Morphological instability of a terrace edge during step-flow growth

Bales, G. S.; Zangwill, Andrew

doi:10.1103/physrevb.41.5500

Cited by 519 publications

(407 citation statements)

References 36 publications

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“…1, [48][49][50] Extensive research can be found in the literature on the kinetic instability. The step edge barriers also modify the mobility for the surface evolution under elastic effects.…”

Section: Introductionmentioning

confidence: 99%

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Zhu

Xiang

2009

Phys. Rev. B

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In heteroepitaxy, the mismatch of lattice constants between the crystal film and the substrate causes misfit strain and stress in the bulk of the film, driving the surface of the film to self-organize into various nanostructures. Below the roughening transition temperature, an epitaxial surface consists of facets and steps and changes its morphology by lateral motion of steps. In this paper, we present a 2 + 1-dimensional continuum model for the long-range elastic interaction on stepped surface of a strained film. The continuum model is derived rigorously from the discrete model for the interaction between steps; thus it incorporates the discrete features of the stepped surfaces. Examples show that our continuum model is much more accurate as an approximation to the discrete model than the traditional continuum approximation. Moreover, in the linear instability of a planar surface, our continuum model gives the transition from step bunching instability to step undulation instability as the distance between adjacent steps increases, which agrees with the experimental observations and the results of discrete models and is missing using the traditional continuum approximation. Numerical simulations of the surface evolution using our model in the nonlinear regime show several different surface morphologies, including the morphology of step bunching which cannot be obtained using the traditional continuum approximation.

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Section: Introductionmentioning

confidence: 99%

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Zhu

Xiang

2009

Phys. Rev. B

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“…Figure 1.1. This asymmetry in attachment and detachment of adatoms to and from terrace boundaries has many important consequences: it induces an uphill current which in general destabilizes nominal surfaces (high symmetry surfaces) [7,30,31], but stabilizes vicinal surfaces (surfaces that are in the vicinity of high symmetry surfaces) with large slope, preventing step bunching [35]; it also leads to the Bales-Zangwill morphological instability of atomic steps [2,29]; Finally, it contributes to the kinetic roughening of film surfaces [17,27,35].…”

Section: Introductionmentioning

confidence: 99%

Thin film epitaxy with or without slope selection

2003

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Abstract. Two nonlinear diffusion equations for thin film epitaxy, with or without slope selection, are studied in this work. The nonlinearity models the Ehrlich-Schwoebel effect-the kinetic asymmetry in attachment and detachment of adatoms to and from terrace boundaries. Both perturbation analysis and numerical simulation are presented to show that such an atomistic effect is the origin of a nonlinear morphological instability, in a roughsmooth-rough pattern, that has been experimentally observed as transient in an early stage of epitaxial growth on rough surfaces. Initial-boundary-value problems for both equations are proven to be well-posed, and the solution regularity is also obtained. Galerkin spectral approximations are studied to provide both a priori bounds for proving the well-posedness and numerical schemes for simulation. Numerical results are presented to confirm part of the analysis and to explore the difference between the two models on coarsening dynamics.

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“…In this "BCF" model, the adatom density solves a diffusion equation with an equilibrium boundary condition (ρ = ρ eq ), and step edges (or island boundaries) move at a velocity determined from the diffusive flux to the boundary. Modifications of this theory were made, for example in [6,11,16,20,23], to include line tension, edge diffusion and nonequilibrium effects. These are "island dynamics" models, since they describe an epitaxial surface by the location and evolution of the island boundaries and step edges.…”

Section: Island Dynamicsmentioning

confidence: 99%

Growth, Structure and Pattern Formation for Thin Films

Caflisch¹

2008

J Sci Comput

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An epitaxial thin film consists of layers of atoms whose lattice properties are determined by those of the underlying substrate. This paper reviews mathematical modeling, analysis and simulation of growth, structure and pattern formation for epitaxial systems, using an island dynamics/level set method for growth and a lattice statics model for strain. Epitaxial growth involves physics on both atomistic and continuum length scales. For example, diffusion of adatoms can be coarse-grained, but nucleation of new islands and breakup for existing islands are best described atomistically. In heteroepitaxial growth, mismatch between the lattice spacing of the substrate and the film will introduce a strain into the film, which can significantly influence the material structure, for example leading to formation of quantum dots. Technological applications of epitaxial structures, such as quantum dot arrays, require a degree of geometric uniformity that has been difficult to achieve. Modeling and simulation may contribute insights that will help to overcome this problem. We present simulations that combine growth and strain showing the structure of nanocrystals and the formation of patterns in epitaxial systems.

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Morphological instability of a terrace edge during step-flow growth

Cited by 519 publications

References 36 publications

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Thin film epitaxy with or without slope selection

Growth, Structure and Pattern Formation for Thin Films

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