Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

Abstract

The formation of coherently strained three-dimensional ͑3D͒ islands on top of the wetting layer in the Stranski-Krastanov mode of growth is considered in a model in 1 ϩ 1 dimensions accounting for the anharmonicity and nonconvexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than expanded overlayers beyond a critical lattice misfit. In expanded overlayers the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. This explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of monoto bilayer, bi-to trilayer islands, etc., after the corresponding critical sizes have been exceeded. The rearrangements are initiated by nucleation events, each one needing to overcome a lower energetic barrier than the one before. The model is in good qualitative agreement with available experimental observations.

Quantum-dot nucleation in strained-layer epitaxy: Minimum-energy pathway in the stress-driven two-dimensional to three-dimensional transformation

“…18,19 The mono-bilayer transformation was considered as the first step of the overall 2D-3D transformation and a critical misfit was determined from the misfit dependence of N 12 . The latter was found to increase with decreasing misfit diverging at a critical value ε 12 .…”

“…The first step in this transformation should be the rearrangement of monolayer into bilayer islands. 18,19 Khor and Das Sarma found by Monte Carlo simulations that during the rearrangement, the material for the bilayer island comes almost completely from the original monolayer island, the bulk of the material for the three-layer island comes from the original two-layer island, etc. 20 Moison et al reported that the coverage suddenly decreases from about 1.75 ML to 1.2 ML when 3D InAs islands begin to form on GaAs.…”

Epitaxial growth of BaTiO3 thin films at a low temperature under 300°C with temperature-controlled BaTiO3 buffer layer

“…Moreover, the second layer nucleation in heteroepitaxy differs markedly from that in homoepitaxy. The reason is that the growth of strained 2D island should be accompanied by the relaxation of strain and the decrease of adhesion of atoms at the island perimeter [21][22][23]. It can lead to the increased adatom concentration on the island top.…”

Various types of growth instabilities in coherent epitaxy

“…If the misfit is weak, growth will take place layer by layer as in the case of a pure crystal. Experimentally, the 2D-3D instability has quite different features at low misfit [11,12] and it has even been suggested [13,14] that growth is two-dimensional below a critical misfit (about 2%). Therefore, it seems reasonable to believe that the nucleation of new terraces has peculiar features above this critical misfit.…”