Nucleation of size calibrated three-dimensional nanodots in atomistic model of strained epitaxy: a Monte Carlo study

Tokar, V. I.

doi:10.1088/0953-8984/25/4/045001

Cited by 4 publications

(22 citation statements)

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“…This is reasonable because the adatoms nucleate an island when meeting at one spatial point in the continuum approximation (or at the nearest sites on the lattice) while according to (44) and (45) the adatom at point x nucleates an island with any other adatom in the system which is unphysical. Secondly, in (44) the nucleation term enters with the coefficient 2, in contrast to our equation (43). The origin of this discrepancy is connected with the last term of (44) that is absent in our equation (43) but is present as the last term in (42)).…”

Section: Comparison With Equations From the Self-consistent Approach mentioning

confidence: 76%

“…As we showed in the present paper, even in the simplest case of the irreversible submonolayer growth in precoalescence regime that has been extensively investigated for about forty years there still remain controversial issues that need further investigation. Obviously that in more complex cases such as the currently hot subject of the quantum dot growth [42,43] the difficulties will enlarge manifold. We expect that the formalism developed in the present paper will prove to be an indispensable tool of derivation of the REs for such cases.…”

Section: Resultsmentioning

confidence: 99%

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Rigorous derivation of the rate equations for epitaxial growth

Tokar

2013

J. Stat. Mech.

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Abstract. In the framework of the second-quantization representation of the master equation governing the irreversible epitaxial growth, exact equations describing the evolution of the island densities has been obtained. Their decoupling within a mean field-type approximation with the unknown correlation functions replaced by capture numbers (CNs) has been used to derive a closed set of rate equations. The latter has been compared with the exact equations to obtain rigorous definitions of the CNs. The CN that describes the nucleation of dimer islands from two mobile monomers has been measured in the exact kinetic Monte Carlo simulations with the use of the rigorous definition. Strong disagreement with the literature values calculated within alternative techniques has been found, especially at low surface coverage. Plausible causes for the discrepancies are suggested.Another important result of the rigorous approach is the rate equation with the term describing the monomer diffusion. The equation significantly differs from the widely used equations of this kind known from literature. Arguments in favour of our approach are given.PACS numbers: 68.55.A-,81.15.Aa

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Section: Comparison With Equations From the Self-consistent Approach mentioning

confidence: 76%

Section: Resultsmentioning

confidence: 99%

Rigorous derivation of the rate equations for epitaxial growth

Tokar

2013

J. Stat. Mech.

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“…Hereafter, the growth behavior with a growth exponent β > 1/2 is called "superepitaxial growth behavior." In the conventional kinetic theory, QDs are generally considered to grow via uphill mass transport of adatoms driven by the latticemismatch strain [189], which can be implemented well in KMC simulations [190][191][192][193][194]. In their KMC simulation of the heteroepitaxial growth (with the elastic property of the system similar to semiconductors) at a lattice mismatch of 5%, Ratsch et al [192] observed the formation of 3D islands that grow according to the super-epitaxial growth law…”

Section: Super-epitaxial Growthmentioning

confidence: 99%

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

Jin

2015

Front. Phys.

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Currently, the nature of self-assembly of three-dimensional epitaxial islands or quantum dots (QDs) in a lattice-mismatched heteroepitaxial growth system, such as InAs/GaAs(001) and Ge/Si(001) as fabricated by molecular beam epitaxy (MBE), is still puzzling. The purpose of this article is to discuss how the self-assembly of InAs QDs in MBE InAs/GaAs(001) should be properly understood in atomic scale. First, the conventional kinetic theories that have traditionally been used to interpret QD self-assembly in heteroepitaxial growth with a significant lattice mismatch are reviewed briefly by examining the literature of the past two decades. Second, based on their own experimental data, the authors point out that InAs QD self-assembly can proceed in distinctly different kinetic ways depending on the growth conditions and so cannot be framed within a universal kinetic theory, and, furthermore, that the process may be transient, or the time required for a QD to grow to maturity may be significantly short, which is obviously inconsistent with conventional kinetic theories. Third, the authors point out that, in all of these conventional theories, two well-established experimental observations have been overlooked: i) A large number of “floating” indium atoms are present on the growing surface in MBE InAs/GaAs(001); ii) an elastically strained InAs film on the GaAs(001) substrate should be mechanically unstable. These two well-established experimental facts may be highly relevant and should be taken into account in interpreting InAs QD formation. Finally, the authors speculate that the formation of an InAs QD is more likely to be a collective event involving a large number of both indium and arsenic atoms simultaneously or, alternatively, a morphological/structural transformation in which a single atomic InAs sheet is transformed into a three-dimensional InAs island, accompanied by the rehybridization from the sp 2-bonded to sp 3-bonded atomic configuration of both indium and arsenic elements in the heteroepitaxial growth system.

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“…Another simplification is to neglect the displacements of the surface atoms in the direction perpendicular to the surface, as suggested in [3,4,31]. This leaves us with onedimensional (1D) chains of atoms lying at the rigid substrate [30,11]. Their relaxation can be described within the harmonic Frenkel-Kontorova model as follows [30].…”

Section: The Model Of Strained Islandsmentioning

confidence: 99%

Size calibration of strained epitaxial islands due to dipole–monopole interaction

Tokar¹

2015

J. Stat. Mech.

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Abstract. Irreversible growth of strained epitaxial nanoislands has been studied with the use of the kinetic Monte Carlo (KMC) technique. It has been shown that the strain-inducing size misfit between the substrate and the overlayer produces long range dipole-monopole (d-m) interaction between the mobile adatoms and the islands. To simplify the account of the long range interactions in the KMC simulations, use has been made of a modified square island model. Analytic formula for the interaction between the point surface monopole and the dipole forces has been derived and used to obtain a simple expression for the interaction between the mobile adatom and the rectangular island. The d-m interaction was found to be longer ranged than the conventional dipole-dipole potential. The narrowing of the island size distributions (ISDs) observed in the simulations was shown to be a consequence of a weaker repulsion of adatoms from small islands than from large ones which led to the preferential growth of the former. Furthermore, similarly to the unstrained case, the power-law behavior of the average island size and of the island density on the coverage has been found. In contrast to the unstrained case, the value of the scaling exponent was not universal but strongly dependent on the strength of the long range interactions. Qualitative agreement of the simulation results with some previously unexplained behaviors of experimental ISDs in the growth of semiconductor quantum dots was observed.

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Nucleation of size calibrated three-dimensional nanodots in atomistic model of strained epitaxy: a Monte Carlo study

Cited by 4 publications

References 50 publications

Rigorous derivation of the rate equations for epitaxial growth

Rigorous derivation of the rate equations for epitaxial growth

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

Size calibration of strained epitaxial islands due to dipole–monopole interaction

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