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**Rhombic planform nonlinear stability analysis of an ion-sputtering evolution equation.**
*(English)*
Zbl 1467.35043

Summary: 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.

### MSC:

35B35 | Stability in context of PDEs |

35B36 | Pattern formations in context of PDEs |

35K25 | Higher-order parabolic equations |

35K58 | Semilinear parabolic equations |

35R35 | Free boundary problems for PDEs |

74A50 | Structured surfaces and interfaces, coexistent phases |

74K35 | Thin films |