Theoretical and Numerical Investigation of Normalized Sensitivity in MEMS Capacitive Pressure Sensors Based on Dimensionless Large-Deflection Governing Equations

MEMS capacitive pressure sensors are one of the major classes of pressure sensors. However, in the non-contact operating mode, their sensitivity often varies nonlinearly with the applied pressure, which increases the difficulty and workload of sensitivity evaluation at multiple pressure points during the design stage. In this study, a normalized sensitivity analysis framework for MEMS capacitive pressure sensors is established based on the large-deflection governing equations. Within this framework, the nonlinear relationship between normalized sensitivity and normalized pressure is characterized by five dimensionless parameters. The results show that, when these dimensionless parameters are identical, sensors with different combinations of structural and material parameters collapse onto nearly identical normalized sensitivity-pressure characteristic curves, with an average relative deviation not exceeding 0.05% in the verification cases. In addition, the effects of each dimensionless parameter on the nonlinear behavior of the characteristic curves are further analyzed. The proposed framework provides a unified and systematic analytical basis for sensitivity comparison, performance evaluation, and structural optimization of MEMS capacitive pressure sensors.