Erasmus Langer
Siegfried Selberherr
Oskar Baumgartner
Markus Bina
Hajdin Ceric
Johann Cervenka
Raffaele Coppeta
Lado Filipovic
Lidija Filipovic
Wolfgang Gös
Klaus-Tibor Grasser
Hossein Karamitaheri
Hans Kosina
Hiwa Mahmoudi
Alexander Makarov
Mahdi Moradinasab
Mihail Nedjalkov
Neophytos Neophytou
Roberto Orio
Dmitry Osintsev
Mahdi Pourfath
Florian Rudolf
Franz Schanovsky
Anderson Singulani
Zlatan Stanojevic
Viktor Sverdlov
Stanislav Tyaginov
Michael Waltl
Josef Weinbub
Yannick Wimmer
Thomas Windbacher
Wolfhard Zisser

Johann Cervenka
Senior Scientist Dipl.-Ing. Dr.techn.
Johann Cervenka was born in Schwarzach, Austria, in 1968. He studied electrical engineering at the Technische Universität Wien, where he received the degree of Diplomingenieur in 1999. He then joined the Institute for Microelectronics at the Technische Universität Wien and received his PhD degree in 2004. His scientific interests include three-dimensional mesh generation, as well as algorithms and data structures in computational geometry.

Deterministic Wigner Approach

To describe the carrier transport processes in novel nanoelectronic devices, an accurate description in the nanometer scale has to be used. Accordingly, in this regime, the effects of quantum mechanics have to be considered as well. The Wigner formulation of quantum mechanics provides a convenient phase space formulation of quantum theory. The main difficulties in the implementation of a deterministic approach to solving the Wigner equation arise due to the huge amount of memory consumption. This issue is solved by stochastic approaches, that are, however, offset by their computational time requirements. Deterministic methods also show difficulties in the discretization of the diffusion term in the differential equation because of rapid variations of the Wigner function in the phase-space. Unfortunately the commonly used higher-order schemes show very different output characteristics. The developed approach uses an integral formulation of the Wigner equation of a single fundamental wave packet. In this method the differentiation can be avoided. We consider the evolution of an initial condition described by the superposition (in phase-space) of particular fundamental packages. To calculate the distribution at desired time steps, all "fundamental evolutions" of the Wigner equation have to be summated. The Wigner equation has to be solved for each packet, which only depends on the initial location (in phase-space) of the packet. As the particular calculations are independent from each other, this method is well suited for parallelization. The calculations have been parallelized by Message Passing Interface over several nodes and OpenMP on each node and show excellent scalability. With this parallelization it was also possible to eliminate another drawback of a sequential procedure. For the calculation of one particular solution of the Wigner equation a convenient history of previous distributions has to be stored. As the amount of stored data rises rapidly with resolution and simulation time, the applicability of the sequential method becomes limited. As each fundamental packet only has to know its own history, the overall history can be split into the history of the tasks on the particular nodes. Further improvements of memory consumption, and consequentially of the resolution, can be achieved by an alternative simulation technique. Originally the solutions for each time step arise sequentially. At end time the history of each distribution in phase-space of all discrete packets is stored. If the separate results are summed at end time, only the distribution history for the currently running simulations has to be stored. This will be the focus of future investigations.

Evolution of a wave packet at a potential barrier at x=0.

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