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We propose an energy-based framework to analyze the statics and dynamics of a ferroelectric negative capacitance-hybrid microelectromechanical system (MEMS) actuator. A mapping function that relates the charge on the ferroelectric to the displacement of the movable electrode is used to obtain the Hamiltonian of the hybrid actuator in terms of displacement. We then use graphical energy&#x2013;displacement and phase portrait plots to analyze static pull-in, dynamic pull-in, and pull-out phenomena of the hybrid actuator. Using these, we illustrate the low-voltage operation of the hybrid actuator to static and step inputs, when compared to the standalone MEMS actuator. The results obtained are in agreement with the analytical predictions and numerical simulations. The proposed framework enables straightforward inclusion of adhesion between the contacting surfaces, modeled using van der Waals forces. We show that the pull-in voltage is not affected, while the pull-out voltage is reduced due to adhesion. The proposed framework provides a physics-based tool to design and analyze negative capacitance-based low-voltage MEMS actuators.

Analysis of Ferroelectric Negative Capacitance-Hybrid MEMS Actuator Using Energy–Displacement Landscape