Linear dynamics of ion sputtered surfaces: instability, stability and bifurcations

Davidovitch, Benny; Aziz, Michael J.; Brenner, Michael P.

doi:10.1088/0953-8984/21/22/224019

Cited by 13 publications

(11 citation statements)

References 40 publications

(111 reference statements)

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“…In the BH and CV theory, a gradient and curvaturedependent stochastic differential equation describes the stability (or instability) of a surface exposed to an oblique incident ion beam. According to recent publications by Madi et al [19], Davidovitch et al [20,21] and Norris et al [22], directed mass redistribution seems to be the dominating contribution to ripple pattern formation with ripple wave vectors parallel to the projected ion beam direction.…”

Section: Introductionmentioning

confidence: 93%

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Surface instability and pattern formation by ion-induced erosion and mass redistribution

Hofsäß

2013

Appl. Phys. A

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The contribution of curvature dependent sputtering and mass redistribution to ion-induced self-organized formation of periodic surface nanopatterns is revisited. Ion incidence angle-dependent curvature coefficients and ripple wavelengths are calculated from 3-dimensional collision cascade data obtained from binary collision Monte Carlo simulations. Significant modifications concerning mass redistribution compared to the model of Carter and Vishnyakov and also models based on crater functions are introduced. Furthermore, I find that curvature-dependent erosion is the dominating contribution to pattern formation, except for very low-energy irradiation of a light matrix with heavy ions. The major modifications regarding mass redistribution and ion-induced viscous flow are related to the ion incidence angle-dependent thickness of the irradiated layer. A smaller modification concerns the relaxation of inward-directed mass redistribution. Ioninduced viscous flow in the surface layer also depends on the layer thickness and is thus strongly angle dependent. Simulation results are presented and compared to a variety of published experimental results. The simulations show that in most cases curvature-dependent erosion is the dominant contribution to surface instability and ripple pattern formation and also determines the pattern orientation transition. The simulations predict the occurrence of perpendicular ripple patterns at larger ion incidence angles, in agreement with experimental observations. Mass redistribution causes stabilization of the surface at near-normal ion incidence angles and dominates pattern formation only at very low ion energies.

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Section: Introductionmentioning

confidence: 93%

“…However, the thickness d of an ionirradiated layer depends on ion energy and ion incidence angle and the correct dependence F S,rad (h, E ion )Ád(h) 3 should be used. Davidovitch et al [20,21] already introduced an angle-dependent relaxation coefficient 3 h. However, such dependence was not used later on.…”

Section: Theorymentioning

confidence: 99%

Surface instability and pattern formation by ion-induced erosion and mass redistribution

Hofsäß

2013

Appl. Phys. A

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“…Besides admitting rimmed craters, this form potentially has more fundamental advantages over traditional treatments of irradiationinduced morphology evolution. Instead of separate, simplified models of the processes of sputter erosion 15,16 and mass redistribution 17,108 -both of which break down as the angle of incidence approaches grazing-the crater function Dh naturally includes components due to both sputtered atoms and redistributed atoms (thus unifying the two approaches) and can in principle be obtained empirically (thus avoiding model inaccuracy at high angles of incidence). Two initial attempts to study Eq.…”

Section: Integro-differential Equationmentioning

confidence: 99%

Ion-induced nanopatterning of silicon: Toward a predictive model

Norris

Aziz

2019

Applied Physics Reviews

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We review recent progress toward the development of predictive models of ion-induced pattern formation on roomtemperature silicon, with a particular emphasis on efforts to eliminate fit parameters in the linear regime by means of experimental measurements or atomistic simulations. Analytical approaches considered include "mechanistic" models of the impactinduced collision cascade, the Crater Function Framework, and continuum treatments of ion-induced stress and viscous flow. Parameter evaluation methods include molecular dynamics and binary collision approximation simulations, as well as wafer curvature measurements and grazing incidence small-angle x-ray scattering. Mathematical detail is provided in the context of key results from pattern formation theory, which are also briefly summarized.

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“…Recently, Harrison and Bradley pointed out that an exact treatment of the BH model within the crater function approach requires also the evaluation of erosion crater functions on curved surfaces [2]. Pattern formation due to directed mass redistribution in the collision cascade volume parallel to the local surface was first introduced by Carter and Vishnyakov (CV) [3] and recently evaluated by Madi et al [4], Davidovitch et al [5,6], Norris et al [7,8] and Hossain et al [9] using the crater function approach. In the BH and CV theories, gradient-and curvature-dependent stochastic differential equations describe the stability (or instability) of a surface exposed to an oblique incident ion beam.…”

Section: Introductionmentioning

confidence: 99%

Model for roughening and ripple instability due to ion-induced mass redistribution [Addendum to H. Hofsäss, Appl. Phys. A 114 (2014) 401, “Surface instability and pattern formation by ion-induced erosion and mass redistribution”]

Hofsäß

2015

Appl. Phys. A

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Carter and Vishnyakov introduced a model (CV model) to describe roughening and ripple instability due to ion-induced mass redistribution. This model is based on the assumption that the irradiated surface layer on a static solid substrate is described by a viscous incompressible thin film bound to the substrate by a ''no slip'' and ''no transport'' kinematic boundary condition, i.e. similar to a thin film of viscous paint. However, this boundary condition is incomplete for a layer under ion irradiation. The boundary condition must allow exchange of atoms between the substrate and the irradiated film, so that the thickness of the film is always determined by the size of the collision cascade, independent of the evolution of the surface height profile. In addition, the film thickness depends on the local ion incidence angle, which leads to a time dependence of the film thickness at a given position. The equation of motion of the surface and interface profiles for these boundary conditions is introduced, and a new curvature-dependent coefficient is found which is absent in the CV model. This curvature coefficient depends on the angular derivative of the layer thickness and the atomic drift velocity at the film surface induced by recoil events. Such a stabilizing curvature coefficient was introduced in Appl. Phys. A 114 (2014) 401 and is most pronounced at intermediate angles.

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Linear dynamics of ion sputtered surfaces: instability, stability and bifurcations

Cited by 13 publications

References 40 publications

Surface instability and pattern formation by ion-induced erosion and mass redistribution

Surface instability and pattern formation by ion-induced erosion and mass redistribution

Ion-induced nanopatterning of silicon: Toward a predictive model

Model for roughening and ripple instability due to ion-induced mass redistribution [Addendum to H. Hofsäss, Appl. Phys. A 114 (2014) 401, “Surface instability and pattern formation by ion-induced erosion and mass redistribution”]

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