Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS
Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS
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DOI：
10.1109/jmems.2004.835773
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发表时间：
2004-10-01
影响因子：
2.7
通讯作者：
Aluru, NR
中科院分区：
文献类型：
--
作者：
De, SK;Aluru, NR
微电子机械系统(MEMS)的动力学分析具有机电耦合的特点。除了静电MEMS中公认的Pull-in现象外，这两个域之间的非线性耦合还引起了一些有趣的动态现象。为了正确理解和深入研究MEMS动力学，有一种可靠有效的物理级仿真方法是非常重要的。在本文中，我们发展了基于拉格朗日描述的机械域和电域的松弛和牛顿格式，用于MEMS动力学分析。将拉格朗日描述应用于机械和静电分析，使该方法比基于标准半拉格朗日格式的MEMS动力学分析更有效。全拉格朗日格式的一个主要优点是可以精确地计算牛顿格式雅可比矩阵中的域间耦合项(力电耦合项)，这是半拉格朗日格式所不能做到的。对悬臂梁和固支MEM梁的模拟结果与已发表的数据进行了比较，验证了基于全拉格朗日松弛格式和牛顿格式的有效性。采用牛顿方法对MEMS中广泛使用的横向和横向两类梳齿传动进行了动力学分析。介绍了几种有趣的MEM动力学现象及其可能的应用。显示了MEM器件的弹簧硬化和软化。分析了不同电信号下MEM器件中多谐振峰的存在，并讨论了其在多带/通带MEM滤波器/振荡器中的可能应用。开关速度是电容型RF-MEM开关的一个严重制约因素。我们已经证明，在谐振频率下，直流偏置和交流偏置可以在相当低的峰值功率需求下实现非常快速的开关。
Dynamic analysis of microelectromechanical systems (MEMS) is characterized by the nonlinear coupling of electrical and mechanical domains. The nonlinear coupling between the two domains gives rise to several interesting dynamic phenomena besides the well established pull-in phenomenon in electrostatic MEMS. For proper understanding and detailed exploration of MEMS dynamics, it is important to have a reliable and efficient physical level simulation method. In this paper, we develop relaxation and Newton schemes based on a Lagrangian description of both the mechanical and the electrical domains for the analysis of MEMS dynamics. The application of a Lagrangian description for both mechanical and electrostatic analysis makes this method far more efficient than standard semi-Lagrangian scheme-based analysis of MEMS dynamics. A major advantage of the full-Lagrangian scheme is in the accurate computation of the interdomain coupling term (mechanical to electrical) in the Jacobian matrix of the Newton scheme which is not possible with a semi-Lagrangian scheme. The full-Lagrangian based relaxation and Newton schemes have been validated by comparing simulation results with published data for cantilever and fixed-fixed MEM beams. The Newton scheme has been used for the dynamic analysis of two classes of comb-drives widely used in MEMS, namely, transverse and lateral comb-drives. Several interesting MEM dynamic phenomena and their possible applications have been presented. Spring-hardening and softening of MEM devices has been shown. The existence of multiple resonant peaks in MEM devices has been analyzed under different electrical signals and their possible applications in multiband/passband MEM filters/oscillators is discussed. Switching speed is a serious constraint for capacitive based RF-MEM switches. We have shown that a dc bias along with an ac bias at the resonant frequency can give very fast switching at a considerably less peak power requirement.