Dresden 2009 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 17: Quantum wires: Optical and transport properties

HL 17.5: Talk

Tuesday, March 24, 2009, 11:15–11:30, BEY 154

Modelling Quantum Transport Through Nano-Structures by Finite Elements: Getting the Boundaries Right — •Stephan Kramer, Oliver Bendix, Kai Bröking, Ragnar Fleischmann, and Theo Geisel — Max-Planck-Institut für Dynamik und Selbstorganisation, 37073 Göttingen

For simulating the electronic transport through a ballistic semiconductor device quantum mechanically, one has to solve the stationary Schrödinger equation in a complex geometry with intricate boundary conditions. We are especially interested in the transmission properties of scattering states, e.g. as in [1]. For their computation we employ higher order finite element methods which make it possible to properly incorporate curvilinear boundaries and spatial adaptivity.

Scattering experiments in semiconductor devices can be described by a finite domain containing scatterers and leads of semi-infinite length providing a source for incoming plane waves and a sink for outgoing scattered waves. As FEMs are capable only of describing problems on a finite domain, the leads must be cut off after some finite distance. Because of this, their infinite extent has to be modelled by suitable boundary conditions. For semi-infinite leads, these are provided by the Sommerfeld radiation condition.

We apply our approach to electron transport in the presence of static magnetic fields and show how to set up the correct boundary conditions for different complex geometries.
[1] Nature Physics 3, 464 - 468 (2007)