Accurate Determination of the Pull-in Voltage for MEMS Capacitive Microphone with Clamped Square Diaphragm

Accurate determination of the pull-in, or the collapse voltage is critical in the design process. In this paper an analytical method is presented that provides a more accurate determination of the pull-in voltage for MEMS capacitive devices with clamped square diaphragm. The method incorporates both the linearized modle of the electrostatic force and the nonlinear deflection model of a clamped square diaphragm. The capacitor structure has been designed using a low stress doped poly silicon diaphragm with a proposed thickness of 0.8 μm and an area of 2.4 mm2, an air gap of 3.0 μm, and a 1.0 μm thick back plate. The value of pull-in voltage calculated using equation is about 6.85V and the finite element analysis (FEA) results show that the pull-in occurs at 6.75V. The resulting pull-in voltage and deflection profile of the diaphragm are in close agreement with finite element analysis results.