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:

## Open subjects for theses

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

2023

### 6165.

Schweitzer, Marcel
Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Linear Algebra Appl., 656 :247-276
2023

### 6164.

Schweitzer, Marcel
Integral representations for higher-order Frechet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Linear Algebra Appl., 656 :247-276
2023

### 6163.

[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Kompetenzförderung durch Erklärvideos in einem Selbstlernbuch zum Einstieg in die Organische Chemie
MNU-Journal, 01.2023 :48-54
2023
ISSN: 0025-5866

### 6162.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Mit Lactase und Lactose zum elektrischen Strom - enzymatische Brennstoffzellen auf Filterpapierbasis für den Chemieunterricht.
CHEMKON, 30 (1) :37-41
Januar 2023

### 6161.

Farkas, Bálint; Jacob, Birgit; Reis, Timo; Schmitz, Merlin
Operator splitting based dynamic iteration for linear infinite-dimensional port-Hamiltonian systems
2023

### 6160.

Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
2023

### 6159.

Asatryan, Hayk; Gaul, Daniela; Gottschalk, Hanno; Klamroth, Kathrin; Stiglmayr, Michael
Ridepooling and public bus services: A comparative case-study
Submitted to Transportation
2023
Herausgeber: arXiv

### 6158.

Schweitzer, Marcel
Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds
2023

### 6157.

Schweitzer, Marcel
Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds
2023

### 6156.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
2023

### 6155.

Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
2023
2022

### 6154.

[english] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Biological Fuel Cells with Drugstore Products
World Journal of Chemical Education, 10 (4) :149-154
Dezember 2022

### 6153.

[German] Zeller, Diana
Heimische Ökosysteme erkunden. Mit Maphub kooperative, ökologische Kartierung umsetzen
In Meier, Monique; Thyssen, Christoph, Editor aus Digital Unterrichten Biologie
Herausgeber: Friedrich Verlag, Hannover
November 2022

### 6152.

[german] Bohrmann-Linde, Claudia; Gökkus, Yasemin; Humbert, Ludger; Kiesling, Elisabeth; Kremer, Richard; Losch, Daniel; Schmitz, Denise; Zeller, Diana
Analyse, Struktur und Darstellung chemiedidaktischer Elemente aus informatischer Perspektive – Entwicklung eines interdisziplinären Lehrkonzeptes
MNU-Journal, 05.2022 :423-429
September 2022

### 6151.

[german] Kremer, Richard; Bohrmann-Linde, Claudia; Tausch, Michael W.
Künstliche Photosynthese im Fokus - Photokatalytische Wasserstofferzeugung in der Eintopfzelle
CHEMKON, 29 (6) :646-653
September 2022

### 6150.

Bohrmann-Linde, Claudia; Siehr, Ilona
CHEMIE Einführungsphase Nordrhein-Westfalen
Herausgeber: C.C.Buchner Verlag, Bamberg
August 2022

ISBN: 9783661060019

### 6149.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Strom aus Bäckerhefe
Nachrichten aus der Chemie, 70 (7-8) :18-21
Juli 2022

### 6148.

[german] Zeller, Diana; Stinken-Rösner, Lisa; Meier, Monique
Interaktive Videoformate für den naturwissenschaftlichen Unterricht. Vom Rezipieren zum Interagieren
Unterricht Biologie, 475 :44-47
07 2022

### 6147.

[german] Zeller, Diana
Medialab – ein dreistufiges Modul zur Entwicklung digitalisierungsbezogener Kompetenzen im Studium des Chemie‐ und Sachunterrichtslehramts
CHEMKON, 29 (S1) :287-292
Juni 2022

### 6146.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Entwicklung eines lowcost Experiments für den Chemieunterricht am Beispiel der enzymatischen Brennstoffzelle mit Lactase
CHEMKON, 29 (S1) :233-238
Juni 2022

### 6145.

[english] Bohrmann-Linde, Claudia; Zeller, Diana; Meuter, Nico; Tausch, Michael W.
Teaching Photochemistry: Experimental Approaches and Digital Media
ChemPhotoChem, 6 (6) :1-11
Juni 2022

### 6144.

[german] Kiesling, Elisabeth; Venzlaff, Julian; Bohrmann-Linde, Claudia
BNE im Chemieunterricht – von der Leitlinie BNE NRW zur exemplarischen Unterrichtseinbindung
CHEMKON, 29 (S1) :239-245
Juni 2022

### 6143.

[german] Zeller, Diana; Meier, Monique
Videos interaktiv erweitern - Forschendes Lernen vielseitig unterstützen
Digital Unterricht Biologie, 4 :10-11
Mai 2022

### 6142.

[german] Gökkus, Yasemin; Tausch, Michael W.
Explorative Studie zur partizipativen und nutzenorientierten Forschung in der Chemiedidaktik
CHEMKON, 29 (3) :117-124
April 2022

### 6141.

Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on {GPU}
JMI, 12 (5)
2022

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