MEMS Model Research Articles

Global bifurcation curves of a regularized MEMS model

The two-parameter differential equation u′′(x)+λ(1−u)2−λε2(1−u)4=0 with the boundary condition u(−1)=u(1)=0 governs the steady-state solutions from a regularized MEMS model. We prove that there exist two constants εˆ(≈0.25458) and εˇ(≈0.29212) such that the bifurcation curve is S-shaped for 0<ε⩽εˆ and is strictly increasing for ε⩾εˇ in the λ,‖u‖∞-plane. This partly confirms the numerical simulations in Lindsay et al. (2014), and also improves a recent result in Iuorio et al. (2019), where the S-shaped curve is proved for sufficiently small ε.

Reinforced Limit of a MEMS Model with Heterogeneous Dielectric Properties

A MEMS model with an insulating layer is considered and its reinforced limit is derived by means of a Gamma convergence approach when the thickness of the layer tends to zero. The limiting model inherits the dielectric properties of the insulating layer.

Variational solutions to an evolution model for MEMS with heterogeneous dielectric properties

<p style="text-indent:20px;">The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with heterogeneous dielectric properties.

Modeling and Simulation of MEMS based Pressure Sensor for Industrial Applications

This paper presents an overview of design, modeling and simulation of MEMS pressure sensor is using COMSOL Multiphysics V4.3b. An attempt has been made to achieve high sensitivity by providing different structures for membrane (Circular, square, rectangle &amp; triangle) with uniform surface area and thickness. Further, simulations have been carried out with various loads ranging from 0.1 to 1MPa assigning three materials viz., InP, GaAs and Silicon. From the analyses of simulation results, it has been observed that the pressure sensor with circular membrane provided InP material found to exhibit more deformation and high sensitivity of 17.3×10-12 for 10 μm thickness and 50.8×10-12 for 7 μm thickness. The reasons for enhancement in the sensitivity are discussed in detail as function of input load, dimensional changes of diaphragm and materials addition. These studies are highly useful to check and compute pressure in various industrial and environmental conditions.

Profile of a touch-down solution to a nonlocal MEMS model

In this paper, we are interested in the mathematical model of MEMS devices which is presented by the following equation on [Formula: see text] : [Formula: see text] where [Formula: see text] is a bounded domain in [Formula: see text] and [Formula: see text]. In this work, we have succeeded to construct a solution which quenches in finite time [Formula: see text] only at one interior point [Formula: see text]. In particular, we give a description of the quenching behavior according to the following final profile [Formula: see text] The construction relies on some connections between the quenching phenomenon and the blowup phenomenon. More precisely, we change our problem to the construction of a blowup solution for a related PDE and describe its behavior. The method is inspired by the work of Merle and Zaag [Reconnection of vortex with the boundary and finite time quenching, Nonlinearity 10 (1997) 1497–1550] with a suitable modification. In addition to that, the proof relies on two main steps: A reduction to a finite-dimensional problem and a topological argument based on index theory. The main difficulty and novelty of this work is that we handle the nonlocal integral term in the above equation. The interpretation of the finite-dimensional parameters in terms of the blowup point and the blowup time allows to derive the stability of the constructed solution with respect to initial data.

Unifying soil organic matter formation and persistence frameworks: the MEMS model

