Simulation of misfit dislocations

In the simplest examples of hetero-epitaxy, adsobate and substrate crystallize in the same lattice types, but with slightly different lattice constants, i.e. inter-atomic distances.
In the early stages of such hetero-epitaxial growth the adsorbate is coherent with the substrate. In such a so-called pseudomorphic film, the crystal topology is that of a perfect crystal, i.e. each particle has the same coordination number and its nearest and next-nearest neighbors form the same geometrical figure with only slightly modified distances.
As the thickness of the adsorbate film increases the elastic energy of the film rises until it is energetically favorable to form misfit dislocations in order to relieve the strain. The lattice structure is locally disturbed, allowing the adsorbate atoms to maintain a spacing which is closer to their undisturbed bulk lattice structure.
Depending on the sign and magnitude of the relative lattice misfit between adsorbate and substrate, dislocations can be found right at the adsorbate/substrate interface, or emerge and remain in the growing film. The following image shows misfit dislocations in the former case, i.e. for fairly large, positive mismatch.

(grey scale values correspond to the average distance to nearest neighbors)


In our work we have studied the emergence of misfit dislocations qualitatively in terms of (1+1)-dimensional models with continuous particle positions. Assuming simple, classical pair-wise interactions, such as Lennard-Jones or Morse potential, we determine for each configuration the rates of, e.g., diffusion processes. This is done by means of the so-called Molecular Static method. The off-lattice KMC simulation method was essentially formulated by D. Wolf and co-workers, see for instance [A. Schindler, PhD thesis, Duisburg, 1999].
Strain effects are not introduced by hand, but result directly from the particle interactions. Effectively long range effects emerge from the elastic deformation of the substrate, for instance.
We determine, for instance, the critical layer thickness for the formation of dislocations as a function of the misfit. Currently we study the influence of buried dislocations on diffusion properties on the surface (M. Walther, PhD thesis work in Würzburg). We find, for instance, correlations between the location of buried misfit dislocations and the formation of mounds in later stages of the growth process.

The following (selected) publications deal with the subject of misfit dislocations:

F. Much, M. Ahr, M. Biehl and W. Kinzel
Kinetic Monte Carlo Simulations of dislocations in heteroepitaxial growth
Europhys. Lett. 56(6), 791 (preprint 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

M. Walther, M. Biehl, W. Kinzel
Formation and consequences of misfit dislocations in heteroepitaxial growth
Physica Status Solidi (C) 4:3210-3220, 2007
preprint version: (PDF)