Energy transfer model for squeeze-film air damping in low vacuum

Abstract

High quality factors are essential for vibratory microsensors. Therefore, the vibrating structure of the sensors is often encapsulated in a housing where the air is evacuated for reduced air damping. However, the vacuum is usually low and the quality factor is still mainly determined by the energy losses to the surrounding air molecules. Air damping in low vacuum is usually estimated using the free molecular model proposed by Christian (Christian R 1966 Vacuum 16 175–8). The major drawback of the model is that the effect of the nearby objects (e.g. the electrodes for electrostatic driving) and the dimensions of the plate cannot be considered. Therefore, the damping effect is often significantly underestimated for real structures.This paper proposes a new model for air damping of microstructures in low vacuum. In this model, the damping effect is calculated by using an energy transfer mechanism instead of the momentum transfer mechanism in Christian's model. For an isolated oscillating plate, the calculated quality factor by the model is the same as that by Christian's model. However, for an oscillating plate with a neighboring object, the damping effect by the new model is related to the dimensions of the vibrating plate and the gap between the plate and the nearby object. The quality factors calculated agree with experimental data better than with Christian's model by about an order of magnitude.