Squeeze-film damping in the free molecular regime: model validation and measurement on a MEMS

Squeeze-film damping (SFD) is important in MEMS oscillators because it determines the quality factor of the oscillators. Published models for predicting SFD gave widely different results in the free-molecule regime, where the distance traveled by gas molecules between collisions in free space is much larger than the thickness of the squeezed gas film. The work presented here provides new experimental data for validating SFD models in that regime. The case studied here is where a rigid plate oscillates vertically while staying parallel to the substrate. The test device was an almost rectangular microplate supported by beam springs. The structure was excited by shaking the base. The velocities of numerous points on the plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. An experimental modal analysis curve-fit the multiple frequency response functions to give the damping ratios. The test structure was contained in a vacuum chamber with air pressures controlled to provide a five-order-of-magnitude range of Knudsen numbers. The damping ratios from the measurements are compared with predictions from various published models. The measured damping ratios are close to predictions from models that are based on the Reynolds equation and take into account the inertia of the gas.