Multiple Timescales and Modeling of Dynamic Bounce Phenomena in RF MEMS Switches

Electrostatically operated RF-MEMS switches are known to suffer from discrete switch bounce events during switch closure that increase wear and tear and lead to increased switching times. Here, we use laser Doppler vibrometer to analyze the switch response of three types of cantilevered dc-contact switches at a 200 ns time resolution. We find that bounce events are multiple time scale events with distinct motion occurring at 10^-1 and 10¹ s timescales in effect high frequency bounces within a bounce. To understand the origin of this effect, we develop a multiple eigenmode model of a cantilever switch with electrostatics, repulsive and adhesive contact forces, and rarefied gas damping and find that the high frequency bounce arises from the transient excitation of the 2nd eigenmode of the cantilever structure of the RF-MEMS switch. This phenomenon not only describes the multiple time scales involved in bounce events, but also shows that the transient excitation of the second mode leads to complex drum roll like dynamics, leading to a series of closely spaced impacts in each actuation cycle. A careful study of the dependence of the phenomenon on contact stiffness and adhesion shows how the landing pad stiffness, adhesion, and actuation voltage in dc contact switches can increase or diminish repeated impacts during actuation.