127978092
The Nonlinear Dynamic Behaviors of Electrostatic Micro-Tweezers
Abstract. This work addresses the nonlinear dynamic behavior of different electrostatic micro-tweezers, a micro electric actuator. This actuator, a cantilever beam electrostatic micro-tweezers, has been extensively used in micro-electro-mechanical systems (MEMS). The importance of micro electric actuators manufactured is higher than the other part of MEMS since it is the power source of the entire micro-electro-mechanical systems. In actual operation, the instability and bad dynamic characteristics of the electric actuators will cause larger displacement mobility error, such as transport behavior and response procedures failure, etc., and even damage the micro-electro-mechanical systems. To improve the actuator dynamic displacement accuracy, the dynamic behavior in the electric actuator system must be studied, especially for nonlinear dynamic behavior of system. In this work, the differential quadrature method (DQM) was employed to solve the problem of nonlinearity in the equation of motion. The results reveal that the proposed DQM model can be used to simulate the nonlinear behavior of the micro-tweezers efficiently Micro-tweezers of various shapes were studied to examine the feasibility of applying the DQM in analyzing their nonlinear responses. The simulated results agree very closely with the calculated and experimental data in the literature.
97028051
Selective chemical vapor deposition of tungsten for microelectromechanical structures
Abstract A selective chemical vapor deposition (CVD) tungsten process is used to fabricate three-dimensional micromechanical structures on a silicon substrate. Patterned structures are formed in silicon dioxide trenches by selective nucleation and growth of tungsten from the bottom of the trench. Examples are shown for selective growth of tungsten on single-crystal silicon, on thin films of silicon and on silicon-implanted, silicon dioxide layers. This high deposition-rate selective CVD tungsten process had been used to fabricate tungsten micromechanical structures greater than 4 μm thick. Tungsten patters with features of 0.3 μm × 0.3 μm in 0.6 μm of tungsten are fabricated using electron beam lithography. As an example of an electromechnical structure, cantilever beams have been fabricated to make micromechanical tweezers that move in two dimensions by the application of potential differences between the beams (lateral motion), and between the beams and the silicon substrate (vertical motion). Tungsten microtweezers 200 μm in length with a cross-section of 2.7 μm × 2.5 μm closed with an applied voltage of less than 150 V.
136575253
Selective chemical vapor deposition of tungsten for microdynamic structures
A selective chemical vapor deposition (CVD) tungsten process is used to fabricate three-dimensional tungsten cantilever beams on a silicon substrate. Two beams form micromechanical tweezers that move in three dimensions by the application of potential differences between the beams, and between the beams and the silicon substrate. A high-deposition-rate selective tungsten CVD process is used to fabricate beams of greater than three microns thickness in patterned CVD SiO/sub 2/ trenches ion-implanted with silicon. Tweezer 200- mu m in length with a cross section of 2.7 mu m*2.5 mu m close with an applied voltage of less than 150 V. The magnitude of the deflection and the beam profile are compared to results obtained using simulations of the electric field and dynamic mechanical simulations of the tweezers.<<ETX>>
122882425
Simulation methods for micro-electro-mechanical structures (MEMS) with application to a microtweezer
Abstract In this paper, we consider the simulation of microelectromechanical structures (MEMS). The objective of this work is to develop reliable numerical procedures that will help improve our understanding of MEMS behaviors, and enable optimal design of MEMS. A hybrid FEM-BEM method is developed to solve the coupled electrostatics and mechanics equations. Sensitivity analysis is carried out using the direct differentiation approach (DDA) to compute the design sensitivity coefficients (DSCs). The DSCs can then be used to drive optimization procedures. The numerical approaches are validated on a simple MEMS device—the tungsten microtweezer. The nonlinearity of the electrostatic force is found to dominate the behavior of this device. Sensitivity analysis and optimization procedures are used to compute critical parameters related to the nonlinear behaviors, as well as to solve inverse problems. The nonlinear behaviors of the tweezer are explained using a simple physical analog which is found to exhibit many of the same behaviors. Quantitative comparisons of the simulated results with experiments are also presented.
