Fluidic damping in micro- and nano-scale mechanical resonators in the molecular flow regime: A momentum transfer based analytical approach

We derived an easy-to-use analytical model in order to predict the fluidic damping forces acting on mechanical resonators in the free molecular flow regime. The model is based on fundamental physical relations, which basically take the momentum transfer between the air molecules and the oscillating mechanical structure into account. The obtained analytical relation for the pressure-dependent damping force is applied to calculate the Q-factor of different mechanical resonators with nanometer-sized gaps underneath the movable structure. The results are compared with data extracted from pressure-dependent Laser-Doppler vibrometric measurements.