Theory of impurity-induced step bunching

Kandel, Daniel; Weeks, John D.

doi:10.1103/physrevb.49.5554

Cited by 90 publications

(85 citation statements)

References 16 publications

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“…Other effects that occur on a real surface are ignored, such as surface diffusion [3], electromigration [72]- [74], the Schwoebel effect [75,76], impurity effects [77]- [79], strain effects [80]- [84], and the effect of surfactants [85]- [86].…”

Section: )) the Energy E(h(i J)) Is Calculated Using The P-rsos Hammentioning

confidence: 99%

Non-universal equilibrium crystal shape results from sticky steps

Akutsu¹

2011

J. Phys.: Condens. Matter

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Abstract. The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z = z(x, y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal GruberMullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) n(p) using the Monte Carlo method, where p = (∂z/∂x, ∂z/∂y), and · represents the thermal average. Using the result of the |p| dependence of n(p) , we derive a |p|-expanded expression for the non-universal surface free energy f eff (p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f eff (p).

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Section: )) the Energy E(h(i J)) Is Calculated Using The P-rsos Hammentioning

confidence: 99%

Non-universal equilibrium crystal shape results from sticky steps

Akutsu¹

2011

J. Phys.: Condens. Matter

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“…Surface evolution is an effect of individual particle jumps and as a result steps join together building bunches at the surface. It was shown that bunching can be caused by Schwoebel barriers 32 , diffusion at step edge 33 , impurities 28 or driven particle flow [8][9][10]34 . In most analytical models step movement factor is neglected 8,10-15 .…”

Section: Introductionmentioning

confidence: 99%

“…Numerically is was studied in the systems with Ehrlich-Schwoebel (E-S) barrier 24 in the chemically etched systems [25][26][27] , with some defects assumed 28 , with electromigration flow of particles 29,30 or for curved steps 31 . In this work we study clean surface with no defects included.…”

Section: Introductionmentioning

confidence: 99%

Step bunching process induced by the flow of steps at the sublimated crystal surface

Załuska‐Kotur

Krzyżewski

2012

Journal of Applied Physics

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Stepped GaN(0001) surface is studied by the kinetic Monte Carlo method and compared with the model based on Burton-Carbera-Frank equations. Successive stages of surface pattern evolution during high temperature sublimation process are discussed. At low sublimation rates clear, well defined step bunches form. The process happens in the absence or for very low Schwoebel barriers at the ideal surface. Bunches of several steps are well separated, move slowly and are rather stiff. Character of the process changes for more rapid sublimation process where double step formations become dominant and together with meanders and local bunches assemble into the less ordered surface pattern. Solution of the analytic equations written for one dimensional system confirms that step bunching is induced by the particle advection caused by step-flow anisotropy. This anisotropy becomes important when due to the low Schwoebel barrier both sides of step are symmetric. Simulations show that in the opposite limit of very high Schwoebel barrier steps fracture and rough surface builds up.

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“…The incorporation of impurities can induce step-disruption, step-bunching, and initiate larger defects. 22 Graphene with multiple layers will have different effects on the surface morphology of copper. To compare the binding between copper substrate and graphene layers, we performed first-principles calculations for both monolayer and bilayer graphene sheets on a copper substrate (see Methods for details).…”

Section: Resultsmentioning

confidence: 99%

Step driven competitive epitaxial and self-limited growth of graphene on copper surface

Fan

et al. 2011

AIP Advances

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The existence of surface steps was found to have significant function and influence on the growth of graphene on copper via chemical vapor deposition. The two typical growth modes involved were found to be influenced by the step morphologies on copper surface, which led to our proposed step driven competitive growth mechanism. We also discovered a protective role of graphene in preserving steps on copper surface. Our results showed that wide and high steps promoted epitaxial growth and yielded multilayer graphene domains with regular shape, while dense and low steps favored self-limited growth and led to large-area monolayer graphene films. We have demonstrated that controllable growth of graphene domains of specific shape and large-area continuous graphene films are feasible

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Theory of impurity-induced step bunching

Cited by 90 publications

References 16 publications

Non-universal equilibrium crystal shape results from sticky steps

Non-universal equilibrium crystal shape results from sticky steps

Step bunching process induced by the flow of steps at the sublimated crystal surface

Step driven competitive epitaxial and self-limited growth of graphene on copper surface

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