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Modelling and simulation of crystal growth

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 Molecular Beam Epitaxy (MBE) is a particular clear-cut realization of epitaxial crystal growth. In this method, one or several adsorbate materials are heated in an oven which is contained in an ultra-high vacuum (UHV) chamber. Evaporated particles form an atomic or molecular beam which is directed onto a substrate crystal. After arrival at the substrate, particales become adatoms which may diffuse on the surface and are finally incorporated into the growing crystal.
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.

Selected review articles:

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 )

both in: A. Voigt (ed.), Multiscale Modeling in Epitaxial Growth
Birkhaeuser, International Series of Numerical Mathematics, Vol. 149 (2005)