MEMS Model Libraries
MEMS+ is based on a library of MEMS building blocks that are used by the MEMS designer to assemble a desired device. Each library component has a 3D view and a corresponding behavioral model. Similar to building an electronic circuit using models from a SPICE model library in IC-Design, MEMS+ has a behavioral model library populated with the latest multi-physics in structural mechanics, electrostatics and damping. The image below depicts the 3-D graphical representation of the MEMS building blocks that make up a MEMS accelerometer. MEMS+ automatically assigns the correct behavioral model to each part.
The MEMS+ component library is strictly hierarchical and builds on top of three different mechanical model families: rigid plates, suspensions and flexible plates.
The rigid plate is used to create arbitrary shapes by assembling parametric geometrical primitives such as rectangular segment, triangular segments, straight and curved comb fingers, etc. The final rigid plate is the result of booleaning the individual segments. The behavioral model of the rigid plate is based on Newton’s law and the Euler equations.
The second group of mechanical elements, the suspensions, includes parametric primitives for straight beams, serpentines, beam paths, vertical beams and many others. All suspension models are based on the Bernoulli beam theory.
The third group of mechanical elements, the flexible plates, include basic shapes like circles, arcs, rectangles and quadrilateral that can be used to create complex flexible structures as seen in the image below:
All flexible plate shapes are modeled by a single, variable-order, finite shell element known as MITC (mixed interpolation of tonsorial components). As for the suspension, great care has been taken to include all process-relevant effects such as side-wall angles, pre-stress, multi-layer support, as well as nonlinear behaviors, such as buckling.
The members of the mechanical model families can be “decorated” with electrostatic, piezo electric and contact models as seen in the image below:
The corresponding behavioral models are based on various different modeling techniques including analytic formulae, numerical integration and finite elements. A detailed description of the underlying models can be found in the comprehensive reference documentation of the MEMS+ design environment.
Background of the MEMS+ Behavioral Model Library
The theoretical background of the multi-physics and multi-domain mathematics for each item in the library has been developed at Coventor over the last 10 years in close collaboration with institutes and MEMS companies. The models have been validated for many different MEMS applications in earlier versions of MEMS+ and the CoventorWare ARCHITECT3D product. Our internal development team continuously updates and improves the MEMS models based on the latest theory and customer requests.
Features in the MEMS+ Behavioral Model Library
Unlike other products on the market, MEMS+ contains a large set of physical models in each of the library components. Some of the library characteristics are:
- linear and non-linear models
- unlimited number of layers
- arbitrary cross-sections and side-wall angle support
- reduced-order models
- variable-order flexible plates based on the latest generation of finite shell elements
- in and out-of-plane contact models
- etch-hole models
- stress and stress-gradient models
- full electrostatic models
- fringing fields support in all electrostatic models
- and more…
MEMS designers are asked to generate MEMS models for circuit or system simulators in order to design control and read-out circuits for MEMS devices. There are three options for creating such models:
- Hand-crafted analytical models, implemented in SPICE or Verilog-A,
- Reduced-order models (macro models) extracted from FEA, or
- Discrete element representation (behavioral models as in MEMS+).
What makes MEMS+ special is that by assembling the models from its component library and defining electrical, mechanical, input and output ports in MEMS+ Innovator, MEMS+ models are ready for simulation. Our MEMS+ integration for Simulink and Cadence is able to automatically and instantaneously convert a given Innovator schematic into a symbol and corresponding model without requiring time-consuming FEM analysis.