Jump to: introduction lattice gas models off-lattice KMC review articles

Note: a few talks (ppt) about some of the topics are available here

One important area within my research activities is the theory, modelling, and simulation of non-equilibrium systems. This concerns, in particular, models of growing crystals and nano-structured surfaces.

The technique of

Growth in an MBE environment is clearly far from equilibrium: the system is constantly driven by the depostion flux and an extremely low pressure is maintained in the UHV chamber. This is different from other situations closer to equilibrium, where the growing film can exchange particles with a vapor, for instance.

MBE growth is therefore highly attractive from a theoretical point of view. The well-defined non-equilibrium situation provides a workshop in which to develop analytical approaches as well as novel computer simulation techniques suitable for more general non-equilibrium systems.

** Lattice gas models and KMC simulations:**
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In our research, we have mainly studied and developed models that allow for the simulation of growth by use of simplifying lattice gas models (click for a review). Examples include the following topics (click for details where available):

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· Mound formation, slope selection, and coarsening dynamics
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· (Non-) Universal scaling behavior in unstable growth
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· Surface reconstructions of II-VI semiconductor materials
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· Atomic Layer Epitaxy of II-VI(001) semiconductor surfaces
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** Off-lattice KMC simulations:**
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For the modelling of hetero-epitaxial systems we employ off-lattice KMC simulations (click for a review) with continuous particle positions. The method combines the ideas of KMC with a determination of transition rates by means of

Our investigations concern the following topics:

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** · Misfit dislocations in strained hetero-epitaxial crystal growth
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· Stranski-Krastanov-like growth: self-organized Quantum Dots
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· The formation of nano-structured surface alloys
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The following two articles appeared as invited contributions in the Proceedings of an MFO Mini-Workshop in Oberwolfach (2004).

M. Biehl

Lattice gas models and Kinetic Monte Carlo simulations
of epitaxial growth.

pages 3-18.
discusses the basic concepts and points at further references)

M. Biehl, F. Much, and C. Vey

Off-lattice Kinetic Monte Carlo simulations of
strained heteroepitaxial growth

pages 41-57
(introduction and example applications )

in: A. Voigt (ed.), *Multiscale Modeling in Epitaxial Growth*

Birkhaeuser, International Series of Numerical Mathematics, Vol. 149 (2005)