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Arbeitsgruppe Angewandte Mathematik / Numerische Analysis
Bergische Universität Wuppertal
Fakultät 04
Gaußstraße 20
D-42119 Wuppertal

Telefon: +49 202 439 5296
Fax: +49 202 439 5201
E-Mail: sek-amna{at}


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Semiconductor devices are solid state bodies, whose electrical conductivity strongly depends on the temperature and other internal properties like the so-called doping. Depending on the temperature or other internal settigns, they can be regarded as insulator or conductor. (Physically speaken: Semiconductor materials have a band gap between.. and .. electron Volt)
This property makes them extremely useful in electronics, since this property can be easily employed to use them as switches. On nowadays computerchips and prozessors, millions of semiconductor devices (especially transistors) are included in an electronic circuit. In order to use common circuit simulation tools to simualte circuits containing those devices, semiconductor devices are often reflected by compact models - subcircuits of basic elements like resistors, capacitors, inductors and current/voltage sources. Those compact models shoul rebuild the input/output behaviour of the semiconductor device.

Ongoing miniaturization and the step from miro- to nanotechnology, however, leads to more powerful prozessors and chips, since higher packing density can be achieved. On the other hand, this higher packing density and miniaturization of the devices makes parasitic effects like heating predominant. Incorporation of those effects into compact models results in large compact models to describe a single semiconductor device. This makes it desireable to include more exact distributed device models - device models based on partial differential equations - into circuit simulation.

Moreover, smaller devices are driven by smaller signals, what makes them more energy efficient. On the other hand this results in a larger noise/signal ratio, what makes inclusion of non-deterministic effects into device models interesting. All in all, this leads to the following recent question in semiconductor/circuit modelling and simulation:

Former and ongoing projects


Open subjects for theses

  • Master Thesis: Two-dimensional thermal-electric simulation of semiconductor MOSFET-devices (M.Brunk)


Markus Brunk; A. Kværnø
Positivity preserving discretization of time dependent semiconductor drift-diffusion equations
Applied Numerical Mathematics, 62(10):1289-1301
Oktober 2012
Sebastian Schöps
Multiscale Modeling and Multirate Time-Integration of Field/Circuit Coupled Problems
aus Elektrotechnik
Herausgeber: VDI Verlag, Düsseldorf
ISBN: 978-3-18-339821-8

Zusammenfassung: This treatise is intended for mathematicians and computational engineers that work on modeling, coupling and simulation of electromagnetic problems. This includes lumped electric networks, magnetoquasistatic field and semiconductor devices. Their coupling yields a multiscale system of partial differential algebraic equations containing device models of any dimension interconnected by the electric network. It is solved in time domain by multirate techniques that efficiently exploit the structure. The central idea is the usage of lumped surrogate models that describe latent model parts sufficiently accurate (e.g. the field model by an inductance) even if other model parts (e.g. the circuit) exhibit highly dynamic behavior. We propose dynamic iteration and a bypassing technique using surrogate Schur complements. A mathematical convergence analysis is given and numerical examples are discussed. They show a clear reduction in the computational costs compared to single rate approaches.

Guiseppe Ali; Andreas Bartel; Markus Brunk; Sebastian Schöps
A convergent iteration scheme for semiconductor/circuit coupled problems
Scientific Computing in Electrical Engineering SCEE 2010
Markus Brunk; Ansgar Jüngel
Heating of semiconductor devices in electric circuits
Roos, Janne and Costa, L., Autoren, Scientific Computing in Electrical Engineering - SCEE 2008. Band 14 aus Mathematics in Industry , Seite 261--272.
Herausgeber: Springer, Berlin
Guiseppe Ali; Giovanni Mascali; Roland Pulch
Hyperbolic {PDAE}s for semiconductor devices coupled with circuits
Roos, Janne and Costa, L., Autoren, Scientific Computing in Electrical Engineering. Mathematics in Industry aus 14 , Seite 305--312.
Herausgeber: Springer, Berlin
Markus Brunk; Ansgar Jüngel
Numerical Coupling of Electric Circuit Equations and Energy-Transport Models for Semiconductors
SIAM Journal on Scientific Computing, 30:873 - 894
Markus Brunk; Ansgar Jüngel
Numerical Coupling of Electric Circuit Equations with the Transient Energy-Transport Equations for Semiconductors
Puccio, Luigia, Autoren, Communications to SIMAI Congress Band 1
Andreas Bartel
Partial Differential-Algebraic Models in Chip Design - Thermal and Semiconductor Problems. Fortschritt-Berichte VDI
aus 20
Herausgeber: VDI-Verlag, Düsseldorf
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