Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation

Rodríguez-Fernández, Enrique; Santalla, Silvia N.; Castro, Mario; Cuerno, Rodolfo

doi:10.1103/physreve.106.024802

Cited by 7 publications

(4 citation statements)

References 58 publications

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“…This special case provides the unexpected insight that even in the super-rough class, both the correlation functions

and

can exhibit time dependence, which according to the existing classification, has been considered as a fingerprint of the intrinsic anomalous roughening class. Given that both

and

are measured close to one, previous experimental results for TiN films [ 26 ], and (possibly) VO 2 films [ 23 ] classified as intrinsic anomalous roughening class, may actually belong to the super-rough class. However, when it comes to the growth of parylene-C film, categorized within the intrinsic anomalous roughening class, it is imperative that the actual

value should be less than one, even though the consistently measured exponent value may appear equal to one (i.e.,

).…”

Section: Resultsmentioning

confidence: 90%

“…In Table 1 , it is interesting to note that the continuum local growth model LDV belongs to the intrinsic anomalous roughening class that satisfies

, despite previous expectations for continuum growth models with local dynamics and spatiotemporal noise. Together with the simulation findings presented for the tensionless KPZ equation [ 26 ], the LDV model departs from the traditional assumptions regarding the role of nonlocal effects associated with the intrinsic anomalous roughening class of the interface. This challenges the conventional belief that intrinsic anomalous roughening is incompatible with local growth models [ 35 ].…”

Section: Resultsmentioning

confidence: 98%

“…Unlike the value of

, which has a mathematical upper limit of 1 according to the definition of

, the value of

can exceed one. This classification scheme, governed by these three roughness exponents, has been widely considered complete [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] and the interface roughening mechanism has been interpreted accordingly. In fact, various film growths by different techniques have been classified into subclasses of anomalous scaling: new class (or faceted surface) [ 17 , 20 ], intrinsic anomalous roughening [ 15 , 22 , 23 , 26 ], and super-rough interfaces [ 16 , 18 , 19 , 21 ].…”

Section: Introductionmentioning

confidence: 99%

“…This classification scheme, governed by these three roughness exponents, has been widely considered complete [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] and the interface roughening mechanism has been interpreted accordingly. In fact, various film growths by different techniques have been classified into subclasses of anomalous scaling: new class (or faceted surface) [ 17 , 20 ], intrinsic anomalous roughening [ 15 , 22 , 23 , 26 ], and super-rough interfaces [ 16 , 18 , 19 , 21 ]. However, as seen in some real-world film growth systems, the application of classification scheme based on the values of roughness exponents (

is not always straightforward and often leads to inconclusive results for various reasons [ 15 , 16 , 17 , 18 , 19 , 20 , 21 ].…”

Section: Introductionmentioning

confidence: 99%

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Surface Evolution of Polymer Films Grown by Vapor Deposition: Growth of Local and Global Slopes of Interfaces

Shin,

Lee

2024

Polymers

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The kinetic roughening of polymer films grown by vapor deposition polymerization was analyzed using the widely accepted classification framework of “generic scaling ansatz” given for the structure factor. Over the past two decades, this method has played a pivotal role in classifying diverse forms of dynamic scaling and understanding the mechanisms driving interface roughening. The roughness exponents of the polymer films were consistently determined as α=1.25±0.09, αloc=0.73±0.02, and αs=0.99±0.06. However, the inability to unambiguously assign these roughness exponent values to a specific scaling subclass prompts the proposal of a practical alternative. This report illustrates how all potential dynamic scaling can be consistently identified and classified based on the relationship between two temporal scaling exponents measured in real space: the average local slope and the global slope of the interface. The intrinsic anomalous roughening class is conclusively assigned to polymer film growth characterized by anomalous “native (background slope-removed) local height fluctuations”. Moreover, the new analysis reveals that interfaces exhibiting anomalous scaling, previously classified as intrinsic anomalous roughening, could potentially belong to the super-rough class, particularly when the spectral roughness exponent αs is equal to 1.

show abstract

“…This special case provides the unexpected insight that even in the super-rough class, both the correlation functions

and

can exhibit time dependence, which according to the existing classification, has been considered as a fingerprint of the intrinsic anomalous roughening class. Given that both

and

value should be less than one, even though the consistently measured exponent value may appear equal to one (i.e.,

).…”

Section: Resultsmentioning

confidence: 90%

“…In Table 1 , it is interesting to note that the continuum local growth model LDV belongs to the intrinsic anomalous roughening class that satisfies

Section: Resultsmentioning

confidence: 98%

“…Unlike the value of

, which has a mathematical upper limit of 1 according to the definition of

, the value of