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- W2283338904 abstract "This theoretic work deals with the dynamics of steps on vicinal surfaces, where thebunching instability on the vicinal Si(111) is the physically relevant phenomenology.Thereby two models are studied in detail. The first one is the standard Burton-Cabrera-Frank model from 1951 with the quasi-static approximation for the adatomconcentrations on the terraces, considered for non-permeable steps and in the limitingcase of fast attachment/detachment kinetics and slow diffusion. In our derivationof the discrete equations we take into account higher order non-linear terms, neglectedin the previous studies. We found, that those terms are present in the caseof sublimation, but not in the case of growth. Analytical and numerical methods areemployed in order to study the impact of these terms on the step dynamics. For bothasymmetry effects, the Ehrlich-Schwoebel effect and the effect of electromigration,there is a change in the dispersion relation obtained from the linear stability analysis,whereas there is no such change in the case of growth. Due to the non-linearterms, the dynamics changes from conservative to non-conservative with respect tothe crystal volume. The continuum limits of the discrete equations for both asymmetrycases yield a hint of slope selection in the so called mechanical analog of thepartial differential equation. As a consequence, the scaling relations of the bunchinggeometry in the case of sublimation differ strongly from those in the case of growth.The numerical simulations of the discrete equations confirm these analytic results.In the non-linear regime there is anti-coarsening or arrested coarsening of the stepbunches and thus there are stationary solutions with bounded maximal slope. Asensitive dependence on the initial conditions is observed. The second model weanalyze was recently introduced by Ranguelov and Stoyanov. It accounts for thecase of strong transparency, fast diffusion and slow attachment/detachment kinetics.This model goes beyond the approximation of quasi-static concentration profiles ofadatoms. Calculations in order to reproduce Ranguelov and Stoyanov’s results forthe gradient of the adatom concentration, depending on the electromigration forceas well as for the linear stability analysis were carried out. Quantitative deviationswere found and the corrections are presented. Finally, the equations are simulatedand the dependence of the maximal slope on the different input parameters in thebunching regime is illustrated." @default.
- W2283338904 created "2016-06-24" @default.
- W2283338904 creator A5016355500 @default.
- W2283338904 date "2012-01-01" @default.
- W2283338904 modified "2023-09-27" @default.
- W2283338904 title "Dynamics of Steps on Vicinal Surfaces" @default.
- W2283338904 hasPublicationYear "2012" @default.
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