Analytical modelling for reliable z-axis FM MEMS accelerometer

Frequency-modulated (FM) accelerometers have recently emerged as promising candidates for high-performance inertial sensing due to their inherent robustness against noise and process variations. While in-plane FM accelerometers have achieved state-of-the-art performance levels, z-axis implementations remain comparatively less mature and still face significant reliability challenges, particularly related to stiction phenomena. In this work, we present an analytical model describing the dynamic response of the newly patented z-axis FM accelerometer fabricated using a dual polysilicon layer commercial process, with the objective of providing a deeper understanding of its operating principles and supporting future redesign efforts. The proposed model enables the decomposition of the device response into physically interpretable contributions, thereby establishing a systematic framework for both the optimization of the current architecture and the development of future FM accelerometer designs. Although local and three-dimensional effects are not captured, the model shows satisfactory agreement with Finite Element simulations performed in COMSOL Multiphysics®. To validate the proposed approach as a viable pathway towards next-generation high-performance z-axis FM accelerometers, the methodology is applied to redesign the device with enhanced robustness against stiction without compromising sensitivity or measurement range. Numerical results demonstrate substantial performance improvements, including a 212% increase in elastic restoring force against adhesion, an 83% extension of the full-scale range, and a 16.8% enhancement in sensitivity.