Fringing Field Effect Research Articles

A Novel Closed-Form Expression Obtained by Using Differential Evolution Algorithm to Calculate Pull-In Voltage of MEMS Cantilever

In this paper, a novel, computationally efficient, and simple closed-form expression has been derived to accurately calculate the pull-in voltage value of microelectromechanical system (MEMS) cantilever. At first, MEMSs actuators with various physical parameters have been simulated by a software that employs the finite element method, and then, the pull-in voltage expression has been derived by using the differential evolution optimization algorithm together with the simulation data. Since the formula is derived from the simulation data, it implicitly contains the fringing field effect. In order to verify the accuracy and robustness, the predictions of closed-form formula proposed in this paper have been compared with those of the theoretical ones through the simulation and experimental studies previously presented in the literature. The key advantage of the presented model is delivering a satisfying estimation of the pull-in voltage in a simple fashion.

An improved analytical model for static pull-in voltage of a flexured MEMS switch

This paper presents the design of low-k meander based MEMS shunt capacitive switch with beam perforations. A closed form model to accurately calculate the pull-in voltage of the designed switch for two cases have been presented viz. a non-uniform meander based MEMS shunt switch and an uniform serpentine meander based MEMS shunt switch with perforated structure. The modified Mejis and Fokkema’s capacitance model have been used to propose a generalized closed form expression for the pull-in voltage which takes care of the nonlinear electrostatic force on the switch as well. The proposed model also takes into account the fringing field effect due to beam thickness and etched holes on the beam. The model is validated by calculating the pull-in voltage for both the meander designs under variation of various design parameters. The results obtained under most design specification variation has been found out to be in the range of 1.5–2.3 V for uniform meander based MEMS shunt switch and 3.2–5.2 V for the non-uniform counterpart. The model based results have been further verified by comparison with simulated results of full 3D FEM solver CoventorWare in a wide range of structural parameter variations. It has been observed that the performance of the proposed model is reasonably satisfactory with an average deviation of 4.73% for uniform serpentine flexure and 3.65% for non-uniform flexure based switch.

Effects of the source gap on transmission efficiency of a quadrupole mass spectrometer.

RationaleRecent trends towards miniature and portable quadrupole mass spectrometry (QMS) entail challenges in instrumental sensitivity, which is influenced by 3D fringe field effects on ion transmission in the Quadrupole Mass Filter (QMF). The relationship of these effects with the gap from the ion source to the QMF entrance (source gap) is significant and little explored. We examine transmission characteristics experimentally and use the results to test the predictive accuracy of a recently developed 3D QMF simulation model. The model is then applied to directly investigate optimal transmission m/z ranges across multiple source gaps.MethodsA portable single filter quadrupole mass spectrometer is used to analyse transmission characteristics across a range of common gases. We use an experimental approach originally proposed by Ehlert, enhanced with a novel method for absolute calibration of the transmission curve. Custom QMF simulation software employs the boundary element method (BEM) to compute accurate 3D electric fields. This is used to study the effects of the source gap on transmission efficiency.ResultsExperimental findings confirm a centrally peaked transmission curve; simulations correctly predict the optimal transmission location (in m/z) and percentage, and extend the experimental trend. We compare several methods for determining fringe field length, demonstrating how the size of the physical source gap influences both the length and the intensity of the fringe field at the QMF entrance. A complex relationship with ion transmission is revealed in which different source gaps promote optimal transmission at differing m/z ranges.ConclusionsThe presented results map the relationship between the source gap and transmission efficiency for the given instrument, using a simulation method transferrable to other setups. This is of importance to miniature and portable quadrupole mass spectrometers design for specific applications, for the first time enabling the source gap to be tailored for optimal transmission in the desired mass range.

