Equilibrium step dynamics on vicinal surfaces

Pimpinelli, Alberto; Villain, Jacques; Wolf, D. E.; Métois, J.J.; Heyraud, J.C.; Elkinani, I.; Uimin, G.

doi:10.1016/0039-6028(93)90190-u

Cited by 165 publications

(115 citation statements)

References 13 publications

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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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Section: Introductionmentioning

confidence: 99%

Thin film epitaxy with or without slope selection

2003

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“…Step displacements are defined by the x coordinate which is perpendicular to the direction of step edge propagation and a function of the y coordinate, which is parallel to the step edge 29 …”

Section: Introductionmentioning

confidence: 99%

Spatial first-passage statistics ofAl∕Si(111)−(3×3)step fluctuations

et al. 2007

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“…For more than a decade it has been recognized that the statistical properties of step fluctuations are determined by the rate-limiting transport mechanism underlying their relaxation [8,9]. When the stochastic time evolution of step edge position x(t) can be accessed, it is possible to determine the temporal correlation function [4,5] ) [ ]…”

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confidence: 99%