Abstract. Soil organic matter (SOM) dynamics in ecosystem-scale biogeochemical models have traditionally been simulated as immeasurable fluxes between conceptually defined pools. This greatly limits how empirical data can be used to improve model performance and reduce the uncertainty associated with their predictions of carbon (C) cycling. Recent advances in our understanding of the biogeochemical processes that govern SOM formation and persistence demand a new mathematical model with a structure built around key mechanisms and biogeochemically relevant pools. Here, we present one approach that aims to address this need. Our new model (MEMS v1.0) is developed from the Microbial Efficiency-Matrix Stabilization framework, which emphasizes the importance of linking the chemistry of organic matter inputs with efficiency of microbial processing and ultimately with the soil mineral matrix, when studying SOM formation and stabilization. Building on this framework, MEMS v1.0 is also capable of simulating the concept of C saturation and represents decomposition processes and mechanisms of physico-chemical stabilization to define SOM formation into four primary fractions. After describing the model in detail, we optimize four key parameters identified through a variance-based sensitivity analysis. Optimization employed soil fractionation data from 154 sites with diverse environmental conditions, directly equating mineral-associated organic matter and particulate organic matter fractions with corresponding model pools. Finally, model performance was evaluated using total topsoil (0–20 cm) C data from 8192 forest and grassland sites across Europe. Despite the relative simplicity of the model, it was able to accurately capture general trends in soil C stocks across extensive gradients of temperature, precipitation, annual C inputs and soil texture. The novel approach that MEMS v1.0 takes to simulate SOM dynamics has the potential to improve our forecasts of how soils respond to management and environmental perturbation. Ensuring these forecasts are accurate is key to effectively informing policy that can address the sustainability of ecosystem services and help mitigate climate change.

Modeling and experimental characterization of an active MEMS based force sensor

Active force sensors are based on the principle of force balancing using a feedback control. They allow, unlike passive sensors, the static characterization of forces without interference of the sensor mechanical properties on the estimated stiffness of the object to be studied. This capability is fundamental when dealing with the mechanical characterization of samples having a wide range of stiffness. This paper deals with the modeling and the experimental characterization of a new active MEMS based force sensor. This sensor includes folded-flexure type suspensions and a differential comb drive actuation allowing a linear force/voltage relationship. A control oriented electromechanical model is proposed and validated experimentally in static and dynamic operating modes using a stroboscopic measurement system. This work is a first step towards new MEMS active force sensor with high resonant frequency (>2kHz) and high linear measurement force range (50 μN). The advantage of this structure is to be able to change the sensor operating point without changing the sensor dynamics. Thus simplifying the control law. Modifying the operating point allows performing an accurate self positioning of the probe in close proximity to the surface to be studied.

Optimum Electromagnetic Modelling of RF MEMS Switches

Radio frequency microelectromechanical systems (RF MEMS) switch technology may have the potential to replace semiconductor technology in future communication systems as well as communication satellites, wireless and mobile phones. RF MEMS switches are being developed for low insertion loss, high isolation loss and high linearity that are required over a broad frequency band application. In wireless mobile communication systems, microstrip transmission lines (t-line) have received attention for their attractive benefits such as low profile, light weight, and easy fabrication. The present work has thus been to explore the design and modelling of low loss RF MEMS switches implemented in a microstrip discontinuity t-line configuration. The electromagnetic modelling of an RF MEMS switch with a microstrip line is presented with a simple analytical model to determine the scattering parameters. This study shows that an RF MEMS switch with a microstrip t-line provided less than 0.01 dB–0.05 dB insertion loss for 50 GHz frequency. Moreover, there is an isolation loss of 50 dB over frequencies up to 50 GHz frequency. This low insertion and high isolation loss in the single beam RF MEMS switch with a microstrip discontinuity t-line contributes to configuring a low loss transmission line for RF communication.DOI: http://dx.doi.org/10.5755/j01.eie.24.5.21842

Analysis of dynamic pull-in voltage of a graphene MEMS model

Bifurcation analysis of dynamic pull-in for a lumped mass model is presented. The restoring force of the spring is derived based on the nonlinear constitutive stress–strain law and the driving force of the mass attached to the spring is based on the electrostatic Coulomb force, respectively. The analysis is performed on the resulting nonlinear spring–mass equation with initial conditions. The necessary and sufficient conditions for the existence of periodic solutions are derived analytically and illustrated numerically. The conditions for bifurcation points on the parameters associated with the second-order elastic stiffness constant and the voltage are determined.

