Hydrodynamic model of wave-ordered structures formed by ion bombardment of solids

Abstract

The model of a wave-ordered structures (WOS) formed by ion-bombardment on a surfaces of amorphous materials is put forward. The model is based on the assumption that amorphous layer under ion-bombardment may be considered as Newtonian fluid on a hard substrate in the field of external force. Within this approach the mathematical model of an amorphous layer is formulated as a boundary value problem for Navier–Stokes and continuity equations for incompressible liquid. Analysis of the problem results in two quasi-stationary spatial-periodic solutions governed by two control parameters: one of them a⊥ is a capillary constant under a vertical ion beam incidence, normalized to layer thickness, another is an angle of incidence Θ. In the general case a capillary constant a⊥(L,Θ) is a convex function of both variables viz. normalized spatial-period L and an angle of incidence Θ. With energy E0=9 keV this function exhibits a local maximum at L=1.77,Θ=50.4∘ which is already global a⊥c=0.375 when E0=5 keV and (as judged by indirect measurements) becomes more convex with further energy reduction. Collation of a⊥(L,Θ) with experimental data reveals that the observed maximum value of capillary constant a⊥ob=0.367, which due to an inherent supercriticality is a little bit lower than a⊥c, falls at Θ=55∘, i.e., with energy diminution angular range should contract to this point. This outcome is consistent with our experimental results on N2+–Si system, manifesting that angular range reduces to a small vicinity of Θcin=55∘ when ion energy tends to minimum energy of WOS formation E0=1.5 keV.