A simple method for calculation of the pull-in voltage and touch-point pressure for the small deflection of square diaphragm in MEMS

Abstract

There are a number of MEMS structures that make use of diaphragms. The deformation of the diaphragm for the purpose of actuation and transduction can be brought about by application of voltage and/or pressure or any other mechanical excitation like acceleration, force, etc. The amount of deformation can be measured by changes in the capacitance between the diaphragm and the fixed electrode. The gap between the electrodes can be an air gap or can have an intervening layer of the dielectric on the fixed electrode along with the air gap. The pull-in voltage and touch-point pressure along with the structural and material properties are critical parameters that decide the behavior of the actuator/transducer. This paper presents a simple methodology, which is capable of representing small deflection of diaphragm with pressure, and/or applied voltage. The method proposed is less complex and less time consuming in comparison with FEM tools. Closed form expressions have been derived for pull-in voltage with/without dielectric between the two electrodes and critical distance for pull-in. The closed form expressions for touch-point pressure have also been derived. The results are compared with those obtained by simulation as well as experiment.