Interfacial Coarsening in Epitaxial Growth Models without Slope Selection

Golubović, Leonardo

doi:10.1103/physrevlett.78.90

Cited by 96 publications

(94 citation statements)

References 18 publications

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“…In contrast to this long time regime where n λ = β, in ion erosion studies on Cu (110) [33,35] it appears that the selected facets of the Rippled state have not yet fully reached the preferred slope magnitude -their slope ∼ w/λ still grows within the experimentally accessible time scale. Such early time regimes are theoretically known to exhibit the coarsening exponent n smaller than β with typically small values [22], as was indeed observed in these experiments on Cu (110) crystal surfaces. We also note that the above analytic discussions of the rippled state ignore the vertical asymmetry (VA) discussed in § 4.2, which produces a contribution to the surface curvature current that is even under vertical reflection h → −h.…”

Section: Large Scale Topological Defects Mediating Surface Growthsupporting

confidence: 55%

“…In contrast to the long time (slope selection dominated) regime with β = n λ , in the experiments the selected facets do not fully reach the selected slope magnitudes as their slope still grows within the experimental time window [35]. Such early time regimes are theoretically known to exhibit the coarsening exponent n < β, with typically small n in the range 0.1 − 0.2 [22].…”

Section: The Multitude Of Interface States On (110) Surfacesmentioning

confidence: 96%

“…Thus Eqs. (3.13) and (3.21) yield 22) and hence from (3.20) 24) and from (3.20) and (3.24) we have another scaling relation…”

Section: Coarsening Of (001) Crystal Surfacesmentioning

confidence: 99%

“…[18,26], § 3.2, § 4.1 and also Fig. 12); and (ii) the relation 22) with q the number of channels for dislocation annihilations -i.e. the number of distinct ways for an annihilation to proceed by continuously changing the edge network (cf.…”

Section: Large Scale Topological Defects Mediating Surface Growthmentioning

confidence: 99%

“…In particular, a combination of numerical simulations and analysis provided the first analytic explanation of the coarsening law exponents seen in MBE growth [18]. The approach was inspired in part by theories of phase ordering processes such as the growth of domains in magnetic systems [20], assuming an underlying effective free energy that governs the film surface dynamics as in earlier work on epitaxial growth [21,22]. Indeed, the dynamics of surface-like elastic manifolds such as membranes are governed by an elastic free energy, exemplified in studies of the buckling dynamics of semi-flexible polymers and membranes [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

Golubović

Levandovsky

Moldovan

2011

East Asian J. Appl. Math.

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Abstract. We review recent theoretical progress in the physical understanding of far-from-equilibrium phenomena seen experimentally in epitaxial growth and erosion on crystal surfaces. The formation and dynamics of various interface structures (pyramids, ripples, etc.), and also kinetic phase transitions observed between these structures, can all be understood within a simple continuum model based on the mass conservation law and respecting the symmetries of the growing crystal surface. In particular, theoretical predictions and experimental results are compared for (001), (110) and (111) crystal surfaces. 81.15.Aa, 89.75.Kd, 05.90.+m PACS (2006):

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Section: Large Scale Topological Defects Mediating Surface Growthsupporting

confidence: 55%

Section: The Multitude Of Interface States On (110) Surfacesmentioning

confidence: 96%

“…Thus Eqs. (3.13) and (3.21) yield 22) and hence from (3.20) 24) and from (3.20) and (3.24) we have another scaling relation…”

Section: Coarsening Of (001) Crystal Surfacesmentioning

confidence: 99%

Section: Large Scale Topological Defects Mediating Surface Growthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

Golubović

Levandovsky

Moldovan

2011

East Asian J. Appl. Math.

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Upper bound on the coarsening rate for an epitaxial growth model

Kohn

Yan

2003

Comm Pure Appl Math

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We study a specific example of energy‐driven coarsening in two space dimensions. The energy is ∫|∇∇u|2 + (1 ‐ | ∇u|2)2; the evolution is the fourth‐order PDE representing steepest descent. This equation has been proposed as a model of epitaxial growth for systems with slope selection. Numerical simulations and heuristic arguments indicate that the standard deviation of u grows like t1/3, and the energy per unit area decays like t‐1/3. We prove a weak, one‐sided version of the latter statement: The time‐averaged energy per unit area decays no faster than t‐1/3. Our argument follows a strategy introduced by Kohn and Otto in the context of phase separation, combining (i) a dissipation relation, (ii) an isoperimetric inequality, and (iii) an ODE lemma. The interpolation inequality is new and rather subtle; our proof is by contradiction, relying on recent compactness results for the Aviles‐Giga energy. © 2003 Wiley Periodicals, Inc.

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Epitaxial phenomena across length and time scales

Vvedensky

2001

Surface & Interface Analysis

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The morphological evolution of an epitaxial film results from atomistic processes such as adatom motion and step-adatom interactions asserting their influence over the macroscopic length and time scales of the growth front. Modelling epitaxial phenomena thus necessitates making a compromise between the detailed information provided by first-principles methods and the computational flexibility afforded by methods such as Monte-Carlo simulations and continuum equations of motion, in which atomistic processes are replaced by coarse-grained effective kinetics. We will review the various approaches that are available for modelling epitaxial phenomena using the (001) surfaces of III-V compound semiconductors as a case study, with a view to making direct comparisons with experimental measurements and to establishing a methodology that is capable of incorporating all pertinent length and time scales.

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Interfacial Coarsening in Epitaxial Growth Models without Slope Selection

Cited by 96 publications

References 18 publications

Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

Upper bound on the coarsening rate for an epitaxial growth model

Epitaxial phenomena across length and time scales

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