Multi field modeling of a microelectromechanical speaker system with electrostatic driving principle

Abstract

The need for computer modeling tools capable of precisely simulating multi-field interactions is increasing. The accurate modeling of an electrostatically actuated Micro-Electro-Mechanical-Systems speaker results in a system of coupled partial differential equations (PDEs), describing the interactions between electrostatic, mechanical and acoustic fields. A finite element (FE) method is applied to solve the PDEs efficiently and accurately. In the first part of this paper, we present the driving technology of an electrostatic actuated Micro-Electro-Mechanical-Systems speaker, where the electrostatic mechanical coupling is realized with reduced order electro mechanical transducer elements. The electrostatic attracting force is derived from the capacity to gap relation of our device. In a second investigation, we focus on generation of the generated sound including open domain characteristics and propagation region optimization. The sound pressure level is computed with Kirchhoff Helmholtz integral as well as with FEM by using CFS++. We use the Kirchhoff Helmholtz model to characterize the interactions of multiple speaker cells in arrays and the FE tool for single speaker cell investigations. At the acoustic FE model, the focus is on mesh generation and optimization of the propagation region using non-conforming grids (Mortar FEM) and in addition at the boundary region to model open domain characteristics. We apply a recently developed perfectly matched layer technique, which allows us to truncate the acoustic propagation domain with open domain characteristics. Finally, we present an optimization method taking advantage of stress induced self-raising realized with various merged layers with different intrinsic pre-stress. The buckling back plate concept can be compared to bimetal characteristics.