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In the last few years, micro-electro-mechanical systems devices vibrating at high frequencies (RF MEMS) (ranging from 1 MHz to 60 GHz) have increasingly been used in various industrial fields. Low-frequency MEMS devices are normally operated at very low pressure in order to minimize the damping due to the internal friction of the gas (viscous damping). This need can be overcome when MEMS devices vibrate at relatively high frequencies, since gas compressibility and inertial forces lead then to another damping mechanism which is related to the propagation of sound waves generated by high-frequency oscillating micro-structures. Very recently, it has been proved in Desvillettes and Lorenzani (2012) for a single-component gas that sound waves propagating between the micro-device walls induce a resonant/antiresonant response of the system. The occurrence of an antiresonance is particularly important since if the device is operated close to the corresponding frequency, the damping due to the gas is considerably reduced. Since gas resonances take place for each value of the rarefaction parameter (inverse Knudsen number), the RF MEMS devices can perform well also at atmospheric pressure, greatly reducing the need for (and cost associated with) vacuum packaging. In the current investigation, we extend the previous analysis carried out for a single species gas (Desvillettes and Lorenzani, 2012) to a gas mixture, by using the unsteady kinetic equation based on the linearized version of the relaxation model of BGK-type presented in Groppi and Spiga (2004). This BGK approximation has already been used as a consistent tool to investigate other physical problems, such as condensation and sublimation in gas mixtures (see Kosuge, Mizuno and Aoki, 2007, Kosuge, Aoki, Inoue, Goldstein and Varghese, 2012). The evaluation of damping forces exerted by different gases assumes a basic relevance in all MEMS fabrication processes. In fact, during the wafer bonding process a gas mixture of noble gases (like Ar, Kr, or Ne) and getterable gases (like N2, O2, or CO2) is usually backfilled into the MEMS sensor package to set its operating pressure, which should exactly match the damping requirements of the micro-device design (“backfilling process”).

DAMPING FORCES EXERTED BY RAREFIED GAS MIXTURES IN MICRO-ELECTRO-MECHANICAL SYSTEM DEVICES VIBRATING AT HIGH FREQUENCIES