Modellierung gekoppelter Effekte in Mikrosystemen auf ...

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systems with a noticeably reduced number of degrees of freedom compared to continuousfield
models.
Based on detailed investigations of various coupled-field effects on continuous-field level
two contrary approaches are compared: system modeling by lumped variables (compact
models, lumped elements) and system modeling by distributed variables, in particular the
Finite Network method. System modeling by physically-based, analytical compact models
and lumped variables turns out to be a powerful method for fast and efficient design
studies. However, the derivation of the compact models needs a lot of effort and expertise
by the designer, which means that the procedure can not be automated. Additionally,
physically-based, analytical compact modeling is mostly limited to device geometries
and/or problems which are not too complex. Therefore, in this work both approaches –
compact modeling and Finite Network method – are combined to form a mixed-level
model. This approach is very flexible, powerful, and especially suited to derive system
models for complex problems, which – by the nature of this modular approach – can be
tailored according to the needs, practicalities and the required accuracy.
The potential of the method has been demonstrated successfully for the simulation of
viscous damping effects in dynamically operated microstructures. This phenomenon can
be exactly described on continuous-field level by fluid-structure interaction, which becomes
prohibitive for most of the practically relevant devices due to the complexity of
the governing equations and the often very complex device geometries (3D, perforations).
Based on the mixed-level method, it was possible to derive a reduced-order model
where the complexity is drastically reduced but which nevertheless is physically based,
scales with all important design parameters, and still provides a high accuracy. Thus, for
the first time, this damping model allows for a predicitive simulation of damping effects
in microsystems even for complex device geometries with an acceptable computational
effort.