Off-Lattice KMC Simulations of Stranski-Krastanov-Like Growth

Abstract

We investigate strained heteroepitaxial crystal growth in the framework of a simplifying (1 + 1)-dimensional model by use of off-lattice kinetic Monte Carlo simulations. Our modified Lennard-Jones system displays the so-called Stranski-Krastanov growth mode: initial pseudomorphic growth ends by the sudden appearance of strain induced multilayer islands upon a persisting wetting layer. IntroductionIn addition to its technological relevance, epitaxial crystal growth is highly attractive from a theoretical point of view. It offers many challenging open questions and provides a workshop in which to develop novel methods for the modeling and simulation of non-equilibrium systems, in general. In particular, strained heteroepitaxial crystal growth attracts significant interest as a promising technique for the production of, for instance, high quality semiconductor films. Recent overviews of experimental and theoretical investigations can be found in, e.g. [1,2,3]. A particularly attractive aspect is the possibility to exploit selforganizing phenomena for the fabrication of nanostructured surfaces by means of molecular-beam epitaxy (MBE) or similar techniques.In many cases, adsorbate and substrate materials crystallize in the same lattice but with different bulk lattice constants. Frequently, one observes that the adsorbate grows layer by layer, initially, with the lateral spacing of atoms adapted to the substrate. The misfit induces compressive or tensile strain in this pseudomorphic film and, eventually, misfit dislocations will appear. These relax the strain and the adsorbate grows with its natural lattice constant far from the substrate, eventually.

Off-lattice Kinetic Monte Carlo Simulations of Strained Heteroepitaxial Growth

“…In simulations with different deposition rates we observe that the kinetic WL thickness increases with R d [20,21]. If the formation of second or third layer nuclei by freshly deposited particles was the driving force, one would expect more frequent nucleation and an earlier 2D-3D-transition at higher growth rates.…”

“…We conclude that, in the main, upward jumps trigger the SK-transition. Further evidence and a more detailed discussion of this important point is given in [21].…”

“…More importantly, we find a significant contribution of particles that jump upward, from the WL atop an island. The rate for such processes is quite small, generally, but becomes significant close to the SK-transition, see [21] for details.…”

“…Several properties of surface diffusion in our model are discussed in [21] in greater detail. Here, we shortly summarize the essential features: a) Adsorbate diffusion right on the substrate is relatively slow, due to the fact that U as is quite large and satisfies U as > U a .…”

“…In the following we will discuss an off-lattice model and the corresponding Kinetic Monte Carlo (KMC) technique, which allows for continuous particle positions and in which strain results directly from the atomic interactions. Schindler and Wolf have essentially formulated the model and simulation method in [17,18], and some of the results presented here have been published previously in [19,20,21]. For a detailed description of the concept and its applications see also [22].…”