Analysis of spring softening effect on the collapse voltage of capacitive MEMS ultrasonic transducers

This paper explained the dependency of collapse voltage on semiconductor device structural features (membrane diameter, membrane thickness and the vertical distance between the electrodes) and physical characteristics (mechanical residual stress of the silicon nitride membrane) considering the electro-mechanical model of MEMS based Capacitive micromachined ultrasonic transducer (CMUT). To have sensitivity comparable to that of piezoelectric ultrasonic transducers (UTs), CMUTs need to be biased close to the collapse voltage. Maximum efficiency is achieved in the conventional mode of operation by biasing the device close to the collapse voltage. The total acoustic output pressure is determined by the efficiency of the device. Hence a careful investigation of the same is decidedly required. Finite element method (FEM) model by PZFlex and analytical model of single element CMUT with 0.75 µm thick silicon nitride membranes suspended on 0.5 µm thick cavity were developed showing resonance frequency at 5 MHz. Through these analyses, it is observed that membrane and vacuum gap thickness are both directly proportional to collapse voltage, while radius of the membrane and also its area are inversely proportional to collapse voltage. Initially the spring softening effect of the membrane has been neglected. Later the effect has been included in the proposed model and analyzed. It has been shown that the spring softening effect cannot be neglected for accurate CMUT modeling. A capacitive micromachined ultrasound transducer can be realized with the model described in this paper.

A Case Study on the Numerical Solution and Reduced Order Model of MEMS

In this paper, we develop a numerical method with a reduced order technique based on the Galerkin procedure to solve nonlinear partial differential equations of MEMS devices. We apply an explicit numerical approach based on the finite difference method (FDM) to a reduced order model of the equation of micro-beams and call it explicit-ROM. As a case study, we obtain the time response of a micro-beam under an electrostatic actuation and a mechanical shock with our method and the reduced order method (ROM) developed in previous papers. We show ROM requires taking the effect of higher order modes into consideration in order to result in accurate response, while explicit-ROM greatly improves both accuracy and speed with only the first mode, hence it is a straightforward approach that can be used in a MEMS software to obtain very fast and accurate results.

Quenching phenomenon for a parabolic MEMS equation

This paper deals with the electrostatic MEMS-device parabolic equation $${u_t} - \Delta u = \frac{{\lambda f(x)}}{{{{(1 - u)}^p}}}$$ in a bounded domain Ω of ℝ N , with Dirichlet boundary condition, an initial condition u0(x) ∈ [0, 1) and a nonnegative profile f, where λ > 0, p > 1. The study is motivated by a simplified micro-electromechanical system (MEMS for short) device model. In this paper, the author first gives an asymptotic behavior of the quenching time T* for the solution u to the parabolic problem with zero initial data. Secondly, the author investigates when the solution u will quench, with general λ, u0(x). Finally, a global existence in the MEMS modeling is shown.

静電ピストンアレイ駆動型MEMS可変形状ミラーの数理解析モデル構築

静電ピストンアレイ駆動型MEMS可変形状ミラーの数理解析モデル構築

On the application of Sturm's theorem to analysis of dynamic pull-in for a graphene-based MEMS model

A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

• A hybrid solution for nonlinear dynamics of microcantilevers has been introduced. • The pure odd-order nonlinear model combined with a distributed parameter system. • A comprehensive model for MEMS before, during and after switching was presented. • Two distinct model for before pull-in and after pull-in regimes are combined. This paper introduces a closed-form approximation of dynamic response of microcantilevers. The applied load on the system was linearized by Taylor series expansion and to obtain approximate solutions, model of a pure odd-order nonlinear oscillator, subjected to constant excitation was assumed. Pull-in voltage was investigated to analyze the different parameters of the examined microbeam. In order to obtain a comprehensive dynamic model for MEMS devices, before, during and after switching, the pure odd-order nonlinear model was combined with a distributed parameter system and solved after reaching the pull-in voltage. The obtained results demonstrate correct prediction of the static pull-in voltage and also the dynamic deflection of microbeams. By using the same approach, the sensitivity of the pull-in voltage to various geometrical parameters was also investigated. The obtained results indicate that excessive increase in the air gap causes substantial increase in the pull-in voltage; while increasing thickness of microcantilever has even greater effect. It was also observed that for a given thickness of microcantilever, increasing its length beyond a certain amount has no effect on the pull-in voltage.

