arXiv subjects

I. Markov

Publications and source records attributed to I. Markov.

11 recordsLinked to original sources

arXiv2017

Stranski-Krastanov mechanism of growth and the effect of misfit sign on quantum dots nucleation

The thermodynamics of the Stranski-Krastanov mode of epitaxial growth and the effect of the sign of the lattice misfit are discussed. The Stranski-Krastanov mode of growth represents a sequence of layer-by-layer or Frank-van der Merwe growth followed by the formation of three-dimensional (3D) islands or Volmer-Weber growth. The occurrence of both growth modes mentioned above is in compliance with the wettability criterion of Bauer. The positive wetting function required for the occurrence of the Volmer-Weber growth is originated by the vertical displacements of the atoms close to the edges of the two-dimensional (2D) islands as a result of the relaxation of the lattice misfit. The monolayer high islands become unstable against bilayer islands, bilayer islands in turn become unstable against trilayer islands, etc. beyond some critical islands sizes. Monolayer islands appear as necessary precursors of three-dimensional (3D) islands. The critical island size for mono-bilayer transformation increases steeply with decreasing lattice misfit and diverges at a critical value of the misfit. This value divides the regions of Frank-van der Merwe and Stranski-Krastanov modes in a phase diagram of coordinates wetting-misfit. The transformation of monolayer to multilayer islands takes place either by consecutive nucleation and growth of 2D islands (layer-by-layer transformation), or by nucleation and lateral (2D) growth of multilayer islands (multilayer 2D transformation). The former occurs in the case of "stiff" overlayer materials and mostly in compressed overlayers. The latter takes place in the case of "soft" materials like Pb and In, mostly in tensile overlayers. Tensile films show non-nucleation transformation compared with the nucleation-like behavior of compressed films.

cond-mat.mtrl-sci↗

arXiv2014

Step energies and equilibrium shape of strained monolayer islands

Using a simple atomistic model of anharmonic nearest-neighbors interaction, we have calculated the step energies of strained hexagonal monolayer islands. These have been found to decrease with the absolute value of the misfit due to the strain relaxation at steps. The effect is significantly more pronounced in the case of positive misfit owing to the stronger repulsive interatomic forces. Furthermore, (111)-faceted steps are favored at positive misfit (compressed islands) and, to a lesser extent, (100)-faceted steps at negative misfits (tensile islands). The result is rationalized in terms of the different bonding geometries at step edges and a comparison with experiments is included. Thus, the equilibrium shape transforms from regular hexagons at zero misfit to threefold symmetric hexagons with increasing misfit.

cond-mat.mtrl-sci↗

arXiv2011

Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots

We have studied the monolayer-bilayer transformation in the case of the coherent Stranski-Krastanov growth. We have found that the energy of formation of a second layer nucleus is largest at the center of the first-layer island and smallest on its corners. Thus nucleation is expected to take place at the corners (or the edges) rather than at the center of the islands as in the case of homoepitaxy. The critical nuclei have one atom in addition to a compact shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with i>1 an integer. When the edge of the initial monolayer island is much larger than the critical nucleus size, the latter is always a rectangle plus an additional atom, adsorbed at the longer edge, which gives rise to a new atomic row in order to transform the rectangle into the equilibrium square shape.

cond-mat.mtrl-sci↗

arXiv2010

Effect of the lattice misfit on the equilibrium shape of strained islands in Volmer-Weber growth

We have studied the effect of the misfit on the equilibrium shape of three-dimensional pyramidal islands grown on a foreign substrate in the case of incomplete wetting (Volmer-Weber mode of growth). We have found that tensile islands have smaller aspect ratios compared with compressed islands owing to its better adhesion to the substrate. The average strains of consecutive layers decrease faster with thickness in compressed than in tensile islands. The strains decrease rapidly with thickness, with the consequence that above a certain height, the upper layers of the pyramid become practically unstrained and does not contribute to a further reduction in the upper base. As a result, the truncated pyramids are not expected to transform into full pyramids. Our results are in good agreement with experimental observations in different systems.

cond-mat.mtrl-sci↗

arXiv2007

Forbidden island heights in stress-driven coherent Stranski-Krastanov growth

The observed height distribution of clusters obtained in strained epitaxy has been often interpreted in terms of electronic effects. We show that some aspects can be explained classically by the interplay of strain and edge energies. We find that soft materials can transform directly from monolayer into thicker islands by two-dimensional (2D) multilayer nucleation and growth. There is a critical thickness decreasing with the force constant. Thinner islands are thermodynamically forbidden, due to the insufficient stress relaxation upon clustering particularly under tensile stress. At sufficiently large misfits the barrier for 2D multilayer nucleation is significantly smaller than the barrier for subsequent single-layer nucleation. The effects are found to be quantitatively reasonable and offer a plausible explanation for the absence of thin islands and 2D growth of flattop islands usually attributed to quantum size effects.

