Coupled substrate-resonator-electrostatic simulation and validation of high-q MEMS resonator performance

Abstract

Vibration energy transmission from MEMS resonator through anchor to substrate, viz., anchor loss, is examined by utilizing the coupled substrate - resonator electrostatic numerical model. The substrate and resonator beam are modeled independently and then integrated by enforcing their interface compatibility condition and the electrostatic force equilibrium to arrive at the multiphysics model. The present model has been validated with several reported sing-beam resonators. The validated model indicates that: the anchor loss is a frequency dependent mechanism that increase with increasing frequency, and the resulting equivalent damping coefficient due to anchor loss is 0.15 % for 71.8 MHz resonator; the resonant frequency of the beam decreases up to 5 % due to substrate flexibilities interacting with the beam at the anchors.