Equivalent Circuit Modeling of Air-Coupled Laterally Actuated Electrostatic Bulk-Mode MEMS

In this paper, a linear lumped-element equivalent circuit model (ECM) for ultrasonic laterally transduced electrostatic bulk-mode air-coupled resonant micro-electro-mechanical systems (MEMS) is described. A single-crystal silicon (SCS) square plate with T-shaped tethers is considered as the geometry of interest with a one-sided electrostatic actuation. This type of sensor can be used for sensitive mass sensing of airborne particles and possesses a large active surface with in-plane vibration modes in the ultrasonic frequency range. Firstly, the eigensolutions and eigenvectors of the problem are obtained using analytical equations and compared with finite-element modeling (FEM) solutions. Secondly, using modal analysis, the number of degrees of freedom is reduced and individual solutions are provided for each vibration mode, leading to various effective masses, stiffnesses and dampings. The first order Taylor expansion of both the electrical current equation and the electrostatic force applied on the resonator allows one to obtain expressions for the additional stiffness and the electro-mechanical transformation coefficient linked to the membrane actuation. Based on theses results, single-input single output (SISO) equivalent circuits are established using electro-mechanical and Butterworth-Van Dyke (BVD) approaches. Electrical admittance simulations resulting from different in-plane vibration modes are proven to be in excellent agreement with FEM simulations. Finally, a numerical mass sensing application is described to evaluate the relevance of both the model and the resonator design to act as a microbalance. The proposed model can be used to design, predict, analyze and optimize the behavior of highly sensitive air-coupled ultrasonic bulk-mode SCS MEMS for various physical applications.