8 Macromodels of Micro - Electro - Mechanical Systems ( М EMS )

Micro-electro-mechanical Systems (MEMS) are components with micron-scale moving parts based on materials and processes of microelectronics fabrication. This is a good example of on-chip integration of electronics, microstructures, microsensors and microactuators. Accurate simulation of MEMS requires precise modeling of all effects of mechanical and damping forces, electrostatic forces and inner stresses, heat transfer, thermal expansion, piezoelectric stresses etc. Modern methodology of MEMS design implies that the entire MEMS can be investigated only at higher abstraction levels such as schematic and system ones, where accurate macromodels can be used [1]. On the other hand, at component or device levels the physical behavior of three-dimensional continuums is described by partial differential equations (PDE) easily solvable by Finite Element or Finite Difference Element Methods (FEM or FDM) [2,3], available in ANSYS –like software. Component level simulations are classified in single domain and coupled domain simulations, both being very computer timeconsuming. The goal of this chapter is to consider methods of automatically obtaining macromodels of MEMS and their mechanical or non-electric components from ANSYS models as equivalent electric circuits or low order differential ordinary equations for further use in circuit design software. This can be done by using different model order reduction techniques developed in recent years. When dealing with the modern MEMS, the possibility for using a single environment to simulate objects, where different physical processes such as electrical, mechanical, optical, thermal etc. take place, plays an important role. Here we have to represent different subsystems of the initial MEMS as equivalent models of the same physical nature permitting to combine them for solution in a single computational process. After that, the complete behavioral model of the entire MEMS and its subsystems can be compiled either in VHDLAMS language (as sets of ODE) or in SPICE-like language (as equivalent electric circuits). The Microsystems design exploits various analytical and numerical methods for virtual prototyping of MEMS. It also demands for libraries of electromechanical, optical models and microfluid components, including springs, bulks, buffers, capacitors, inductances, operational amplifiers, transistors etc. Three basic possible approaches of MEMS design procedure are illustrated below: FEM/FDM Model, Reduced Order Model (ROM), Coupled system-level model.