A Macro Model of Squeeze-Film Air Damping in the Free-Molecule Regime

Abstract

A three-dimensional Monte Carlo ͑MC͒ 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.

On the modified Reynolds equation model for the prediction of squeeze-film gas damping in a low vacuum

“…For this reason, extensive research efforts have been devoted to the development of modeling approaches and tools for the accurate prediction of squeeze-film damping. Some relevant work can be found in (Andrews et al 1993;Pan et al 1998;Hutcherson and Ye 2004;Gallis and Torczynski 2004;Nayfeh and Younis 2004;Veijola et al 1995Veijola et al , 2005Bao and Yang 2007;Pandey and Pratap 2008;Sujilen et al 2009;Hong and Ye 2010;Leung et al 2010;Bidkar et al 2009;Guo and Alexeenko 2009;Veijola 2004;Lee et al 2009) and references cited in a review article by Bao and Yang (2007). Depending on the ambient pressure level and the characteristic length of the resonators, gas between the resonant structure and the fixed substrate could be in a rarefied flow regime and therefore be governed by fundamentally different physics.…”

“…Compared with continuum methods, non-continuum methods, although more accurate, are computationally intensive and may not be practical to be used for the design of micro-resonators. One way to circumvent this difficulty is to develop efficient compact models based on non-continuum simulations (Guo and Alexeenko 2009;Hong and Ye 2010).…”

Effect of oscillation mode on the free-molecule squeeze-film air damping

“…Even when the device is packaged inside a vacuum enclosure, air damping can still be a significant factor when ambient pressure is as low as 1 torr [1]. For this reason, the study of air damping in the free-molecule gas regime has attracted many researchers' attention and numerous papers have been published [2][3][4][5][6][7][8][9][10][11].…”

“…Unfortunately, an accurate viscosity model without empirically adjusted parameters is yet to come [9]. Approaches based on individual molecular transport have the advantage of being accurate and theoretically sound [10,11]. However, all the existing models/studies based on the molecular approaches assume a rigid resonator motion.…”