Stability of crystals that grow or evaporate by step propagation

Ghez, R.; Cohen, Hirsh; Keller, Joseph B.

doi:10.1063/1.103016

Cited by 12 publications

(6 citation statements)

References 10 publications

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“…The instability occurs if [28] k + − k − > 0 or equivalently (since k + + k − < 0 for w > 0), when the anisotropy ratio ρ = k + k − < 1. This analysis is similar to the work of Ghez et al [29] which includes an external flux with the electromigration force being absent.…”

Section: A Relevance To Electromigration Experimentssupporting

confidence: 70%

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Calculated Schwoebel barriers on Si(111) steps using an empirical potential

1996

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Motivated by the recent investigations on instabilities caused by Schwoebel barriers during growth and their effects on growth or sublimation by step flows, we have investigated, using the Stillinger-Weber potential, how this step edge barrier arises for the two high symmetry steps on 1×1 reconstructed Si(111). Relative to a barrier of 0.97 ± 0.07 eV on the surface, we find additional (Schwoebel) barriers of 0.61 ± 0.07 eV and 0.16 ± 0.07 eV for adatom migration over the [211] and the [112] steps respectively. The adatom potential energy is found to be strongly correlated with that derived from the local geometry of atoms on the adatom-free surface or step edges. This correlation preserves a strict correspondence between the barrier determining features in the spatial variation of the adatom potential energy and the same derived from the local geometry for the Si( 111) surface and the [211] step. It is therefore argued that the Schwoebel barrier on the [211] step is robust i.e. a feature that would survive in more satisfactory ab initio or tight binding calculations. Using a diffusion equation for the adatom concentration the relevance of the barrier to electromigration of steps has been explored. Data from such experiments on Si(111) has been used to place an upper bound on the Schwoebel barrier and a lower bound on the electromigration force.

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Section: A Relevance To Electromigration Experimentssupporting

confidence: 70%

“…The diffusion equation for non-interacting adatoms subliming in the presence of an electromigration force F perpendicular to the step edge and the absence of an external flux may be written in the "adiabatic approximation" (which neglects the time derivative of the density) as follows: [14,29]…”

Section: Motionmentioning

confidence: 99%

Calculated Schwoebel barriers on Si(111) steps using an empirical potential

1996

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“…(1.1) 1 -is developed in Ghez et al (1990Ghez et al ( , 1993; Keller et al (1993). In this work, the authors write the perturbation equations on the domain of the steady-state solutions and correct the inadequacy of the domain of definition through Taylor expansions of the boundary conditions about the steady-state position of the interface.…”

Section: The Different Approaches To the Effect Of Dynamicsmentioning

confidence: 99%

“…Using the vocabulary used for stability problems in fluid-structure interaction-where the same issue of both function and domain perturbation arises-their approach is referred to as the transpiration method by contrast with ours makes use of the arbitrary Lagrangian-Eulerian formulation (see e.g., Fanion et al, 2000). However, in the formulation of the step governing equations by Ghez et al (1990Ghez et al ( , 1993; Keller et al (1993), the dynamics terms are missing from the boundary conditions (1.1) 2,3 as those were only included in the step-flow problem at later times (see e.g., Pierre-Louis, 2003;Ranguelov and Stoyanov, 2007;Dufay et al, 2007).…”

Section: The Different Approaches To the Effect Of Dynamicsmentioning

confidence: 99%

Revisiting step instabilities on crystal surfaces. Part II: General theory

Guin,

Jabbour,

Shaabani-Ardali

et al. 2021

Preprint

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The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on stability of different mechanisms and their interplay: elastic step-step interactions, the Schwoebel barrier, and the chemical coupling of the diffusion fields on adjacent terraces. In this second part, we present a stability analysis of the general problem without recourse to the quasistatic approximation. This analysis reveals the existence of a supplementary mechanism, which we label the "dynamics effect" as it follows from accounting for all the convective and transient terms in the governing equations. This effect can be stabilizing or destabilizing depending on the ratio of step attachment/detachment kinetics to terrace diffusion kinetics. Further, we find that this dynamics effect remains significant in the slow deposition/evaporation regime, thereby invalidating the classical postulate underlying the quasistatic approximation. Finally, revisiting experiments of crystal growth on Si(111)-7×7 and GaAs(001), our analysis provides an alternative explanation of the observed step bunching, one that does not require the mechanisms previously invoked in the literature.

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“…In both growth modes surface diffusion is responsible for material transfer [1][2][3][4][5][6]. Although various experimental efforts have been made [1,[7][8][9] to examine surface diffusion, the dependence of the surface diffusion length on growth conditions (temperature and impingement rate) is still controversial .…”

Section: Introductionmentioning

confidence: 99%

Growth Morphologies of Steps on Vicinal Surfaces in Molecular-Beam Epitaxy

Xiao

1992

MRS Proc.

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A Monte Carlo model has been used to study growth morphologies of steps on vicinal surfaces in molecular-beam epitaxy. The model accounts for molecule attachment, detachment, and surface diffusion. Through variation of surface temperature, impingement rate of source molecules, and the orientation of vicinal surface, we have explored the surface diffusion and the conditions under which two dimensional nucleation (2DN) growth and step flow (SF) growth occur. We have found optimum growth windows for 2DN growth and SF growth. For SF growth we have found that morphological stabilitity of steps are closely dependent on their step height. Steps with multi-molecular-layers are seen to be less stable than single-layer steps in a surface diffusion field, due to a decrease in the attachment of growth units from the upper terrace.

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Stability of crystals that grow or evaporate by step propagation

Cited by 12 publications

References 10 publications

Calculated Schwoebel barriers on Si(111) steps using an empirical potential

Calculated Schwoebel barriers on Si(111) steps using an empirical potential

Revisiting step instabilities on crystal surfaces. Part II: General theory

Growth Morphologies of Steps on Vicinal Surfaces in Molecular-Beam Epitaxy

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