Lumped Modeling of Contact Resistance upon Pull-In or Lift-Off of MEMS Beam Elements

J.V. Clark, H. Rost, K.S.J. Pister
Auburn University,
United States

Keywords: pull-in, lift-off, contact resistance, switch, relay, simulation, compact modeling, lumped modeling


We present a compact model of a microelectromechanical system (MEMS) beam element that includes electrical current upon gap closure. Simulation includes quasi-static analysis of pull-on and lift-off. The compact beam element (without contact) is a key building block for many types of MEMS. By including mechanical and electrical contact physics to the beam model, then the computationally-efficient design of many other types of microsystems may be also explored. Examples include RF MEMS switches or relays, analog to digital converters, low-power potential energy stores, mechanical memory, gap stops, high-acceleration impact, torsional switches or digital light projection micromirrors, vertical diffraction gratings, double-beam switches, curved-beam pull-in, comb drive instability, etc. Prior efforts by others include closed-form pull-in analytical models, simulations of pull-in and lift-off without electrical contact, and the modeling of separate gate/drain pull-in switches have been reported. A comprehensive review of electrostatic pull-in instability is given here. To our best knowledge, a compact model of contact resistance of the gate electrode upon pull-in has not been reported. Our parameterized compact model includes an electrostatic attractive force for pull-in, a short-range repulsive force to prevent beam elements from passing through each other, a short-range force similar to van der Waals that models stiction during lift-off, and a simple conductive element that is switched on when the gap is smaller than a threshold value. In the full paper, we will present a full description of our model and quasi-static simulation method. We will also demonstrate the use of our compact model by comparing simulations to results of real MEMS devices found in the literature.