Functional aspects as well as the influence of integration technology on the system behavior have to be considered in the 3D integration design process of micro systems. Therefore, information from different physical domains has to be provided to designers. Due to the variety of structures and effects of different physical domains, efficient modeling approaches and simulation algorithms have to be combined. The article describes a modular approach which covers detailed analysis with PDE solvers and model generation for system level simulation

In the development of microsystems, FEM simulators are used to investigate the behavior of system components with high accuracy. Generally, FEM simulations are time consuming. System-level models of all components are needed to allow a fast but sufficiently exact investigation of the system behavior to simulate entire microsystems. Typically, microsystems consist of nonelectrical components and electronic circuits. Providing models for electronic components and languages to describe the behavior of nonelectrical subsystems, simulators like Eldo, Saber, and VHDL-AMS simulators become more and more popular in the development of microsystems. For simple structures such as mechanical beams, models of microsystem components can be derived from analytical descriptions. Another possibility to consider more complex structures is to use FEM descriptions to generate models for system simulation. Some FEM simulators like ANSYS allow to access the numerical values of the system matrices. They are established based on the description of geometry and material data. Usually, these system matrices are very large (10 000 up to 100 000 system variables or more). For system simulation, models with about 10 up to 100 variables are often required. Therefore, methods for order reduction are applied to derive smaller system matrices. An improvement of an order reduction method based on a projection method is introduced in the paper. Using the reduced systems, behavioral models in languages like MAST, HDL-A or VHDL-AMS can be generated automatically. The described method was applied successfully to simulate mechanical microsystem components on system level.

Sensor development in the field of microsystem technology is driven by steadily increasing demands on sensor resolution and performance and the need to reduce costs. Thus, interactions between mechanical and electronic components of a complex sensor system become more important and have to be considered in the design process, preferably already in early design steps. That is why a system simulation of the entire sensor system is necessary to be able to verify different design steps and to decrease the number of expensive prototyping cycles. Due to typical combinations of different physical domains (mechanics, electronics, thermodynamics, etc.) a simulation of the entire system based on partial differential equations using e.g. finite element methods (FEM) is often impossible or too expensive concerning computing time. Furthermore, many details of the component behavior calculated by FEM are not needed at system level. A successful approach to system simulation of sensor systems is to derive behavioral models from FEM descriptions and to combine them with system level models of electronics. In the following a method for automatic generation of behavioral models for micromechanical components using order reduction methods will be introduced.

Computer aided MEMS optimization regarding performance, power consumption, and reliability is an important design task due to high prototyping costs. In the MEMS design flow, a variety of specialized tools is available. FEM tools (e.g. ANSYS, CFD-ACE+) are widely used for simulation on component level. Simulations on system level are carried out with simplified models using simulators like Saber, ELDO, or Spice. A few simulators offer tool-specific optimization capabilities but there is a lack of simulator-independent support of MEMS optimization. The paper presents a modular approach for simulation-based optimization which aims at a flexible combination of simulators and optimization algorithms by partitioning the optimization cycle into separate modules for model generation, simulation, error calculation, and optimization. Available optimization algorithms include direct and indirect methods as well as stochastic approaches. Interfaces to the simulators ANSYS, ELDO, Saber, MATLAB, and SPICE are implemented. Thus the optimization task can be solved on different levels of model abstraction (FEM, ordinary differential equations, generalized networks, ...). A graphical user interface (GUI) supports control and visualization of the optimization progress. The modules of the optimization system may communicate via the internet (webbased optimization, distributed optimization).

The importance of MEMS optimization concerning performance, power consumption, and reliability increases. In the MEMS design flow a variety of specialized tools is available. For simulation on component level FEM tools (e.g. ANSYS, CFD-ACE+) are widely used. Simulations on system level are carried out with simplified models using simulators like Saber, ELDO or Spice. A few simulators offer tool-specific optimization capabilities but there is a lack of simulator independent support of MEMS optimization. Our approach aims at a flexible combination of simulators and optimization algorithms by partitioning the optimization cycle. This new method is translated into a modular optimization system implemented in JAVA. The main parts (modules) are: • Simulation: System behavior is calculated with the actual design parameters. This computation can be a simple evaluation of equations or a complex simulation with a FEM tool or a system simulator, respectively. • Error calculation: Simulation results and the specified system behavior are used to calculate the error value (the design objective function) in the actual optimization step. • Optimization: The error value is used to compute the new vector of design parameters. • Model instantiation: The new parameter values are used to modify the generic model for a new simulation run. The implemented optimization algorithms are: • methods without derivatives (e.g. Nelder-Mead-Simplex), • methods using derivatives (e.g. Conjugate Gradient or Quasi-Newton) and • stochastic approaches (e.g. Simulated Annealing). Interfaces to the simulators ANSYS, ELDO, Saber, and SPICE are implemented. Thus the optimization task can be solved on different levels of model abstraction (FEM, ordinary differential equations, generalized networks, ...). A graphical user interface (GUI) supports control and visualization of the optimization progress. The modules of the optimization system may communicate via the internet (web-based optimization, distributed optimization). The paper covers the partitioning of optimization cycle, the interaction between the modules of the optimization system, first experiences in web-based optimization, and the application of the approach to MEMS optimization.