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

Prieto, J. E.; Markov, Ivan

doi:10.1103/physrevb.72.205412

Cited by 13 publications

(32 citation statements)

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“…The rearrangement of mono-to bilayer islands was found to be a true nucleation process in compressed overlayers, in the sense that a small critical nucleus of the second layer is initially formed and then grows further up to the completion of the transformation. The associated energy displays a maximum at some number of atoms in the second level, which becomes very small for high enough values of the lattice misfit [17]. However, bilayer islands of expanded overlayers tend to require unrealistically high values of the lattice strain and of the island size to become stable against ML islands.…”

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confidence: 99%

“…However, bilayer islands of expanded overlayers tend to require unrealistically high values of the lattice strain and of the island size to become stable against ML islands. Their transformation curves show an increase of the energy up to large second layer cluster sizes, making nucleation unlikely [17]. Also compressed overlayers of softer materials, or at lower misfits, are not expected to show nucleation behavior through this mechanism.…”

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confidence: 99%

“…5b of Ref. 17. The energy tends to increase all the way (the departure from monotonic behavior depends on the exact atomistic processes related to filling and depleting of atomic rows during the transformation process) and shows at the very end a sudden collapse due to the disappearance of the single and double steps to produce low-energy facets.…”

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confidence: 99%

“…The second is the relaxation of strain at steps and the third is the reduction of interlayer adhesion at steps due to the edge atoms climbing up in the potential valley created by their neighbors underneath. Only the strain relaxation favors the process of clustering [17,22]. The other two contributions oppose it, in addition to the step repulsion energy.…”

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confidence: 99%

“…islands [17,20]: the direct nucleation of multilayer clusters whose thickness depends on the values of the force constant and the lattice misfit. We have studied this mechanism: Fig.…”

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confidence: 99%

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Forbidden Island Heights in Stress-Driven Coherent Stranski-Krastanov Growth

Prieto

Markov

2007

Phys. Rev. Lett.

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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.PACS numbers: 68.35. Md, 68.43.Hn, 68.55.Ac, 68.65.Hb Nanostructures are very promising for optoelectronic and magnetic applications. For efficient operation, the shape, size and thickness distribution of small clusters are important parameters. Therefore it is crucial to understand the factors which control them. The epitaxy of metals on semiconductor surfaces at low temperatures (130K -180K) has been intensively studied in the last years [1,2,3,4]. Some important observations are: (i) flat-top Pb islands with steep edges and a preferred height of 7 monolayers (ML) grow on the wetting layer on Si(111)7 × 7 [1, 2, 3, 5], (ii) islands with thicknesses from 1 to 3 MLs are never observed [3,6,7]; (iii) flat-top Pb islands are preceded by pyramidal or dome-like clusters; clusters thinner than 3 MLs are never registered [8]; (iv) 2-ML thick flat-top Ag islands on Si(111) increase linearly in size with increasing coverage whereas ML islands preserve a nearly constant size of about 5 nm 2 [8]; (v) flat-top islands with a preferred height grow laterally without thickening [1,7,9]; (vi) Vertical growth of Pb/Si(111) takes place by bilayer increments [7,10].The above observations were explained in terms of the energy lowering due to electron confinement and spilling of charge through the metal-semiconductor interface by Zhang, Niu and Shih, who coined for this reason the term "electronic growth" [11]. However, classical effects associated to strain relaxation are expected to contribute, as assumed to explain the fact that the increase of the aspect ratio of flat-top Pb islands is mediated by the formation and growth of strips (or rings) around the outer edges of the islands [12]. The aim of this paper is to show that some of the observations listed above, in particular (ii), (iii), (iv) and (v), can be explained classically in terms of the interplay of strain and edge energies.Two mechanisms have been invoked to address the instability of planar growth against clustering. The first is the nucleationless development of instabilities of a certain wavelength that evolve into faceted three-dimensional (3D...

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confidence: 99%

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confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

“…islands [17,20]: the direct nucleation of multilayer clusters whose thickness depends on the values of the force constant and the lattice misfit. We have studied this mechanism: Fig.…”

mentioning

confidence: 99%

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Forbidden Island Heights in Stress-Driven Coherent Stranski-Krastanov Growth

Prieto

Markov

2007

Phys. Rev. Lett.

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Nucleation at Surfaces

Markov

2010

Springer Handbook of Crystal Growth

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

Cited by 13 publications

References 42 publications

Forbidden Island Heights in Stress-Driven Coherent Stranski-Krastanov Growth

Forbidden Island Heights in Stress-Driven Coherent Stranski-Krastanov Growth

Nucleation at Surfaces

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

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