Modeling and physical analysis of an out-of-plane capacitive MEMS transducer with dynamically coupled electrodes

Abstract

This paper presents a physics-based system-level compact model of a novel out-of-plane capacitive MEMS transducer for detection of mechanical forces, pressure variations or acceleration. This innovative device, which could be used e.g., as a MEMS microphone for consumer electronics applications—the use case addressed in this work—employs a capacitive read-out scheme based on a combination of plate and comb capacitors. In contrast to conventional plate capacitor transducers both electrodes of this novel device are movable. This feature results in device dynamics analogous to a weakly coupled two-degree-of-freedom oscillator system. An analysis of the governing electromechanical and fluidmechanical coupling effects is presented together with the description of the dynamics of the coupled electrodes. The proposed model, which is based on generalized Kirchoffian networks, can be simulated with the help of standard circuit simulation software. Dynamic measurements performed on two different prototype devices in a low-pressure environment are used to calibrate and validate the model. The resonance frequency shift due to electrostatic spring softening is self-consistently included in the model since the interaction among mechanical, electrical, and fluidic domain is implemented on a physical basis. The presented study also contains an analytical derivation of the dynamics of the device for the small-signal working regime. All in all, the presented analysis provides accurate physical understanding of the device, which can be employed to analyze and improve the transducer characteristics. The energy-coupled and modular modeling approach enables the extension of the model to investigate the performance of the device under the impact of the surrounding atmosphere and the effects of device packaging.