Multidegree-of-Freedom State-Space Modeling of Nonlinear Pull-in Dynamics of an Electrostatic MEMS Microphone

Abstract

Capacitive micromachined ultrasound transducers (CMUTs) are most frequently used to generate ultrasound by superimposing the stimulus waveform and a steady bias voltage. This results in the best signal linearity, but limits the maximum displacement to which the diaphragm can be driven. Operating in the collapse-snapback excitation mode involves applying a voltage larger than the electrostatic pull-in threshold, and allows the diaphragm to traverse the entire depth of the air gap. Modeling the dynamics of the pull-in process is complicated by the inherent nonlinearity of the electrostatic transduction, nonlinearity of viscous damping with respect to the diaphragm displacement, and coupling between the electrical, mechanical, and acoustical domains. We have developed a multi-degree-of-freedom numerical model, using lumped elements to discretize the mechanical diaphragm and acoustic components. Simple one-dimensional lumped element models fail to accurately account for the varying contact between diaphragm and backplate, and the change in effective diaphragm area over the course of the cycle. Our discretized model is in excellent agreement with LDV measurements made on a commercially-developed MEMS microphone in air, and shows promise for using collapse-snapback mode as a means of generating impulsive ultrasound signals in air. [2021-0216]