Tracking of bifurcations and hysteresis in electrostatically actuated resonators by motion-induced current

In this work, we present an experimental technique to detect the onset of bifurcation and measure the extent of hysteresis in electrostatic MEMS. The device-under-test comprises a microcantilever beam actuated via a side electrode. The beam vibrations result in varying the resonator's capacitance, therefore inducing a current that can be measured and used for characterization and performance analysis. The motion-induced current is measured, and its harmonics are extracted using a lock-in amplifier. Locking on the third harmonic of the induced current enables us to bypass parasitic capacitance and extract a signal directly related to the resonator motions. We show that this signal can be used to investigate the nonlinear dynamic behavior of MEMS resonators undergoing large motions. Specifically, our experiments demonstrate our technique's ability to detect various bifurcations, to track the onset of hysteresis, and to measure the hysteresis bandwidth. We also use our technique to analyze the quantitative relationships between the actuation voltage, the location of the bifurcation point, and the hysteretic bandwidth. Finally, we show that our technique can be used to generate the calibration curves for inertial MEMS sensors.