Squeeze-film damping of microbeam and microplate resonators in the free molecular regime

Correct modeling of squeeze-film damping (SFD) is an important consideration in the design of high-Q microresonators. In 2002, using the molecular dynamics (MD) approach, Bao et al. developed an analytical MD model for the evaluation of the SFD of a parallel-plate device in the free molecular regime. Their model was based on the energy exchange between the oscillating plate and gas molecules. Bao’s model is now widely used in microsystem design. However, Bao’s model cannot reduce to the air damping model in free space and is unsuitable for flexible microbeams. This paper first presents a more accurate analytical model for the evaluation of the SFD of the parallel plate. Then the present analytical model is extended to model the SFD of flexible microbeams with deformed shapes. This paper is based on the momentum transfer between the vibration plate and gas molecules. Results: The analytical results of the present model have shown a good agreement with the available experimental results. The limitations in the previous model are overcome.