Conference Paper

Efficient mixed-domain analysis of electrostatic MEMS

Dept. of Mech. & Ind. Eng., Univ. of Illinois, Urbana-Champaign, IL, USA
DOI: 10.1109/TCAD.2003.816210 Conference: Proceedings of the 2002 IEEE/ACM International Conference on Computer-aided Design, 2002, San Jose, California, USA, November 10-14, 2002
Source: IEEE Xplore


We present efficient computational methods for scattered point and meshless analysis of electrostatic microelectromechanical systems (MEMS). Electrostatic MEM devices are governed by coupled mechanical and electrostatic energy domains. A self-consistent analysis of electrostatic MEMS is implemented by combining a finite cloud method-based interior mechanical analysis with a boundary cloud method (BCM)-based exterior electrostatic analysis. Lagrangian descriptions are used for both mechanical and electrostatic analyses. Meshless finite cloud and BCMs, combined with fast algorithms and Lagrangian descriptions, are flexible, efficient, and attractive alternatives compared to conventional finite element/boundary element methods for self-consistent electromechanical analysis. Numerical results are presented for MEM switches, a micromirror device, a lateral comb drive microactuator, and an electrostatic comb drive device. Simulation results are compared with experimental and previously reported data for many of the examples discussed in this paper and a good agreement is observed.

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Available from: G. Li, Aug 23, 2015
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    • "However, due to practical limitations, it is not always possible to tightly control tolerances and this results in very different behavior, going from one device to the next. Although several advances have been made in the development of high-fidelity numerical methods to model microsystems [1] [2] [3] [4] [5] [6], there is a pressing need to augment the capability of these methods to handle the uncertainties that are encountered in a realistic device model. "
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    ABSTRACT: This paper presents a unified framework for uncertainty quantification (UQ) in microelectromechanical systems (MEMS). The goal is to model uncertainties in the input parameters of micromechanical devices and to quantify their effect on the final performance of the device. We consider different electromechanical actuators that operate using a combination of electrostatic and electrothermal modes of actuation, for which high-fidelity numerical models have been developed. We use a data-driven framework to generate stochastic models based on experimentally observed uncertainties in geometric and material parameters. Since we are primarily interested in quantifying the statistics of the output parameters of interest, we develop an adaptive refinement strategy to efficiently propagate the uncertainty through the device model, in order to obtain quantities like the mean and the variance of the stochastic solution with minimal computational effort. We demonstrate the efficacy of this framework by performing UQ in some examples of electrostatic and electrothermomechanical microactuators. We also validate the method by comparing our results with experimentally determined uncertainties in an electrostatic microswitch. We show how our framework results in the accurate computation of uncertainties in micromechanical systems with lower computational effort.
    Preview · Article · Oct 2011 · Computer Methods in Applied Mechanics and Engineering
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    • "To address these issues, accurate modeling of MEMS dynamics is required. Based on the level of abstraction, MEMS modeling approaches can be categorized into three groups: analytical/semi-analytical approach [Daqaq, Reddy, and Nayfeh (2008); Mukherjee (2000)], reduced-order approach [Rewienski and White (2003); Bettini, Brusa, Munteanu, Specogna, and Trevisan (2008)], and full numerical approach [Li and Aluru (2003); Chen, Lai, and Liu (2009)]. Compared to the first two types of approaches, the full numerical approach solves the governing partial differential equations directly. "
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    ABSTRACT: Input-shaping is an open-loop control technique for dynamic control of electrostatic MEMS. In MEMS applications, open-loop control is attractive as it computes a priori the required system input to achieve desired dynamic behavior without using feedback. In this work, a 3-D computational electromechanical analysis is performed to preshape the voltage commands applied to electrostatically actuate a torsional micromirror to a desired tilt angle with minimal residual oscillations. The effect of higher vibration modes on the controlled response is also investigated. It is shown that, for some structural design parameters, the first bending mode of the micromirror can have a significant effect on the dynamic response. If not accounted for in the control algorithm, these bending vibrations could have an adverse effect on the controlled response of the mirror. To resolve this issue, a numerical optimization procedure is employed to shape the input voltage from the real time dynamic response of the mirror structure. The optimization scheme yields a periodic nonlinear input voltage design that can effectively suppress the bending mode.
    Full-text · Article · Jun 2009 · Computer Modeling in Engineering and Sciences
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    • "The design and analysis of micro-electromechanical systems (MEMS) requires considering the interaction of various physical fields such as mechanical, electrical and possibly fluidic. In recent years, the advances in numerical simulation methods have increased the ability to accurately model these devices [1] [2] [3] [4]. These simulation methods assume that the material properties and various geometrical parameters of the device are known in a deterministic sense. "
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    ABSTRACT: This work proposes a stochastic framework based on generalized polynomial chaos (GPC), to handle uncertain coupled electromechanical interaction, arising from variations in material properties and geometrical parameters such as gap between the microstructures, applicable to the static analysis of electrostatic MEMS. The proposed framework comprises of two components – a stochastic mechanical analysis, which quantifies the uncertainty associated with the deformation of MEM structures due to the variations in material properties and/or applied traction, and a stochastic electrostatic analysis to quantify the uncertainty in the electrostatic pressure due to variations in geometrical parameters or uncertain deformation of the conductors. The stochastic analysis is based on a stochastic Lagrangian approach, where, in addition to uncertain input parameters and unknown field variables, the random deformed configuration is expanded in terms of GPC basis functions. The spectral modes for the unknown field variables are finally obtained using Galerkin projection in the space spanned by GPC basis functions. The stochastic mechanical and electrostatic analyses are performed in a self-consistent manner to obtain the random deformation of the MEM structures. Various numerical examples are presented to study the effect of uncertain parameters on performance of various MEMS devices. The results obtained using the proposed method are verified using rigorous Monte Carlo simulations. It has been shown that the proposed method accurately predicts the statistics and probability density functions of various relevant parameters.
    Preview · Article · Aug 2008 · Computer Methods in Applied Mechanics and Engineering
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