Modeling and modification of the parallel plate variable MEMS capacitors considering deformation issue

For electrostatically actuated parallel plate variable capacitors in conventional theory, pull-in occurs when the deflection of the movable plate is one-third of the original air gap. However, the electrostatic force is nonlinear, only the center of the movable plate nearly fully reached their maximum displacement when pull in occurs. In this paper, formulas for calculating the capacitance of two plates with an angle are presented. We model the deformation of the movable plate and analyze the mechanical behavior of the capacitors. We fabricated the parallel plate variable MEMS capacitors and used WYKO NT1100 optical surface profiler to measure the displacement related with deformation. The results show that the theoretical deviations of the capacitance and pull-in voltage in conventional theory and in this work are more than 2.6% and 1.3%. The model presented in this paper can be used for the design, analysis and optimization of electrostatically actuated parallel plate variable MEMS capacitors.