Numerical and experimental validation of out-of-plane resonance closed formulas for MEMS suspended plates with square holes

Abstract

A compact analytical model for out-of-plane resonance evaluation is proposed for large diffuse MEMS vibrating plates with squared holes. A closed form expression was developed from a structural reduced order model with equivalent concentrated mass and stiffness parameters. Results were validated through FEM models and experimental modal analysis. Numerical FEM simulations were performed by 1D, 2D and 3D FEM models; experiments on polysilicon test structures were conducted using an interferometric microscope. Specimens were designed ad hoc to highlight the sensitivity of proposed formulas to main structural dimensional parameters of vibrating plates. Experiments and models helped investigate the sensitivity of the proposed reduced linearized model when exposed to electrostatic non-linear coupling effects and fluidic damping coupling. Both numerical results and experiments are in good agreement with analytical results predicted by closed formulas.