Compact modeling of inertial and rarefaction effects on quality factor of MEMS torsional structures in continuum to molecular flows under low operating frequencies

The applicability of an existing compact model that captures the effect of rarefaction and inertia is studied in this paper. In order to ascertain the accuracy of the model, we take two different configurations of a torsional MEMS structure from the literature which operate under different frequencies and have different air-gap thicknesses. For the structure with large air-gap and low operating frequency, the analytical model based on the equivalent length captures the effect well under the continuum, slip, transition and the molecular regimes. On the other hand, for the structures with high operating frequencies but low air-gap thickness, the analytical model breaks down in the transition regime.