Static Pull-in Analysis of Electrostatically Actuated Functionally Graded Micro-Beams Based on the Modified Strain Gradient Theory

In this paper, the static pull-in behavior of electrostatically actuated functionally graded (FG) micro-beams resting on an elastic medium is studied using the modified strain gradient (MSG) theory. To this end, the equilibrium equation along with classical and non-classical boundary conditions is obtained by considering the fringing field and elastic foundations effects within the principle of minimum total potential energy. Also, the elastic medium is composed of a shear layer (Pasternak foundation) and a linear normal layer (Winkler foundation). The governing differential equation is solved for cantilever and doubly fixed FG beams using an iterative numerical method. This method is a combination of the reduced-order technique, the fourth-order Runge–Kutta and shooting methods. The pull-in voltages of silicon beams obtained from the present model are compared with the experimental and theoretical results reported in the literature. It is seen that the MSG theory is able to reduce significantly the difference between pull-in voltages predicted by theoretical approaches based on the classical continuum theory and the experimental observations. Finally, a parametric study is carried out to analyze in detail the influences of power index, length scale parameters, coefficients of elastic foundations and boundary conditions on the pull-in behavior of FG micro-beams. Findings indicate that the size effect on the pull-in instability of FG micro-beams with both boundary conditions is significant; however, it is seen that the variation with the normalized length scale parameter of static pull-in voltages for doubly fixed beams is larger than cantilever beams. Also, it is shown that the increase of ceramic volume fraction can improve the pull-in resistance of beams. However, this influence becomes smaller with rise of power index for both cases.

A corrected model for static and dynamic electromechanical instability of narrow nanotweezers: Incorporation of size effect, surface layer and finite dimensions

Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin–Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

Fringing field effects in negative capacitance field-effect transistors with a ferroelectric gate insulator

We study the effects of fringing electric fields on the behavior of negative-capacitance (NC) field-effect transistors (FETs) with a silicon-on-insulator body and a gate stack consisting of an oxide film, an internal metal film, a ferroelectric film, and a gate electrode using our own device simulator that can properly handle the complicated relationship between the polarization and the electric field in ferroelectric materials. The behaviors of such NC FETs and the corresponding metal–oxide–semiconductor (MOS) FETs are simulated and compared with each other to evaluate the effects of the NC of the ferroelectric film. Then, the fringing field effects are evaluated by comparing the NC effects in NC FETs with and without gate spacers. The fringing field between the gate stack, especially the internal metal film, and the source/drain region induces more charges at the interface of the film with the ferroelectric film. Accordingly, the function of the NC to modulate the gate voltage and the resulting function to improve the subthreshold swing are enhanced. We also investigate the relationships of these fringing field effects to the drain voltage and four design parameters of NC FETs, i.e., gate length, gate spacer permittivity, internal metal film thickness, and oxide film thickness.

Enhancement of the Multipactor Threshold Inside Nonrectangular Iris

Multipactor breakdown is studied inside the capacitive iris of a rectangular waveguide with a skewed slot along its longitudinal cross section. Both the iris length and height are assumed to be small compared to the electromagnetic wavelength. Therefore, the quasi-static approximation is applied so as to describe the RF field distribution inside the iris gap, whereas a 2-D model is used to analyze the electron motion. The peculiarities of RF field structure are studied using the conformal mapping approach, which shows that the electric field lines can be approximated by circular arcs when the iris length is much larger than its height. The electron motion inside the iris gap is analyzed using different analytical approaches as well as numerical simulations. The simplest analytical consideration is based on the general theory of multipactor between curved surfaces. Within the more sophisticated model, the fringing field effect on electron motion inside the iris is calculated assuming circular structure of electric field lines. It is demonstrated within all approaches that the electron losses within the iris gap increase considerably with the skew angle, deviating from the rectangular iris shape. As a result, the multipactor becomes impossible at a relatively small value of this angle.

