Influence of Operating Air Pressure on the Frequency Shift of an Electrostatic MEMS Micromirror: Theoretical Modeling and Experimental Investigation

This work investigates the influence and mechanism of operating air pressure on the frequency shift characteristics of an electrostatically actuated micromirror. The dependence of air damping and air additional inertia moment of the micromirror on air pressure are investigated through fluid theory and computational fluid dynamics (CFD) simulations. The results show that the air damping and air additional inertia moment of the micromirror decrease with the decrease of air pressure. The influence of the damping, additional inertia moment, and air pressure on the frequency response shift is investigated by numerically solving the established dynamic model of the micromirror. The numerical simulation frequency responses reveal that the downward sweep jump frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> of the micromirror linearly decreases with the decrease of damping and linearly increases with the decrease of additional inertia moment. Furthermore, the numerical results also show that the downward sweep jump frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> linearly increases with the decrease of air pressure. The measured data provide good validation for the numerical results. The results demonstrate that the downward sweep jump frequency under different air pressures is primarily influenced by the inertial effect of air, while the air damping mainly affects the amplitude.