Transition States Between Pyramids and Domes During Ge/Si Island Growth

Ross, FM; Tromp, R. M.; Reuter, M. C.

doi:10.1126/science.286.5446.1931

Cited by 448 publications

(233 citation statements)

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“…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.…”

mentioning

confidence: 92%

“…However, asymmetric shapes are also seen on nominally singular surfaces, [3][4][5] i.e. with the surface oriented in a high-symmetry direction.…”

mentioning

confidence: 99%

“…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 simulations using a 2D kinetic Monte…”

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confidence: 99%

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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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mentioning

confidence: 92%

“…However, asymmetric shapes are also seen on nominally singular surfaces, [3][4][5] i.e. with the surface oriented in a high-symmetry direction.…”

mentioning

confidence: 99%

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Symmetry breaking in shape transitions of epitaxial quantum dots

Spencer

Tersoff²

2013

Phys. Rev. B

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“…Relatively flat islands called pre-pyramids start to emerge at 3 monolayers (MLs) of Ge coverage [5,6,7]. Upon further deposition, they quickly grow into truncated pyramids bounded by four (105) facet planes on the sides and subsequently into fully grown pyramids which are also called hut islands.…”

Section: Pacs Numbersmentioning

confidence: 99%

Fast Kinetic Monte Carlo Simulation of Strained Heteroepitaxy in Three Dimensions

2008

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Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Green's function formalisms for boundary values in the associated lattice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm. PACS numbers:Epitaxial growth techniques enable deposition of a dislocation-free thin film on a substrate of a different material with a mismatched lattice constant. For film-substrate combinations such as Ge/Si, InAs/GaAs and InAs/InP, arrays of three-dimensional (3D) coherent islands self-assemble spontaneously beyond certain film thicknesses under appropriate growth conditions [1,2,3,4]. These studies are of much current interest since they are expected to find applications in future microelectronic devices.One of the most widely studied examples is Ge/Si(100) with a 4% lattice misfit. Relatively flat islands called pre-pyramids start to emerge at 3 monolayers (MLs) of Ge coverage [5,6,7]. Upon further deposition, they quickly grow into truncated pyramids bounded by four (105) facet planes on the sides and subsequently into fully grown pyramids which are also called hut islands. Upon still further deposition, they become dome islands bounded mainly by (113) facet planes. Finally, large dislocated islands appear. For the closely related alloy variant Si 1−x Ge x /Si(100) with a generally lower 4x% misfit, the development is rather similar and goes through stages characterized by ripples, hut islands, dome islands and finally dislocated islands [8,9,10]. The structures are however larger and each transition is postponed to occur at a larger film thickness. The islands are also more closely packed.Islands self-assemble because they can relieve the elastic stress in the heteroepitaxial films. There is theory for island formation that emphasizes nucleation. It suggests that islands must overcome an energy barrier associated with a critical size so that the elastic energy gained can balance the extra surface energy cost [11]. The theory is reasonably consistent with experiments at relatively high misfit. At low misfit, the critical island size and hence the energy barrier are expected to increase and make nucleation prohibitively difficult. Island formation mechanisms which do not have a barrier then offer a more promising explanation. For example, according to the Asaro-Tiller-Grinfeld (ATG) theory [12,13,14], strained surfaces are unstable at sufficiently long wavelengths. Therefore, shallow ripples first develop from small random initial perturbations and then into islands. For this mechanism to oper...

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“…Dome (or lens-shaped) Ge QDs [15,16] belong to this case. This approximation requires that all physical parameters of a crystalline lattice possess this symmetry, which means that all the relevant quantities of the problem do not depend on the angular coordinate ϕ of the cylindrical coordinates (r, ϕ, z).…”

Section: Linear Elastic Theorymentioning

confidence: 99%

Mechanical Strain in Capped and Uncapped Self-Assembled Ge/Si Quantum Dots

2015

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In this study we numerically calculate the spatial profile of mechanical strain on self-assembled germanium (Ge) quantum dots (QDs) grown on a silicon (Si) substrate. Although the topic has been exhaustively studied, interesting features have not been explained or even mentioned in the literature yet. We studied the effect of the cap layer considering two cases: capped QDs (where a Si cap is present above the Ge QDs) and uncapped QDs (where no Si is present above the Ge QDs). We observed that Ge in the capped QDs is more strained compared with the the uncapped QDs. This expected effect is attributed to the additional tension from the Si cap layer. However, the situation is opposite for the Si substrate, it is more strained in the uncapped QD because the Ge layer is less strained in this case. We also calculated the band-edge alignment for the electrons and holes.Keywords quantum dots · mechanical strain · uncapped quantum dot · capped quantum dot 1 Introduction

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Transition States Between Pyramids and Domes During Ge/Si Island Growth

Cited by 448 publications

References 13 publications

Symmetry breaking in shape transitions of epitaxial quantum dots

Symmetry breaking in shape transitions of epitaxial quantum dots

Fast Kinetic Monte Carlo Simulation of Strained Heteroepitaxy in Three Dimensions

Mechanical Strain in Capped and Uncapped Self-Assembled Ge/Si Quantum Dots

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