Surface dynamics of the Wolf-Villain model for epitaxial growth in 1 + 1 dimensions

Park, K.; Kahng, B.; Kim, S.S.

doi:10.1016/0378-4371(94)00094-8

Cited by 15 publications

(3 citation statements)

References 22 publications

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“…1, with the crossover to the EW value ␤Ϸ1/4 clearly demonstrated. 35 Recently, Park et al 36 found further evidence that the asymptotic behavior is of the EW type.…”

Section: B Results In 1؉1 Dimensionsmentioning

confidence: 97%

Nonuniversality in models of epitaxial growth

Kotrla

Šmilauer

1996

Phys. Rev. B

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Kinetic roughening in two variants of a solid-on-solid model of epitaxial growth, a ''toy'' relaxation model and a collective diffusion model, is studied and compared, using extensive computer simulations in different spatial dimensions. We have studied the Wolf-Villain ͑WV͒ model and its modifications, and a full diffusion ͑FD͒ model with Arrhenius dynamics. The WV model shows nonuniversal features and its asymptotic behavior switches between the Edwards-Wilkinson type and a morphological instability, depending on the spatial dimension, a lattice coordination, or a minor modification of the model rules. The results for the FD model in 1ϩ1 and 2ϩ1 dimensions are not consistent with any of the continuum equations proposed to describe epitaxial growth; in particular, we observe too low values of the roughness exponent measured from the height-difference correlation function. In 1ϩ1 dimensions, the results obtained for both models are very similar for more than 10 6 monolayers deposited with an ''incorporation'' radius in the WV model corresponding to the substrate temperature in the FD model. Such a close correspondence is not found in 2ϩ1 dimensions. Asymptotic behavior of the WV and FD models is different in all spatial dimensions. Both FD and WV models show anomalous scaling in all dimensions studied. The anomalous scaling in the FD model is very weak ͑logarith-mic͒ in the physically relevant case of 2ϩ1 dimensions.

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“…1, with the crossover to the EW value ␤Ϸ1/4 clearly demonstrated. 35 Recently, Park et al 36 found further evidence that the asymptotic behavior is of the EW type.…”

Section: B Results In 1؉1 Dimensionsmentioning

confidence: 97%

Nonuniversality in models of epitaxial growth

Kotrla

Šmilauer

1996

Phys. Rev. B

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“…[77] was the prediction of a crossover to Edwards-Wilkinson scaling for the Wolf-Villain (WV) model both in one and two substrate dimensions ; the crossover time was estimated to be t, ti 10 6 monolayers in d = 1, and t~ 2 x 104 ML in d = 2 . Direct numerical evidence for such a crossover has been presented in two recent studies [253,254] . Moreover, the measurement of surface currents for a variety of limited mobility rules introduced by Das Sarma and Ghaisas [133] indicates that JNE is nonzero generically for these models [255].…”

Section: Computer Simulationsmentioning

confidence: 96%

Origins of scale invariance in growth processes

Krug

1997

Advances in Physics

985

1,358

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“…In the continuum limit, the WV model in d = 1 is expected to belong to the EW class. Indeed, many works have already analyzed the long crossover to the asymptotic exponents in that case [25,26,27,9,24]. Krug et al [30] and Siegert [9] observed a crossover to the EW class in d = 2, but the recent works of Das Sarma and collaborators [14,15,16] suggested the unstable (mounded morphology) universality class in that case.…”

Section: Introductionmentioning

confidence: 99%

Scaling of local interface width of statistical growth models

Chame

Reis

2004

Surface Science

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We discuss the methods to calculate the roughness exponent alpha and the dynamic exponent z from the scaling properties of the local roughness, which is frequently used in the analysis of experimental data. Through numerical simulations, we studied the Family, the restricted solid-on-solid (RSOS), the Das Sarma-Tamborenea (DT) and the Wolf-Villain (WV) models in one- and two dimensional substrates, in order to compare different methods to obtain those exponents. The scaling at small length scales do not give reliable estimates of alpha, suggesting that the usual methods to estimate that exponent from experimental data may provide misleading conclusions concerning the universality classes of the growth processes. On the other hand, we propose a more efficient method to calculate the dynamic exponent z, based on the scaling of characteristic correlation lengths, which gives estimates in good agreement with the expected universality classes and indicates expected crossover behavior. Our results also provide evidence of Edwards-Wilkinson asymptotic behavior for the DT and the WV models in two-dimensional substrates.Comment: To appear in Surface Scienc

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Surface dynamics of the Wolf-Villain model for epitaxial growth in 1 + 1 dimensions

Cited by 15 publications

References 22 publications

Nonuniversality in models of epitaxial growth

Nonuniversality in models of epitaxial growth

Origins of scale invariance in growth processes

Scaling of local interface width of statistical growth models

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