Coupling of morphology to surface transport in ion-beam-irradiated surfaces: normal incidence and rotating targets

Abstract

Continuum models have proved their applicability to describe nanopatterns produced by ion-beam sputtering of amorphous or amorphizable targets at low and medium energies. Here we pursue the recently introduced 'hydrodynamic approach' in the cases of bombardment at normal incidence, or of oblique incidence onto rotating targets, known to lead to self-organized arrangements of nanodots. Our approach stresses the dynamical roles of material (defect) transport at the target surface and of local redeposition. By applying results previously derived for arbitrary angles of incidence, we derive effective evolution equations for these geometries of incidence, which are then numerically studied. Moreover, we show that within our model these equations are identical (albeit with different coefficients) in both cases, provided surface tension is isotropic in the target. We thus account for the common dynamics for both types of incidence conditions, namely formation of dots with short-range order and long-wavelength disorder, and an intermediate coarsening of dot features that improves the local order of the patterns. We provide for the first time approximate analytical predictions for the dependence of stationary dot features (amplitude and wavelength) on phenomenological parameters, that improve upon previous linear estimates. Finally, our theoretical results are discussed in terms of experimental data.

Self-organized nanopatterning of silicon surfaces by ion beam sputtering

“…Namely, the time for instability onset, the ripple wavelengths within linear stage and after coarsening interruption, and the ripple amplitude at long times, for all of which approximate theoretical predictions exist which are given in terms of the parameters in Eq. (12) [230]. In order to see how such an agreement can be obtained, note that continuum equations of the type we are describing apply to the large-scale behavior of the system.…”

“…Capitalizing on these ideas, a ''hydrodynamic'' approach has been developed for the cases of normal [28,230] and oblique incidence [231,232]. Note that this is not a full implementation of the Navier-Stokes equations, see in contrast Section 5.3.…”

“…This provides the dependencies on phenomenological parameters for e.g. the ripple wavelength and the velocity of in-plane ripple transport [232,230]. Very recently, such predictions have been argued to successfully account for ripple propagation on glass surfaces, as induced by FIB irradiation with 30 keV Ga þ ions [233].…”

“…As discussed in [28,230], Eq. (12) leads to a nanodot pattern with short-range order, whose typical wavelength coarsens at intermediate times [234].…”

Hydrodynamic approach to surface pattern formation by ion beams

“…Despite the fact that we have not considered the dynamics of the amorphouscrystalline interface, here we want to note that, in the shallow-water limit, one can reduce the present full hydrodynamical formulation, making contact with previous theories of erosion, specifically with the two-field model approach pioneered in [43] and further developed in [25][26][27][28], see an overview in [7].…”