Integrated modeling of nonlinear dynamics and contact mechanics of electrostatically actuated RF-MEMS switches

Abstract

In this work, a novel nonlinear dynamic model is developed to investigate the bouncing and deformation behaviors of an electrostatically actuated, ohmic-contact RF-MEMS switch. The model accounts for a real geometry, the electrostatic actuation, squeeze-film damping effect, and the nonlinear elastic-plastic contact mechanics using Hertz theory. A lowcomplexity formulation based on finite differential analysis is employed to solve the model equations in the time-domain. The proposed methodology is validated using a real four-contact RF-MEMS switch with complex geometry. The simulation results of the switch performance in the on-stage (closure) are in good agreement with experimental measurements demonstrating that the model is very effective in capturing the bouncing and contact deformation phenomena accurately. It is foreseen that the proposed approach will be instrumental in providing a better insight into the reliability of MEMS switches and will, ultimately, found a basis of developing and implementing control strategies to maximize their lifetime.

Micromechanical vibro-impact systems: a review

“…The FETD method is popular in the MEMS field using commercial software, such as RF switches using ANSYS [39,40,193] and COMSOL Multiphysics [164]. The FDTD method has also been used in studying the time-dependent behavior of switches [37,155,[159][160][161][162] and tapping-mode AFM [148,149]. However, both methods require extensive time integration of second-order ODEs, making themselves computationally expensive and nearly impossible for systematic investigation and device optimization.…”

“…Distributed-parameter approach is commonly used to analyze MEMS vibro-impact systems that maintains the continuous nature of the structure and represents the response in terms of continuous variables. Based on this approach, MEMS vibro-impact systems are usually modeled as a timevarying, spatially distributed partial differential equation (PDE) coupled with the nonlinear terms and most of them are based on the Euler-Bernoulli theory [18,37,115,117,141,148,149,160,163]. A widely used method to treat these PDEs is to reduce them to tractable ordinary differential equations (ODEs) through modal analysis [18,115,117,141,163], resulting in a lumped reduced-order model.…”

Model identification for impact dynamics of a piezoelectric microactuator

“…Forcing Dynamics Damping Impact Adhesion Experimentally validated Wang et al [6] ES L SF Asperity -Threshold for bouncing Decuzzi et al [7] ES D SF VdW VdW -Do et al [8] ES D SF Elastic/plastic -Periods of contact Park et al [9] ES suggested novel impact/bounce models over various substrate conditions, which are used to inform the lumped-parameter modeling in this paper. Additionally, for models based on an assumption that the geometry of the contact surfaces is well known, close estimation of the short-ranged forces was conducted in several studies, including use of the Reynolds equation for squeeze-film damping [3,6,7,10,11] and various adhesion/contact force models such as Johnson-Kendall-Roberts (JKR) [3] or Lennard-Jones force [12].…”

“…This is especially true for studies of scanning probe technologies, as in atomic force microscopy [1] or probe storage research [2], which has allowed extremely detailed studies of contact dynamics for such instruments. For applications with larger interacting surfaces, on the order of 10-1000 μm, the most prevalent area of contact modeling is for micro-electromechanical switches [3,[6][7][8][9][10][11][12][13], with additional work being done on certain vibration scavenging [4] or miniature gear devices [5]. Table 1 shows a summary of many contact models from the literature for interacting surfaces at this scale.…”

“…A variety of models for impact, adhesion and damping behavior have been utilized, and these have enabled accurate predictions of certain specific phenomena during one or more impact events. More specifically, among closely related models in table 1, Decuzzi [7] and Do [8] investigated trends in adhesion/contact force for different environments and Do [8], LaRose [10] and McCarthy [11] Table 1. Comparison of features included in contact models for impact of fixed surface and actuated device 0.01-1 mm in size.…”