Delayed pull-in transitions in overdamped MEMS devices

Journal article

We consider the dynamics of overdamped MEMS devices undergoing the pull-in instability. Numerous previous experiments and numerical simulations have shown a significant increase in the pull-in time under DC voltages close to the pull-in voltage. Here the transient dynamics slow down as the device passes through a meta-stable or bottleneck phase, but this slowing down is not well understood quantitatively. Using a lumped parallel-plate model, we perform a detailed analysis of the pull-in dynamics in this regime. We show that the bottleneck phenomenon is a type of critical slowing down arising from the pullin transition. This allows us to show that the pull-in time obeys an inverse square-root scaling law as the transition is approached; moreover we determine an analytical expression for this pull-in time. We then compare our prediction to a wide range of pull-in time data reported in the literature, showing that the observed slowing down is well captured by our scaling law, which appears to be generic for overdamped pull-in under DC loads. This realization provides a useful design rule with which to tune dynamic response in applications, including stateof-the-art accelerometers and pressure sensors that use pull-in time as a sensing mechanism. We also propose a method to estimate the pull-in voltage based only on data of the pull-in times.

Authors: Gomez, M; Moulton, D; Vella, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Journal of Micromechanics and Microengineering
• Volume: 28
• Issue: 1
• Pages: 015006
• Publication date: 2017-12-12
• Acceptance date: 2017-11-14
• DOI: 10.1088/1361-6439/aa9a70
• EISSN: 1361-6439
• ISSN: 0960-1317
• Keywords: pull-in transitions; critical slowing down; MEMS