cond-mat.mtrl-sci↗

arXiv2006

Formation and self-assembly of coherent quantum dots: some thermodynamic aspects

Quantum dots have promising properties for optoelectronic applications. They can be grown free of dislocations in highly mismatched epitaxy in the coherent Stranski-Krastanov mode. In this chapter, some thermodynamic aspects related to the wetting in the growth and self-assembly of three-dimensional (3D) coherent islands are studied using an energy minimization scheme in a 1+1-dimensional atomic model with anharmonic interactions. The conditions for equilibrium between the different phases are discussed. It is found that the thermodynamic driving force for 3D-cluster formation is the reduced adhesion of the islands to the wetting layer at their edges. In agreement with experimental observations, for values of the lattice mismatch larger than a critical misfit, a critical island size for the 2D-3D transition is found. Beyond it, monolayer islands become unstable against bilayer ones. Compressed coherent overlayers show a greater tendency to clustering than expanded ones. The transition to 3D islands takes place through a series of intermediate stable states with thicknesses discretely increasing in monolayer steps. Special emphasis is made on the analysis of the critical misfit. Additionally, the effect of neighbouring islands mediated through a deformable wetting layer is considered. The degree of wetting of the substrate by a given island depends on the size and shape distributions of the neighbouring islands. Implications for the self-assembled growth of quantum dots are discussed.

cond-mat.mtrl-sci↗

arXiv2005

Quantum-dot nucleation in strained-layer epitaxy: minimum-energy pathway in the stress-driven 2D-3D transformation

The transformation of monolayer islands into bilayer islands as a first step of the overall two-dimensional to three-dimensional (2D-3D) transformation in the coherent Stranski-Krastanov mode of growth is studied for the cases of expanded and compressed overlayers. Compressed overlayers display a nucleation-like behavior: the energy accompanying the transformation process displays a maximum at some critical number of atoms, which is small for large enough values of the misfit, and then decreases gradually down to the completion of the transformation, non-monotonically due to the atomistics of the process. On the contrary, the energy change in expanded overlayers increases up to close to the completion of the transformation and then abruptly collapses with the disappearance of the monoatomic steps to produce low-energy facets. This kind of transformation takes place only in materials with strong interatomic bonding. Softer materials under tensile stress are expected to grow predominantly with a planar morphology until misfit dislocations are introduced, or to transform into 3D islands by a different mechanism. It is concluded that the coherent Stranski-Krastanov growth in expanded overlayers is much less probable than in compressed ones for kinetic reasons.

cond-mat.mtrl-sci↗

arXiv2004

Self-assembly of quantum dots: effect of neighbor islands on the wetting in coherent Stranski-Krastanov growth

The wetting of the homogeneously strained wetting layer by dislocation-free three-dimensional islands belonging to an array has been studied. The array has been simulated as a chain of islands in 1+1 dimensions. It is found that the wetting depends on the density of the array, the size distribution and the shape of the neighbor islands. Implications for the self-assembly of quantum dots grown in the coherent Stranski-Krastanov mode are discussed.

cond-mat.mtrl-sci↗

arXiv2003

Some thermodynamic aspects of self-assembly of arrays of quantum dots

We have studied the relative adhesion (the wetting) of dislocation-free three-dimensional islands belonging to an array of islands to the wetting layer in Stranski-Krastanov growth mode. The array has been simulated as a chain of islands in 1+1 dimensions placed on top of a wetting layer. In addition to the critical size of the two-dimensional islands for the 2D-3D transformation to occur, we find that the wetting depends strongly on the density of the array, the size distribution and the shape of the islands.

cond-mat.mtrl-sci↗

arXiv2002

Thermodynamic driving force of formation of coherent three-dimensional islands in Stranski-Krastanov growth

The formation of coherent three-dimensional islands in highly mismatched epitaxy is discussed in terms of the traditional concept of wetting. It is shown that the wetting layer and the 3D islands represent different phases which cannot be in equilibrium with each other, and the transfer of matter from the stable wetting layer to the 3D islands is thermodynamically unfavored. The experimentally observed critical misfit for coherent 3D islanding to occur and the coexistence of pyramids with discrete heights of two, three, four... monolayers can be explained assuming that the thermodynamic driving force of formation of coherent 3D islands on the surface of the wetting layer of the same material is the reduced average adhesion of the islands to that layer and that the islands height is a discrete variable.

cond-mat.mtrl-sci↗

arXiv2000

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

The formation of coherently strained three-dimensional islands on top of the wetting layer in Stranski-Krastanov mode of growth is considered in a model in 1+1 dimensions accounting for the anharmonicity and non-convexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than in expanded overlayers beyond a critical lattice misfit. In the latter case 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 the 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. The latter explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after exceeding the corresponding critical sizes. The rearrangements are initiated by nucleation events each next one requiring to overcome a lower energetic barrier. The model is in good qualitative agreement with available experimental observations.

cond-mat.mtrl-sci↗