108953397
OYSTER, a three-dimensional structural simulator for microelectromechanical design
Abstract As microelectromechanical systems become more complex, designers will find it useful to derive models of the geometry of their device structures directly from the process description and planar mask patterns. OYSTER simulates the geometric effects of sequential IC process stages, including patterning of photoresists with planar masks, in order to produce three-dimensional polyhedral representations of all material structures in a design cell after each process stage. The polyhedral models may be used with various analytic procedures as sources of geometric data for finite-element calculations, or they may be subjected to interference calculations, or inspected to detect structural anomalies. OYSTER has been developed for IC simulation, but is applicable to microelectromechanical systems manufactured using similar processes. In addition, because it uses basic functions of a solid modeling program developed for mechanical systems, it provides access to features like dimensioning and tolerancing and kinematics.
110402611
A computer-aided design system for microelectromechanical systems (MEMCAD)
The authors describe the MIT microelectromechanical computer-aided design system (MEMCAD), in which selected commercial software packages are linked with specialized database and numerical programs to allow designers to quickly perform both mechanical and electrical analyses of structures either described directly, or derived from the design specification (mask data plus process flow). The system architecture, the various modules, and their present status are described, and present system performance is demonstrated with several examples. >
110619607
Self-consistent simulation and modelling of electrostatically deformed diaphragms
Design of MEMS devices which apply electrostatic forces to deformable structures is complicated by the fact that as the structure deforms, the charges redistribute, thereby modifying the mechanical loads. This paper reports three different levels of model used to simulate such structures: a very simple lumped parallel-plate-capacitor-plus-spring model, a one-dimensional numerical model based on beam and/or plate theory with loads derived from an incrementally parallel-plate capacitor, and a fully self-consistent three-dimensional numerical simulation combining finite-element structural modeling with multipole-accelerated boundary element capacitance analysis. The relative merits of each model are described, and several specific examples are examined. The lumped model has the advantage of simplicity plus a full analytic description, which permits assessment of stability of solutions. The one-dimensional numerical model, in the specific cases examined, agrees with the full 3-D model, and is computationally far less costly However, the simple structures examined here have nearly parallel conductors which remain in the small-deflection regime up to the pull-in voltage. For non-parallel conductors, and for structures which involve large deflections, the full 3-D model will be required. Furthermore, the full 3-D model is extremely valuable in identifying the limitations of the beam-theory simulation, some of which could be critical to a design.
110070246
M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures
A set of electrostatically actuated microelectromechanical test structures is presented that meets the emerging need for microelectromechanical systems (MEMS) process monitoring and material property measurement at the wafer level during both process development and manufacturing. When implemented as a test chip or drop-in pattern for MEMS processes, M-Test becomes analogous to the electrical MOSFET test structures (often called E-Test) used for extraction of MOS device parameters. The principle of M-Test is the electrostatic pull-in of three sets of test structures [cantilever beams (CB's), fixed-fixed beams (FB's), and clamped circular diaphragms (CD's)] followed by the extraction of two intermediate quantities (the S and B parameters) that depend on the product of material properties and test structure geometry. The S and B parameters give a direct measure of the process uniformity across an individual wafer and process repeatability between wafers and lots. The extraction of material properties (e.g., Young's modulus, plate modulus, and residual stress) from these S and B parameters is then accomplished using geometric metrology data. Experimental demonstration of M-Test is presented using results from MIT's dielectrically isolated wafer-bonded silicon process. This yielded silicon plate modulus results which agreed with literature values to within /spl plusmn/4%. Guidelines for adapting the method to other MEMS process technologies are presented.
15181787
Electrostatic curved electrode actuators
This paper presents the design and performance of an electrostatic actuator consisting of a laterally compliant cantilever beam and a fixed curved electrode, both suspended above a ground plane. A theoretical description of the static behavior of the cantilever as it is pulled into contact with the rigid fixed-electrode structure is given. Two models are presented: a simplified semi-analytical model based on energy methods, and fully three-dimensional (3-D) coupled electromechanical numerical simulations using CoSolve-EM. The two models are in qualitative agreement with each other, and predict stable actuator behavior when the beam deflection becomes constrained by the curved electrode geometry before electrostatic pull-in can occur. The pull-in behavior depends on the shape of the curved electrode. Test devices have been fabricated by polysilicon surface micromachining techniques. Experimental results confirm the basic theoretical results. Stable behavior with relatively large displacements and forces can be generated by these curved electrode actuators. Depending on the design, or as a result of geometrical imperfections, regions of unstable (pull-in) deflection behavior are also observed.
