Viscous air damping in laterally driven microresonators

A systematic experimental study of viscous air damping in laterally moving planar microstructures is reported. Previous studies indicated that Couette and Stokes flow models underestimate microstructural damping. To investigate this discrepancy, a series of lateral resonant microstructures with different damping plates and combs was fabricated by polysilicon surface micromachining. The resonant frequencies and quality factors of the structures were measured electrically. By analyzing these data, the damping effects due to different geometries were elucidated and compared to theory. The results indicated that if edge and finite-size effects are included in the model, reasonably accurate predictions of the quality factors can be obtained even for small geometries and comb drives. An empirical formula that predicts the quality factor for a range of plate sizes and comb designs was derived. The damping effects as functions of structural thickness and structure-to-substrate separation are also reported.