An approach to the coupling effect between torsion and bending for electrostatic torsional micromirrors

A general theoretical model using the coupling effect between the torsion and bending is presented in this paper, which characterizes the static properties of the electrostatic torsional micromirror, especially its pull-in effect. A set of normalized equations governing the static actuation properties of the torsional micromirror based on the parallel plate capacitor model is derived to demonstrate the relationships between the parameters of static characteristics, such as torsion angle, vertical displacement, and applied voltage. Thereafter, the pull-in effect is investigated specifically to predict pull-in voltage, pull-in angle, and pull-in displacement, which highly depend on the electrode size and position, and ratio of the bending and torsion effect of the torsion beam. The ratio of the bending and torsion effect plays a key role in the pull-in phenomena. It also determines the instability mode of torsional micromirrors dominated by either the torsion or bending effect. Then, a group of torsional micromirrors is fabricated using three-layer-polysilicon micromachining process and measured using an optical projection method to verify the static actuation relation and pull-in effect respectively. The experimental data are processed and analyzed, and the theoretical analysis is in good agreement with the experimental results.