Relationship between Macrostep Height and Surface Velocity for a Reaction-Limited Crystal Growth Process

Akutsu, Noriko

doi:10.1021/acs.cgd.9b00168

Cited by 19 publications

(27 citation statements)

References 51 publications

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“…The obtained results do not depend on the initial configuration. This is in contrast to the mean-height of a faceted macrostep n , which is known to be sensitive to the history of the surface configuration 63,64 . As seen from Fig.…”

Section: Resultsmentioning

confidence: 89%

“…Here, �µ R (L) is the crossover point from a vicinal surface with (111) faceted macrosteps to a tilted surface with locally merged steps, and �µ (poly) co (L) is the crossover point from single nucleation growth to poly-nucleation growth at the lower edge of a faceted macrostep 63 . In the region �µ (poly) co (L) < �µ < �µ R (L) , the vicinal surface of the p-RSOS model grows in a step-detachment process in the manner of 2D poly-nucleation at the lower edge of a faceted macrostep 63,64 . Figure 2 shows a typical morphology of a vicinal surface in the region �µ (poly) co (L) < �µ < �µ R (L) (see also Figs.…”

Section: Resultsmentioning

confidence: 99%

“…Inset: Illustration of a step-detachment mode in a poly-nucleation process at the edge of a faceted macrostep. edge of the faceted macrostep 63,64 . At steady state, ∂�n�/∂t = 0 , and n + = n − .…”

Section: Resultsmentioning

confidence: 99%

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Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Akutsu

2021

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To clarify whether a surface can be rough with faceted macrosteps that maintain their shape on the surface, crystal surface roughness is studied by a Monte Carlo method for a nucleation-limited crystal-growth process. As a surface model, the restricted solid-on-solid (RSOS) model with point-contact-type step–step attraction (p-RSOS model) is adopted. At equilibrium and at sufficiently low temperatures, the vicinal surface of the p-RSOS model consists of faceted macrosteps with (111) side surfaces and smooth terraces with (001) surfaces (the step-faceting zone). We found that a surface with faceted macrosteps has an approximately self-affine-rough structure on a ‘faceted-rough surface’; the surface width is strongly divergent at the step-disassembling point, which is a characteristic driving force for crystal growth. A ‘faceted-rough surface’ is realized in the region between the step-disassembling point and a crossover point where the single nucleation growth changes to poly-nucleation growth.

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Section: Resultsmentioning

confidence: 89%

Section: Resultsmentioning

confidence: 99%

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Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Akutsu

2021

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“…This attraction, which is the microscopic origin of the discontinuous surface tension, is considered to result from quantum interactions between steps at step meeting points [10]. Our non-equilibrium steady-state study [11][12][13] showed that the height of the faceted macrosteps decreases as the degree of non-equilibrium increases.…”

Section: Introductionmentioning

confidence: 79%

Surface Roughness Changes Induced by Stoichiometric Deviation in Ambient Phase for Two-Component Semiconductor Crystals

2020

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The effects of a deviation in the fraction of the components in the ambient phase of a stoichiometric AB compound, such as GaN or SiC crystals, on the surface roughness and step self-assembly and disassembly on a vicinal surface are studied using the Monte Carlo method based on a staggered restricted solid-on-solid (st-RSOS) model at equilibrium. The (001) and (111) surfaces are typical examples of non-polar and polar surfaces, respectively. Although a stoichiometric deviation of the ambient phase does not affect the surface energy of a non-polar surface, it affects that of polar surfaces such as the (111) A and (111) B surfaces. We found that the vicinal surface of an AB compound is atomically smooth and globally rough. Globally, the vicinal surface is not affected by a stoichiometric deviation in the ambient phase. In contrast, in a small area, the structure of the vicinal surface is affected by a stoichiometric deviation in the ambient phase. The vicinal surface consists of local double and quadruple steps. The characteristic length L MFL , which separates the global length scale region and the local length scale region, has a maximum value of 156a in the present study, where a is the lattice constant. When temperature decreases, L MFL can become large.

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“…The RSOS model with point-contact-type step-step attraction (p-RSOS model) partially accounts for the 2nn attractions between atoms. In the p-RSOS model, mono-atomic steps self-assemble to form faceted macrosteps at low temperatures at equilibrium [37][38][39][40][41][42][43][44][45] . In that case, the surface width is different from the results near equilibrium reported in the present paper.…”

Section: Discussionmentioning

confidence: 99%

Crossover from BKT-rough to KPZ-rough surfaces for interface-limited crystal growth/recession

Akutsu

2020

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the crossover from a Berezinskii-Kosterlitz-thouless (BKt) rough surface to a Kardar-parisi-Zhang (KpZ) rough surface on a vicinal surface is studied using the Monte carlo method in the non-equilibrium steady state in order to address discrepancies between theoretical results and experiments. the model used is a restricted solid-on-solid model with a discrete Hamiltonian without surface or volume diffusion (interface limited growth/recession). The temperature, driving force for growth, system size, and surface slope dependences of the surface width are calculated for vicinal surfaces tilted between the (001) and (111) surfaces. The surface velocity, kinetic coefficient of the surface, and mean height of the locally merged steps are also calculated. In contrast to the accepted theory for (2 + 1) surfaces, we found that the crossover point from a BKT (logarithmic) rough surface to a KPZ (algebraic) rough surface is different from the kinetic roughening point for the (001) surface. the driving force for crystal growth was found to be a relevant parameter for determining whether the system is in the BKT class or the KPZ class. It was also determined that ad-atoms, ad-holes, islands, and negative-islands block surface fluctuations, which contributes to making a BKT-rough surface.

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Relationship between Macrostep Height and Surface Velocity for a Reaction-Limited Crystal Growth Process

Cited by 19 publications

References 51 publications

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Surface Roughness Changes Induced by Stoichiometric Deviation in Ambient Phase for Two-Component Semiconductor Crystals

Crossover from BKT-rough to KPZ-rough surfaces for interface-limited crystal growth/recession

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