Shape transitions of metastable surface nanostructures

Vine, D. J.; Jesson, D. E.; Morgan, Michael J.; Shchukin, V. A.; Bimberg, D.

doi:10.1103/physrevb.72.241304

Cited by 11 publications

(34 citation statements)

References 29 publications

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“…Finally, the most interesting theoretical development would be an extension of the model that transitions smoothly into a kinetic model at high temperature and coverage where ripening and alloying become very important. The recent work of Vine et al 24 is a step in this direction, but clearly there is much to be done. Ge/Si(001) and θ = 11.9 ML were given in Rudd et al 2 The bimodal size distribution is characteristic of two island types.…”

Section: Discussionmentioning

confidence: 99%

Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots

Rudd¹,

Briggs²,

Sutton³

et al. 2007

Jnl of Comp & Theo Nano

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We present in detail a thermodynamic equilibrium model for the growth of nanostructures on semiconductor substrates in heteroepitaxy and its application to ger- * robert.rudd@llnl.gov 1 manium deposition on silicon. Some results of this model have been published previously, but the details of the formulation of the model are given here for the first time.The model allows the computation of the shape and size distributions of the surface nanostructures, as well as other properties of the system. We discuss the results of the model, and their incorporation into a nanostructure diagram that summarizes the relative stability of domes and pyramids in the bimodal size distributions.

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Section: Discussionmentioning

confidence: 99%

Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots

Rudd¹,

Briggs²,

Sutton³

et al. 2007

Jnl of Comp & Theo Nano

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“…The consequences of this finding for the growth kinetics have been worked out. 30,49 In brief, it gives rise to an anomalous island size distribution characterized by a few islands that have passed the transition point and continue to grow quickly, while a large number of smaller, pyramidal islands are left behind in their evolution. While the smallest islands shrink ͑as seen in Ref.…”

Section: B Chemical Potential Of In Atoms In the Qdmentioning

confidence: 99%

Shape transition during epitaxial growth ofInAsquantum dots onGaAs(001): Theory and experiment

et al. 2006

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For heteroepitaxial growth of InAs islands on GaAs͑001͒, a transition of shapes is observed experimentally by scanning-tunneling microscopy and analyzed theoretically in terms of the thermodynamic stability of the islands. The experiments show the coexistence of small islands bound predominantly by shallow facets of the ͕137͖ family and large islands that show a variety of steeper facets, among them the ͕101͖, ͕111͖, and ͕111͖ orientations. The calculations of island stability employ a hybrid approach, where the elastic strain relief in the islands is calculated by continuum elasticity theory, while surface energies and surface stresses are taken from density-functional theory calculations that take into account the atomic structure of the various side facets, as well as of the InAs wetting layer on GaAs͑001͒. With the help of the theoretical analysis, we interpret the observed coexistence of shapes in terms of a structural phase transition accompanied by a discontinuous change of the chemical potential in the islands. Consequences of this finding are discussed in analogy with a similar behavior of GeSi islands on silicon observed previously.

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“…In the prototypical Ge/Si system, small islands have a pyramidal shape with a rectangular base, called 'pyramid'; large islands have a multifaceted shape which has multiple steep facets near the foot of the pyramid, called 'dome'. Because of the complexity of the epitaxial growth process, a large amount of research [3,5,[11][12][13][14][15][16][17][18][19][20][21][22][23][24] has been done to study the size and shape distribution of QDs in an array of islands during growth in order to get control on the QD distribution in production.…”

Section: Introductionmentioning

confidence: 99%

“…The thermodynamic model [11][12][13] suggests that the coexistence and the bimodal distribution of pyramid and dome reflects two minima in the island energy at two different volumes. On the other hand, the kinetic model [3,[14][15][16][17][18][19][20][21][22] considers the evolution of the island distribution as a result of a kinetically limited process. In this kinetic process, a coarsening process is observed [5] where islands larger than a critical size are growing while smaller islands are shrinking, which results in the bimodal distribution without the need of energy minima.…”

Section: Introductionmentioning

confidence: 99%

A Fokker–Planck reaction model for the epitaxial growth and shape transition of quantum dots

Wei¹,

Spencer²

2017

Proc. R. Soc. A.

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We construct a Fokker-Planck reaction (FPR) model to investigate the dynamics of the coupled epitaxial growth and shape transition process of an array of quantum dots (QDs). The FPR model is based on a coupled system of Fokker-Planck equations wherein the distribution of each island type is governed by its own Fokker-Planck equation for growth, with reaction terms describing the shape transitions between islands of different types including asymmetric shapes. The reaction terms for the shape transitions depend on the island size and are determined from explicit calculations of the lowest barrier pathway for each shape transition. This mean-field model enables us to consider the kinetics of asymmetric shape transitions and study the evolution of island shape distributions during the coupled growth and transition process. Asymmetric metastable shapes play a crucial role in the dynamics, with asymmetric QDs comprising up to 10% of the population, and with up to 100% of the shape transitions passing through asymmetric shapes. Moreover, we find that the characteristic multimodal distribution of pyramid/dome QD coarsening can be eliminated at sufficiently high temperature and deposition rate.

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Shape transitions of metastable surface nanostructures

Cited by 11 publications

References 29 publications

Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots

Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots

Shape transition during epitaxial growth ofInAsquantum dots onGaAs(001): Theory and experiment

A Fokker–Planck reaction model for the epitaxial growth and shape transition of quantum dots

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