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Simulation of Stranski-Krastanov growth


In very thin hetero-epitaxial films with positive misfit, strain can be relaxed by the spontaneous formation of 3D-islands on the surface. In the mounds and in particular on the mounds surface, particles can assume larger distances than in a flat, pseudomorphic layer.
In the so-called Stranski-Krastanov (SK) growth mode the scenario is, somewhat idealized, as follows:

· the first few monolayers of adsorbate grow coherently with the substrate,
  a so-called wetting layer (WL) is formed

· at a characteristic kinetic WL thickness 3D islands emerge,
  this has been termed the Stranski-Krastanov transition

· the growth of these islands is fed by further deposition and by
  the incorporation of wetting layer particles

· if deposition stops after depostion of a few monolayers of adsorbate material
  one observes well separated islands of roughly the same size on top
  of a stationary WL

This growth mode has been observed in a variety of materials, including semi-conductor systems such as Ge/Si or compound materials like InGaAs. In this context, SK-growth can be exploited in the self-organized formation of Quantum Dots. But even in the deposition of large organic molecules on metal surfaces, SK-like growth occurs. This supports that the idea that the basic mechanisms that trigger the SK-transition should not be material specific and might be apparent in simpliftying models already.

In our off-lattice Kinetic simulations of a simple (1+1) dimensional model of strained hetero-epitaxy we observe indeed the formation of a WL and self-organized islands along the lines of the SK scenario. The following image displays a system with a relative misfit of 4%. After a mean film thickness of 4ML of adsorbate, deposition was stopped and one finds clearly separated islands on a persisting wetting layer.


(color coded mean distance from neighbors
blue = bulk substrate, orange = bulk adsobat spacing)

We are aiming at a principled understanding of the SK transition. Within the frame of our model we can study the dependence of critical and stationary wetting layer thickness on misfit, temperature and deposition rate. For different choices of the very few model parameters (temperature, flux, misfit, adsorbate-adsorbate and substrate-adsorbate interactions) the system should also display Volmer-Weber and Layer-by-Layer growth. We are currently performing studies in this direction (M. Walther, PhD project, Würzburg).

The following (selected) publications deal with the self-organized formation of islands in Stranski-Krastanov growth:

F. Much and M. Biehl
Simulation of wetting-layer and island formation in heteroepitaxial growth
preprint version of Europhys. Lett. 63, 14 (2003)

(PS version)    (PDF version)

M. Biehl and F. Much
Off-lattice Kinetic Monte Carlo simulations of Stranski-Krastanov-like growth
preprint version of an invited contribution to the NATO-ARW on
Quantum Dots: Fundamentals, Applications, and Frontiers, June 2003,
eds. B. Joyce, P. Kelires, A. Naumovets, and D.D. Vvedensky,
NATO Sciences Series II: Mathematics, Physics, and Chemistry Vol. 190, Springer (2005)
(PS version)    (PDF version)

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


Off-lattice Kinetic Monte Carlo simulations of strained heteroepitaxial growth
preprint version of an invited contribution to an MFO Mini-Workshop (Oberwolfach, 2004),
in: Multiscale Modeling in Epitaxial Growth,
ed. A. Voigt, Int. Series of Numerical Mathematics 149 (Birkhaeuser, 2005), 41-57