Device-oriented Behavior Of Mems Macro Modeling Approach

Due to the nonlinear coupled energy domain behavior of MEMS (Micro Electro Mechanical System) devices, the development of MEMS CAD tools becomes a more challenging task. The coupled relevant field quantities (mechanical, thermal, electric, magnetic, optical, chemical, etc.) are consistently described by a set of time-dependent partial differential equations, direct simulation based on fully meshed structures involves thousands of degrees of freedom. In order to perform efficient prediction on system level, it is essential to build accurate macro models for MEMS devices on device level.In the thesis, three methods of semi-analytic macro modeling compatible with different terms are studied and realized to solve the questions of typical MEMS devices such as the torsion micro mirror, fixed-fixed micro beam, capacitive pressure sensor, etc. The main contents in this thesis are described as follows:1) Based on a modal representation of coupled domains, the behavior of a coupled system can be assembled in Lagrange equation. In the mode superposition method, the thousands of original system freedoms are reduced to several generalized coordinates (mode coordinates). With the example of a torsion micro mirror, the efficient and accuracy is verified. Because of the modularization of the energy domain, the method isn't available to the energy dissipation system.2) Arnoldi algorithm does not need to solve the original large scale ODEs but directly reduce it to a lower order model by computing an orthogonal subspace which spans the same Krylov subspace. With the Taylor series expansion and the Arnoldi process, weakly nonlinear MEMS devices model is efficiently reduced via a second order system. Unfortunately it can not be used to handle strong nonlinear system accurately.3) To solve the question of strongly nonlinear MEMS devices, the KL decomposition method is studied. In the method, the first and most important is the signals (data shots), which are required to represent the behaviors of the original system well. By the KL decomposition on the signals, the global basis functions are gained. With the Galerkin method, the time-dependent coefficients of each basis function are chosen. A capacitive pressure sensor is used to verify the method.