Simulation of formation of nanostructures during sputtering of the surface by ion bombardment

Rudyi, A. S.; Куликов, А. Н.; Metlitskaya, A. V.

doi:10.1134/s1063739711020089

Cited by 4 publications

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“…Nanostructures other than WNST were not considered in this paper. For example, the formation of terraces was consid ered in [19], which addressed a boundary value problem different from a periodic one for the generalized Kuramoto-Sivashinsky equation.…”

Section: Discussionmentioning

confidence: 99%

Formation of wavy nanostructures on the surface of flat substrates by ion bombardment

Куликов

Kulikov

2012

Comput. Math. and Math. Phys.

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A popular mathematical model for the formation of an inhomogeneous topography on the surface of a plate (flat substrate) during ion bombardment was considered. The model is described by the Bradley-Harper equation, which is frequently referred to as the generalized Kuramoto-Sivashin sky equation. It was shown that inhomogeneous topography (nanostructures in the modern terminol ogy) can arise when the stability of the plane incident wavefront changes. The problem was solved using the theory of dynamical systems with an infinite dimensional phase space, in conjunction with the integral manifold method and Poincaré-Dulac normal forms. A normal form was constructed using a modified Krylov-Bogolyubov algorithm that applies to nonlinear evolutionary boundary value problems. As a result, asymptotic formulas for solutions of the given nonlinear boundary value prob lem were derived.A. N. KULIKOV, D. A. KULIKOV we showed (emphasizing once again) that, in the case of an oblong substrate, the problem can sometimes be reduced to a periodic boundary value problem, i.e., to a system in which the "basic role" is played by the Ginzburg-Landau equation, which is a model equation in various fields of physics and continuum mechanics. CONCLUSIONSA possible explanation for the formation of wavy nanostructure topography (WNST) was proposed. Recently, much interest has been given to self organized nanostructures in condensed systems. Examples are WNST, ripples, terraces, and etched cavities on semiconductor surfaces induced by ion bombardment. Of all these structures, WNST is of greatest interest, since it can be used as a nanomask. Nanostructures other than WNST were not considered in this paper. For example, the formation of terraces was consid ered in [19], which addressed a boundary value problem different from a periodic one for the generalized Kuramoto-Sivashinsky equation.

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Section: Discussionmentioning

confidence: 99%