Universality class of discrete solid-on-solid limited mobility nonequilibrium growth models for kinetic surface roughening

Sarma, S. Das; Chatraphorn, P.; Toroczkai, Zoltán

doi:10.1103/physreve.65.036144

Cited by 48 publications

(66 citation statements)

References 17 publications

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“…For high enough temperatures activated surface diffusion delays this instability, but eventually the surface becomes unstable even if surface diffusion strongly dominates over WV relaxation processes at atomistic scales. Indeed, our results provide an analytic justification for the conclusion reached by KMC simulations [44][45][46] that a given relaxation mechanism can lead to qualitatively different surface morphologies depending on the dimensionality of the substrate (i.e. nonuniversal behavior) and the length and time scales considered.…”

Section: Introductionsupporting

confidence: 63%

“…Indeed, it is well known [10,57] that even for relatively small system sizes KMC simulations of the EW model show scaling behavior consistent with Eq. (45). Moreover, the 1D EW equation has been derived previously [89] as an asymptotic description of the 1D EW model.…”

Section: B Continuum Langevin Equationmentioning

confidence: 99%

“…A more accurate multiscale analysis of the EW model therefore necessitates the inclusion of the term ν 6 ∇ 6 u in the calculation of the RG trajectories from the initial conditions in Table I [53]. As discussed (21), (45), and (56) for the EW model on substrates of dimension d obtained with the representative choice δ = 0.01. We have set a ⊥ = a = τ0 = 1 and we have D2 = 0 for d = 1 and d = 2.…”

Section: B Continuum Langevin Equationmentioning

confidence: 99%

“…Moreover, experiments and computer simulations only access transient regimes of morphological evolution, whereas universality, which is often invoked [10,11] to justify a particular continuum equation for a given experimental setup, is appropriate only in the limit of infinitely large length and time scales. Indeed, the difficulties encountered with the description of recent computer simulations [45][46][47] and experiments [30][31][32][33][48][49][50] of homoepitaxial growth in terms of the standard equations of surface growth show that this program remains problematic. This is exacerbated by the fact that, from a technological perspective [29][30][31][32][33], the initial, rather than the asymptotic behavior of homoepitaxial surfaces, is of primary interest.…”

Section: Introductionmentioning

confidence: 99%

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Renormalization of stochastic lattice models: Epitaxial surfaces

Haselwandter

Vvedensky

2008

Phys. Rev. E

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We present the application of a method [Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial new technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the EdwardsWilkinson (EW) model [Proc. Roy. Soc. London Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding to the equation proposed by Villain [J. Phys. I 1, 19 (1991)] and by Lai and Das Sarma [Phys. Rev. Lett. 66, 2899 (1991)]. We conclude with a discussion of the application of our methodology to other growth settings.

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Section: Introductionsupporting

confidence: 63%

Section: B Continuum Langevin Equationmentioning

confidence: 99%

Section: B Continuum Langevin Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Renormalization of stochastic lattice models: Epitaxial surfaces

Haselwandter

Vvedensky

2008

Phys. Rev. E

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“…The exponents in this case are known only numerically in one and two dimensions [277]. For example in d = 1, α ≈ 1, β ≈ 1/3 and z ≈ 3 [277][278][279].…”

Section: • Molecular Beam Epitaxy (Mbe) Equation: This Is a 4-th Ordementioning

confidence: 99%

Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

531

669

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In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

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Stochastic Equations for Thin Film Morphology

Vvedensky

2005

Handbook of Materials Modeling

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Universality class of discrete solid-on-solid limited mobility nonequilibrium growth models for kinetic surface roughening

Cited by 48 publications

References 17 publications

Renormalization of stochastic lattice models: Epitaxial surfaces

Renormalization of stochastic lattice models: Epitaxial surfaces

Persistence and first-passage properties in nonequilibrium systems

Stochastic Equations for Thin Film Morphology

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