Air damping in laterally oscillating microresonators: a numerical and experimental study

In this paper, we investigate computing air damping in a comb-drive resonator by numerically solving the three-dimensional (3-D) Stokes equation for the entire resonator using the FastStokes Solver. In addition, we used a recently developed computer microvision system to directly measure resonator frequency response. By comparing the measured results to those generated by one dimensional analytic models and by numerical solution of the 3-D Stokes´ equation, we demonstrate that numerically solving the Stokes´ equation is fast and also generates a model that matches quality the factor to within 10%. We also show that results based on one-dimensional (1-D) models mispredict quality factor by more than a factor of two. In addition, the detailed drag force distribution generated by the FastStokes solver is used to identify sources of errors in the 1-D models.