A Simple Displacement Function to Determine the Response of a Micro Capacitive Pressure Sensor

The response of a capacitive pressure sensor is generally represented by a fourth order partial differential equation which is complex to solve and does not possess an exact solution. Several attempts have been made earlier through various techniques such as the Galerkin method, Finite Difference Method etc.... In this paper an attempt has been made to develop a simple approximate analytical approach to determine the response of a micro capacitive pressure sensor whose diaphragm is designed to undergo very small deflections (typically less than 25% of the thickness). The non-uniform gap between the electrodes is mathematically expressed as a combination of the initial gap between the electrodes (in the undeformed state) and a displacement function in (x,y). The proposed displacement function is then utilized in evaluating the capacitance as a function of the applied pressure. The results obtained from the analytical approach are benchmarked against those obtained from COMSOL Multiphysics®, a popular Finite Element Analysis tool in the MEMS industry. It is observed that the results obtained from COMSOL Multiphysics® and those from the analytical approach are in good agreement with a maximum deviation of about 8.66%.