Electrothermomechanical and torsion-bending-stretching coupling micromirrors: Numerical and analytical modeling, parametric analysis and experimental characterization method

Abstract

Considering the combined effect of electrothermomechanical coupling and torsion-bending-stretching coupling in the electrostatically driven tilting micromirror, a numerical model is developed to calculate the rotation angle and vertical displacement of the bars-plate structure over the entire operating range, and for the critical state at which an arbitrary small increment of driving voltage will make the plate contact the substrate, an analytical model is developed to judge its type and calculate the critical driving voltage, critical rotation angle and critical vertical displacement. An approximately linear relationship between the rotation angle and the vertical displacement is found and calculated. The positive, negative or non-monotonic correlation of each dimension parameter, temperature variation or bending-induced midplane stretching with each performance parameter is presented, and ways to optimize the mirror's performances by adjusting dimension parameters or by making the mirror have the second type of critical state are proposed. A nondestructive experimental method is designed for fast characterizing the fabricated mirror's performances over its entire operating range and at its critical state, and this method only needs to measure a rotation angle and a vertical displacement both induced by one driving voltage, or two rotation angles induced by two driving voltages, without a need to know the mirror's material property parameters which usually change significantly with microfabrication method and structure size, and without a need to know some dimension parameters.