Layer-by-layer epitaxy in limited mobility nonequilibrium models of surface growth

Chatraphorn, P.; Sarma, S. Das

doi:10.1103/physreve.66.041601

Cited by 12 publications

(14 citation statements)

References 51 publications

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“…An alternative class of systems to model nonequilibrium surface growth are discrete lattice growth models which are known as limited mobility (LM) models [57][58][59][60][61]. Due to their simplicity, these models are especially suitable to investigate scaling properties, to study kinetic surface roughening and morphological properties as well as to investigate details like crossover and longlived transient effects in nonequilibrium surface growth [62,63,68,69]. In LM models, the process rates that are used in KMC simulations are replaced by a certain set of stochastic rules for particle movements that depend on the local environment of the position of particle adsorption.…”

Section: Introductionmentioning

confidence: 99%

“…This would enable us, for example, to study the asymptotic regime of the surface growth where we expect to observe scaling behavior of the growing surface. In particular, one would like to extract the corresponding critical exponents describing the scaling of the surface roughness [85] without being limited by finite-size effects or computational manipulations like the noise reduction technique (NRT) [80][81][82][83][84].…”

Section: Introductionmentioning

confidence: 99%

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Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

Martynec

Klapp

2019

Phys. Rev. E

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Kinetic Monte-Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy (MBE) experiments. In parallel, simplified approaches such as limited mobility (LM) models characterized by a fixed diffusion length have been studied. Here, we investigate an extended LM model to gain deeper insight into the role of diffusional processes concerning the growth morphology. Our model is based on the stochastic transition rules of the Das Sarma-Tamborena (DT) model, but differs from the latter via a variable diffusion length. A first guess for this length can be extracted from the saturation value of the meansquared displacement calculated from short KMC simulations. Comparing the resulting surface morphologies in the sub-and multilayer growth regime to those obtained from KMC simulations, we find deviations which can be cured by adding fluctuations to the diffusion length. This mimics the stochastic nature of particle diffusion on a substrate, an aspect which is usually neglected in LM models. We propose to add fluctuations to the diffusion length by choosing this quantity for each adsorbed particle from a Gaussian distribution, where the variance of the distribution serves as a fitting parameter. We show that the diffusional fluctuations have a huge impact on cluster properties during submonolayer growth as well as on the surface profile in the high coverage regime. The analysis of the surface morphologies on one-and two-dimensional substrates during sub-and multilayer growth shows that the LM model can produce structures that are indistinguishable to the ones from KMC simulations at arbitrary growth conditions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

Martynec

Klapp

2019

Phys. Rev. E

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“…Studies of the kinetic surface roughening models for molecular beam epitaxy (MBE) growth has long been an interesting research topics [1][2][3][4][5][6][7][8][9][10][11][12][13]. This is because MBE technique is very effective in growing high quality films.…”

Section: Introductionmentioning

confidence: 99%

“…A substantial amount of works have been done to incorporate the ES barrier into MBE growth model [2,3,[9][10][11][12][13]. One of the earliest works studied a stochastic SOS Monte Carlo model in the presence of a potential barrier [5].…”

Section: Introductionmentioning

confidence: 99%

Effects of the Ehrlich–Schwoebel potential barrier on the Wolf–Villain model simulations for thin film growth

Rangdee¹,

Chatraphorn²

2006

Surface Science

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Wolf-Villain (WV) model is a simple model used to study ideal molecular beam epitaxy (MBE) growth by using computer simulations. In this model, an adatom diffuses instantaneously within a finite diffusion length to maximize its coordination number. We study statistical properties of thin films grown by this model. The morphology of the WV model is found to be kinetically rough with a downhill particle diffusion current. In real MBE growth, however, there are additional factors such as the existence of a potential barrier that is known as the Ehrlich-Schwoebel (ES) barrier. The ES barrier is an additional barrier for an adatom that diffuses over a step edge from the upper to a lower terrace which is known to induce an uphill particle current. We found that with the addition of the ES barrier, the WV-ES model morphology is rough with mound formation on the surface when the barrier is strong enough. To confirm these results, the correlation function is also studied. We find no oscillation in the correlation function in the WV model. For the WV-ES model, the correlation function oscillates. These results confirm that a strong enough ES barrier can cause mound formation on the WV surface in our study.

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“…The presence of mound morphology, a missing feature in one spatial dimension, suggests that a given model may belong to a different universality class in a different dimension, thus rendering the universality class concept futile. [27][28][29] In this paper we propose, in addition to ES barrier, a competing mechanism for mound formation as a consequence of probabilistic terrace currents due to the geometry of a film's crystalline structure. We begin, in Section II, by describing the helical boundary conditions essential for constructing representations of various crystal structures.…”

Section: Introductionmentioning

confidence: 99%

Growth instability due to lattice-induced topological currents in limited-mobility epitaxial growth models

2010

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The energetically driven Ehrlich-Schwoebel barrier had been generally accepted as the primary cause of the growth instability in the form of quasiregular moundlike structures observed on the surface of thin film grown via molecular-beam epitaxy (MBE) technique. Recently the second mechanism of mound formation was proposed in terms of a topologically induced flux of particles originating from the line tension of the step edges which form the contour lines around a mound. Through large-scale simulations of MBE growth on a variety of crystalline lattice planes using limited-mobility, solid-on-solid models introduced by Wolf-Villain and Das Sarma-Tamborenea in 2+1 dimensions, we show that there exists a topological uphill particle current with strong dependence on specific lattice crystalline structure. Without any energetically induced barriers, our simulations produce spectacular mounds very similar, in some cases, to what have been observed in many recent MBE experiments. On a lattice where these currents cease to exist, the surface appears to be scale invariant, statistically rough as predicted by the conventional continuum growth equation.

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Layer-by-layer epitaxy in limited mobility nonequilibrium models of surface growth

Cited by 12 publications

References 51 publications

Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

Effects of the Ehrlich–Schwoebel potential barrier on the Wolf–Villain model simulations for thin film growth

Growth instability due to lattice-induced topological currents in limited-mobility epitaxial growth models

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