The stability of rapidly growing or evaporating crystals

Keller, Joseph B.; Cohen, Hirsh; Merchant, G. J.

doi:10.1063/1.352929

Cited by 15 publications

(13 citation statements)

References 2 publications

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“…Here, one should note the efforts of Ghez et al [1] and Keller et al [2] to clarify the stability of a step flow in the more complex situation when the surface diffusion of the adatoms is not assumed to be very fast. Their mathematical treatment is more sophisticated than the original Burton, Cabrera and Frank theory [3] in the sense that the quasi-static approximation is replaced by a Stefan-like problem for moving steps.…”

Section: Introductionmentioning

confidence: 99%

Evaporation and growth of crystals: Propagation of step-density compression waves at vicinal surfaces

Ranguelov

Stoyanov

2007

Phys. Rev. B

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We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachmentdetachment at the steps. For this limit we formulate a model free of the quasi-static approximation in the calculation of the adatom concentration on the terraces at the crystal surface. Such a model provides a relatively simple way to study the linear stability of a step train in a presence of step-step repulsion and an absence of destabilizing factors (as Schwoebel effect, surface electromigration etc.). The central result is that a critical velocity of the steps in the train exists which separates the stability and instability regimes. Instability occurs when the step velocity exceeds its critical valuewhere K is the step kinetic coefficient, Ω is the area of one atomic site at the surface, and the energy of step-step repulsion iswhere l is the interstep distance. Integrating numerically the equations for the time evolution of the adatom concentrations on the terraces and the equations of step motion we obtained the step trajectories. When the step velocity exceeds its critical value the plot of these trajectories manifests clear space and time periodicity (step density compression waves propagate on the vicinal surface). This ordered motion of the steps is preceded by a relatively short transition period of disordered step dynamics.

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Section: Introductionmentioning

confidence: 99%

Evaporation and growth of crystals: Propagation of step-density compression waves at vicinal surfaces

Ranguelov

Stoyanov

2007

Phys. Rev. B

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“…In this model, the adatom density solves a diffusion equation with an equilibrium boundary condition, and steps move at a velocity determined from a twosided diffusive flux of adatoms to the edges. Modifications of the BCF model have been made in [3,10,11,13,15] to incorporate into the boundary conditions additional effects, such as the curvature of the step or boundary and in particular the Ehrlich-Schwoebel barrier-a higher energy barrier that must be overcome by an adatom in order for it to stick to the boundary from an upper terrace [8,20,21], cf. Figure 2.…”

Section: Introductionmentioning

confidence: 99%

Stability of a circular epitaxial island

Rätz

Voigt

2004

Physica D: Nonlinear Phenomena

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The morphological stability of a single, epitaxially growing, circular adatom island with a radially symmetric adatom distribution is studied using a BurtonCabrera-Frank type island dynamics model. Various kinds of boundary conditions for the adatom density that include the thermodynamic equilibrium value, line tension, and attachment-detachment kinetics, and different velocity formulas with or without the one-dimensional "surface" diffusion are examined. Rigorous analysis shows that the circular island is always stable if its normalized area A is larger than a critical value. If A is less than such a critical value, and if neither the line tension nor surface diffusion is present, then there exists a critical wavenumber k c = k c (A) such that the island is only stable for wavenumbers less than k c . When the line tension or surface diffusion is present, small islands are always stable. In particular, the Bales-Zangwill instability for straight steps due to the kinetic asymmetry does not exist for small circular islands.PACS numbers: 68.35.J (Surface dynamics); 68.55.a (Thin film structure and morphology); 81.10.Aj (Theory and models of crystal growth).

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“…The equations we obtain therefore form a coupled system for both the heightfunction and the adatom density. The difficulties in defining appropriate boundary conditions in similar approaches to derive such a coupled system in [9,15] are no longer present.…”

Section: Introductionmentioning

confidence: 96%

Phase-field model for island dynamics in epitaxial growth

Rätz¹,

Voigt²

2004

Applicable Analysis

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A phase-field model is proposed to describe epitaxial growth. In this model the motion of island boundaries of discrete atomic layers is determined by the time evolution of an introduced phase-field variable. We use formally matched asymptotic expansion to determine the asymptotic limit of vanishing interfacial thickness and show the reduction to classical sharp interface models of Burton-Cabrera-Frank type.

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The stability of rapidly growing or evaporating crystals

Cited by 15 publications

References 2 publications

Evaporation and growth of crystals: Propagation of step-density compression waves at vicinal surfaces

Evaporation and growth of crystals: Propagation of step-density compression waves at vicinal surfaces

Stability of a circular epitaxial island

Phase-field model for island dynamics in epitaxial growth

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