In this chapter, the quick review of different structures, modes, and excitation mechanisms is given in the beginning. The mechanical model for the RF MEMS resonator is discussed and ways to extract the important device parameters are given along with the electrical equivalent model. The importance of the physical modeling of a MEMS device is established and various governing partial differential equations (PDEs) are discussed. A brief introduction to the FEM for solving PDEs is given to give the reader a glimpse of the FEM machinery running behind the screens of commercial simulation tools. It discusses a finite element assembly for the Poisson's equation and its solution for demonstration purpose followed by the details of a few commercial tools such as CoventorWare, Intellisuite, and COMSOL Multiphysics with specific examples.

Chapter Contents:

• 5.1 Classification of RF MEMS resonators
• 5.1.1 Structure
• 5.1.2 Shapes
• 5.1.3 Vibration modes
• 5.1.4 Actuation mechanisms
• 5.1.5 Coupling mechanisms
• 5.2 Modeling of RF MEMS resonators
• 5.2.1 Mechanical model
• 5.2.2 Electrical equivalent model
• 5.2.3 Numerical simulation
• 5.3 Governing PDEs
• 5.3.1 Beam mechanics
• 5.3.2 Solid mechanics
• 5.3.3 Electrostatics
• 5.3.4 Thermal domain
• 5.3.5 Fluid domain
• 5.3.6 Coupled-domain analysis
• 5.4 Finite element method
• 5.4.1 Preprocessing
• 5.4.1.1 Variational method
• 5.4.1.2 Galerkin method
• 5.4.1.3 Meshing
• 5.4.1.4 Shape functions
• 5.4.1.5 Matrix assembly
• 5.4.2 Weak formulation of Poisson's equation
• 5.4.3 Processing
• 5.4.3.1 Eigenvalue equation solvers
• 5.4.4 Postprocessing
• 5.4.5 Examples of Poisson's equation solved using FEM
• 5.4.5.1 Triangular charge density in X direction
• 5.4.5.2 Laplace equation
• 5.5 Commercial MEMS design tools
• 5.5.1 CoventorWare
• 5.5.1.1 Meshing
• 5.5.1.2 Solver and visualizer
• 5.5.1.3 Integrator
• 5.5.2 Intellisuite
• 5.5.2.1 IntelliFAB
• 5.5.2.2 Builder
• 5.5.2.3 Thermoelectromechanical analysis—device analysis
• 5.5.3 COMSOL Multiphysics
• 5.6 Summary
• References

Inspec keywords: finite element analysis; Poisson equation; micromechanical resonators

Other keywords: partial differential equations; excitation mechanisms; physical modeling; PDE; commercial simulation tools; Poisson equation; electrical equivalent model; RF MEMS resonators; FEM; MEMS device; finite-element modeling; device parameters

Subjects: Microwave circuits and devices; Differential equations (numerical analysis); Numerical approximation and analysis; Micromechanical and nanomechanical devices and systems; Finite element analysis; Design and modelling of MEMS and NEMS devices