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

Schmidt, Sydney; Kolden, Stephanie; Dichone, Bonni; Wollkind, David

Involve 14, No. 1, 119-142 (2021).

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

Keywords:

ion-sputtered erosion; Kuramoto-Sivashinsky equation; Swift-Hohenberg equation; nonlinear stability analysis; rhombic pattern formation