matched electrostatic z-axis MEMS gyroscope considering the foundry constraints of relatively low cost and commercially available silicon-on-insulator multi-user MEMS processes (SOIMUMPs) microfabrication process. The novelty of the proposed MEMS gyroscope design lies in the implementation of two separate masses for the drive and sense axis using a unique mechanical spring configuration that allows minimizing the cross-axis coupling between the drive and sense modes. For frequency mismatch compensation between the drive and sense modes due to foundry process uncertainties and gyroscope operating temperature variations, a comb-drive-based electrostatic tuning is implemented in the proposed design. The performance of the MEMS gyroscope design is verified through a detailed coupled-field electric-structural-thermal finite element method (FEM)-based analysis.

MEMS-actuated metasurface Alvarez lens

Miniature lenses with a tunable focus are essential components for many modern applications involving compact optical systems. While several tunable lenses have been reported with various tuning mechanisms, they often face challenges with respect to power consumption, tuning speed, fabrication cost, or production scalability. In this work, we have adapted the mechanism of an Alvarez lens – a varifocal composite lens in which lateral shifts of two optical elements with cubic phase surfaces give rise to a change in the optical power – to construct a miniature, microelectromechanical system (MEMS)-actuated metasurface Alvarez lens. Implementation based on an electrostatic MEMS generates fast and controllable actuation with low power consumption. The utilization of metasurfaces – ultrathin and subwavelength-patterned diffractive optics – as optical elements greatly reduces the device volume compared to systems using conventional freeform lenses. The entire MEMS Alvarez metalens is fully compatible with modern semiconductor fabrication technologies, granting it the potential to be mass-produced at a low unit cost. In the reported prototype operating at 1550 nm wavelength, a total uniaxial displacement of 6.3 µm was achieved in the Alvarez metalens with a direct-current (DC) voltage application up to 20 V, which modulated the focal position within a total tuning range of 68 µm, producing more than an order of magnitude change in the focal length and a 1460-diopter change in the optical power. The MEMS Alvarez metalens has a robust design that can potentially generate a much larger tuning range without substantially increasing the device volume or energy consumption, making it desirable for a wide range of imaging and display applications.

Analysis of Electrostatic MEMS Using Energy-Charge Landscape

A common way to analyze electrostatic microelectromechanical systems (MEMS) actuators is to use their energy-displacement landscape. Here, we describe an alternative approach to analyze electrostatic MEMS actuators using their energy-charge landscape. This technique involves coordinate transformation from displacement to charge, thereby formulating the Hamiltonian of electrostatic MEMS actuators in terms of charge. We investigate the use of the energy-charge landscape to analyze static pull-in, dynamic pull-in, and pull-out phenomena. The voltage expressions derived using this method are identical with those derived using the conventional energy-displacement landscape. In addition, we also obtain the expressions for charge under static and dynamic pull-in conditions. This work can aid in the design and analysis of electrostatic MEMS devices. As a case study, the analysis of a feedback capacitor-MEMS actuator system is presented to illustrate the application of the energy-charge landscape.

A Study of Noise Impact on the Stability of Electrostatic MEMS

Abstract Noise-induced motions are a significant source of uncertainty in the response of micro-electromechanical systems (MEMS). This is particularly the case for electrostatic MEMS where electrical and mechanical sources contribute to noise and can result in sudden and drastic loss of stability. This paper investigates the effects of noise processes on the stability of electrostatic MEMS via a lumped-mass model that accounts for uncertainty in mass, mechanical restoring force, bias voltage, and AC voltage amplitude. We evaluated the stationary probability density function (PDF) of the resonator response and its basins of attraction in the presence noise and compared them to that those obtained under deterministic excitations only. We found that the presence of noise was most significant in the vicinity of resonance. Even low noise intensity levels caused stochastic jumps between co-existing orbits away from bifurcation points. Moderate noise intensity levels were found to destroy the basins of attraction of the larger orbits. Higher noise intensity levels were found to destroy the basins of attraction of smaller orbits, dominate the dynamic response, and occasionally lead to pull-in. The probabilities of pull-in of the resonator under different noise intensity level are calculated, which are sensitive to the initial conditions.

Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope

This paper presents microfabrication process-driven design of a multi-degree of freedom (multi-DoF) non-resonant electrostatic microelectromechanical systems (MEMS) gyroscope by considering the design constraints of commercially available low-cost and widely-used silicon-on-insulator multi-user MEMS processes (SOIMUMPs), with silicon as a structural material. The proposed design consists of a 3-DoF drive mode oscillator with the concept of addition of a collider mass which transmits energy from the drive mass to the passive sense mass. In the sense direction, 2-DoF sense mode oscillator is used to achieve dynamically-amplified displacement in the sense mass. A detailed analytical model for the dynamic response of MEMS gyroscope is presented and performance characteristics are validated through finite element method (FEM)-based simulations. The effect of operating air pressure and temperature variations on the air damping and resulting dynamic response is analyzed. The thermal stability of the design and corresponding effect on the mechanical and capacitive sensitivity, for an operating temperature range of −40 °C to 100 °C, is presented. The results showed that the proposed design is thermally stable, robust to environmental variations, and process tolerances with a wide operational bandwidth and high sensitivity. Moreover, a system-level model of the proposed gyroscope and its integration with the sensor electronics is presented to estimate the voltage sensitivity under the constraints of the readout electronic circuit.