New Formulation for Finite Element Modeling Electrostatically DrivenMicroelectromechanical Systems

The increased complexity and precision requirements of microelectromechanical systems(MEMS) have brought about the need to develop more reliable and accurate MEMS simulation tools. To better capture the physical behavior encountered, several finite elementanalysis techniques for modeling electrostatic and structural coupling in MEMS devices havebeen developed in this project. Using the principle of virtual work and an approximationfor capacitance, a new 2-D lumped transducer element for the static analysis of MEMS hasbeen developed. This new transducer element is compatible to 2-D structural and beamelements. A novel strongly coupled 3-D transducer formulation has also been developed tomodel MEMS devices with dominant fringing electrostatic fields. The transducer is compatible with both structural and electrostatic solid elements, which allows for modeling complexdevices. Through innovative internal morphing capabilities and exact element integrationthe 3-D transducer element is one of the most powerful coupled field FE analysis tools available. To verify the accuracy and effectiveness of both the 2-D and 3-D transducer elements a series of benchmark analyses were conducted. More specifically, the numerically predicted results for the misalignment of lateral combdrive fingers were compared to available analytical and modeling techniques. Electrostatic uncoupled 2-D and 3-D finite element models werealso used to perform energy computations during misalignment. Finally, a stability analysisof misaligned combdrive was performed using a coupled 2-D finite element approach. Theanalytical and numerical results were compared and found to vary due to fringing fields