Effect of the roughening transition on the vicinal surface in the step droplet zone

Akutsu, Noriko

doi:10.1016/j.jcrysgro.2016.10.014

Cited by 10 publications

(11 citation statements)

References 22 publications

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“…The kinetically roughened state for |∆µ|/ > ∆µ R is somewhat different from the state in step droplet zone II [43,44]. In step droplet zone II, the (001) surface is rough because the temperature is higher than its roughening transition temperature.…”

Section: Discussionmentioning

confidence: 87%

“…In contrast, when the mean surface slope satisfies p 1,eq <p < √ 2, homogeneous stepped surfaces are thermodynamically unstable [40]. Then, the surface is realized through two-surface coexistence; the two surfaces are the surface with a slope equal to p 1,eq and the (111) surface [40][41][42][43][44][45]. This is illustrated in Figure 5a.…”

Section: Macrostep Size and Surface Growth Ratementioning

confidence: 99%

“…They Moreover, the plot of the roughening transition temperature of the (001) surface divides the step droplet and GMPT zones into step droplet zones I and II and GMPT zones I and II, respectively [43,44]. Step-faceting (QI Bose solid +Vacuum)…”

Section: Introductionmentioning

confidence: 99%

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Disassembly of Faceted Macrosteps in the Step Droplet Zone in Non-Equilibrium Steady State

Akutsu¹

2017

Crystals

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A Wulff figure-the polar graph of the surface tension of a crystal-with a discontinuity was calculated by applying the density matrix renormalization group method to the p-RSOS model, a restricted solid-on-solid model with a point-contact-type step-step attraction. In the step droplet zone in this model, the surface tension is discontinuous around the (111) surface and continuous around the (001) surface. The vicinal surface of 4H-SiC crystal in a Si-Cr-C solution is thought to be in the step droplet zone. The dependence of the vicinal surface growth rate and the macrostep size n on the driving force ∆µ for a typical state in the step droplet zone in non-equilibrium steady state was calculated using the Monte Carlo method. In contrast to the known step bunching phenomenon, the size of the macrostep was found to decrease with increasing driving force. The detachment of elementary steps from a macrostep was investigated, and it was found that n satisfies a scaling function. Moreover, kinetic roughening was observed for |∆µ| > ∆µ R , where ∆µ R is the crossover driving force above which the macrostep disappears.

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Section: Discussionmentioning

confidence: 87%

Section: Macrostep Size and Surface Growth Ratementioning

confidence: 99%

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Disassembly of Faceted Macrosteps in the Step Droplet Zone in Non-Equilibrium Steady State

Akutsu¹

2017

Crystals

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“…The anomaly in surface tension is caused microscopically by step-step attraction. This prior work employed the restricted solidon-solid (RSOS) model in conjunction with point contact step-step attraction, termed the p-RSOS model [14][15][16][17][18][19]. Point contact step-step attraction is considered to result from the energy gain associated with the point at which neighboring steps meet.…”

Section: Introductionmentioning

confidence: 99%

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

Akutsu

2019

Crystal Growth & Design

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This work examined the effect of macrostep height on the growth velocity of a vicinal surface during reaction-(interface-) limited crystal growth under non-equilibrium steady state conditions. The Monte Carlo method was employed, based on a restricted solid-onsolid (RSOS) model with point-contacttype step-step attraction (termed the p-RSOS model). Although this is a simple lattice model, the model surface shows a variety of distinctive configurations depending on the temperature and the driving force for crystal growth. The results demonstrate that the surface velocity decreases as the height of the faceted macrostep increases. In addition, the significant variation in surface velocity recently reported by Onuma et al. in a study based on 4H-SiC was reproduced. This work also shows that the terrace slope, elementary step velocity and elementary step kinetic coefficient are all affected by the faceted macrostep height.

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“…The microscopic model considered in this study is the p-RSOS model ( Fig. 1) [19][20][21][22][23][24][25]. In this model, "an atom" corresponds to a unit cube.…”

Section: A the P-rsos Modelmentioning

confidence: 99%

Height of a faceted macrostep for sticky steps in a step-faceting zone

Akutsu

2018

Phys. Rev. Materials

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The driving force dependence of the surface velocity and the average height of faceted merged steps, the terrace-surface-slope, and the elementary step velocity in the non-equilibrium steady-state are studied using the Monte Carlo method. The Monte Carlo study is based on a lattice model, the restricted solid-on-solid model with point-contact type step-step attraction (p-RSOS model). The temperature is selected to be in the step-faceting zone where the surface is surrounded by the (001) terrace and the (111) faceted step at equilibrium. Long time simulations are performed at this temperature to obtain steady-states for the different driving forces that influence the growth/recession of the surface. A Wulff figure of the p-RSOS model is produced through the anomalous surface tension calculated using the density-matrix renormalization group method. The characteristics of the faceted macrostep profile at equilibrium are classified with respect to the connectivity of the surface tension. This surface tension connectivity also leads to a faceting diagram, where the separated areas are respectively classified as a Gruber-Mullins-Pokrovsky-Talapov zone, step droplet zone, and step-faceting zone. Although the p-RSOS model is a simplified model, the model shows a wide variety of dynamics in the step-faceting zone. There are four characteristic driving forces, ∆µy, ∆µ f , ∆µco, and ∆µR. For the absolute value of the driving force, |∆µ| is smaller than Max[∆µy, ∆µ f ], the step attachment-detachments are inhibited, and the vicinal surface consists of (001) terraces and the (111) side surfaces of the faceted macrosteps. For Max[∆µy, ∆µ f ] < |∆µ| < ∆µco, the surface grows/recedes intermittently through the two-dimensional (2D) heterogeneous nucleation at the facet edge of the macrostep. For ∆µco < |∆µ| < ∆µR, the surface grows/recedes with the successive attachment-detachment of steps to/from a macrostep. When |∆µ| exceeds ∆µR, the macrostep vanishes and the surface roughens kinetically. Classical 2D heterogeneous multi-nucleation was determined to be valid with slight modifications based on the Monte Carlo results of the step velocity and the change in the surface slope of the "terrace". The finite size effects were also determined to be distinctive near equilibrium.

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Effect of the roughening transition on the vicinal surface in the step droplet zone

Cited by 10 publications

References 22 publications

Disassembly of Faceted Macrosteps in the Step Droplet Zone in Non-Equilibrium Steady State

Disassembly of Faceted Macrosteps in the Step Droplet Zone in Non-Equilibrium Steady State

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

Height of a faceted macrostep for sticky steps in a step-faceting zone

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