Electrostatic MEMS actuators suffer from an instability called pull-in, wherein the movable electrode snaps onto the fixed electrode beyond a certain applied voltage. Thus, the entire allowed range is not utilized for stable operation. We propose pull-in free, low-voltage operation by using a cubic non-linear spring with a ferroelectric negative-capacitance hybrid MEMS actuator. We use a physics-based framework based on the energy landscape to illustrate the stability improvement. This framework uses energy-displacement and voltage-displacement plots for analysis. We predict that the actuator can operate in three distinct modes: (a) monostable, (b) bistable and (c) always-stable, based on the value of the cubic spring constant. We also estimate the threshold values of the cubic spring constant that demarcate the three modes of operation. By proper design of the cubic spring constant, we predict pull-in free, low-voltage operation of the hybrid actuator, as compared to the standalone MEMS actuator. The results obtained are in agreement with the numerical simulations. This work will aid in the design of electrostatic MEMS actuators for low-voltage applications without pull-in instability.

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 displacement of the movable electrode, is used to obtain the Hamiltonian of the hybrid actuator in terms of displacement. We then use graphical energy-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, as 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 force. 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.