Coupling of morphology to surface transport in ion-beam irradiated surfaces: Oblique incidence

Abstract

We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering ͑IBS͒ at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in which a single evolution equation is posed for the surface height, we overcome ͑some of͒ them by explicitly formulating the dynamics of the species that transport along the surface and by coupling it to that of the surface height proper. In this, we follow recent proposals inspired by "hydrodynamic" descriptions of pattern formation in aeolian sand dunes and ion-sputtered systems. From this enlarged model and by exploiting the time-scale separation among various dynamical processes in the system, we derive a single height equation in which coefficients can be related to experimental parameters. This equation generalizes those obtained by previous continuum models and is able to account for many experimental features of pattern formation by IBS at oblique incidence, such as the evolution of the irradiation-induced thin amorphous layer, transverse ripple motion with nonuniform velocity, ripple coarsening, onset of kinetic roughening, and others. Additionally, the dynamics of the full two-field model is compared with that of the effective interface equation.

Ion impact energy distribution and sputtering of Si and Ge

“…[4][5][6][7] An assumed ellipsoidal energy deposition and a hypothesized linear relation to sputtering are the basis of Sigmund's 4,5 model, which leads to curvature dependent sputtering and within Bradley and Harper's stability analysis predicts the formation of a rich range of nanometerscale surface morphologies. 6,[8][9][10][11] These models are consistent with several erosion related surface behaviors. However, they fail to explain particular observations, including the formation of ripples at lower angles as observed during low-energy ion bombardment.…”

Self-organized nanopatterning of silicon surfaces by ion beam sputtering

“…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].…”

“…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.…”

Stress-induced solid flow drives surface nanopatterning of silicon by ion-beam irradiation

“…22 Notice that, e.g., the surface roughness W grows in the linear unstable regime as W ∼ h(t) ∝ e t/τ . This exponential behavior will eventually be interrupted by nonlinear mechanisms (coming, for instance, from stress 19 or from purely erosive effects [34][35][36] ) at sufficiently long times. Hence, the time duration of the validity of the linear approximation is also safely characterized by τ .…”