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 Delta 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 ti, but significantly underestimate the actual switching time which in fact coincides with tf. It has been predicted that as the actuation voltage increases, ti and tf reduce, whereas Delta 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.