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.

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)