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

This paper investigates efficient actuation methods of shunt MEMS switches and other parallel-plate actuators. We start by formulating a multi-physics model of the micro switch, coupling the nonlinear Euler–Bernoulli beam theory with the nonlinear Reynolds equation to describe the structural and fluidic domains, respectively. The model takes into account fringing field effects as well as mid-plane stretching and squeeze film damping nonlinearities. Static analysis is undertaken using the differential quadrature method (DQM) to obtain the pull-in voltage, which is verified by means of the finite element model and validated experimentally. We develop a reduced order model employing the Galerkin method for the structural domain and DQM for the fluidic domain. The proposed waveforms are intended to be more suitable for integrated circuit standards. The dynamic response of the micro switch to harmonic, square and triangular waveforms are evaluated and compared experimentally and analytically. Low voltage actuation is obtained using dynamic pull-in with the proposed waveforms. In addition, global stability analysis carried out for the three signals shows advantages of employing the square signal as the actuation method in enhancing the performance of the micro switch in terms of actuation voltage, switching time, and sensitivity to initial conditions.

Developing a temperature measuring system model for agriculture dryer with consideration of fringing field effect in mathematical modeling

Thermometer accuracy at small rise in temperature leads to increasing the knowledge about products process especially in drying of plants, fruits and biological laboratories. This developed model a thermometer based on capacitance change resulting from deflection of a bimetal cantilever. The effect of fringing field is included in the model. The deflection of the theoretical model is simulated and results are shown to closely follow the previously published results. Finally, the complete theoretical model, including the effect of fringing field, is simulated using an example. The Taguchi method with analysis of S/N ratio is used to obtain the optimal design of the sensor. Using the optimum settings, the S/N ratio improved by 24.11 dB.

Analytical Modelling and Analysis of Spacer Induced Shallow Source/Drain Extension Junction-Less Double Gate (SDE-JLDG) MOSFET Incorporating Fringing Field Effects

Analytical Modelling and Analysis of Spacer Induced Shallow Source/Drain Extension Junction-Less Double Gate (SDE-JLDG) MOSFET Incorporating Fringing Field Effects

Design and performance analysis of soil temperature and humidity sensor

In view of the current soil layer temperature and humidity measurement, there are some problems such as difficult installation and changing soil structure. Therefore the soil temperature and humidity measurement sensor based on high frequency fringe field effect is designed. The measuring principle is based on LC oscillating circuit and soil dielectric constant. Through this method the functional relation between soil humidity and output frequency can be deduced. Numerical analysis technique is used to get the curve of oscillator frequency output with the change of soil humidity. Based on a large number of measured data, the functional relation between output frequency and soil moisture is obtained by data fitting method. Sensors can output data through serial port, GSM and Bluetooth. The soil temperature and humidity sensor is stable through many experiments. It provides an efficient acquisition and measurement method for real-time acquisition of multi-layer soil temperature and humidity.

Grain size and nanoscale effects on the nonlinear pull-in instability and vibrations of electrostatic actuators made of nanocrystalline material

Presented herein is the study of grain size, grain surface energy and small scale effects on the nonlinear pull-in instability and free vibration of electrostatic nanoscale actuators made of nanocrystalline silicon (Nc-Si). A Mori–Tanaka micromechanical model is utilized to calculate the effective material properties of Nc-Si considering material structure inhomogeneity, grain size and grain surface energy. The small-scale effect is also taken into account using Mindlin’s strain gradient theory. Governing equations are derived in the discretized weak form using the variational differential quadrature method based on the third-order shear defamation beam theory in conjunction with the von Kármán hypothesis. The electrostatic actuation is modeled considering the fringing field effects based upon the parallel plate approximation. Moreover, the Casimir force effect is considered. The pseudo arc-length continuation technique is used to obtain the applied voltage-deflection curve of Nc-Si actuators. Then, a time-dependent small disturbance around the deflected configuration is assumed to solve the free vibration problem. By performing a numerical study, the influences of various factors such as length scale parameter, volume fraction of the inclusion phase, density ratio, average inclusion radius and Casimir force on the pull-in instability and free vibration of Nc-Si actuators are investigated.

