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Prof. Caren Tischendorf
| Speaker: |
Prof.dr. Caren Tischendorf
(University of Köln)
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| Date: |
Wednesday February 14, 2007 |
| Title: |
Numerical
Analysis for Coupled Circuit and Device Simulation
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Abstract
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For a coupled circuit and device simulation,
circuits are modelled by (charge oriented) modified nodal analysis and
semiconductors by nonstationary drift diffusion equations.
Consequently, the circuit equations are described by a system of
differential algebraic equations (DAEs). The drift diffusion equations
represent a system of one elliptic and two parabolic differential
equations. Both systems are coupled via boundary conditions and
integral relations.
We present structural properties of the equation systems for individual
parts as well as for the complete coupled system. This allows us to
describe the solution behaviour with respect to perturbations by
circuit topological conditions.
For the coupled simulation, we introduce an approach discretizing the
semiconductor equations first in space. This implies a differential
algebraic equation system for the whole system that can be solved by
time varying DAE solvers. We discuss different discretizations in space
with respect to solvability and index of the resulting DAE.
Finally, we present some simulation results for small test circuits.
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