Automatic Mixed-Dimensional MEMS Modeling

Abstract

The process of modeling and simulation of MEMS devices aims to reduce the design cycle time. The pre- processing stage of creating and preparing the mesh for analysis poses some challenges. Firstly, hexahedral mesh generation is usually manual or semi-automatic, hence there is a need for a true automatic hexahedral mesh generation algorithm. Secondly, it is computationally more efficient to model thin sections of the model using two-dimensional elements, hence there is a need for automatic model reduction. Thirdly, provision must be made to support coupled-domain analysis. This paper presents an automatic process to generate the mesh of a MEMS model by using a geometric transformation, known as the block Cartesian abstraction, which can be further decomposed into a mixed-dimensional equivalent. This representation is then meshed using a new grid-based algorithm resulting in a mixed quadrilateral and hexahedral mesh, which will reduce the computational requirement during analysis as compared to using a full hexahedral mesh. As the mesh is structured, it can also be used as a platform for coupled-domain analysis. cycle time for MEMS devices. To further reduce the time-to- market, efforts have been made to streamline the simulation and analysis processes, which involve a pre-processing stage, a numerical processing stage and a post processing stage. The pre-processing stage entails the discretization of the analysis domain for Boundary Element Analysis (BEA) or Finite Element Analysis (FEA). This process, otherwise known as mesh generation, has been identified as the bottleneck of the whole simulation process, and much research efforts have been directed at developing automatic mesh generation algorithms. Moreover, a typical geometric model usually consists of both solid parts and thin-walled sections. By using a suitable dimensional reduction algorithm, the model can be reduced to a non-manifold model consisting of solid portions and two-dimensional portions which represent the mid-surfaces of the thin-walled sections. To reduce computational time, it is desirable to mesh the solid entities using three-dimensional elements and the surface entities using two-dimensional elements. Also, due to the scale and nature of the problem associated with the simulation and analysis of MEMS devices, coupled- domain analysis is often encountered. In such cases, traditional Boundary Element Method (BEM) and Finite Element Method (FEM) are not sufficient. This work focuses on automatic mixed-dimensional mesh generation based on quadrilateral and hexahedral elements. To achieve mixed-dimensional non-manifold geometric representation, reduction techniques are employed to simplify thin portion of the geometric domains into surfaces. This geometric representation is subsequently meshed with automatic algorithms. The proposed scheme can also be used as a platform that is suitable for coupled electrostatic- mechanical analysis.