Motion Measurement Methods for Nonlinear Analysis of Electrostatic MEMS Resonators

In this paper, we compare two measurement techniques to analyze the dynamic response of a MEMS resonator, made of a microcantilever beam, that is electrostatically actuated via a side electrode. The first method is based on a combination of Michelson interferometry, knife-edge analysis, and stroboscopic imaging, and is used to dissect the in-plane and out-of-plane motions of the resonator. The second approach follows the motion-induced current method and is based on a transduction mechanism that converts the movement of the resonator to a current signal. The third harmonic of said current is directly related to the in-plane motion of the resonator. Motion-induced current measurements enable the detection of the nonlinear dynamics associated with the motion of the resonator when actuated with high excitation voltages. The optical and electrical measurements show similar nonlinear features in terms of the location of the cyclic-fold bifurcation in the parameter space and the hysteretic region associated with it. These dynamic features can be exploited for sensing purposes.