A simple computationally efficient closed-form model has been developed to determine the pull-in voltage of a cantilever beam actuated by electrostatic force. The approach is based on a linearized uniform approximate model of the nonlinear electrostatic pressure and the load deflection model of a cantilever beam under uniform pressure. The linearized electrostatic pressure includes the electrostatic pressure due to the fringing field capacitances and has been derived from Meijs and Fokkema's highly accurate empirical expression for the capacitance of a VLSI on-chip interconnect. The model has been verified by comparing the results with published experimentally verified 3D finite element analysis results and also with results from similar closed-form models. The new model can evaluate the pull-in voltage for a cantilever beam with a maximum deviation of ±2% from the finite element analysis results for wide beams, and a maximum deviation of ±1% for narrow beams (extreme fringing field).

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A highly accurate mathematical method has been presented for analytical characterization of capacitive micromachined ultrasonic transducers (CMUTs) built with square diaphragms. The method uses a new two-dimensional polynomial function to more accurately predict the deflection curve of a multilayer square diaphragm subject to both mechanical and electrostatic pressure and a new capacitance model that takes into account the contribution of the fringing field capacitances. Both of the models have been experimentally verified by comparing the models predicted values with measurement results and are found to be in excellent agreement with a maximum deviation of less than 2% for experimentally measured capacitance values. 3-D electromechanical finite element analysis (FEA) for a wide range of material properties, geometric specifications, and loading conditions show that the presented method is highly consistent in accuracy over the typical square-diaphragm CMUT design space.

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