Applied and Computational Mathematics (ACM)

Semiconductor

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

Cooperations

Open subjects for theses

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

Publications



2024

6990.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Spectral analysis of a class of linear hyperbolic partial differential equations
03 2024

6989.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Linear-Quadratic optimal control for boundary controlled networks of waves
02 2024

6988.

Celik, I. E.; Mittendorf, Fabia; Gómez-Suárez, Adrián; Kirsch, S. F.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 9
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X

6987.

Bensberg, Kathrin; Savvidis, Athanasios; Ballaschk, Frederic; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry - A European Journal, 2024 :e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-6539

6986.

[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 2024

6985.

Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics

6984.

Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital

6983.

Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital

6982.

Ehrhardt, M; Günther, M; Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

6981.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6980.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6979.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6978.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6977.

Petrov, Pavel S; Ehrhardt, Matthias; Kozitskiy, Sergey B
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration :118304
2024
Herausgeber: Elsevier

6976.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6975.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

6974.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

6973.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

6972.

Putek, Piotr; PAPLICKI, Piotr; Pulch, Roland; Maten, Jan; Günther, Michael; PA{\L}KA, Ryszard
NONLINEAR MULTIOBJECTIVE TOPOLOGY OPTIMIZATION AND MULTIPHYSICS ANALYSIS OF A PERMANENT-MAGNET EXCITED SYNCHRONOUS MACHINE

6971.

Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs

6970.

Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model

6969.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

6968.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

6967.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

6966.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

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