The dynamic response of resistive microswitches: switching time and bouncing

The dynamic response of a cantilever-based microswitch has been analyzed employing a one-degree-of-freedom model, placing particular emphasis on the interaction between the cantilever tip and the substrate which has been modeled introducing a general Lennard–Jones force. Five dimensionless key parameters have been identified, the most important being A 1 —the ratio of the electrostatic actuation force versus the elastic restoring force—and Q —the quality factor which is inversely proportional to the damping coefficient of the system. From dynamic analysis three characteristic times have been derived: the time t i for establishing the first tip/substrate contact, the time t f for the final permanent contact and switch closure and the time interval Δ t (= t f − t i ) during which the beam tip bounces several times over the substrate before achieving a full effective contact. It has been shown that the formulae currently available for the switching time, which neglect bouncing and damping, accurately estimate t i , but significantly underestimate the actual switching time which in fact coincides with t f . It has been predicted that as the actuation voltage increases, t i and t f reduce, whereas Δ t and the number of bounces increase favoring mechanical damage as the tip/substrate interface. On the other hand, as the damping coefficient of the system increases, the number of bounces reduces monotonically, whereas t f has a biphasic behavior showing a minimum for an optimal Q . Maps have been presented which can be used in a preliminary design process of the cantilever-based switch.