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:
- Thermal effects in semiconductor devices
- Noise in semiconductor devices (SDEs)
- Quantum Effects in semiconductor devices
- Electro-thermal coupling of optoelectronic semiconductor devices with electric circuits
- Efficient Co-Simulation of circuit/semiconductor problems (Dynamic Iteration schemes)
Former and ongoing projects
Cooperations
- Vittorio Romano, Università degli studi di Catania, Italy
- Giuseppe Ali, Universitá della Calabria, Italy
- Ansgar Jüngel, TU Vienna, Austria
- Pina Milisic, University of Zagreb, Croatia
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: 2692-45605399.
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, 2451-93085398.
Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A Space Mapping approach for the calibration of financial models with the application to the Heston model
20255397.
Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems5396.
Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations5395.
High order tensor product interpolation in the Combination Technique
preprint, 14 :255394.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 3885393.
Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers5392.
Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics5391.
Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics5390.
Ehrhardt, Matthias; Günther, Michael
Mathematical Study of Grossman's model of investment in health capital5389.
Bartel, PD Dr A
Mathematische Modellierung in Anwendungen5388.
Model Order Reduction Techniques for Basket Option Pricing5387.
Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance5386.
Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 3775385.
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 :5875384.
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 MACHINE5383.
Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs5382.
Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model5381.
Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options5380.
Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit
Operator Splitting and Multirate Schemes5379.
Vázquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 3905378.
Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions5377.
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 895376.
Putek, PA; Ter Maten, EJW
Reliability-based Low Torque Ripple Design of Permanent Magnet Machine