An experimental and theoretical investigation of dynamic pull-in in MEMS devices actuated electrostatically

In this work, we investigate dynamic pull-in in MEMS devices actuated with a DC voltage superimposed to an AC harmonic voltage. We focus on the role of the AC frequency and amplitude in triggering instabilities. Dynamic pull-in is treated here in the context of a broader concept in nonlinear dynamics, which is the escape-from-potential-well phenomenon. The escape is defined where, for specific AC frequency and amplitude, the system exhibits the pull-in instability. We investigate dynamic pull-in experimentally in a polysilicon microcantilever beam, a cantilever and clampedclamped microbeams made of gold, and a capacitive accelerometer. It is found experimentally that, despite the differences in their structures, the tested devices exhibit similar escape behavior near their fundamental natural frequency (primary resonance). A series of experiments are conducted using the capacitive accelerometer to study the effect of pressure (damping), excitation amplitude and frequency, resonance type (primary and subharmonic at twice the device's natural frequency), and sweeping type (sweeping the AC amplitude or sweeping the AC frequency) on the escape zones. It is found that, except for the sweeping type, these factors have significant effect on shaping the escape zones. A nonlinear lumped-parameter model is used to capture the dynamics of the capacitive accelerometer. A shooting method is utilized to predict the theoretical zones of inevitable escape, where it is impossible for a resonator to oscillate in a stable state. An attempt has been made to relate the inevitable escape bands to the pull-in bands measured experimentally. We found that both pull-in bands and inevitable escape bands are correlated. However, we concluded that experimental testing is still needed to estimate accurately the instability bounds of each electrostatically actuated resonator.