A Non-Linear Lumped Model for the Electro-Mechanical Coupling in Capacitive MEMS Microphones

Abstract

This work provides an analytical non-linear model for the capacitive transduction in MEMS transducers with perforated counter-electrodes, especially applicable to capacitive MEMS microphones. Starting from an electrostatic description of a perforated unit cell of the transducer, analytical formulations of the variable capacitance and electrostatic forces are derived, accounting for the deflection profile of a clamped circular plate. A lumped implementation into conventional circuit simulations tools is enabled via behavioral modeling based on hardware description languages, such as Verilog-A. Therefore, the analytical model is approximated via Taylor series expansions, allowing for a stable and non-linear behavioral implementation. The resulting model finally enables both a small- and large-signal analysis of capacitive MEMS microphones, precisely accounting for non-linearities in the capacitive transduction. This allows to simulate the harmonic distortion of the microphone's output signal and to account for electrostatic spring-softening in simulations of its bias voltage dependent sensitivity.