Implementation of MEMCAD system for electrostatic and mechanical analysis of complex structures from mask descriptions

Abstract

We report the development of a first implementation of the MEMCAD system (version 1.0). The system is composed of three commercial mechanical CAD software packages integrated with our specialize structure generation and electrostatic analysis programs. In this paper we describe the system and demonstrate its capabilities using a comb drive example constructed directly from a CIF description of its mask set. We received the CIF file from U.C.Berkeley [l]. The analysis of the comb drive takes just a few hours, all the way from generating a full 3D model from mask descriptions to calculating comb levitation forces.INTRODUCTION MEMS designers are making increasing use of commercially available computer simulation packages as design aids [2,3,4]. Modeling a MEMS device involves three basic tasks: creation of the 3D structure, simulation of some physical behavior of the model device, and visualization and analysis of the results. Commercial tools exist in all these areas; however, the geometric complexity of MEMS structures often makes using such tools cumbersome. An architecture for a MEMCAD (MEM Computer-Aided Design) system has been proposed [5] which would both simplify and accelerate the process of simulating novel MEMS structures.We have developed a first implementation of the MEMCAD system (version 1.0). The system is composed of three commercial mechanical CAD software packages integrated with our specialize structure generation and electrostatic analysis programs. We describe the system and demonstrate its capabilities by using it to analyze a comb drive example from U.C.Berkeley.In Figure 1 we sketch the MEMCAD 1.0 system in the context of those three tasks. The shaded boxes represent the commercial CAD tools: ProEngineer [6], PATRAN [7], and ABAQUS [8]. They cooperate through their common use of the PATRAN Neutral File (PNF)[7] for interchange of 3D structures. The open boxes represent codes written at MIT. They are STS (or cif2iges)[9] and FASTCAPII+[lO]. The three bubbles on the left of Figure 1 represent the basic user inputs to the process of creating a 3D structure. Figure 1 also summarizes the application of the MEMCAD system to the comb drive example. STS 1.0 converts mask layouts to IGES format. ProEngineer, a solid modeling package, is used to read the IGES file, to extrude the mask to build a 3D structure, and to automatically generate coarse analysis meshes. Visualization on geometric structures is done with PATRAN. Mechanical analysis is done with ABAQUS, and electrostatic analysis with FASTCAPII+.This paper contains three sections corresponding to the tasks above: creation of 3D structure, visualization, and simulation and modeling. In each section we briefly describe the parts of MEMCAD 1.0 in that area, and illustrate them with example of the comb drive. The bulk of our remarks are found in the sections on creation of 3D structure and simulation and modeling, since it is in those areas that we have added both software codes and methods to what is available commercially.CREATION OF 3D STRUCTURE...

M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures

“…The method used to develop these models is extendable to other test-structure geometries. Each model is ultimately based on detailed 3-D numerical quasi-static self-consistent simulation of the deformation of the test structure under the combined effect of linear elastic forces and nonlinear electrostatic forces, using the MIT MEMCAD system [10], [11]. However, because the M-Test structures are highly symmetric, indeed, nearly 2-D, it was determined that a much simpler 2-D finite-difference model, initially reported in [13] (with some important typographical errors, which are corrected here), was sufficiently precise in comparison with 3-D simulation to permit its use over a wide design space.…”

“…This work presents: 1) the development of closed-form quantitative models for the pull-in of M-Test structures derived from two-dimensional (2-D) and three-dimensional (3-D) numerical simulations using the Massachusetts Institute of Technology's software package for the computer-aided design of microelectromechanical systems (MIT MEMCAD) [10], [11]; 2) an experimental procedure and associated data-reduction method, which removes geometrically correlated statistical variation in order to improve the precision of the results and uses geometric data on the test-structure dimensions (such as beam thickness and undeformed gap) to extract material properties from the pull-in data; and 3) experimental verification of the M-Test method using data from MIT's dielectrically isolated single-crystal silicon wafer-bonded process [12].…”

Emerging simulation approaches for micromachined devices

“…For this reason, there has been a steady effort over the last decade to develop nearly automatic approaches for generating accurate macromodels of micromachined devices starting from only layout and process descriptions. Most efforts is this area are following a three step approach [18], [11], [19].…”

“…Finally, the electrostatic force is approximated assuming nearly parallel plates and is given by where is the applied voltage. Spatial discretization of (17) and (18) leads to a large nonlinear system of the form (19) where is an -length state vector, in this case the vector of displacements and their time derivatives. The function , which maps an -length vector to an -length vector, represents the spatially discretized partial differential equation.…”

“…Then, the matrix represents a transformation from the original to the reduced coordinate system. Substituting the change of variables in (19) and multiplying the resulting equation by yields (21) It should be noted that the dynamical system could have been multiplied by a second transformation matrix, , leading to a wider range of algorithms. Buried in (21) are the two key model-order reduction issues.…”