Simulation and Synthesis of MicroElectroMechanical Systems


This thesis presents a MEMS simulation method based on modified nodal analysis (MNA) and a synthesis method for MEMS devices using evolutionary techniques. Modified nodal analysis (MNA) is demonstrated to be successfully applied to MEMS simulation in multi-energy domains. Nodal equations of coupled linear and nonlinear ordinary differential equations in mechanical and electrical domains are formed and solved. Physical models that fit into MNA framework are presented for anchors, force and displacement generators, two dimensional (2D) linear beams, three dimensional (3D) linear beams, 2D electrostatic gaps, 2D comb drives, 2D rigid beams. Algorithms for static (DC), steady state and modal frequency analysis are developed. The modified nodal analysis framework together with analysis routines and physical models are implemented as a simulation tool called SUGAR in Matlab. The accuracy of the program is compared with analytical solutions, experimental data and finite element method simulations. The verification shows that this MNA approach could lead to an accurate, fast, higher level simulation package in multi-energy domains for MEMS. The second part of the thesis incorporates this simulation method into an evolutionary algorithm loop to automatically synthesize MEMS designs. Given a higher-level description of the device's desired behavior, both the topology and sizing of the devices are generated using a Multi-Objective Genetic Algorithm (MOGA). An initial population of candidate designs is generated randomly from a number of available components such as anchors, beams, electrostatic gaps, combs and springs. Each design is checked for geometrical validity and its performance is evaluated by SUGAR. MOGA is then applied to the initial population to iteratively search for functional designs that meet constraints and optimize the performance. Variations of design coding schemes, random design generation, selection, crossover, elitism and immigration are implemented to test their effectiveness in producing superior designs in the MOGA implementation. The obtained results on a 2D spring design, a 2D resonator design and a 2D actuator design demonstrated the feasibility of this approach to MEMS functional structure synthesis.