scholarly journals A Semi-Linear Elliptic Model for a Circular Membrane MEMS Device Considering the Effect of the Fringing Field

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5237
Author(s):  
Mario Versaci ◽  
Alessandra Jannelli ◽  
Francesco Carlo Morabito ◽  
Giovanni Angiulli
Keyword(s):  
Membrane Curvature ◽  
Circular Membrane ◽  
Electromechanical Properties ◽  
Differential Model ◽  
Convergence Conditions ◽  
Box Scheme ◽  
Fringing Field ◽  
Elliptic Model ◽  
Uniqueness Of The Solution ◽  
Mems Device

In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller–Box scheme, and the III/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.

scholarly journals A 2D Membrane MEMS Device Model with Fringing Field: Curvature-Dependent Electrostatic Field and Optimal Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 465
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Optimal Control ◽  
Electrostatic Field ◽  
Circular Membrane ◽  
Differential Model ◽  
Field Curvature ◽  
Fringing Field ◽  
Uniqueness Of The Solution ◽  
Stable Equilibrium Position ◽  
The One ◽  
Fringing Field Effect

An important problem in membrane micro-electric-mechanical-system (MEMS) modeling is the fringing-field phenomenon, of which the main effect consists of force-line deformation of electrostatic field E near the edges of the plates, producing the anomalous deformation of the membrane when external voltage V is applied. In the framework of a 2D circular membrane MEMS, representing the fringing-field effect depending on |∇u|2 with the u profile of the membrane, and since strong E produces strong deformation of the membrane, we consider |E| proportional to the mean curvature of the membrane, obtaining a new nonlinear second-order differential model without explicit singularities. In this paper, the main purpose was the analytical study of this model, obtaining an algebraic condition ensuring the existence of at least one solution for it that depends on both the electromechanical properties of the material constituting the membrane and the positive parameter δ that weighs the terms |∇u|2. However, even if the the study of the model did not ensure the uniqueness of the solution, it made it possible to achieve the goal of finding a stable equilibrium position. Moreover, a range of admissible values of V were obtained in order, on the one hand, to win the mechanical inertia of the membrane and, on the other hand, to ensure that the membrane did not touch the upper disk of the device. Lastly, some optimal control conditions based on the variation of potential energy are presented and discussed.

scholarly journals Recovering of the Membrane Profile of an Electrostatic Circular MEMS by a Three-Stage Lobatto Procedure: A Convergence Analysis in the Absence of Ghost Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 487 ◽  
Author(s):  
Mario Versaci ◽  
Giovanni Angiulli ◽  
Alessandra Jannelli
Keyword(s):  
Convergence Analysis ◽  
Electrostatic Field ◽  
Mean Curvature ◽  
Mechanical Systems ◽  
Numerical Approach ◽  
Second Order ◽  
Circular Membrane ◽  
Differential Model ◽  
The Mean

In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic field is considered proportional to the mean curvature of the membrane, a collocation procedure, based on the three-stage Lobatto formula, is derived. The convergence is studied, thus obtaining the parameters operative ranges determining the areas of applicability of the device under analysis.

scholarly journals A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1193 ◽  
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Steady State ◽  
Mean Curvature ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Circular Membrane ◽  
Mems Devices ◽  
Differential Model ◽  
Non Linear ◽  
The Mean ◽  
State Case

In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.

scholarly journals On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1200
Author(s):  
Sanda Micula
Keyword(s):  
Numerical Methods ◽  
Integral Equations ◽  
Trapezoidal Rule ◽  
Picard Iteration ◽  
Fredholm Integral Equations ◽  
Convergence Conditions ◽  
One Dimensional ◽  
Cubature Formulas ◽  
Uniqueness Of The Solution ◽  
Iterative Numerical Methods

In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed.

scholarly journals Electrostatic Circular Membrane MEMS: An Approach to the Optimal Control

Computation ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 41
Author(s):  
Mario Versaci ◽  
Francesco Carlo Morabito
Keyword(s):  
Optimal Control ◽  
Stable Equilibrium ◽  
Equilibrium Configuration ◽  
Micro Electro Mechanical System ◽  
Circular Membrane ◽  
Differential Model ◽  
Equilibrium Configurations ◽  
Electrostatic Effect ◽  
The Mean ◽  
The Stability

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.

Micromachined LCP Connectors for Packaging MEMS Devices in Biological Environments

2007 ◽  
Vol 4 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Robert Dean ◽  
Jenny Weller ◽  
Mike Bozack ◽  
Brian Farrell ◽  
Linas Jauniskis ◽  
...  
Keyword(s):  
Mems Devices ◽  
Electromechanical Properties ◽  
Optical Signals ◽  
Mems Packaging ◽  
Fine Pitch ◽  
Chemical Inertness ◽  
Mems Technology ◽  
Mems Device ◽  
Electrical Connections ◽  
Implanted Device

Micro- and nano-MEMS technology is being increasingly exploited in biological applications, such as large electrode-count neural prosthesis probe arrays. However, a bottleneck in fully utilizing this technology has been the interconnect between the implanted MEMS device and the external system connected to the implanted device. Since the implanted MEMS device is capable of having a large number of elements, the interconnect must have a sufficient number of electrical connections to communicate with each and every element. Complicating this is the fact that the interconnect requirements may include electrical signals, microfluidics transport and optical signals, all packaged in a miniature biocompatible interconnect cable. Micromachined liquid crystal polymer (LCP) is a promising technology for this application, due to LCP's biocompatibility, chemical inertness, electromechanical properties and its ability to be micromachined. This paper presents the results from the development of MEMS packaging technology suitable for use in biological environments, and is demonstrated in the realization of a prototype micromachined LCP biomedical interconnect device. In particular, the development of the interconnect device demonstrates the realization of biocompatible connectors with high-density ultra-fine pitch electrical traces.

Characterization of RF Sputtered ZnO Piezoelectric Films Using Transmission Electron Microscope

1975 ◽  
Vol 33 ◽  
pp. 86-87
Author(s):  
Kemining W. Yeh ◽  
Richard S. Muller ◽  
Wei-Kuo Wu ◽  
Jack Washburn
Keyword(s):  
Integrated Circuit ◽  
Acoustic Waves ◽  
New Technology ◽  
Surface Acoustic Waves ◽  
Electromechanical Properties ◽  
Leading Role ◽  
Saw Devices ◽  
Transmission Electron ◽  
High Degree

Considerable and continuing interest has been shown in the thin film transducer fabrication for surface acoustic waves (SAW) in the past few years. Due to the high degree of miniaturization, compatibility with silicon integrated circuit technology, simplicity and ease of design, this new technology has played an important role in the design of new devices for communications and signal processing. Among the commonly used piezoelectric thin films, ZnO generally yields superior electromechanical properties and is expected to play a leading role in the development of SAW devices.

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