Microelectromechanical Systems Cantilever Resonators: Pressure-Dependent Gas Film Damping

Abstract

Under near-vacuum conditions, the fluid frictional dissipation or approximately the inverse of the quality factor of a microcantilever once the intrinsic dissipation can be neglected is proportional to the low pressure. We shall investigate the dynamic behavior of micro-electromechanical systems (MEMS) devices via the calculation of the quality factor or frictional damping forces resulting from surrounding gases. Here, we illustrated some specific examples relevant to the computation of the quality factor or dynamical friction for an oscillating microcantilever in air via measurements of the paper of Okada et al. (Okada, H., Itoh, T., and Suga, T., 2008, Wafer Level Sealing Characterization Method Using Si Micro Cantilevers, Sens. Actuators A, 147(2), pp. 359–364) considering the quality factors of the CM (a label for a microcantilever: 500 × 90 × 5 μm3 Si microcantilever (the measured resonance frequency: 23.7 kHz) and the paper of Kara et al. (Kara, V., Yakhot, V., and Ekinci, K. L., 2017, Generalized Knudsen Number for Unsteady Fluid Flow, Phys. Rev. Lett., 118(7), p. 074505) in rarefied gases regime. We present the corrected quality factor or dynamical friction over the whole range of the Knudsen number considering the CM part by Okada et al. Our new plot considering the quality factor which is proportional to the inverse of the dissipative friction parameter per unit length, pressure as well as the Knudsen number over the whole range should be useful to researchers in this field.