Berlin 2008 – wissenschaftliches Programm
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HL: Fachverband Halbleiterphysik
HL 28: Transport properties
HL 28.10: Vortrag
Dienstag, 26. Februar 2008, 11:45–12:00, ER 164
Adaptive Finite Element Simulations of Ballistic Semiconductor Devices — •Stephan Kramer1, Oliver Bendix2, Kai Bröking2, Ragnar Fleischmann2, and Theo Geisel2 — 1Institut für Theoretische Physik, 37077 Göttingen — 2Max-Planck-Institut für Dynamik und Selbstorganisation, 37073 Göttingen
Simulating the quantum mechanics of a ballistic semiconductor device requires the treatment of a stationary Schrödinger equation in a complex geometry with a great variety of boundary conditions. The presence of strong magnetic fields induce steep gradients on the wave function which impose high demands on the numerical methods.
We have implemented a finite-element simulation based on deal.II [1] equipped with several adaption schemes for the triangulation of the domain of the physical problem. This allows for resolving the details of the wave function on different length scales in different parts of the geometry. Especially in the area of the contacts of the device, where we have to calculate the wave function with great accuracy, we can locally employ a high grid resolution, whereas in other regions the mesh is kept coarse. This decreases the computational effort, only making it possible to run simulations for a sufficiently large number of magnetic fields to reproduce experimental results.
We use the computation of the transmission properties of a magnetic focussing device [2] from the scattering matrix as an example to demonstrate the benefits of a locally adaptive simulation code.
[1] www.dealii.org
[2] Nature Physics 3, 464 - 468 (2007)