A macromodel for squeeze-film air damping in the free-molecule regime

A three-dimensional Monte Carlo (MC) simulation approach is developed for the accurate prediction of the squeeze-film air damping on microresonators in the free-molecule gas regime. Based on the MC simulations and the analytical traveling-time distribution, a macromodel, which relates air damping directly with device dimensions and operation parameters, is constructed. This model provides an efficient tool for the design of high-performance microresonators. The accuracy of the macromodel is validated through the modeling of the quality factors of several microresonators. It has been found that the relative errors of the quality factors of two resonators, as compared with experimental data, are 3.9% and 5.7%, respectively. The agreements between the macromodel results and MC simulation results, on the other hand, are excellent in all cases considered.