73563010
Nonlinear electromechanical behaviour of an electrostatic microrelay
In this paper experiments on the quasistatic and dynamic behaviour of the electrostatic polysilicon microrelay fabricated at IMT are presented together with new nonlinear dynamical models. The models simulate the pull-in voltage, the resonance frequency, the quality factor, the switching time and the electrostatic spring softening of the microrelay. Simulation of the pull-in voltage has been done with MIT's MEMCAD system, the resonance frequency has been simulated with Abaqus/sup TM/, while macro-models developed at MIT have been used to simulate the dynamics of the nonlinear actuator in the presence of squeeze-film damping.
108568470
Extending the travel range of analog-tuned electrostatic actuators
The pull-in instability limits the travel distance of elastically suspended parallel-plate electrostatic microactuators to about 1/3 of the undeflected gap distance. In this paper, we examine the "leveraged bending" and "strain-stiffening" methods for extending the travel range of electrostatic actuators. The leveraged bending effect can be used to achieve full gap travel at the cost of increased actuation voltage. The strain-stiffening effect can be used to minimize actuation voltage for a given travel range. An analytical approximation shows that the strain-stiffening effect can be used to achieve a stable travel distance up to about 3/5 of the gap. A tunable reflective diffraction grating known as the polychromator has been designed using these actuation techniques, and selected designs have been fabricated and tested for actuation behavior. Gratings with 1024 flat, closely packed grating-element actuators have been fabricated with over 1-cm-long mirrors, achieving stable vertical travel distances of more than 1.75 /spl mu/m out of a 2-/spl mu/m gap.
109405031
Fabrication and investigation of in-plane compliant SU8 structures for MEMS and their application to micro valves and micro grippers
Abstract This paper demonstrates the versatile application potential of SU8 photoepoxy for micromechanical components. Its outstanding aspect ratio and attainable film thicknesses enable the design of structures such as beams and hinges that are compliant in the wafer plane. The applicability of this technology is demonstrated on shape memory alloy and pneumatically actuated micro grippers [1] , [2] as well as a micro fluidic channel with integrated check valve. Besides reporting on the improved technology for 300–400 μm SU8 structures, we will present elastic material properties measured on micro compliant beams and flexural hinges employing a tactile force sensor [3] . The material properties measured on micro specimen are compared to large scale standard tensile test results.
6007885
Multi-axial micromanipulation organized by versatile micro robots and micro tweezers
In this paper, we describe development of the multi-axial micromanipulation organized by versatile micro robots using micro tweezers. To conduct microscopic operations, a unique locomotion mechanism composed of four piezoelectric actuators and two electromagnets is proposed. Here two legs arranged to cross each other are connected by four piezoelectric actuators so that the robot can move in any direction, i.e. in X and Y directions as well as rotate at the specified point precisely in the manner of an inchworm. To manipulate micro objects by these versatile micro robots, we have developed micro tweezers driven by 3 piezoelectric actuators. We have also developed an electromagnetic spherical micromanipulator to position the micro tweezers. The electromagnetic spherical micromanipulator rotates in yaw, roll and pitch directions independently. The electromagnetic spherical micromanipulator is a 1-inch cube size, so we can easily attach them on top of the versatile micro robots. We have developed the multi-axial micromanipulation organized by 3 versatile micro robots with the electromagnetic spherical micromanipulator and micro tweezers. The whole manipulation device is very small, 200 mm in diameter and 70 mm in height, so we can easily attach the device to micro processing instruments even if the working area is very small. This device has 21 DOF with less than 100 nm resolution. In experiments, we have demonstrated flexible handling of miniscule glass spheres with a diameter of 20 mum. We have also succeeded in fixing miniscule glass spheres on a sample table by an ultraviolet cure adhesive. The design procedure, basic performance and micro-assembling applications of this tiny robot are also discussed as part of the new field of micro robotics requiring especially high precision in certain regions.
