Behavioral Modeling in Viscous Damping in MEMS

MicroElectroMechanicalSystemMEMS are often characterized by structures that are a few microns in size, separated by micron-sized gaps. At these sizes and gaps, viscous air damping dominates other energy dissipation mechanisms at atmospheric pressure, thus, affecting the dynamic behavior of the devices. Also, the number of such gaps can be very large in a MEMS device. Hence, fast and accurate behavioral simulation of the dynamics of MEMS systems necessitates accurate, low-order damping models. Further, to be useful in the design flow, these models need to be parameterized, so that they can be used to model damping for a wide range of structure size, gap, frequency and amplitude of motion. Viscous damping due to the fluid surrounding the moving structures can be of two types squeeze film damping and lateral damping. In squeeze film damping, there are two parallel structures as shown in Fig. 1.1. They are in relative motion perpendicular to the plane, thus squeezing the air film between the structures. The air counters the motion by exerting an opposing force. Fig. 1.2 shows the case of lateral damping. Here the motion of the plate is parallel to the plane of the structure. The resulting fluid flow causes energy dissipation and exerts an opposing force which is a function of the velocity of the moving plate, the dimensions of the plate, its distance from other parallel structures, and the viscosity of the fluid. This report presents lumped parameter models for squeeze film and lateral damping. The accuracy of these models down to MEMS scaled structures, and their parameterized nature makes them useful for design and simulation of MEMS devices. With the edge-effect contribution to the damping force becoming significant in micron-scaled structures, emphasis is laid on including these effects.