Fringing Field Effect Research Articles

Studying fringe field effect of a field emitter array

Field emitter arrays on heavy As-doped Si wafer are studied in vacuum nanoelectronics diode configuration. Different shapes of emitters are considered: cone-shaped point-emitters and cylinder-shaped sharp-edge-emitters are compared. Micro scale field enhancement factor on the edge of cylindrical emitter was calculated via home-developed Matlab application and the results are presented. Two types of anode geometry are proposed: plane anode and spherical anode. Experimental and modelling results of surface electric field distribution are presented. The spherical shape of anode allows higher voltage (and higher field emission current) without destructive arcs risk.

Effects of quadrupole fringe fields in final focus systems for linear colliders

Quadrupole fringe fields in the final focus system can be a source of aberrations in the interaction point transverse beam sizes. This paper investigates the fringe field impact on the transverse beam size in the ATF2, ILC, and CLIC lattices in the linear and non-linear regimes. The linear effects are studied by replacing the hard-edge quadrupolar field by the more realistic gradient fall-off. To address the nonlinear effects, the fringe fields are represented as high order kicks added to both sides of the hard-edge magnets. It will be shown that the linear fringe fields effects can be easily cured by tuning the quadrupole strengths. On the other hand, mitigation of the nonlinear fringe fields effects is more difficult and requires use of octupole magnets or, alternatively, increasing the value of interaction point horizontal beta function ${\ensuremath{\beta}}_{x}^{*}$.

Fringing field suppression for liquid crystal gratings using equivalent capacitance configuration

A liquid crystal grating with high spatial frequency and equivalent capacitance configuration is proposed, where two layers of periodical ground electrodes are interlaced and aligned with the addressing electrodes. The equivalent capacitance configuration can reduce the fringing field effect efficiently owing to the generated electric field resisting the fringing field and redistributing the equivalent voltage exerting on the liquid crystal layer. The phase modulation depth and far-field diffraction patterns both for conventional and novel configurations were simulated. The results show that phase modulation is greatly enhanced and the maximum diffraction efficiency for a sinusoidal phase grating is 33.86%, which indicates that the equivalent capacitance configuration provides a good solution for suppressing the fringing field effect.

The effects of magnetic fringe fields on beam dynamics in a beam transport line of a terahertz FEL source

The transport line used in a terahertz FEL device has to transport electron beam through the entire system efficiently and meet the requirements of the beam parameters at the undulator entrance. Due to space limitations, the size of the magnets (five quadrupoles and two bending magnets) employed in the transport line was limited, and some devices were densely packed. In this paper, analyses of the effect of fringe fields and magnetic interference of magnets are presented. 3D models of these magnets are built and their linear optical properties are compared with those obtained by hard edge models. The results indicated that the effects of these factors are significant and they would cause a mismatch of the beam at the exit of the transport line under the preliminary lattice design. To solve this problem, the beam was re-matched using the particle swarm optimization algorithm.

Parallel plate capacitor analogy of equatorial plasma bubble and associated fringe fields with implications to equatorial valley region irregularities

AbstractVHF radar echoes from the valley region plasma irregularities, displaying ascending pattern, are often observed during the active phase of equatorial plasma bubble in the close vicinity of the geomagnetic equator and have been attributed to bubble‐related fringe field effect. These irregularities however are not observed at a few degrees away from the equator. In this paper, we attempt to understand this contrasting observational result by comparing fringe field at the geomagnetic equator and low latitudes. We use parallel plate capacitor analogy of equatorial plasma bubble and choose a few capacitor configurations, consistent with commonly observed dimension and magnetic field‐aligned property of plasma bubble, for computing fringe field. Results show that fringe field decreases significantly with decreasing altitude as expected. Further, fringe field decreases remarkably with latitude, which clearly indicates the role of magnetic field‐aligned property of plasma bubble in reducing the magnitude of fringe field at low latitudes compared to that at the geomagnetic equator. The results are presented and discussed in the light of current understanding of plasma bubble‐associated fringe field‐induced plasma irregularities in the valley region.

Fringe electric fields of flat and cylindrical deflectors in electrostatic charged particle storage rings

(Received 10 September 2013; revised manuscript received 13 June 2014; published 18 July 2014) Analytic expressions for the potentials and fields offlat and cylindrical plates, including the fringe fields, are given. The present analysis extends and simplifies the current expression for the fields of flat plates and develops expressions for the fringe fields of cylindrical plates in terms of polar coordinates. The development of a FORTRAN program to output the field strength at a given location within the Proton Electric Dipole Moment (Proton EDM) ring is then described. Fourth-order Runge-Kutta integration is used to investigate the effect of fringe fields on particle and spin dynamics with precision tracking in the proposed Proton EDM experiment.

