Coupling of hierarchical fluid models with electrostatic and mechanical models for the dynamic analysis of MEMS

The dynamical behavior of MEMS (micro-electro-mechanical systems) is often strongly affected by viscous fluid/air damping effects from the surrounding. These fluid/air damping effects have to be carefully taken into account during the design and optimization process, in order to get a realistic and reliable description of the device operation. In this paper, two hierarchical fluid models (the 2D compressible Reynold's squeeze film equation and the 2D compressible Navier-Stokes equations) are coupled with a 2D electro-mechanical solver for the dynamic analysis of MEMS to simulate and understand the effect of fluid damping on microstructures. The different physical domains (electrical, mechanical and fluidic) are coupled together using a Newton method for faster convergence. A Lagrangian description of all the physical domains makes it possible to compute the inter-domain coupling terms in the Jacobian matrix of the Newton method exactly. Several MEMS devices (a micromirror, a piggyback actuator, a lateral comb drive and a cantilever beam in air) have been simulated using the coupled electro-mechanical-fluidic solver and numerical results on the resonant frequency and the quality factor are compared with experimental data. The two hierarchical fluid models can be used judiciously (based on speed and accuracy) along with the electro-mechanical solver, depending on the type of MEMS device under consideration, thereby making the dynamic analysis of MEMS devices more efficient.