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



2023

6843.

[english] Venzlaff, Julian; Kosumi, Kaltrina; Zeller, Diana; Bohrmann-Linde, Claudia
Education for Sustainable Development and Experiments involving Titanium Dioxide
World Journal of Chemical Education, 11 (3) :80-86
August 2023

6842.

[english] Brunnert, Rainer; Tausch, Michael W.
Green Chemistry in STEM Education: Light for Basic Concepts
World Journal of Chemical Education, 11 (3) :65-73
August 2023

6841.

[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit
August 2023

6840.

[german] Venzlaff, Julian; Bohrmann-Linde, Claudia
Photoreformierung – grüner Wasserstoff aus Alkohol, Zucker und Stärke
CHEMKON, 30 (6) :254-259
Juni 2023

6839.

Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry
05 2023

6838.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Dem Apfel ans Leder
Nachrichten aus der Chemie, 71 :12-14
März 2023

6837.

Fatoorehchi, Hooman; Zarghami, Reza; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
2023

6836.

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

6835.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6834.

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

6833.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6832.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6831.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csomós, Petra; Faragó, István; Fekete, Imre; others
Invited Papers

6830.

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

6829.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csom{\'o}s, Petra; Farag{\'o}, Istv{\'a}n; Fekete, Imre; others
Invited Papers

6828.

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

6827.

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

6826.

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

6825.

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

6824.

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

6823.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6822.

Al{\i}, G; Bartel, A; Günther, M
Electrical RLC networks and diodes

6821.

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

6820.

Fatoorehchi, Hooman; Zarghami, Reza; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
2023

6819.

Akramov, ME; Yusupov, JR; Ehrhardt, M; Susanto, H; Matrasulov, DU
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters A :128611
2023
Herausgeber: North-Holland

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