Pull-in Dynamics of Electrostatically-actuated Beams

We report the experimental measurement and simulation of the transient electrostatic pull-in characteristics of microstructural beams fabricated with silicon surface micromachining. Pull-in dynamics are investigated under the influence of compressible squeezed-film damping (CSQFD) for large amplitude motion. A linearized one-dimensional model, using a fitted damping constant, and a two-dimensional finitedifference model, based on the compressible isothermal ReynoldÕs equation, are used to simulate the experimental data. INTRODUCTION Elastically supported microstructures become unstable under a nonlinear electrostatic force beyond an applied voltage called the pull-in voltage. In mechanically static situations, this voltage is termed the static pull-in voltage (VPI). Models for VPI have been used for extraction of material properties and for process monitoring from microelectromechanical system (MEMS) test structures. [1-4] In mechanically dynamic situations, MEMS devices over small air gaps are subject to CSQFD. This effect has been simulated for large amplitude motion by Yang and Senturia using the nonlinearized form of the compressible isothermal ReynoldÕs equation. [5] Here we investigate the coupled elastomechanical-electrostatic-CSQFD problem for the large dynamic motion of microstructural fixed-fixed beams by measuring their pull-in times after step voltage applications. EXPERIMENTS AND SIMULATIONS Two fixed-fixed polysilicon beams, 610Êμm long and 710Êμm long, 2.12Êμm thick and 40Êμm wide over a 2.07Êμm gap are placed in a circuit similar to that in Figure 1. [6] A zero-topeak step input voltage is applied between the beam and a fixed bottom conductor. Similar to that shown in Figure 2, the pullin time is measured as the delay between the application of the step input and the sharp increase in Vout after the beam makes contact to the conductor. Rs = 1 MΩ Co ≈ 0.15pF Vin