  We propose a framework to model ferroelectric negative capacitance:
electrostatic Micro Electro Mechanical Systems (MEMS) hybrid actuators and
analyze their dynamic (step input) response. Using this framework, we report
the first proposal for reduction in the dynamic pull-in and pull-out voltages
of the hybrid actuators due to the negative capacitance of the ferroelectric.
The proposed model also reveals the effect of ferroelectric thickness on the
dynamic pull-in and pull-out voltages and the effect of ferroelectric damping
on the energy dissipated during actuation. We infer from our analysis that the
hybrid actuators are better than the standalone MEMS actuators in terms of
operating voltage and energy dissipation. Further, we show that one can
trade-off a small part of the reduction in actuation voltage to achieve
identical pull-in times in the hybrid and standalone MEMS actuators, while
still consuming substantially lower energy in the former as compared to the
latter. The circuit compatibility of the proposed hybrid actuator model makes
it suitable for analysis and evaluation of various heterogeneous systems
consisting of hybrid MEMS actuators and other electronic devices.
