A Highly accurate method to calculate capacitance of MEMS sensors with circular membranes

A highly accurate analytical method to calculate capacitance of MEMS capacitive type sensors with circular membranes has been presented. The method determines the center deflection of the membrane by taking account of the electrostatic pressure due to the bias voltage, external pressure, residual stress, and nonlinear spring hardening effect during large deflection. A new deflection shape function uses this center deflection to calculate a highly accurate deflection profile of the membrane which is then used to calculate the capacitance between the deformed membrane and the fixed backplate for any deformed profile of the membrane. The model has been verified by comparing the results with experimental and 3-D electromechanical finite element analysis (FEA) results with excellent agreement. The model predicted values deviate by a maximum of 2.2% for the membrane center deflection and 3.4% for capacitance values for different external pressure loading and electrostatic bias voltage.