Model for Gas Damping in Air Gaps of RF MEMS Resonators

Damping in air gaps is studied at RF frequencies and modelled with a viscoelastic wave propagation model, since the traditional squeezed-film damping model is not valid in the MHz regime. The FEM study shows that above a certain frequency the wave propagation in the air gap can be modelled assuming closed damper borders. This closed-border problem is solved analytically from the linearized Navier-Stokes equations in 1D. This results in a compact model for the mechanical impedance that includes the damping, inertial, and spring forces. The model produces the gas resonances in the air gap when the wavelength of the acoustic wave is smaller than the gap dimensions. The model is applicable in cases where the frequency of oscillation in a squeezed-film damper is so high that the gas is trapped in the gap. The model is applied in calculating damping due to air in a RF MEMS disk resonator.