Development of Nonlinear Electromechanical Coupled Macro Model for Electrostatic MEMS Cantilever Beam

The deployment of MicroElectroMechanical System (MEMS) cantilever in the electronic systems is continuously increasing. These devices are usually interfaced with electronic circuits. It is important to build its macro model for rapid system design and simulation. This paper proposes development of an electromechanical coupling macro model of electrostatically actuated MEMS cantilever for straight and curled beam configurations. It consists of linear electrical components and nonlinear dependent sources, which represent mechanical parameters and electromechanical coupling in the system. In order to model device mechanics, analytical formulations are done and calculations are adapted to macro model. A methodology to derive electromechanical coupling as a function of bias voltage is developed. This electrical model is capable of predicting the device characteristic behaviour before the onset of pull-in instability region and estimates pull-in voltage. Such macro model can be easily implemented in any circuit simulation platform and be used to demonstrate the possible advantage of using this scheme for device and system dynamics optimization. To arrive at equivalence, an analytical formulation for spring constant and pull-in voltage of cantilever based on the partial load distribution and curling is derived. It utilizes the methodology based on nonlinear electrostatic pressure approximated by its linearized uniform counterpart and mechanical force-deflection model. An electrical characterization of fabricated MEMS cantilever is done to obtain the experimental value of pull-in voltage. Simulation Program with Integrated Circuit Emphasis (SPICE) simulations results for the developed model is obtained for actual device dimensions and is in good agreement with analytical and experimental results.