Metastable states of surface nanostructure arrays studied using a Fokker-Planck equation

Munt, Timothy P; Jesson, D. E.; Shchukin, V. A.; Bimberg, D.

doi:10.1103/physrevb.75.085422

Cited by 7 publications

(22 citation statements)

References 29 publications

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“…This stationary distribution occurs clearly at larger sizes than the spontaneously (i.e. without external flux) selected distribution [8,10]. It is notable, that increasing the ion bombardment flux F does not improve the size selection, but in- The results of current model are in agreement with experimental results [6], where the ratio x c =x p ¼ ðL c =L p Þ 3 % 21, where x c and x p are the stationary sizes for continuous and pulsed IBAD, and L p and L c are the nanodot base lengths, respectively.…”

Section: The Predictions Of Analytical Modelmentioning

confidence: 92%

“…A net mass flux Jðs; tÞ is found between dots of sizes s and s þ 1: [8,20,21] Jðs; tÞ ¼ r s n s ðtÞ À c sþ1 n sþ1 ðtÞ; ðA:3Þ where t is time and n s and n sþ1 are the non-equilibrium distributions. At the continuum limit the size variable s !…”

Section: Appendix a The Continuous Growth Modelmentioning

confidence: 99%

“…(5)-(7) one can derive the continuous growth equation for the time dependent nanodot size distribution nðtÞ [8,10]. The details of the derivation are found in Appendix A.…”

Section: The Continuous Growth Equationmentioning

confidence: 99%

“…We use a mesoscopic, continuous growth model of Fokker-Planck type. Similar reaction kinetic based model has previously succeeded in describing the stationary state which occurs as an interplay of kinetics and thermodynamics, when the kinetically driven growth pushes the distribution mean over the free energy difference minimum [8][9][10][11]. The thermodynamical energy in IBAD growth has a feature of double-well type potential, where the first well corresponds to the IBAD state of growth and the second well is the equilibrium state of strained nanodots which is also present in MBE growth.…”

Section: Introductionmentioning

confidence: 98%

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Size selected growth of nanodots: Ion beam assisted deposition and transition from 2D to 3D growth

Riekki

Koponen

2012

Nuclear Instruments and Methods in Physics Research Section B:

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Section: The Predictions Of Analytical Modelmentioning

confidence: 92%

Section: Appendix a The Continuous Growth Modelmentioning

confidence: 99%

“…(5)-(7) one can derive the continuous growth equation for the time dependent nanodot size distribution nðtÞ [8,10]. The details of the derivation are found in Appendix A.…”

Section: The Continuous Growth Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Size selected growth of nanodots: Ion beam assisted deposition and transition from 2D to 3D growth

Riekki

Koponen

2012

Nuclear Instruments and Methods in Physics Research Section B:

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“…The dynamical behavior of this regime is generally described in terms of n(s, t), the cluster size distribution as a function of time t and the number of atoms s contained in a cluster. In general, the time evolution of n(s, t) is controlled by the discrete BeckerDoring equations [65] or continuum Fokker-Planck equation [66]. In the third stage, the coarsening stage, all the material in the old phase has been consumed by the formation of the new phase, and the system now consists entirely of an ensemble of stable-state clusters of various sizes.…”

Section: First-order Phase Transformationmentioning

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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