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



2025

5400.

Asya, Berçin V.; Wang, Sitao; Euchler, Eric; Khiêm, Vu Ngoc; Göstl, Robert
Optical Force Probes for Spatially Resolved Imaging of Polymer Damage and Failure
Aggregate, 6 :e70014
Februar 2025
ISSN: 2692-4560

5399.

Hahmann, Johannes; Schüpp, Boris N.; Ishaqat, Aman; Selvakumar, Arjuna; Göstl, Robert; Gräter, Frauke; Herrmann, Andreas
Sequence-specific, mechanophore-free mechanochemistry of DNA
Chem, 11 :102376
Januar 2025
ISSN: 2451-9294, 2451-9308

5398.

Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A Space Mapping approach for the calibration of financial models with the application to the Heston model
2025

5397.

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

5396.

Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations

5395.


High order tensor product interpolation in the Combination Technique
preprint, 14 :25

5394.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388

5393.

Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers

5392.

Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics

5391.

Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics

5390.

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

5389.

Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

5388.


Model Order Reduction Techniques for Basket Option Pricing

5387.

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

5386.

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

5385.

Gjonaj, Erion; Bahls, Christian Rüdiger; Bandlow, Bastian; Bartel, Andreas; Baumanns, Sascha; Belzen, F; Benderskaya, Galina; Benner, Peter; Beurden, MC; Blaszczyk, Andreas; others
Feldmann, Uwe, 143 Feng, Lihong, 515 De Gersem, Herbert, 341 Gim, Sebasti{\'a}n, 45, 333
MATHEMATICS IN INDUSTRY 14 :587

5384.

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

5383.

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

5382.

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

5381.

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

5380.

Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit
Operator Splitting and Multirate Schemes

5379.

Vázquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 390

5378.

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

5377.

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

5376.

Putek, PA; Ter Maten, EJW
Reliability-based Low Torque Ripple Design of Permanent Magnet Machine