Pull-in-free design of electrically actuated carbon nanotube-based NEMS actuator assuming non-parallel electrodes arrangement

In this numerical investigation, the nonlinear structural response of an electrostatic carbon nanotube (CNT) based nano-actuator assuming a non-parallel (out-of-plane) plates actuation configuration is examined. The actuating force is initiated by the asymmetry of the resultant electric fringing-fields caused mainly due to the non-parallel electrodes scheme. The nano-actuator is designed based on a carbon nanotube flexible moving electrode and two symmetrically located actuating stationary rectangular-shaped out-of-plane electrodes. First, the electrical problem of the nano-actuator is numerically solved to acquire the resultant actuating force. The force is then mathematically approximated from the outcomes of a 2D numerical solution of the electric problem via a finite-element-based numerical analysis. Then, the structural behavior of the CNT-based nano-actuator under the effect the resultant non-parallel electric fields is investigated numerically via a modal expansion process. The electro-mechanical model was constructed based on an Euler–Bernoulli continuous nonlinear beam model, where both the mid-plane stretching (geometric nonlinearity) and the electric non-parallel fringing-fields effects have been taken into consideration. The reduced-order model (ROM) was derived using the Galerkin decomposition via modal decomposition process. The resultant nonlinear equations are solved numerically to get the static response of the considered CNT-based nano-actuator for various DC voltages. The eigenvalue problem is afterward derived and studied to get the variation of the fundamental as well as higher-order natural frequencies when the system is deflected by a non-zero DC amplitude. A detailed parametric study indicates an opportunity of having larger stroke as well as higher fundamental natural frequency for such CNT-based nano-actuator function of the assumed DC voltage amplitude, enabling it to be used as a tunable NEMS-based device without any pull-in scenario.

Closed-form solution for static pull-in voltage of electrostatically actuated clamped–clamped micro/nano beams under the effect of fringing field and van der Waals force

This investigation provides an accurate prediction of static pull-in voltage for clamped–clamped micro/nano beams based on distributed model. The Euler–Bernoulli beam theory is used adapting geometric non-linearity of beam, internal (residual) stress, van der Waals force, distributed electrostatic force and fringing field effects for deriving governing differential equation. The Galerkin discretisation method is used to make reduced-order model of the governing differential equation. A regime plot is presented in the current work for determining the number of modes required in reduced-order model to obtain completely converged pull-in voltage for micro/nano beams. A closed-form relation is developed based on the relationship obtained from curve fitting of pull-in instability plots and subsequent non-linear regression for the proposed relation. The output of regression analysis provides Chi-square (χ2) tolerance value equals to 1 × 10−9, adjusted R-square value equals to 0.999 29 and P-value equals to zero, these statistical parameters indicate the convergence of non-linear fit, accuracy of fitted data and significance of the proposed model respectively. The closed-form equation is validated using available data of experimental and numerical results. The relative maximum error of 4.08% in comparison to several available experimental and numerical data proves the reliability of the proposed closed-form equation.

A novel expression obtained by using artificial bee colony algorithm to calculate pull-in voltage of fixed-fixed micro-actuators

In this paper, a novel, computationally efficient and simple closed-form expression has been derived to accurately calculate the pull-in voltage value of fixed-fixed micro-actuator. At first, microelectromechanical systems actuators with various physical parameters have been simulated by a software that employs the finite element method, the pull-in voltage expression has been derived by using the artificial bee colony optimization algorithm together with the simulation data. Since the formula is derived from the simulation data, it implicitly contains the fringing field, mid-plane stretching and size effects. In order to verify the accuracy and robustness, the predictions of closed-form formula proposed in this work have been compared with those of the theoretical ones through the simulation and experimental studies previously presented in the literature. The key advantage of the presented method is delivering a satisfying estimation of the pull-in voltage with a simple and easy way.

Enhancement of Transient Two-States Characteristics in Metal-Insulator-Semiconductor Structure by Thinning Metal Thickness

In this work, the Al/SiO2/p-Si metal-insulator-semiconductor structures with various metal thicknesses were fabricated. The charging/discharging transient current behaviors during sweeping or switching the voltages have been studied. By thinning down partial portion of the gate metal to 10 nm, the steady state leakage current was found decreased because the high resistivity of the ultrathin metal causing lower fringing field effect. Also, the transient currents were found enhanced. The reasons were that there were minority carriers under the ultrathin metal contributing to the transient currents. The above properties make the device having better volatile memory characteristics.

