Micro resonators have been extensively applied in MEMS industry over the past recent three decades. However, their resolution is significantly affected by the energy dissipation which therefore attracts many researchers to study. The air damping squeezed between two parallel-plate beams/plates is dominant in the free-molecule regime among all energy dissipation mechanisms and measured by one dimensionless parameter, quality factor. The literature reviews show that both the existing classes of models, continuum models and molecule models, fail to predict quality factor within 50% error with experimental measurements due to some unreasonable assumptions included in these models. In this study, a 3D Monte Carlo (MC) simulation approach, which tracks every individual gas molecule’s motion a...[ Read more ]

Micro resonators have been extensively applied in MEMS industry over the past recent three decades. However, their resolution is significantly affected by the energy dissipation which therefore attracts many researchers to study. The air damping squeezed between two parallel-plate beams/plates is dominant in the free-molecule regime among all energy dissipation mechanisms and measured by one dimensionless parameter, quality factor. The literature reviews show that both the existing classes of models, continuum models and molecule models, fail to predict quality factor within 50% error with experimental measurements due to some unreasonable assumptions included in these models. In this study, a 3D Monte Carlo (MC) simulation approach, which tracks every individual gas molecule’s motion and its interaction with the resonator, is developed based on molecular kinetic theory. Comparing with some experimental measurements, the MC approach is by far the most accurate modeling approach for the modeling of squeeze-film damping in the free-molecule regime because it employs the fewest assumptions.

Based on MC simulation and analytical derivation, a macro model for air damping with rigid beam resonator and pure specular gas-surface reflection is proposed, whose accuracy is verified to be less than 1% error to MC simulations; furthermore, a compact approximate model is derived from the macro model based on small oscillation amplitude and frequency assumptions.

Gas-surface interaction is very important for gas transfer study in the free-molecule regime. One phenomenological and yet practically useful model for gas-wall interaction is the Maxwell model which includes two ideal gas-surface collisions (specular and diffuse reflection). The fraction of these reflections is characterized by accommodation coefficients. In this study, the accommodation coefficients effect on air damping is studied by MC simulation. It is found that the quality factor is increased with the increasing accommodation coefficient; and accommodation coefficients effect on quality factor when resonator operating at high oscillation frequency is more than that at low oscillation frequency. Based on qualitative analysis, it is found that the difference in the quality factor between specular and diffuse reflection is largely caused by the different traveling time in two reflections.

Due to different oscillation structure, some resonators oscillate with rigid beam, while others oscillate at their deformed shapes. The effect of oscillation mode on air damping is studied by MC simulation. It is found that quality factors of flexible beam with the 1st and 2^nd oscillation mode are both higher than that of rigid beam at the same frequency. The quantitative analysis shows that unlike free-space damping which is caused by the resonators oscillating in an unbounded space, squeeze film damping is very sensitive to the mode shape. This implies that some of the existing modeling approaches based on rigid-resonator assumption may not be accurate when applied to model resonators oscillating at their deformed shape.