Liquid Crystal Compensator Using Dual-Layer Electrodes for the Optical Pickup Head Application

This paper proposes a novel dual-layer electrode configuration for the liquid crystal compensator design. It has the feature of two conducting transparent electrode layers separated by a dielectric insulation layer, which sustains the electric isolation. With the design, the adjacent electrodes with almost no gap width could be performed. The proposed device was fabricated and verified. Experimental results show the expected feature. It could effectively reduce the fringe field effect of the compensator and provide the optical compensation of the focusing spot of an optical pickup head.

Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories

In recent years, extensive experiments have shown that classical continuum theory cannot predict the behavior of mechanical microstructures with small size. To accurately design and analyze micro- and nano-electro-mechanical systems, size-dependent continuum theories should be used. These theories model micro- and nano-electro-mechanical systems with higher accuracy because they include size-dependent parameters. In this paper, polysilicon nano-beam is modeled using modified couple stress and Eringen’s nonlocal elasticity theories. First, partial differential equations governing the vibration of nano-beams are converted to a one D.O.F. differential equations using Galerkin method, resulting in the lumped model of the system. Then, an analytical solution for the static pull-in voltage is derived from the lumped model of the system and Taylor expansion of the electrostatic force with fringing field effect. Both clamped-free and clamped–clamped beams are considered in the analysis where the mid-plane stretching and axial force are taken into account in clamped–clamped case. The method and model are validated by comparing the results with previously reported ones in the literature. Size-dependent parameters of polysilicon are chosen in order to minimize the difference between calculated and experimental values for static pull-in voltages. Natural frequencies of several micro-beams are calculated using derived non-classical models and results are compared to the experimental ones. The results demonstrate that modified couple stress theory coincides experimental results better than Eringen’s nonlocal elasticity and classical theories.

Modeling and Optimization of an Electrostatic Energy Harvesting Device

Modeling of energy harvesting devices is complicated by the coupling between electrical and mechanical domains. In this paper, we present a coupled electromechanical model for electret-based resonant energy harvesters where the two output pads are placed on the same device side (single-sided). An analytical analysis is complemented by 2-D finite element method simulations, where the fringing field effect on a plane capacitor is studied and accounted for by an effective area that is well fitted by a sinusoidal function of the displacement of the proof mass. From analytical calculations, we prove that the electrostatic transducer force is related to the voltage output and cannot be approximated by viscous damping or a Coulomb force as reported previously. The coupled model with two simultaneous differential equations is numerically solved for the voltage output and transduction force with given parameters. The model was verified both by practical measurements from our own fabricated device and results from a reference. An optimization study is carried out using this model to achieve the maximum output power by tuning the allowable movement (X M ) of the proof mass. Finally, the effect of a standard power-conditioning circuit is investigated for both continuous and burst power supply applications.

18.2: Color Filter LCOS with Double Mirror Structure

AbstractHigh PPI color filter LCOS is a challenging research topic. Such kind of device will induce several problems such as Fringing Field Effect, Low reflectance and Low color saturation. In this paper, a so‐called Double Mirror structure is proposed. It is found that all mentioned issues can be handled by such mirror structure. The full pixel size of the color filter LCOS can be shrunk down to 8um from 13.5um.

Pull-in behavior analysis of vibrating functionally graded micro-cantilevers under suddenly DC voltage

The present research attempts to explain dynamic pull-in instability of functionally graded micro-cantilevers actuated by step DC voltage while the fringing-field effect is taken into account in the vibrational equation of motion. By employing modern asymptotic approach namely Homotopy Perturbation Method with an auxiliary term, high-order frequency-amplitude relation is obtained, then the influences of material properties and actuation voltage on dynamic pull-in behavior are investigated. It is demonstrated that the auxiliary term in the homotopy perturbation method is extremely effective for higher order approximation and two terms in series expansions are sufficient to produce an acceptable solution. The strength of this analytical procedure is verified through comparison with numerical results.

