Kinetic Monte Carlo simulation of shape transition of strained quantum dots

Lam, Chi Hang

doi:10.1063/1.3483248

Cited by 13 publications

(20 citation statements)

References 39 publications

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“…However, at the atomic scale, the new facet is believed to form by bunching of atomic steps 18 as an intermediate state before coalescing into facets. 6,19 This process can be seen in KMC simulations. 6 However, it…”

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confidence: 98%

“…1 These islands are typically symmetrical in shape, but asymmetrical islands are also observed in experiment [2][3][4][5] and in simulations. 6,7 The presence of asymmetry has important implications for both the growth process and the island properties. Asymmetry in quantum dots is particularly significant for optical applications, as it can split degeneracies of quantum dot states and provide a source of optical anisotropy.…”

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confidence: 99%

“…6 The asymmetrical transition state can have important consequences for the structure of the final stable island. Due to intermixing with substrate material during growth, islands typically have large internal composition gradients reflecting the growth history.…”

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Symmetry breaking in shape transitions of epitaxial quantum dots

Spencer

Tersoff²

2013

Phys. Rev. B

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During heteroepitaxial growth, coherently strained islands form. These "self-assembled quantum dots" then undergo a series of shape transitions with increasing size. The best-known examples are the transitions of Ge on Si(001) and InAs on GaAs(001) from pyramidal islands to multi-facetted domes. Here we examine the transition pathway, using a simple two-dimensional model. We find that the transition occurs via sequential nucleation of individual facets. While the stable states are symmetrical, the transition states are highly asymmetrical. The calculated transition path can pass through a metastable half-dome island shape, consistent with experimental observations. The broken symmetry of the transition state can be "locked in" by intermixing with substrate material, leading to asymmetrical islands.1 Nanoscale islands form spontaneously during the growth of strained heteroepitaxial semiconductor films. This process has attracted intense study as a route to self-assembly of quantum dots. 1 These islands are typically symmetrical in shape, but asymmetrical islands are also observed in experiment 2-5 and in simulations. 6,7 The presence of asymmetry has important implications for both the growth process and the island properties. Asymmetry in quantum dots is particularly significant for optical applications, as it can split degeneracies of quantum dot states and provide a source of optical anisotropy.The complexity of the growth process has made it difficult to identify precisely how asymmetry arises. Both experiments 2 and calculations 8 showed that when the substrate has a modest miscut, islands can have qualitatively asymmetric shapes even in equilibrium.However, asymmetric shapes are also seen on nominally singular surfaces, 3-5 i.e. with the surface oriented in a high-symmetry direction.We therefore study the energetics of heteroepitaxial islands on singular substrates, using a fully faceted two-dimensional (2D) model. 8,9 We focus on the transition from pyramids to domes, the two most-studied shapes for Ge and InAs islands. 1 For any given volume, we calculate the energies of all possible shapes. In this way we determine the entire energy surface, and the transition path and barrier heights along this surface.As expected, with increasing island size there is a first-order transition from symmetric pyramid shapes to symmetric domes. However, we find that shape transitions occur via highly asymmetric transition states, typically involving nucleation of a steeper facet on only one side of the island. The activation barrier for this transition is much smaller than for a symmetrical transition pathway.In addition, we find that the reaction pathway can pass through a metastable asymmetrical "half-dome" shape. If sufficiently long-lived, such a state could appear stable in experiment. Indeed, Ross et al. 3 using in situ microscopy clearly observed the shape transition to occur via such asymmetrical shapes by sequential nucleation of facets. Evidence of metastable half-dome states has also been observed in sim...

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Symmetry breaking in shape transitions of epitaxial quantum dots

Spencer

Tersoff²

2013

Phys. Rev. B

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“…We point out that more sophisticated bond counting models have been proposed in Refs. [23,24] in the context of heteroepitaxy.…”

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confidence: 99%

Kinetic Monte Carlo simulation of heteroepitaxial growth: Wetting layers, quantum dots, capping, and nanorings

Schulze

Smereka

2012

Phys. Rev. B

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A new kinetic Monte Carlo algorithm that efficiently accounts for elastic strain is presented and applied to study various phenomena that take place during heteroepitaxial growth. For example, it is demonstrated that faceted quantum dots occur via the layer-by-layer nucleation of pre-pyramids on top of a critical layer with faceting occurring by anisotropic surface diffusion. It is also shown that the dot growth is enhanced by the depletion of the critical layer which leaves behind a wetting layer. Capping simulations provide insight into the mechanisms behind dot erosion and ring formation. The algorithm used for the simulations presented here is based on the observation that adatom and dimer motion is essentially decoupled from the elastic field. This is exploited by decomposing the film into two parts: the weakly bonded portion and the strongly bonded portion. The weakly bonded portion is taken to evolve independent of the elastic field. In this way the elastic field need only be updated infrequently. Extensive validation reveals that there is little loss of fidelity but the algorithm is fifteen to twenty times faster.

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“…Worst, diffusion processes at semiconductor surfaces are typically influenced by local changes in orbital hybridization, so that reliable estimates of diffusion rates call for refined and computationally demanding ab initio calculations [48]. Nevertheless, it is worth mentioning some significant progress based on empirical approaches exploiting Kinetic Monte-Carlo schemes [49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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Kinetic Monte Carlo simulation of shape transition of strained quantum dots

Cited by 13 publications

References 39 publications

Symmetry breaking in shape transitions of epitaxial quantum dots

Symmetry breaking in shape transitions of epitaxial quantum dots

Kinetic Monte Carlo simulation of heteroepitaxial growth: Wetting layers, quantum dots, capping, and nanorings

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

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