A nonlinear lumped parameter model for designing a capacitive MEMS microphone

Abstract

The MEMS microphone, which is widely used for mobile devices, includes electro-mechanical energy conversion as well as acousto-mechanical conversion through the structures such as the back plate with many holes and an extremely flexible membrane with nonlinear characteristics. Hence, it is a time-consuming job to build an appropriate finite element model to predict the dynamic behaviors of the microphone. The equivalent circuit models are frequently used to check the linear behaviors of the MEMS microphone. However, it is sometimes inadequate to predict the nonlinear behaviors due to the nonlinear deformation of the sensing membrane, which usually determine the acoustic overload point. In this study, a nonlinear four-degree-of-freedom model is developed to design the MEMS microphone. Instead of the conventional equivalent circuit model, a model based on mechanical analysis is constructed and the state equations for the model is derived in the form of a set of ordinary differential equations. The responses of the model can be easily predicted in the time and frequency domain both by solving the equations numerically. With the time domain analysis used, the sensitivity can be easily shown as a function of frequency even including the nonlinear dynamic behaviors. [Work supported by DB Kim Jun-ki Cultural Foundation.]