Numerical Algorithms and their Application to MEMS Electrostatic Actuators

iii Microelectromechanical systems (MEMS) are small mechanical devices of dimensions from a few µm to a few mm fabricated by microelectronics manufacturing techniques. RF MEMS devices, such as microswitches, are microsystems with functions for high-frequency electro-magnetic systems. Within the field of MEMS, simulations are used both as a design tool and for understanding complex device behaviour. Simulations are important, since fabrication and physical evaluation of devices are expensive and time-consuming activities. A commonly used principle to drive MEMS devices is electrostatic actuation. It is based on the electrostatic force between elements with a potential difference. A class of electrostatic actuators consists of a a fixed electrode and a movable cantilever electrode. When an actuation voltage is applied between the electrodes the cantilever moves. In this thesis, a numerical algorithm has been developed for simulating complex electro-static MEMS actuators. The algorithm employs a time-efficient quasi-static non-linear corotational finite element solver, using a direct substitution iteration scheme. A general actuator model has been developed. The model consists of a movable cantilever electrode with non-uniform thickness and multiple material layers between one or two fixed electrodes. The algorithm allows for special features such as rolling mechanical contact (multiple contact points), robust handling of the highly non-linear electrostatic forces, material pre-stress, and contact hysteresis with individual adhesion force for each contact point. Simulation of these phenomena is not directly possible in commercially available simulation software. The simulation algorithm has been used to evaluate two structures: an S-shaped film actuator switch developed at the Royal Institute of Technology (KTH) in Stockholm, Swe-den, and a mechanically bistable switch developed by a joint effort of Nanyang Technologica