A simple capacitance calculation formula for MEMS capacitive type sensors with square membranes

A simple highly accurate mathematical method has been developed to calculate capacitance change for MEMS capacitive type sensors with square membranes. The method improves the accuracy of existing methods as it takes account of the membrane deflection due to the electrostatic pressure in addition to the external mechanical pressure, considers the fringing field effects, and is also applicable to large deflection cases. The model has been verified by 3-D electromechanical finite element analysis for a wide range of loading conditions. The model predicted values are found to be in excellent agreement with the FEA results with a maximum deviation of 5.08% for the membrane center deflection and 5.76% for capacitance values for different external pressure loading and electrostatic bias voltage.