Multiple-domain Coupling Analysis And Multidisciplinary Design Optimization Of MEMS

With the rapid progress in microelectromechanical systems (MEMS) technology, MEMS-specific modeling and simulation environments are increasingly needed to improve performance of MEMS device before costly and time-consuming prototyping. In addition, more and more MEMS fabrication processes are standardized to meet the requirement of commercialization of MEMS products which accelerate the development of modeling and simulation.Generally speaking, MEMS couple multiple physical domains such as mechanical, electrical, fluidic, optical, magnetic and thermal to implement their functions. The inherent coupled property poses difficult challenges for modeling and simulation of MEMS. It is necessary to require an effective method to predict the behavior of MEMS device through researching on these tightly coupling effects. On the other hand, most of MEMS integrate micro-transducers with readout and control circuit on a common board, design and optimization of MEMS require comprehensive consideration for the coupling effects of fabrication process, structure physical parameters, operational environments, and electronics.In the thesis, electrostatically-actuated microbeam and micromachined gyroscope are taken as examples to demonstrate the procedure of multi-domain coupling analysis and system design optimization of MEMS. The main contents in this thesis are described as follows:1) Model order reduction (MOR) techniques are proposed to quickly solve the coupling problems existing in MEMS. Parameterized macromodeling method based on nodal analysis technique, nonlinear macromodeling method based on Churn process, and automatically macromodeling method based on Arnoldi algorithm are detailedly discussed. Their appropriate applications are identified through comparison among these macromodeling methods.2) In the case of non-damping and nonlinear condition, electrostatic-structural coupling analysis is performed for the flexible electrostatic fixed-fixed microbeam using Churn process. When damping and nonlinear conditions are concerned, discretized ordinary differential equations (ODEs) are firstly derived from the original partial differential equations using finite differential method (FDM), and then Arnoldi process based onKrylov subspace is applied to generate reduced order model (ROM). Electrical-structural-fluidic multi-domain coupling analysis is implemented using the generated ROM. The results prove that macromodeling methods can quickly solve the coupling problem with little compromising accuracy.3) The multiple domains can be decomposed into elastic field, electrostatic field and air-damping field. The lumped parameter macromodeling method for every domain, therefore, is utilized to analyze coupling effects in micromachined gyroscope based on physically numerical simulation. The obtained lumped models can be described using hardware description language (HDL) and then inserted into system level model to do transient analysis of micromachined gyroscope.4) The electrostatic numerical analysis is performed to capture fringing effect in micro structural capacitance so that the relationship of capacitance with displacement can be accurately extracted. The principle of thermal-fluidic analogy is used to extract lumped parameters (damping coefficient and squeeze stiffness) of squeeze film damping in perforation plate structure. Modal analysis technology is used to extract the effective stiffness and mass in driving and sensing modes of gyroscope.5) Multidisciplinary design optimization idea is introduced for the overall preliminary design of micromachined gyroscope. To optimize the whole performance of microgyroscope such as sensitivity a multidisciplinary design model is proposed with consideration of the coupling effects of fabrication process, structure physical parameters, environmental quality factor, and electronics.6) Genetic algorithm is applied to optimize the proposed MDO problem and obtain the global trade-off optimum. The prototype of microgyroscope is fabricated with optimal parameters, and test results for the gyroscope show that MDO methodology is a promising approach to effectively explore system trade-off and design space for complex MEMS.