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



6805.

Calvo-Garrido, MC; Ehrhardt, M; V{\'a}zquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 390

6804.

Calvo-Garrido, MC; Ehrhardt, M; Vázquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 390

6803.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

6802.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

6801.

Carmen Calvo-Garrido, Mar{\i}a; Ehrhardt, Matthias; V{\'a}zquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89

6800.

Carmen Calvo-Garrido, Mar{\i}a; Ehrhardt, Matthias; Vázquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89

6799.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6798.

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

6797.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6796.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6795.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6794.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6793.

Günther, M; Ehrhardt, M; Knechtli, F; Shcherbakov, D; Striebel, M; Wandelt, M
Symmetric \& Volume Preserving Projection Schemes

6792.

Putek, Piotr; Günther, Michael
Topology Optimization and Analysis of a PM synchronous Machine for Electrical Automobiles

6791.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Vorhersage-Modelle am Beispiel des Corona-Virus COVID-19

6790.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Vorhersage-Modelle am Beispiel des Corona-Virus COVID-19

6789.

Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas
Operator Splitting and Multirate Schemes

6788.

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

6787.

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

6786.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems
2023

6785.

Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
2023

6784.

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

6783.

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

6782.

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

6781.

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

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