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)

2022

### 6140.

Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-nume\-rical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
J. Energy Storage, 45 :103746
2022
Herausgeber: Elsevier

### 6139.

Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 507 (1) :125761
2022

### 6138.

Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
2022

### 6137.

Tordeux, Antoine; Totzeck, Claudia
Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems
2022

### 6136.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Multi-objective Matroid Optimization with Ordinal Weights
Discrete Applied Mathematics
2022

### 6135.

Doganay, Onur Tanil; Klamroth, Kathrin; Lang, Bruno; Stiglmayr, Michael; Totzeck, Claudia
Modeling Minimum Cost Network Flows With Port-Hamiltonian Systems
{PAMM}
2022
Herausgeber: Wiley

### 6134.

Bartel, Andreas; Günther, Michael
Multirate Schemes -- An Answer of Numerical Analysis to a Demand from Applications
In Michael Günther and Wil Schilders, Editor, Novel Mathematics Inspired by Industrial Challenges
Seite 5--27
Herausgeber: Springer
2022
5--27

### 6133.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
2022

### 6132.

Jäschke, J.; Skrepek, N.; Ehrhardt, M.
Mixed-Dimensional Geometric Coupling of Port-{Hamiltonian} Systems
IMACM preprint 22/04
2022

### 6131.

J.R. Yusupov, M. Ehrhardt; Matrasulov, D.U.
Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
IMACM preprint 22/12
2022

### 6130.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

### 6129.

Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
2022

### 6128.

Daners, Daniel; Glück, Jochen; Mui, Jonathan
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
2022

### 6127.

[german] Tausch, Michael W.
LED statt Gasbrenner - Mehr Licht für nachhaltigen Chemieunterricht
Chemie in unserer Zeit, 56 (3/2022) :188–196
2022

### 6126.

Agasthya, L.; Bartel, A.; Biferale, L.; Ehrhardt, M.; Toschi, F.
Lagrangian instabilities in thermal convection with stable temperature profiles
IMACM preprint 22/10
2022

### 6125.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
2022

### 6124.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

### 6123.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

### 6122.

Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
On intertwining of maxima of sum of translates functions with nonsingular kernels
Trudy Inst. Mat. Mekh. UrO RAN
2022

### 6121.

Muniz, M.; Ehrhardt, M.; Günther, M.; Winkler, R.
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
IMACM preprint 22/14
2022

### 6120.

Petrov, {Pavel S.}; Ehrhardt, Matthias; Trofimov, {M. Yu.}
On the decomposition of the fundamental solution of the {Helmholtz} equation via solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215--228
2022
Herausgeber: IOS Press

### 6119.

Arora, Sahiba; Glück, Jochen
Stability of (eventually) positive semigroups on spaces of continuous functions
C. R., Math., Acad. Sci. Paris, 360 :771--775
2022

### 6118.

Glück, Jochen; Martin, Florian G.
Uniform convergence of stochastic semigroups
Israel J. Math., 247 (1) :1--19
2022

### 6117.

Sabirov, K.K.; Yusupov, J.R.; Ehrhardt, M.; Matrasulov, D.U.
Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line
Physics Letters A, 423 :127822
2022
Herausgeber: Elsevier

### 6116.

Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Tracing locally Pareto optimal points by numerical integration
SIAM Journal on Control and Optimization, 59 (5) :3302-3328
2022

Weitere Infos über #UniWuppertal: