The kinetics of fast steps on crystal surfaces and its application to the molecular beam epitaxy of silicon

Ghez, R.; Iyer, Subramanian S.

doi:10.1147/rd.326.0804

Cited by 113 publications

(80 citation statements)

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“…This method neglects the possible energy barrier for particles to cross downward over the step. One can incorporate this "Ehrlich-Schwoebel barrier" by specifying the particle current j = −D ∇ρ at the boundary [18,19], without changing the conclusions of this paper.…”

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confidence: 99%

Multiple Time Scales in Diffraction Measurements of Diffusive Surface Relaxation

et al. 2006

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We grew SrTiO3 on SrTiO3 (001) by pulsed laser deposition, using x-ray scattering to monitor the growth in real time. The time-resolved small angle scattering exhibits a well-defined length scale associated with the spacing between unit cell high surface features. This length scale imposes a discrete spectrum of Fourier components and rate constants upon the diffusion equation solution, evident in multiple exponential relaxation of the "anti-Bragg" diffracted intensity. An Arrhenius analysis of measured rate constants confirms that they originate from a single activation energy.

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confidence: 99%

Multiple Time Scales in Diffraction Measurements of Diffusive Surface Relaxation

et al. 2006

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“…With few exceptions [64][65][66], most theoretical studies of step dynamics work in the quasistatic approximation, which implies that the dynamics of the diffusing adatoms on the terraces separating the steps is assumed to be much faster than the step motion. As a consequence a step reacts instantaneously to the motion of its neighbors, which mathematically leads to coupled first-order equations for the step positions such as (1.14).…”

Section: Beyond the Quasistatic Approximationmentioning

confidence: 99%

Nonlinear Dynamics of Surface Steps

Krug

2010

Nonlinear Dynamics of Nanosystems

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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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The kinetics of fast steps on crystal surfaces and its application to the molecular beam epitaxy of silicon

Cited by 113 publications

References 2 publications

Multiple Time Scales in Diffraction Measurements of Diffusive Surface Relaxation

Multiple Time Scales in Diffraction Measurements of Diffusive Surface Relaxation

Nonlinear Dynamics of Surface Steps

Growth, Structure and Pattern Formation for Thin Films

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