Hallmarks of the Kardar–Parisi–Zhang universality class elicited by scanning probe microscopy

Alves, Sidiney G.; Araujo, C. I. L. de; Ferreira, Silvio C.

doi:10.1088/1367-2630/18/9/093018

Cited by 11 publications

(5 citation statements)

References 66 publications

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“…Finally, the KPZ mechanism in CdTe films comes from the packing of grains, which yields a velocity excess in the growth, as explained in refs 19 , 21 . Obviously, results presented here do not have any relation with a possible artificial KPZ scaling induced by AFM tip effects 52 . Note that typical tip radius ( r ) is r ≈ 10–20 nm , corresponding to the size of our image pixel ( a ≈ 19.5 nm ), while the average CdTe grain size is l g ≈ 0.7 μm in the asymptotic KPZ regime.…”

Section: Summary and Final Discussionmentioning

confidence: 51%

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

Almeida

Ferreira

Ferraz

2017

Sci Rep

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The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A pseudo-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of ~10 4 monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors.The Kardar-Parisi-Zhang (KPZ) equationoriginally describes interface motion under conditions of no bulk conservation and exponentially fast relaxation 2 . The height field h(x, t) is measured from a d s -dimensional substrate at location x, with x ∈  d s at time t ≥ 0. ν, λ and D are phenomenological parameters, physically representing the surface tension, the excess of velocity in the growth, and the amplitude of a space-time white noise η, respectively.Although posed 30 years ago, outstanding advances on the understanding of the KPZ class have been made quite recently. Following seminal works on multiple-meaning stochastic models 3, 4 , long-awaited analytical solutions 2,5 , experiments 6, 7 and numerical simulations 7-9 came out to confirm that asymptotic 1D-KPZ height distributions (HDs) are related to statistics of the largest eigenvalues of random matrices 10 , while spatial covariances are dictated by the time-correlation of Airy processes 11 . Noteworthy, both HDs and covariances exhibit sensibility to initial conditions (ICs) 4, 11 , splitting the KPZ class into subclasses according to the ICs. This unanticipated feature was recently observed also in models for nonlinear molecular beam epitaxy class 12 . Similar scenario has been found for the 2D-KPZ case, based on numerical simulations [13][14][15] , although no analytical result is known for 2D-KPZ HDs and covariances and the existing theoretical approaches 16,17 for the scaling exponents disagree with numerical outcomes. In such arid landscape, the rare reliable experimental evidences of 2D-KPZ universality [18][19][20][21] turns to be precious achievements.The short-time roughening of systems exhibiting asymptotic KPZ scaling is also rich in behavior. For example, a transient scaling in the Edwards-Wilkinson 22 (EW) class, might appear whenev...

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Section: Summary and Final Discussionmentioning

confidence: 51%

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

Almeida

Ferreira

Ferraz

2017

Sci Rep

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“…We expect that our results will be of relevance for experimental analyses, in which mounded morphologies are commonly observed [1] and the resolution of the universality class is challenging. As a perspective, it would be interesting to consider the role played by the intrinsic smoothening of the surfaces obtained by the widely used scanning probe microscopy techniques that can markedly interfere in the roughness exponent determination [38] or even indicate a misleading universality class [39].…”

Section: Discussionmentioning

confidence: 99%

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

2017

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We present an optimal detrended fluctuation analysis (DFA) and applied it to evaluate the local roughness exponent in non-equilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations computing the shortest distance of each point of the profile to a detrending curved that fits the surface within the investigated interval. We compare the optimal DFA (ODFA) with both the standard DFA and nondetrended analysis. We validate the ODFA method considering a one-dimensional model in the Kardar-Parisi-Zhang universality class starting from a mounded initial condition. We applied the methods to the Clarke-Vvdensky (CV) model in 2 + 1 dimensions with thermally activated surface diffusion and absence of step barriers. It is expected that this model belongs to the nonlinear Molecular Beam Epitaxy (nMBE) universality class. However, an explicit observation of the roughness exponent in agreement with the nMBE class was still missing. The effective roughness exponent obtained with ODFA agrees with the value expected for nMBE class whereas using the other methods it does not. We also characterized the transient anomalous scaling of the CV model and obtained that the corresponding exponent is in agreement with the value reported for other nMBE models with weaker corrections to the scaling.

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“…Our findings constitute an important step for confirm-ing the nMBE as a general universality class. Moreover, the scarcity of experimental evidences for nMBE could be explained by the almost unavoidable presence of strong corrections to the scaling due to limitations for growth times and resolution in scanning probe microscopes [41,42], which might be addressed using suitable methods such as ODFA [34]. This method can be easily extended to the analysis of self-affine objects not related to surface growth such as time series modulated for seasonal changes [43].…”

Section: Discussionmentioning

confidence: 99%

Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one dimension

et al. 2019

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We report local roughness exponents, α loc , for three interface growth models in one dimension which are believed to belong the non-linear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval α loc ∈ [0.96, 0.98] consistent with renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form α loc = 1 − of the one-loop renormalization group analysis of the VLDS equation.

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Hallmarks of the Kardar–Parisi–Zhang universality class elicited by scanning probe microscopy

Cited by 11 publications

References 66 publications

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one dimension

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