High-fidelity modeling of MEMS resonators. Part II. Coupled beam-substrate dynamics and validation

A computational multiphysics model of the coupled beam-substrate-electrostatic actuation dynamics of MEMS resonators has been developed for the model-based prediction of Q-factor and design sensitivity studies of the clamped vibrating beam. The substrate and resonator beam are modeled independently and then integrated by enforcing their interface compatibility condition and the force equilibrium to arrive at the multiphysics model. The present model has been validated with several reported single-beam clamped resonators. The validated model indicates that: the anchor loss is primarily engendered through coupling between the resonant modes and the waves propagating through the substrate inner layers; the resonant frequency of the beam decreases up to 5% due to substrate flexibilities interacting with beam at the anchors; and, for a given design the beam mass and its relative compliance with respect to the substrate are key parameters that influence the Q-factor degradation. In addition, the coupled model has also been used to predict the Q-factor of a paired-beam mechanical filter device with high fidelity when compared with the experimentally observed Q-factor.