Modeling and Measurement of a Bistable Beam in a Microelectromechanical System

Design and fabrication of microelectromechanical systems (MEMS) can be costly, time consuming, and necessitating accurate models for their behavior. Current theoretical models of bistable beams in MEMS devices are limited to numerical or small deformation models and current measurement techniques are unable to fully characterize these devices as they only determine thresholds or have resolutions that are too coarse to adequately explore the force-deflection relationship of bistable mechanisms. Two analytical models are developed: a stepped Euler-Bernoulli beam and a large deformation model. To validate these models, a new technique for measuring in-plane mechanical properties of MEMS devices is introduced that measures normal and lateral forces against a probe tip, while electrostatic actuation and a force-feedback loop maintain the desired tip position. This allows true displacement-controlled measurements along two axes and facilitates automated positioning. Measurements validate the large deformation model and show that Euler-Bernoulli beam theory is inadequate for modeling the mechanism's bistable behavior. A parameter study in edge width using the large deformation model accounts for discrepancies between predicted and measured forces. The model's utility is further demonstrated by an optimization study that redesigns the mechanism to be less sensitive to the edge width variation introduced in the manufacturing process.