A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.