110923815
Characterization of an electro-thermal micro gripper and tip sharpening using FIB technique
A micromachined electro-thermal gripper, first introduced by Ivanova et al. (Microelectron Eng 83:1393–1395, 2006), represents a promising candidate for the manipulation and handling of micro or even nano-scaled objects. To further optimize the performance of the device, a detailed electrical and mechanical characterization is needed. Due to the so-called duo-action gripper approach (i.e., a separate actuator for closing and opening action) these investigations focused on the maximum (minimum) opening width being 11.5 μm (3.3 μm), while in rest position a value of 4 μm is feasible. The maximum, electrical input power is limited to 80 mW/actuator element, resulting in a current density of up to 1.27 MA cm−2 in the corresponding metal layers. When applying, however, larger current densities the probability of device failure increases substantially as in combination with an enhanced temperature of about 200°C electromigration effects occur in the metallization. Furthermore, the cut-off frequency and parasitic effects during actuation such as the z-deflection and the increase in length of each arm both showing values of up to 3 μm have been investigated as a function of operation parameters. Finally, the tips of the gripper were sharpened using Focused Ion Beam technique to a radius of less than 1 μm for gripping operations in space-restricted environments or for the manipulation or handling of sub-μm scaled objects.
122053474
DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
Abstract The numerical solution of nonlinear partial differential equations plays a prominent role in numerical weather forecasting, optimal control theory, radiative transfer, and many other areas of physics, engineering, and biology. In many cases all that is desired is a moderately accurate solution at a few points which can be calculated rapidly. In this paper we wish to present a simple direct technique which can be applied in a large number of cases to circumvent the difficulties of programming complex algorithms for the computer, as well as excessive use of storage and computer time. We illustrate this technique with the solution of some partial differential equations arising in various simplified models of fluid flow and turbulence.
121467458
Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam
The quadrature method (OM) has been used in structural analysis only in recent years. In this study, OM is applied to flexural vibration analysis of a geometrically nonlinear beam. The numerical results by OM agree with the results by the finite element method. It is believed that this is the first attempt to solve a nonlinear dynamic problem by the quadrature method.
122885193
FREE VIBRATION ANALYSIS OF TAPERED RECTANGULAR PLATES BY DIFFERENTIAL QUADRATURE METHOD: A SEMI-ANALYTICAL APPROACH
Abstract The particular type of thin rectangular plate configurations considered in the present work are the ones having two opposite edges simply supported and are of varying thickness between the other two edges. The boundary conditions at these two edges may be quite general. The plates may isotropic or specially orthotropic. For the numerical solution to evaluate the free vibration characteristics of such plates, a semi-analytical approach is adopted. First, by using the trigonometric sine functions for the mode shape between the simply supported edges, the eigenvalue partial differential equation is reduced to an ordinary differential equation. The solution of the reduced equation is then carried out by the differential quadrature method. On the basis of comparison with the available results in the published literature, it is believed that this solution method is capable of yielding highly accurate results. Moreover, the very small computation times required for the evaluation of the vibration characteristics demonstrate the high computational efficiency of the method and point to its possible use in the real time analysis and design of vibrating plate systems.
15241409
The Study on the Nonlinear Computations of the DQ and DC Methods
This article points out that the differential quadrature (DQ) and differential cubature (DC) methods, due to their global domain property, are more efficient for nonlinear problems than the traditional numerical techniques such as finite element and finite difference methods. By introducing the Hadamard product of matrices, we obtain an explicit matrix formulation for the DQ and DC solutions of nonlinear differential and integro-differential equations. Due to its simplicity and flexibility, the present Hadamard product approach makes the DQ and DC methods much easier to use. Many studies on the Hadamard product can be fully exploited for the DQ and DC nonlinear computations. Furthermore, we first present the SJT product of matrixandvectortocomputeaccuratelyandefficientlytheFrechetderivativematrixintheNewton{Raphson method for the solution of the nonlinear formulations. We also propose a simple approach to simplify the DQ or DC formulations for some nonlinear differential operators and, thus, the computational efficiency of these methods is significantly improved. We give the matrix multiplication formulas to efficiently compute the weighting coefficient matrices of the DC method. The spherical harmonics are suggested as the test functionsintheDCmethodtohandlethenonlineardifferentialequationsoccurringinglobalandhemispheric weather forecasting problems. Some examples are analyzed to demonstrate the simplicity and efficiency of the presented techniques. It is emphasized that the innovations presented are applicable to the nonlinear computations of the other numerical methods as well. c 1997 John Wiley & Sons, Inc.
