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Rhombic
planform nonlinear stability analysis of an ion-sputtering
evolution equation
Sydney Schmidt, Stephanie Kolden, Bonni Dichone and David Wollkind
Vol. 14 (2021), No. 1, 119–142
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Abstract |
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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. |
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Keywords
ion-sputtered erosion, Kuramoto–Sivashinsky equation,
Swift–Hohenberg equation, nonlinear stability analysis,
rhombic pattern formation
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Mathematical Subject Classification
Primary: 35B35, 35B36, 35R35, 74A50, 74K35
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Milestones
Received: 28 June 2020
Revised: 30 September 2020
Accepted: 10 October 2020
Published: 4 March 2021
Communicated by Martin J. Bohner
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Authors |
| Sydney Schmidt | |
| Department of Mathematics Gonzaga University Spokane, WA United States |
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| Stephanie Kolden | |
| Department of Mathematics Gonzaga University Spokane, WA United States |
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| Bonni Dichone | |
| Department of Mathematics Gonzaga University Spokane, WA United States |
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| David Wollkind | |
| Department of Mathematics Washington State University Pullman, WA United States |
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