Modeling heterogeneity and memory effects on the kinetic roughening of silica films grown by chemical vapor deposition

Ojeda, F.; Cuerno, Rodolfo; Salvarezza, Roberto Carlos; Vázquez, Luís

doi:10.1103/physrevb.67.245416

Cited by 8 publications

(5 citation statements)

References 28 publications

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“…One possibility is that the crossovers induced by the instabilities are so long lived as to prevent actual asymptotic scaling from being accessed by experiments. Such a possibility seems to occur in conceptually similar growth techniques, such as chemical vapor deposition [33,34]. However, standard symmetry arguments [6] lead to the expectation of generic KPZ behavior for such non-conserved growth phenomena as provided by ECD systems.…”

Section: J Stat Mech (2009) P02036mentioning

confidence: 99%

Kinetic roughening in a realistic model of non-conserved interface growth

2009

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We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-slopes (interfacial) theories and the interplay between the emergence of morphologically instabilities in the aggregate dynamics, and its kinetic roughening properties. Taking for definiteness electrochemical deposition as our experimental field of reference, our theoretical approach makes use of two complementary approaches: interfacial effective equations and a phase-field formulation of the electrodeposition process. Both descriptions allow us to establish a close quantitative connection between theory and experiments. Moreover, we are able to correlate the anomalous scaling properties seen in some experiments with the failure of the small slope approximation, and to assess the effective re-emergence of standard kinetic roughening properties at very long times under appropriate experimental conditions.

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Section: J Stat Mech (2009) P02036mentioning

confidence: 99%

Kinetic roughening in a realistic model of non-conserved interface growth

2009

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“…We propose that based upon these findings a control tool should be developed which might be useful in experimental setups. The work of Ojeda et al [7,8] gives some indication that the KPZ nonlinearity is tunable via the temperature.…”

Section: Discussionmentioning

confidence: 96%

Time delayed feedback control in growth phenomena

Block

Schöll

2007

Journal of Crystal Growth

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“…The KPZ equation has been discussed in many different contexts, including thin film growth [18,19,20,21], fluctuating hydrodynamics [22], driven diffusive systems [23,24], tumor growth in biophysics [25,26], propagating fire fronts [27,28] and econophysics [29]. In the following, we will use the language of surface growth, but our findings are easily translated into these other contexts and just as relevant there.…”

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confidence: 99%

“…We thus hope to develop a control tool which might also be useful in experimental setups. The work of Ojeda et al [18,19] gives some indications that the KPZ nonlinearity is tunable via the temperature. Hence, it seems feasable to implement a time-delayed feedback loop and stabilize desired growth exponents by suitable adjustments of the…”

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confidence: 99%

“…Even if such control can only be sustained in a finite window of time, its experimental potential is undiminished since the growth process can simply be terminated when the desired characteristics have been achieved, thanks to today's precise in situ characterization capabilities. Moreover, paradigmatic growth models, such as the KardarParisi-Zhang ͑KPZ͒ equation, 11 find applications in many diverse areas of science, e.g., thin film growth, [12][13][14][15] fluctuating hydrodynamics, 16 driven diffusive systems, [17][18][19] tumor growth in biophysics, [20][21][22] propagating fire fronts, 23 and econophysics. 24 Therefore, broad implications can be expected if methods from control theory can be successfully implemented in this vast context.…”

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confidence: 99%

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Controlling surface morphologies by time-delayed feedback

2007

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We propose a method to control the roughness of a growing surface via a time-delayed feedback scheme. The method is very general and can be applied to a wide range of nonequilibrium growth phenomena, from solid-state epitaxy to tumor growth. Possible experimental realizations are suggested. As an illustration, we consider the Kardar-Parisi-Zhang equation ͓Phys. Rev. Lett. 56, 889 ͑1986͔͒ in 1 + 1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval ͓0.25, 0.33͔, for a significant length of time. DOI: 10.1103/PhysRevB.75.233414 PACS number͑s͒: 68.35.Rh, 05.10.Gg, 02.30.Ks, 02.60.Cb The control of unstable states in chaotic or patternforming nonlinear dynamical systems has attracted much interest recently. 1,2 Time-delayed feedback control 3 has been especially successful in stabilizing a variety of dynamic and spatial structures, including noise-induced oscillations and patterns found, e.g., in semiconductor nanostructures. [4][5][6][7] Here, we propose to apply these control techniques to a completely new class of dynamical phenomena, namely, farfrom-equilibrium surface growth. [8][9][10] The goal is to stabilize desired surface characteristics, such as spatiotemporal height-height correlations or the surface roughness, during the growth process. Even if such control can only be sustained in a finite window of time, its experimental potential is undiminished since the growth process can simply be terminated when the desired characteristics have been achieved, thanks to today's precise in situ characterization capabilities. Moreover, paradigmatic growth models, such as the KardarParisi-Zhang ͑KPZ͒ equation, 11 find applications in many diverse areas of science, e.g., thin film growth, 12-15 fluctuating hydrodynamics, 16 driven diffusive systems, [17][18][19] tumor growth in biophysics, [20][21][22] propagating fire fronts, 23 and econophysics. 24 Therefore, broad implications can be expected if methods from control theory can be successfully implemented in this vast context.In this Brief Report, we provide an exploration of these ideas. We choose the most promising type of control, timedelayed feedback, and study its effects on the KPZ equation. 11 Specifically, we attempt to control the effective dynamic growth exponent ␤ associated with the roughness of the growing surface. By implementing two realizations of the control scheme, we will see below that we can, indeed, stabilize ␤ in a range of values between the two universal limits, 1 / 4 and 1 / 3, over at least one to two decades in time. In the following, we will use the language of surface growth, but our findings are just as relevant in the context of all other applications of the KPZ equation. For instance, in recent work on tumor growth, 20 it has been shown that an efficient method to influence the proliferation of tumor cells at the border is coupled to the growth exponents and the universality class of growth. The authors suggest and establish a therapy which rests on th...

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Modeling heterogeneity and memory effects on the kinetic roughening of silica films grown by chemical vapor deposition

Cited by 8 publications

References 28 publications

Kinetic roughening in a realistic model of non-conserved interface growth

Kinetic roughening in a realistic model of non-conserved interface growth

Time delayed feedback control in growth phenomena

Controlling surface morphologies by time-delayed feedback

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