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The diffusion type is determined not only by microscopic dynamics but also by the environment properties. For example, the environment's fractal structure is responsible for the emergence of subdiffusive scaling of the mean square…

Statistical Mechanics · Physics 2021-10-26 Piotr Kubala , Michał Cieśla , Bartłomiej Dybiec

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically…

Statistical Mechanics · Physics 2007-05-23 Daniele Vilone , Claudio Castellano , Paolo Politi

We model an apparent instability seen in recent experiments on current induced step bunching on Si(111) surfaces using a generalized 2D BCF model, where adatoms have a diffusion bias parallel to the step edges and there is an attachment…

Soft Condensed Matter · Physics 2009-10-31 Da-Jiang Liu , John D. Weeks , Daniel Kandel

We report numerical results for two models of vicinal motion. The first, LW, aims at crystal evaporation when the detachment from steps is slow [Liu and Weeks, PRB 57, 23 (1998) 14891]. The source of destabilization is electromigration…

Materials Science · Physics 2010-05-06 Diana Staneva , Bogdan Ranguelov , Vesselin Tonchev

The step bunching instability is studied in three models of step motion defined in terms of ordinary differential equations (ODE). The source of instability in these models is step-step attraction, it is opposed by step-step repulsion and…

Materials Science · Physics 2016-04-20 Anna Krasteva , Noriko Akutsu , Vesselin Tonchev

Adatom incorporation into the ``faceted'' steps bordering the 2D nanoislands is analyzed. The step permeability and incorporation coefficients are derived for some typical growth situations. It is shown that the step consisting of…

Materials Science · Physics 2015-06-25 Sergey N. Filimonov , Yuri Yu. Hervieu

The stacking sequence of hexagonal close-packed and related crystals typically results in steps on vicinal {0001} surfaces that have alternating A and B structures with different growth kinetics. However, because it is difficult to…

We present results for collective diffusion of adatoms on a stepped substrate with a submonolayer coverage. We study the combined effect of the additional binding at step edge, the Schwoebel barrier, the enhanced diffusion along step edges,…

Condensed Matter · Physics 2009-10-28 Juha Merikoski , See-Chen Ying

We propose a one-dimensional model based on the Burton-Cabrera-Frank equations to describe the electromigration-induced step bunching instability on vicinal surfaces. The step drift resulting from atomic evaporation and/or deposition is…

Materials Science · Physics 2009-11-13 Matthieu Dufay , Thomas Frisch , Jean-Marc Debierre

Using the plane wave pseudopotential method we performed density functional theory calculations on the stability of steps and self-diffusion processes on Ag(100). Our calculated step formation energies show that the {111}-faceted step is…

Materials Science · Physics 2009-10-28 Byung Deok Yu , Matthias Scheffler

Two mechanisms for the breakdown of step flow growth, in the sense of the appearance of steps of opposite sign to the original vicinality, are studied by kinetic Monte Carlo simulations and scaling arguments. The first mechanism is the…

Statistical Mechanics · Physics 2009-11-10 J. Kallunki , J. Krug

Images of the morphology of GaN (0001) surfaces often show half-unit-cell-height steps separating a sequence of terraces having alternating large and small widths. This can be explained by the $\alpha \beta \alpha \beta$ stacking sequence…

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…

Materials Science · Physics 2021-08-25 L. Guin , M. E. Jabbour , L. Shaabani-Ardali , N. Triantafyllidis

The morphology of a growing crystal surface is studied in the case of an unstable two-dimensional step flow. Competition between bunching and meandering of steps leads to a variety of patterns characterized by their respective instability…

Statistical Mechanics · Physics 2012-07-19 A. Verga

We show that a variety of non-monotonic ratchet effects can arise when mesophase pattern-forming systems, which exhibit anisotropic crystal, stripe, and bubble reigmes, are coupled to one-dimensional asymmetric substrates under ac driving.…

Statistical Mechanics · Physics 2024-09-10 C. Reichhardt , C. J. O. Reichhardt

Step meandering during growth of gallium nitride (0001) surface is studied using kinetic Monte Carlo method. Simulated growth process, conducted in N-rich conditions are therefore controlled by Ga atoms surface diffusion. The model employs…

Statistical Mechanics · Physics 2011-10-24 Magdalena A. Załuska-Kotur , Filip Krzyżewski , Stanisław Krukowski

We introduce two hybrid models of step bunching on vicinal crystal surfaces. The model equations for step velocity are constructed by the two possible exchanges of terms between the equations of two primary models MM2 and LW2…

Materials Science · Physics 2011-10-13 Diana Staneva , Bogdan Ranguelov , Vesselin Tonchev

We report the results of computer simulations of epitaxial growth in the presence of a large Schwoebel barrier on different crystal surfaces: simple cubic(001), bcc(001), simple hexagonal(001) and hcp(001). We find, that mounds coarse by a…

Statistical Mechanics · Physics 2009-10-31 M. Ahr , M. Biehl , M. Kinne , W. Kinzel

We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit we formulate a model free of the quasi-static…

Chemical Physics · Physics 2009-11-13 Bogdan Ranguelov , Stoyan Stoyanov

Concerted experimental and numerical studies of step bunching on vicinal crystal surfaces resulting from step-down electromigration of partially charged adatoms, confirmed the theoretical prediction of scaling dependence of the minimal…