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2021 Rhombic planform nonlinear stability analysis of an ion-sputtering evolution equation
Sydney Schmidt, Stephanie Kolden, Bonni Dichone, David Wollkind
Involve 14(1): 119-142 (2021). DOI: 10.2140/involve.2021.14.119

Abstract

A damped Kuramoto–Sivashinsky equation describing the deviation of an interface from its mean planar position during normal-incidence ion-sputtered erosion of a semiconductor or metallic solid surface is derived and the magnitude of the gradient in its source term is approximated so that it will be of a modified Swift–Hohenberg form. Next, one-dimensional longitudinal and two-dimensional rhombic planform nonlinear stability analyses of the zero deviation solution to this equation are performed, the former being a special case of the latter. The predicted theoretical morphological stability results of these analyses are then shown to be in very good qualitative and quantitative agreement with relevant experimental evidence involving the occurrence of smooth surfaces, ripples, checkerboard arrays of pits, and uniform distributions of islands or holes once the concept of lower- and higher-threshold rhombic patterns is introduced based on the mean interfacial position.

Citation

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Sydney Schmidt. Stephanie Kolden. Bonni Dichone. David Wollkind. "Rhombic planform nonlinear stability analysis of an ion-sputtering evolution equation." Involve 14 (1) 119 - 142, 2021. https://doi.org/10.2140/involve.2021.14.119

Information

Received: 28 June 2020; Revised: 30 September 2020; Accepted: 10 October 2020; Published: 2021
First available in Project Euclid: 22 April 2021

Digital Object Identifier: 10.2140/involve.2021.14.119

Subjects:
Primary: 35B35 , 35B36 , 35R35 , 74A50 , 74K35

Keywords: ion-sputtered erosion , Kuramoto–Sivashinsky equation , nonlinear stability analysis , rhombic pattern formation , Swift–Hohenberg equation

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 1 • 2021
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