Quantum Semiconductors
The progress in material sciences and process technologies allows for the realization of novel semiconductor devices whose functionality is based on quantum mechanical effects. Examples are resonant tunneling diodes, quantum cascade structures, and quantum dots (single-electron transistor). These devices may be modeled by particular partial differential equations, such as Schrödinger-Poisson systems, Wigner models, and Pauli master equations.
Challenging problems are the modeling of Schrödinger solvers with closed and open boundary conditions, the computation of electronic band structures, and the simulation of carbon-nanotube field-effect transistors. Mathematically, efficient numerical discretizations and algorithms will be developed. The Ph.D. projects will be conducted with the participation of the following professors from electro-engineering and mathematics: Arnold, Jüngel, Kosina, Melenk.
Particle density in a 2D quantum stub transistor