New formulation for finite element modeling electrostatically driven microelectromechanical 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 element analysis techniques for modeling electrostatic and structural coupling in MEMS devices have been developed in this project. Using the principle of virtual work and an approximation for capacitance, a new 2-D lumped transducer element for the static analysis of MEMS has been developed. This new transducer element is compatible to 2-D structural and beam elements. A novel strongly coupled 3-D transducer formulation has also been developed to model MEMS devices with dominant fringing electrostatic fields. The transducer is compatible with both structural and electrostatic solid elements, which allows for modeling complex devices. Through innovative internal morphing capabilities and exact element integration the 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 were also used to perform energy computations during misalignment. Finally, a stability analysis of misaligned combdrive was performed using a coupled 2-D finite element approach. The analytical and numerical results were compared and found to vary due to fringing fields.