Erratum: Self-Assembled Quantum Dots: Crossover from Kinetically Controlled to Thermodynamically Limited Growth [Phys. Rev. Lett. 87, 236101 (2001)]

Meixner, M.; Schöll, Eckehard; Shchukin, V. A.; Bimberg, D.

doi:10.1103/physrevlett.88.059901

Cited by 51 publications

(74 citation statements)

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“…Alternative routes, e.g. the evaluation of the strain energy for a given lattice configuration, have been suggested and used in the literature, see for instance [31].…”

Section: Summary and Discussionmentioning

confidence: 99%

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Volkmann¹,

Much²,

Biehl³

et al. 2005

Surface Science

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We study the formation of nanostructures with alternating stripes composed of bulk-immiscible adsorbates during submonolayer heteroepitaxy. We evaluate the influence of two mechanisms considered in the literature: (i) strain relaxation by alternating arrangement of the adsorbate species, and (ii) kinetic segregation due to chemically induced diffusion barriers. A model ternary system of two adsorbates with opposite misfit relative to the substrate, and symmetric binding is investigated by off-lattice as well as lattice kinetic Monte Carlo simulations. We find that neither of the mechanisms (i) or (ii) alone can account for known experimental observations. Rather, a combination of both is needed. We present an off-lattice model which allows for a qualitative reproduction of stripe patterns as well as island ramification in agreement with recent experimental observations for CoAg/Ru(0001) [R. Q. Hwang, Phys. Rev. Lett. 76, 4757 (1996)]. The quantitative dependencies of stripe width and degree of island ramification on the misfit and interaction strength between the two adsorbate types are presented. Attempts to capture essential features in a simplified lattice gas model show that a detailed incorporation of non-local effects is required.

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“…Alternative routes, e.g. the evaluation of the strain energy for a given lattice configuration, have been suggested and used in the literature, see for instance [31].…”

Section: Summary and Discussionmentioning

confidence: 99%

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Volkmann¹,

Much²,

Biehl³

et al. 2005

Surface Science

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“…26 Alternatively, KMC simulations can also be performed efficiently using more approximate forms of elastic interactions. [27][28][29] This paper is organized as follows. Section II explains our multistate model for elastic solids which can account for both a shallow and a steep facet.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Monte Carlo simulation of shape transition of strained quantum dots

Lam

2010

Journal of Applied Physics

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The pyramid-to-dome transition in Ge x Si 1−x on Si͑100͒ initiated by step formation on pyramidal quantum dots is atomistically simulated using a multistate lattice model in two-dimensions incorporating effective surface reconstructions. Under quasiequilibrium growth conditions associated with low deposition rates, the transition occurs at island size n c following ͱ n c ϳ x −1.69 independent of temperature and deposition rate. The shape transition is found to be an activated process. Results are explained by a theory based on simple forms of facet energies and elastic energies estimated using a shallow island approximation. An asymptotic scaling relation n c 1/d ϳ x −2 for x → 0 applicable to d = 2 or 3 dimensions is derived. The shape transition energy barrier can be dominated by the interface energy between steep and shallow facets.

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“…More importantly, it is exact for arbitrary morphologies. This is in sharp contrast to half-space Green's functions in the small slope approximation which are often applied [11,26,27].…”

Section: Exact Green's Function Methodsmentioning

confidence: 98%

“…All of these studies work for general film morphologies. Alternatively, one can limit the study to the evolution of only shallow structures and solve the elastic problem using the halfspace Green's function in the small-slope approximation [26,27].…”

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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Erratum: Self-Assembled Quantum Dots: Crossover from Kinetically Controlled to Thermodynamically Limited Growth [Phys. Rev. Lett. 87, 236101 (2001)]

Cited by 51 publications

References 0 publications

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys

Kinetic Monte Carlo simulation of shape transition of strained quantum dots

Fast Kinetic Monte Carlo Simulation of Strained Heteroepitaxy in Three Dimensions

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