There is CAD and than there is MEMS CAD
Posted by Josephus van Kuijk on Wed, Nov 11, 2009 @ 07:59 AM
Choosing the right structural analysis method for MEMS simulations
MEMS designers are asked to generate MEMS models for circuit simulators such as SPICE in order for IC-designers to design control and read-out circuits for MEMS devices and optimize the two together. The three options available for creating such MEMS models are:
- Hand-crafted analytical models
- Create macro models extracted from Finite Element simulations
- Discrete element representation using Network Models
These MEMS models need to describe the MEMS behavior accurately in the mechanical domain and electrical domain.
Each method has its advantages and disadvantage:
Analytical hand-crafted models
- Easy model creation - NO (depending on complexity and knowledge)
- Fast simulations - YES (for simple models)
- Accuracy - NO (Idealized models, lots of assumptions)
- Parametric - YES
- Complexity - NO
- Easy integration into IC tools - NO (manually)
FEM based macro-modeling
- Easy model creation - NO (Long simulation time and model validation)
- Fast simulation - YES (only for linear, simple models)
- Accuracy - NO (missing non-linearity, multi-physics)
- Parametric - NO
- Complexity - NO (partitioning in abstract macro-models)
- Easy integration into IC tools - NO (manually)
Network Models
- Easy model creation - YES (the geometry defines the models)
- Fast simulation - YES (fastest models compatible with ICs)
- Accuracy - YES (includes non-linearity, coupled multi-physics)
- Parametric - YES (100% parameterization of models)
- Complexity - YES (unlimited 3-D stacking and layouts)
- Easy integration into IC tools - YES (fully automated)
The diagram below shows the different methods of mechanical structural analysis along with other methods of analysis as described in [1].
Methods of structural analysis
The analytical method (1) is usually limited to simple models for which a closed form solution can be found; for example one dimensional linear deflection of an idealized beam under a point load. Usually these models are not sufficient to be used for MEMS design. These models also lead to misconceptions; it is for example often assumed that the pull-in voltage of a MEMS device occurs at 1/3 of the gap width which is only true for idealized "mass-spring-parallel plate capacitor" system.
The numerical solution of differential equations is usually limited to simple structures.
Also Finite Element based simulators (2) have their limitations and are not compatible with circuit simulators. There are clear disadvantages of using Reduced Order Modeling or Macro-Model extraction techniques since the resulting models are non-parameterized, often limited to structural analysis only and can not model non-linearity very well.
Since the goal is to connect the MEMS models with IC simulators the most natural choice is the "network method (3)" since it can be directly integrated with circuit simulations. In order to use the network method the MEMS device or structure is decomposed into an assembly of discrete structural elements with assumed form of displacement and the complete solution is then obtained by combining these individual approximate displacements in a manner which satisfies the force-equilibrium at the junctions of these elements. Methods based on this approach appear to be suitable for the analysis of complex structures. The theory of matrix structural analysis is ideally suited to numerically solve this type of analysis.
"the theory of matrix structural analysis" by J. S. Przemieniecki (1985).