A Semi-Analytical and Computationally Efficient Method to Calculate the Touch-Point Pressure and Pull-In Voltage of a MEMS Pressure Sensor With a Circular Diaphragm

Micro-Electromechanical Systems (MEMS) based capacitive pressure transducers have a pivotal role in transducer devices for real-world applications. Thus, the efficient analysis for modelling these transducers is increasingly becoming important. These transducers use diaphragms of various geometries, however for the same active area, circular diaphragms are more sensitive as compared to square diaphragms. Pull-in voltage and touch-point pressure are two parameters which determine the performance of a micro- electromechanical systems device. In this work a complete analysis is presented for evaluating these parameters along with the mechanical and capacitive sensitivity for a circular diaphragm based capacitive pressure transducer. The effect of thickness and radius of the diaphragm has been illustrated, as they form the essential design parameters for fabricating the micro-electromechanical systems devices. Literature review suggests that relatively less work has been reported for this analysis and more complicated and computationally complex methods have been used. The semi-analytical approach presented in this research is less complex and computationally efficient, in comparison to finite element method (FEM). Critical differentiator of this formulation is related to its applicability for analysing sensor parameters with or without considering the effect of electrostatic pressure on diaphragm deflection. Furthermore, this analysis eliminates the need for determining spring constant k which is used in lumped element methods. MATLAB has been used to compute and simulate the results. The mathematical model developed is verified with a standard Finite Element Analysis (FEM) using COMSOL v5.5.