Experimental analysis of pull-out voltage of electrostatically actuated microcantilever beam based on contact-stiction model

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

“…The proposed graphical approach based on energy landscape gives physical insight into understanding the effect of adhesion. We model the adhesion between the contacting surfaces using the van der Waals force [16]- [18], [43], based on the Lennard-Jones potential and given by…”

“…As a result, there exists an effective gap at contact, g c , between the two contacting surfaces. Assuming σ t and σ s are the standard deviations of the thickness of the top electrode and the height of the stopper respectively, we can define g c = σ 2 t + σ 2 s [18], [44]. Therefore, after pull-in, owing to the surface roughness, the top electrode settles effectively at g o −h s −g c .…”

“…However, for many applications, displacement is a more natural coordinate used to analyze MEMS actuators [13]. Analysis based on displacement is convenient to include effects such as adhesion [16]- [18] and a non-linear spring [19], that are directly described in terms of displacement. We had developed [20] a numerical model to analyze both the statics and dynamics of the hybrid actuator, based on displacement.…”

“…Adhesion plays a major role when the top electrode comes in contact with the bottom surface. We include the effect of adhesion between contacting surfaces, by adding a term corresponding to the van der Waals force [16]- [18] into the Hamiltonian of the system. We show that adhesion reduces the pull-out voltage but does not affect the pull-in voltage.…”

Design and implementation of micro-machined cantilever structures for MEMS-based digital inverter and electron tunneling sensor

“…Static response of the cantilevers under electrostatic actuation mechanism has been analyzed based on the Euler-Bernoulli beam theory. An integro-differential semi-numerical technique to solve the Euler-Bernoulli equation to find the static deflection of micro-cantilevers under electrostatic actuation has been presented [2]. An analytical technique to account for the effects of stiction forces on the static response of the beams has also been developed based on the above formulation [3].…”