60284
The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates
The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen. In this study, they are applied to the diAerential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simplified, while the SJT product approach minimizes the eAort to evaluate the Jacobian derivative matrix in the Newton‐Raphson method for solving the resultant nonlinear formulations. In addition, the coupled nonlinear formulations for the present problems can easily be decoupled by means of the Hadamard and SJT product. Therefore, the size of the simultaneous nonlinear algebraic equations is reduced by two-thirds and the computing eAort and storage requirements are greatly alleviated. Two recent approaches applying the multiple boundary conditions are employed in the present DQ nonlinear computations. The solution accuracies are significantly improved in comparison to the previously given by Bert et al. The numerical results and detailed solution procedures are provided to demonstrate the superb eAciency, accuracy and simplicity of the new approaches in applying DQ method for nonlinear computations. # 1999 Elsevier Science Ltd. All rights reserved.
122628839
DIFFERENTIAL QUADRATURE METHOD: APPLICATION TO INITIAL- BOUNDARY-VALUE PROBLEMS
Two non-linear dynamical systems have been considered. In both cases, the governing equation of motion is reduced to two second-order non-linear non-autonomous ordinary differential equations using the differential quadrature method with a careful distribution of sampling points. To check the numerical results, a comparison with those obtained using the Galerkin approach is proposed.
121502267
THE GENERALIZED DIFFERENTIAL QUADRATURE RULE FOR INITIAL-VALUE DIFFERENTIAL EQUATIONS
Abstract The generalized differential quadrature rule (GDQR) proposed recently by the authors is applied here to solve initial-value differential equations of the 2nd to 4th order. Differential quadrature expressions are derived based on the GDQR for these equations. The Hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the GDQR. The numerical solutions for example problems demonstrate that the GDQR has high efficiency and accuracy. A detailed discussion on the present method is presented by comparing with other existing methods. The present method can be extended to other types of differential equation systems.
119791446
Simulating non-linear coupled oscillators by an iterative differential quadrature method
Abstract An iterative method based on differential quadrature rules is proposed as a new unified frame of resolution for non-linear two-degree-of-freedom systems. Dynamical systems with Duffing-type non-linearity have been considered. Differential quadrature rules have been applied with a careful distribution of sampling points to reduce the governing equation of motion to two second-order non-linear, non-autonomous ordinary differential equations and to solve the time-domain problem. The time domain of the problem is discretized by means of time intervals, with the same distribution of sampling points used to discretize the space domain (which can be seen as a single interval). It will be shown that accurate solutions depend not only on the choice of the distribution of sampling points, but also on the length of the time interval one refers to in the computations. The numerical results, utilized to draw Poincare maps, are successfully compared with those obtained using the Runge–Kutta method.
120906218
Application of the generalized differential quadrature rule to initial–boundary-value problems
Partial differential equations (PDEs) for the forced vibration of structural beams are solved in this paper using the recently proposed generalized differential quadrature rule (GDQR). The GDQR techniques are first applied to both spatial and time dimensions simultaneously as a whole. No other classical methods are needed in the time dimension. The objective of this paper is to formularize the GDQR expressions and corresponding explicit weighting coefficients, while the derivation of explicit weighting coefficients is one of the most important aspects in the differential quadrature methods. It should be emphasized that the GDQR expressions and weighting coefficients for two-dimensional problems are not a direct application of those for one-dimensional problems, and they are distinctly different for PDEs of different orders. An Euler beam and a Timoshenko beam are employed as examples. Accurate results are obtained. The proposed procedures can be applied to problems in other disciplines of sciences and technology, where the problems may be governed by other PDEs with different orders in the time or spatial dimension.