A modeling and analysis of spring-shaped torsion micromirrors for low-voltage applications

An electrostatic torsion micromirror is designed using the optimized spring-shaped torsion beams and U-shaped groove supporters. The main advantages of this design will be a reduction in the pull-in voltage for low-voltage applications and the function as a switch of the instability mode by adjusting the effective bending stiffness of the torsion beam. In this design, a theoretical model is developed to demonstrate the static characteristics of the electrostatic torsion micromirror. The pull-in effect is investigated specifically to predict the pull-in voltage, pull-in angle, and pull-in displacement. These parameters depend significantly on the electrode size and position, position of the groove, and ratio of the bending and torsion effect of the torsion beam. In addition, the effective torsion and bending stiffness model is provided using the energy method with the objectives to optimize the spring-shaped geometries of the torsion beams and to decrease the pull-in voltage below 2 V. The U-shaped groove supporters are applied in the theoretical model to adjust the effective bending stiffness of the torsion beam and to switch the instability mode of the torsion micromirror. The theoretical analysis is consistent with the numerical simulation using MEMCAD and experimental results measured by an optical projection method.