Columnar growth and kinetic roughening in electrochemical deposition

Kahanda, G. L. M. K. S.; Zou, Xiao-qun; Farrell, Robert E.; Wong, Po‐zen

doi:10.1103/physrevlett.68.3741

Cited by 105 publications

(112 citation statements)

References 23 publications

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“…Eq. (8). Consequently, they will describe the GKE system for dimensions d > d c , where the trivial FP is stable, cf.…”

Section: Resultsmentioning

confidence: 99%

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Growth equation with a conservation law

Lauritsen

1995

Phys. Rev. E

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A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows for a unified investigation of growth equations. From a dynamic renormalization-group analysis critical exponents and universality classes are determined for growth models with a conservation law.

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“…Eq. (8). Consequently, they will describe the GKE system for dimensions d > d c , where the trivial FP is stable, cf.…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, one can speculate whether some growth experiments, which yield exponents that do not agree with the KPZ exponents, may contain nonlocal growth effects such as, e.g., the experiments on electrochemical deposition reported in Refs. [8,9].…”

Section: Introductionmentioning

confidence: 99%

Growth equation with a conservation law

Lauritsen

1995

Phys. Rev. E

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“…This is the well-known Mullins-Sekerka dispersion relation [26], that appears in many other di usive problems like solidiÿcation and, what is more signiÿcative, in several ECD experiments like [8,27]. Nevertheless, these experiments were made at constant overpotential instead of constant current density, which is one of the hypothesis made in proposing (3) - (6).…”

Section: Instantaneous Surface Kineticsmentioning

confidence: 89%

“…The generality of KPZ scaling would be a consequence of the phenomenon of universality observed for the scaling properties of rough surfaces. However, despite some attempts at measuring KPZ scaling in, e.g., IBS [7] or ECD [8], to date very few experiments have been reported which are unambiguously described by the KPZ equation [9 -11]. The identiÿcation of the physical mechanisms responsible for this paradoxical (termed "anomalous" in some early studies of kinetic roughening) non-KPZ scaling behavior has been complicated by two main reasons: on the one hand, while detailed derivations of the KPZ equation have actually been achieved, they apply to discrete or continuous theoretical models [12] which are indirectly related with experiments, or else the derivations themselves need resort to approximations which are not free from ambiguities.…”

Section: Introductionmentioning

confidence: 99%

Possible origin for the experimental scarcity of KPZ scaling in non-conserved surface growth

Cuerno

Castro

2002

Physica A: Statistical Mechanics and its Applications

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The Kardar-Parisi-Zhang (KPZ) equation is generically expected to describe the scaling properties of rough surfaces growing in the absence of conservation laws. However, very few experimental realizations are known of this universality class. Here we focus on the role of instabilities, whether of di usional origin or other, as physical mechanisms hindering the observation of KPZ scaling. Examples are drawn from various growth processes, such as electrochemical deposition (ECD), chemical vapor deposition (CVD), and erosion by ion-beam sputtering. We moreover consider an interface equation which, starting from the corresponding constitutive equations, can be derived to describe growth by either ECD or CVD depending on the interpretation of the quantities appearing. This approach makes contact with phenomenological parameters, and suggests that a more generic description of non-conserved growth may be provided by the KuramotoSivashinsky equation and generalizations thereof. In this case, the experimental scarcity of KPZ scaling would be due to exceedingly long transients determined by the instabilities that occur.

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“…The exponents found in our study for high pressure data were x = 0.40 and /? = 0.40 (2). One of the key features for the dynamic scaling behavior is the fact that the value does not change over time.…”

Section: Discussionmentioning

confidence: 99%

X-ray reflectivity study of gold films during sputter-deposition

Chiarello¹,

You²,

Roberts³

1994

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May 1994Submitted to Physical Review B Ism 1-2. 4.M We performed in-situ x-ray reflectivity measurements of gold films during sputter-deposition on polished silicon substrates. T h e measurements were performed at several substrate temperatures and under two argon pressures.The gold surfaces were also examined by scanning tunneling microscopy after deposition to obtain their real-space topographic images. These images were used to complement tlie s-ray reflectivity measurements in determining the effect of argon pressure on tlie gold surface and its height-height differencefunctions. An approximation for height-height difference functions was cnipioycd to analyze the x-ray rcflcctivity data. The nieasureti intcrfacc widt 11 during growtli follows a siinplc po\vcr-la\v behavior consistcnt witli rccciitly developed dynamic scaling behavior. The scaling exponents, however, do not agree well with predictions based on some models in 2 + 1 dimensions.

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Columnar growth and kinetic roughening in electrochemical deposition

Cited by 105 publications

References 23 publications

Growth equation with a conservation law

Growth equation with a conservation law

Possible origin for the experimental scarcity of KPZ scaling in non-conserved surface growth

X-ray reflectivity study of gold films during sputter-deposition

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