**Unstable epitaxial crystal growth**

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One can assume that in many materials, inter-layer diffusion is hindered
by an additional energy barrier at terrace edges.
While such additional barriers are irrelevant for equilibrium properties,
in principle, this so-called Ehrlich-Schwoebel
causes a strong kinetic instability: particles will preferentially stay on top
of existing terraces. Ultimately flat surfaces become unstable and mounds
will form in the growth process.

Slope dependent downhill currents, on the other hand, can counter-balance
the Schwoebel effect. As a result, the system can select a stable angle
after the initial formation of mounds.

Thereafter, mounds on the surface will coarsen, i.e. merge into larger structures.
The coarsening can be due to different mechanisms. Deposition noise can lead
to the random dominanca of mounds over their neighbors resulting in noise
driven coarsening. Other effects, such as the diffusion of adatoms along terraces
at the base of mounds, lead to a mass transport which can speed up the coarsening
process.

Such systems constitute a special case of self-affine surfaces, their properties
are described by dynamical scaling laws and the corresponding set of exponents.
Often, one hypothesizes the existence of * universality classes*: groups
of models that differ in microscopic details but display the same, robust
scaling behavior and set of exponents.
For an overview of this field, see, for instance,
A.-L. Barabasi and H.E. Stanley, *Fractal Concepts in Surface Growth* (Cambridge
University Press, 1995).

We have investigated mound formation and slope selection in the framework of simplifying lattice gas models. As one example, we have addressed the question to what extent the microscopic details of adatom diffusion along step edges determines the morphology and scaling of the growing surface. Recently we have studied, furthermore, the influence of an Ehrlich-Schwoebel like barrier at corners and kink-sites.

The following __selected__ key publications concern mound formation, slope selection and
the scaling behavior of self-affine growth. For a more complete list of references
go here.

M.Biehl, M. Walther, and S. Weber
__Corner barrier controlled morphology and scaling behavior of unstable epitaxial growth__

(in preparation)

M.Biehl, M. Ahr, M. Kinne, W. Kinzel, and S. Schinzer

Particle currents and the distribution of terrace
sizes in unstable epitaxial growth

preprint version of Phys. Rev. B ** 64 ** (Brief Reports), 113405 (2001)

(PS version)
(PDF version)

M. Ahr and M.Biehl,hr, M. Biehl, M. Kinne, W. Kinzel,

The influence of the crystal lattice on coarsening in unstable epitaxial growth

preprint version of Surface Science ** 465 **, 339 (2000)

(PS version)
(PDF version)

M. Ahr and M. Biehl
*
Singularity spectra of rough growing surfaces from wavelet analysis*

preprint version of Phys. Rev. **E 62**, 1773 (2000)

S. Schinzer, M.Kinne,
M.Biehl, and W. Kinzel,
*The
role of step edge diffusion in epitaxial crystal growth*

preprint version of Surface Science **439**, 191 (1999)

M. Biehl, W. Kinzel, and S. Schinzer
*A
simple model of epitaxial growth*

preprint version of Europhys. Lett. **41** (1998), 443