Design and Investigation on Bioinverter and Bioring-Oscillator for Dielectrically Modulated Biosensing Applications

In this work, an inverter-based biomolecule detection strategy has been introduced for dielectrically modulated biosensing applications that show a clear output logic-state transition after conjugation. Subsequently, a bioring-oscillator has been realized based on such bioinverters, where biomolecules can be detected from the oscillation frequency amplification with conjugation. To optimize the detection efficiency, a dielectrically modulated fringing field effect transistor based transducer has been incorporated as the pull-up/pull-down elements of such bioinverter. The underlying physics of such structure has been investigated and subsequent electrical response has been estimated for various biomolecule sample specifications. This work explores different bioinverter configurations, and subsequently the suitable choice of bioinverter has been indicated for charged and charge-neutral biomolecule detection. Similar studies have been performed for bioring oscillator, and the roles of supply voltage scaling and oscillator stage enhancement have been investigated in this context.

Application of Homotopy Analysis Method for the Pull-In and Nonlinear Vibration Analysis of Nanobeams Using a Nonlocal Euler–Bernoulli Beam Model

Abstract In this investigation, the homotopy analysis method (HAM) is utilized for the pull-in and nonlinear vibration analysis of nanobeams based on the stress-driven model (SDM) of nonlocal elasticity theory. The physical properties of nanobeams are assumed not to vary through the thickness. The nonlinear equation of motion and the corresponding boundary condition are derived on the basis of the Euler–Bernoulli beam theory. For the solution purpose, the Galerkin method is employed for reducing the nonlinear partial differential equation to a nonlinear ordinary differential equation in the time domain, and then, the resulting equation is analytically solved using the HAM. In the results section, the influences of different parameters, including nonlocal parameter, electrostatic and intermolecular van der Waals forces and fringing field effect changes on the pull-in and nonlinear vibration response are investigated.

Novel analytical model for optimizing the pull-in voltage in a flexured MEMS switch incorporating beam perforation effect

This paper presents a new method for the design, modelling and optimization of a uniform serpentine meander based MEMS shunt capacitive switch with perforation on upper beam. The new approach is proposed to improve the Pull-in Voltage performance in a MEMS switch. First a new analytical model of the Pull-in Voltage is proposed using the modified Mejis-Fokkema capacitance model taking care of the nonlinear electrostatic force, the fringing field effect due to beam thickness and etched holes on the beam simultaneously followed by the validation of same with the simulated results of benchmark full 3D FEM solver CoventorWare in a wide range of structural parameter variations. It shows a good agreement with the simulated results. Secondly, an optimization method is presented to determine the optimum configuration of switch for achieving minimum Pull-in voltage considering the proposed analytical mode as objective function. Some high performance Evolutionary Optimization Algorithms have been utilized to obtain the optimum dimensions with less computational cost and complexity. Upon comparing the applied algorithms between each other, the Dragonfly Algorithm is found to be most suitable in terms of minimum Pull-in voltage and higher convergence speed. Optimized values are validated against the simulated results of CoventorWare which shows a very satisfactory results with a small deviation of 0.223V. In addition to these, the paper proposes, for the first time, a novel algorithmic approach for uniform arrangement of square holes in a given beam area of RF MEMS switch for perforation. The algorithm dynamically accommodates all the square holes within a given beam area such that the maximum space is utilized. This automated arrangement of perforation holes will further improve the computational complexity and design accuracy of the complex design of perforated MEMS switch.

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam affected by an electric field including the fringing field effect, based on strain gradient elasticity, couple stress and classical theory was obtained. Influences of different parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin’s method via mode summation. The resulting non-linear differential equation was also solved by using the homotopy analysis method (HAM). The influence of HAM parameters on accuracy was studied specifically in the vicinity of the pull-in voltage. Comparison of the results for pull-in voltage indicated at low voltages good agreement existed between numerical and semi-analytical methods while at high voltages HAM results deviated from those of numerical methods. Findings indicate that considering strain gradient and couple stress effects results in a stiffer microbeam than with classical theory. Effects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at different voltages and orders of HAM approximation