Abstract

The nonlinear nature of electrostatic fields in micromachined structures, such as, cantilevers, bridges or plates, makes it difficult to achieve desired deflection shapes. The objective of this thesis is to develop an efficient analytical approach to predict the static deflection and dynamic behavior of microstructures subjected to electrostatic fields of multiple electrostatic actuators so that the microdevices can be effectively optimized and controlled in real time operation. The non-classical boundary conditions which result from various microfabrication processes are modeled with artificial springs. A classical energy method using boundary characteristic orthogonal polynomials was applied to formulate the equation of motion of the microsystems. Based on this method, influence functions were built and Least Squares Fitting method was used to optimize the applied voltage for each of electrostatic actuators so as to generate desired static deflections. The proposed method is simple and can be easily extended to complicated configurations which are suitable for adaptive optics applications. Reduced Order Modeling (ROM) method in ANSYS was used to confirm the results obtained using the proposed method. Static and dynamic behaviors were predicted with finite element analysis (FEA) using ROM method. This study found that the static and dynamic behaviors predicted from the proposed method were highly consistent with those calculated from FEA in the region not close to pull-in condition. Softening effect of the electrostatic field, in terms of electrostatic stiffness, is demonstrated in the dynamic simulation results. However, the proposed method is simpler and more efficient than FEA and can be conveniently used for any structures with non-classical boundary conditions. These features make the proposed method useful to effectively control and optimize the shape of a microstructure under multiple electrostatic actuators. The proposed modeling method was further verified and validated with the fabricated devices using SOI (silicon on insulator) based Micragem technology. The devices fabricated include different designs of microbridges and microplates with multiple electrodes and support boundary conditions. The out of plane deflections were measured by interference fringe patterns localized near the test surface using a Mirau interferometry method. After the boundary conditions were characterized, the predicted deflections were presented and compared with the experimental results that were post processed by Fringe Processor(TM) using Fourier transform method. It is clearly demonstrated that Rayleigh Ritz method is simple and can predict the behavior of microdevices with multiple electrostatic actuators considering both non-classical boundary conditions and electromechanical coupling effect. Both the theoretical and experimental methods proposed in this thesis are very simple and easily implementable