Squeeze film damping in the free molecular flow regime with full thermal accommodation

We introduce an analytical model for the gas damping of a MEMS resonator in the regime of free molecular flow. Driving force in this model is the change in density in the gap volume due to the amplitude of the oscillating microstructure, which is counteracted by the random walk diffusion in the gap that tries to restore the density to its equilibrium value. This results in a complex-valued force that contributes to both the damping as well as the spring constant, depending on the value of ωτωτ with ωω the resonance frequency and ττ the random walk diffusion time. The diffusion time is calculated analytically using the model for random walk Brownian motion and numerically by a Monte Carlo simulation of the ballistic trajectories of the molecules following Maxwell–Boltzmann statistics and full thermal accommodation in gas-surface collisions. The model is verified by comparison to accurate data on the pressure dependency of the damping of three MEMS resonators, showing agreement within 10%.