SSCS Saintgits Student Chapter Holds Workshop on Modeling and Simulation of MEMS Using Intellisuite Software [Chapters

SSCS Saintgits Student Chapter Holds Workshop on Modeling and Simulation of MEMS Using Intellisuite Software [Chapters

Highly Sensitive MEMS Based Capacitive Pressure Sensor Design Using COMSOL Multiphysics &amp; Its Application in Lubricating System

Capacitive pressure sensors are making themselves the leader among its market competitors since they consume less power with less temperature sensitivity. This paper includes the design and development possibilities to increase the sensor sensitivity by optimizing the device dimension and including different types of materials. The figure of merits (FOMs) such as displacement, capacitance, electric potential with variation in temperature and pressure are thoroughly analyzed. This paper includes the unique developments, possible challenges with respect to design, modelling, simulation and analysis of MEMS based capacitive pressure sensors. As the range of application level of different sensors is increasing, it is indispensable to review the technological advancement and future possibilities of MEMS capacitive pressure sensors. This paper also focuses on the available reviews of various types of capacitive pressure sensor principles, geometrical design; physics based modelling, parameters analysis to consider, materials that can be used in fabrication process. The 3-D simulation is performed using COMSOL Multiphysics 5.0. During device development all the standards are followed according to the simulation standard set by COMSOL.

Vanishing aspect ratio limit for a fourth-order MEMS model

So far most studies on mathematical models for microelectromechanical systems are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the aspect ratio equal to zero in a more complex model involving a moving boundary. A rigorous justification of this derivation is provided here when bending is taken into account.

Modelling and Design Analysis for Nonlinear 3D Dynamic Simulation of Triangular Microspring for MEMS based SAM

This paper reports the design and modelling of triangular shaped microspring which is proposed to be used for munition purpose. The simulation results are obtained for Safe and Arm mechanism for different 'g' for MEMS based Rocket SAM. Design for MEMS based technology for Rocket SAM chip is structured in such a way that it has both movable and non-movable parts which utilizes mechanical properties, structural properties and material properties that may be and may not be electronically controlled. The design proposed for Rocket SAM in this research is aimed to achieve reliability, safety and cost effectiveness for mass-production. Our motive is to design, simulate and derive its results using metal alloy MEMS based Rocket SAM using SOLIDWORKS Multiphysics software is used which propounds a prodigious environs to solve this problem. Thus, this research presents the design analysis, modelling and nonlinear 3D dynamic simulation of MEMS based metal alloy for Rocket SAM using SOLIDWORKS Multiphysics GUI tool.

Analytical Study of Highly Sensitive Mems Based Bragg Grating Pressure Sensor

A model of MEMS based Bragg Grating Pressure Sensor is analytically proposed in this paper. In MEMS pressure sensor, the shift of wavelength of only one Bragg grating incorporated into a waveguide gives an erroneous outcome because of the cross sensitivity rendered by different parameters including temperature. In this design, the sensor consisting of dual identical Waveguide Bragg Gratings (WBGs) integrated in a curved waveguide in silicon micro-machined circular diaphragm is presented. The pitch of the Bragg gratings changes upon the application of pressure on the diaphragm, and hence, the corresponding wavelength is shifted. As the wavelength shifts because of the temperature, in the two identical waveguide gratings in equal amount, the error occurs due to the change of temperature can be eliminated. So, the Pressure Sensitivity (PS) can be measured correctly. A parametric analysis of this proposed sensor is performed utilizing MATLAB 2015a programming. Pressure sensitivities are found to be 2.0 and 1.8 picometre per Pascal for the two Bragg gratings.