Formation and consequences of misfit dislocations in heteroepitaxial growth

Abstract

We investigate the formation of misfit dislocations in strained heteroepitaxial crystal growth and their influence on the structure of the growing layers. We use Kinetic Monte Carlo simulations for an off-lattice model in 1+1 dimensions with Lennard-Jones interactions. Two different types of the formation of dislocations are found, depending on the sign and the magnitude of the misfit. Misfit dislocations affect the lateral and the vertical lattice spacing in heteroepitaxial growth. In addition, we observe a correlation between the lateral position of buried dislocations and grown mounds, depending on the sign of the misfit.1 Introduction Due to its high technological relevance, epitaxial growth of semiconductor interfaces has become a field of intensive study in the past years. From a theoretical point of view, epitaxial growth is an example of cooperative behavior far from thermal equilibrium which is still an active field of research. Epitaxial layers of atoms and molecules can be realized by molecular beam epitaxy which allows to design high quality semiconductor structures on an atomic scale. In the case of heteroepitaxy, substrate and adsorbate consist of different materials and may differ in their lattice constants. This leads to interesting structures of the growing atomic layers. The first few adsorbate layers can grow pseudomorphically, i.e. coherently with the crystal structure of the substrate. But due to strain the elastic energy of the system rises with increasing adsorbate film thickness. At a critical layer thickness the strain is released by forming misfit dislocations.In this work the detailed mechanisms of the formation of dislocations are investigated with means of Kinetic Monte Carlo Simulations [1][2][3]. It is obvious that dislocations cannot be modelled properly with predefined lattice structures, hence we use an off-lattice model. Since we are interested in the general phenomenon of epitaxial growth competing with strain and dislocations, we use Lennard-Jones interactions. As a starting point, we investigate (1+1)-dimensional models with classical pair-interactions and lateral extensions of a few hundred lattice spacings. Even in this fairly limited framework we observe complex phenomena which can be compared with experiments and yield qualitative insights into heteroepitaxial growth. Following previous studies [3-6], we choose a pair potential to model the interactions between substrate and adsorbate particles and we apply an off-lattice algorithm to the simulation of the growth of heteroepitaxial layers in 1+1 dimensions.We have investigated the formation of dislocations as well as their influence on the vertical and the lateral lattice spacings. In addition, we found that buried dislocations have a pronounced influence on the surface structure of the subsequent growth.

Simulation of self-assembled nanopatterns in strained 2D alloys on the face centered cubic (111) surface

“…The atomistic structure now naturally emerges from the symmetry of the particle interactions used, and the symmetry of the substrate. This type of model has been employed in previous investigations of heteroepitaxial growth, at first in the simpler 1 + 1-dimensional case, for instance in the context of strain relief through misfit dislocations [16][17][18][19] or the so-called StranskiKrastanov growth mode [20]. The method was applied, also to 2 + 1-dimensional systems, for the study of the effect of strain on diffusion barriers in [21], however, for a simple cubic lattice.…”

Crossing the mesoscale no-man<U+2019>s land via parallel kinetic Monte Carlo.

“…For the general amorphous case, it may be possible to use bond length and angle expectations to significantly reduce the volume of space that need be probed for potential vacant sites near an occupied site. Not surprisingly, most off lattice models of surface deposition and diffusion in the literature are 2D [6,57,58,85] and existing 3D models are for a simple cubic lattice [69,81].…”

Effect of misfit dislocation on surface diffusion

“…In heteroepitaxial growth, for example, the first few deposited layers grow pseudomorphically (following the substrate geometry) until the strain due to the lattice mismatch is released at a critical thickness leading to the formation of misfit dislocations. [7][8][9] In several works 10-13 the formation of such misfit dislocations for heteroepitaxial Lennard Jones systems was documented using molecular static calculations of system energetics and activation energy barriers coupled with either off-lattice kinetic Monte Carlo simulations [10][11][12] or application of spherical repulsive potentials 13 to activate the nucleation process. More recently Trushin et al 14 have applied semi empirical interaction potentials from the embedded atom method (EAM) 15 to generate misfit dislocation in heteroepitaxial growth of Pd/Cu(100) and Cu/Pd(100).…”