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