Atomistic and Continuum Elastic Effects in Heteroepitaxial Systems

Schindler, A. C.; Vvedensky, Dimitri D.; Gyure, Mark F.; Simms, Geoffrey; Caflisch, Russel E.; Connell, Cameron

doi:10.1007/978-94-010-0391-9_26

Cited by 2 publications

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“…The physical reason for the ocurrence of this 2D-3D transition is well established as the gain of strain energy at the expense of surface energy. [1][2][3][4][5][6][7][8] However, the mechanism of formation of 3D islands on the planar wetting layer in the case of coherent (dislocationless) SK growth is still an unsolved problem in spite of intensive studies in the last two decades.…”

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

Prieto

Markov

2011

Phys. Rev. B

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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. The Stranski-Krastanov (SK) mode of epitaxial growth is a nice example of an instability of planar, two-dimensional (2D) growth against three-dimensional (3D) islanding due to a nonzero lattice misfit between the deposit and the substrate materials. This leads to the formation of arrays of self-assembled small crystallites. In the case of semiconductor overgrowth, these are known as quantum dots and have important applications in optoelectronic devices. The physical reason for the occurrence of this 2D-3D transition is well established as the gain of strain energy at the expense of surface energy.1-8 However, the mechanism of formation of 3D islands on the planar wetting layer in the case of coherent (dislocationless) SK growth is still an unsolved problem in spite of intensive studies in the last two decades.Voigtländer and Zinner 9 observed by scanning tunneling microscopy (STM) that faceted 3D Ge islands form at the same locations on a Si(111) surface at which 2D islands were observed in the initial stage of deposition immediately after exceeding the critical thickness of the wetting layer. Ebiko et al. 10 found that the scaling function of the volume distribution of 3D InAs quantum dots on the surface of GaAs coincide with the scaling function for 2D submonolayer homoepitaxy with critical cluster size i = 1. Mo et al. 11 observed Ge islands representing elongated pyramids (hut clusters) bounded by {105} facets inclined by 11.3• to the substrate. The authors suggested that the hut clusters are a step in the pathway to the formation of larger islands with steeper side walls known in the literature as (rounded) domes and (faceted) barns.12 Chen et al. 13 studied the earliest stages of Ge islanding on Si(001) and established that Ge islands smaller than the hut clusters are not bounded by discrete {105} facets. This result was later confirmed by Vailionis et al. 14 who observed the formation of three to four monolayers (ML)-high prepyramids with rounded bases, which exist over a narrow interval of a Ge coverage in the beginning of the 2D-3D transition. Also Arapkina and Yuryev found that the formation of the second layer of Ge clusters results in rearrangement of the f...

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confidence: 99%

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

Prieto

Markov

2011

Phys. Rev. B

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“…Furthermore, diffusion is restricted to adsorbate particles at the surface whereas jumps of substrate particles onto the surface are not considered. As we will demonstrate in a forthcoming publication, these simplifications are justified for small misfits ǫ in the LJ-system because the corresponding rates are extremely low, see also [8,9].…”

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“…Following earlier investigations of related phenomena, e.g. [8][9][10][11], we choose a classical pair potential ansatz to represent the interactions between atoms in our model. Here, we restrict our studies to the fairly simple case of a modified Lennard-Jones (LJ) system in 1 + 1 spatial dimensions, i.e.…”

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

Biehl

Much

Quantum Dots: Fundamentals, Applications, and Frontiers

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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.

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Atomistic and Continuum Elastic Effects in Heteroepitaxial Systems

Cited by 2 publications

References 45 publications

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

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

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

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