Nonlinear-electrostatic analysis of micro-actuated beams based on couple stress and surface elasticity theories

Abstract In this paper, a size-dependent electrostatic model for cantilever micro-actuated beams is investigated considering the microstructure and surface energy effects. The modified couple stress theory is used to capture the microstructure effects while surface effects are incorporated into the model based on the Gurtin and Murdoch surface elasticity model. The electrostatic energy considering the fringing field effect forces the beam to a self-excited nonlinear beam. The governing nonlinear ordinary differential equation (ODE) of micro-actuated beams is derived, in which additional stiffnesses are added to incorporate surface energy and microstructure effects. Two solutions are proposed for the governing equation: linear exact solution and nonlinear numerical solution. At first, a linearization scheme is suggested to simplify the ODE to obtain an exact analytical solution. Then, a numerical technique, based on a finite difference method, is proposed to solve the general nonlinear ODE. The exact analytical solution of the linear ODE is used as an initial guess to numerically solve the extracted set of equations using Newton׳s method. The present model is verified by comparing its estimations with the available numerical, analytical and experimental results. Finally, a parametric study is provided to show effects of the couple stress and surface energy on the electrostatic behavior of micro-beams. Moreover, a comparison between the two proposed solution schemes is provided which allows defining the limit of applicability of each one of the proposed solutions.

Influence of High-k Gate Dielectric on Nanoscale DG-MOSFET

Influence of dielectric materials as gate oxide on various short channel device parameters using a 2-D device simulator has been studied in this paper. It is found that the use of high-k dielectrics directly on the silicon wafer would degrade the performance. This degradation is mainly due to the fringing field effect developed from gate to source/drain. This fringing field will further generate electric field into the channel region from source/drain region which weakens the gate control. Therefore, by taking the gate stack engineering into account it has been shown that the induced electric field along the channel can be minimized as well as the device performance can be enhanced. This paper examined various parameters of the device like potential distribution from source and drain, threshold voltage (Vth), drain induced barrier lowering (DIBL), subthreshold slope (SS), on-current (Ion), off-current (Ioff) and Transconductance (gm) by taking different dielectric materials [SiO2(=3.9), Si3N4 (=7.5), HfO2 (=24) and Ta2O5 (=50) ] as gate oxide (s).

Analysis of nonlinear dynamic behavior of electrically actuated micro-beam with piezoelectric layers and squeeze-film damping effect

An analytical model based on a nonlinear deflection equation and the Reynolds equation is proposed to describe the dynamic behavior of an electrically actuated micro-beam with two piezoelectric layers. The proposed model takes explicit account of the fringing field effect, the axial stress effect, the residual stress effect, and the squeeze-film damping effect between the micro-beam and the lower electrode. The nonlinear governing equation of the micro-beam is solved using a hybrid computational scheme comprising the differential transformation method and the finite difference method. The validity of the analytical model and numerical solution procedure is demonstrated by comparing the result obtained for the pull-in voltage of a micro-beam actuated by a DC voltage only with that presented in the literature. It is shown that the nonlinear dynamic response of the micro-beam can be controlled using a combined driving scheme consisting of both the magnitude and the frequency of the AC actuating voltage and a DC driving voltage. The effects of the AC/DC actuating conditions, micro-beam geometry parameters, and squeeze-film damping force on the center-point displacement of the micro-beam are systematically examined. In addition, the actuating conditions which ensure the stability of the micro-beam are identified by means of phase portraits and Poincare maps. In general, the results show that the analytical model and hybrid numerical scheme provide a feasible means of analyzing the dynamic response of a variety of electrostatically-actuated microstructures.

Photo-induced tunneling currents in MOS structures with various HfO2/SiO2 stacking dielectrics

In this study, the current conduction mechanisms of structures with tandem high-k dielectric in illumination are discussed. Samples of Al/SiO2/Si (S), Al/HfO2/SiO2/Si (H), and Al/3HfO2/SiO2/Si (3H) were examined. The significant observation of electron traps of sample H compares to sample S is found under the double bias capacitance-voltage (C-V) measurements in illumination. Moreover, the photo absorption sensitivity of sample H is higher than S due to the formation of HfO2 dielectric layer, which leads to larger numbers of carriers crowded through the sweep of VG before the domination of tunneling current. Additionally, the HfO2 dielectric layer would block the electrons passing through oxide from valance band, which would result in less electron-hole (e−-h+) pairs recombination effect. Also, it was found that both of the samples S and H show perimeter dependency of positive bias currents due to strong fringing field effect in dark and illumination; while sample 3H shows area dependency of positive bias currents in strong illumination. The non-uniform tunneling current through thin dielectric and through HfO2 stacking layers are importance to MOS(p) tunneling photo diodes.

Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams

Conventional continuum theory does not account for contributions from length scale effects which are important in modeling of nano-beams. Failure to include size-dependent contributions can lead to underestimates of deflection, stresses, and pull-in voltage of electrostatic actuated micro and nano-beams. This research aims to use nonlocal and strain gradient elasticity theories to study the static behavior of electrically actuated micro- and nano-beams. To solve the boundary value nonlinear differential equations, analogue equation and Gauss---Seidel iteration methods are used. Both clamped-free and clamped---clamped micro- and nano-beams under electrostatical actuation are considered where mid-plane stretching, axial residual stress and fringing field effect are taken into account for clamped---clamped cases. The accuracy of solution is evaluated by comparison of the pull-in voltages of different micro-electro-mechanical systems with those results previously published in the literature. A main drawback of the previous theoretical researches using nonlocal or strain gradient methods was that they don't account for effects of the size on the Young modulus of the beam and merely they adjust the length scale parameters for small sizes to fit data with experimental results. In the present study, the experimental voltages for static pull-in of different micro- and nano-beams are used to estimate the silicon Young's modulus, nonlocal and length scale parameters. Using the estimated parameters, pull-in voltages of silicon micro- and nano-beams based on strain gradient and nonlocal theories are compared with respect to each other and also with the experimental and previous theoretical results. The conducted results demonstrate that the predicted pull-in voltages using proposed strain gradient theory will give the best fit with experimental observations.

Modeling and Analysis of an Electrically Actuated Microbeam Based on Nonclassical Beam Theory

This work investigates the mechanical behavior of a clamped-clamped microbeam modeled within the framework of the strain-gradient elasticity theory. The governing equation of motion gives proper account of both the effect of the nonlinear midplane stretching and of an applied axial load. An electric-voltage difference, introducing into the model a further source of nonlinearity, is considered, including also a correction term for fringing field effects. The electric force acting on the microbeam is rearranged by means of the Chebyshev method, verifying the accuracy of the proposed approximation. The results show that a uniform error on the whole domain can be achieved. The static solution is obtained by a numerical differential quadrature method. The paper looks into the variation of the maximal deflection of the microbeam with respect to several parameters. Study of the pull-in limit on the high-order material parameters introduced by the nonclassical approach and a comparison with respect to the classical beam theory are also carried out. The numerical simulation indicates that the static response is larger, affected by the use of a nonclassical theory near the pull-in instability regime. The dynamical problem is, finally, analyzed, deriving the multi degree-of-freedom problem through a Galerkin-based approach. The study on the single degree-of-freedom model enables us to note the large influence of the nonlinear terms.

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

In this paper, we provide a unified and self-consistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam,the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The non-uniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam. For the clamped-clamped case, care must be taken to account for the effective use of thermal loading in the design of microbeams. It is also observed that uniform thermal loading will lead to a reduction in the pull-in voltage of a FGM microbeam for all the three boundary conditions considered.

The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect

Dynamic pull-in instability of vibrating nano-actuators in the presence of actuation voltage is studied in this paper through introducing the closed form expression for the fundamental frequency of beam-type nano-structure. The fringing field effect and dispersion forces (Casimir and van der Waals attractions) are taken into account in the dynamic governing equation of motion. The influences of initial amplitude of vibration, applied voltage and intermolecular forces on the dynamic pull-in behavior and fundamental frequency are investigated by a modern asymptotic approach namely Parameter Expansion Method (PEM). It is demonstrated that two terms in series expansions are sufficient to produce an acceptable solution of the actuated nano-structure. The obtained results from numerical methods by considering three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of system dynamic shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the nano-beam actuator exhibit periodic and homoclinic orbits.

Proposed transport beam line for DESIR

In this paper the detailed structure of the transport beam line design is proposed, quadrupoles and deflectors specifications in order to transport the beam from the optic adaptation point in the SPIRAL2 production building up to the adaptation point in the DESIR hall. All optical elements, in beam line, are electrostatic and so, settings are independent of the ratio q/m of the particle. The calculations are done by COSY INFINITY computer code in first order of approximation and without fringe field effects. The beam emittances at the starting point (adaptation point in the SPIRAL2 production building) in horizontal and vertical planes are 80p mm mrad. The beam line is designed in such a way that the beam sizes, in both planes, at the end (adaptation point in the DESIR hall) are kept the same as they are at the starting point; the horizontal and vertical displacements from the optic axis at starting and ending points are the same, ?6 mm. In such case the efficiency of transport of the beam is high.