Stress-driven nonlinear dynamics of ion-induced surface nanopatterns

Abstract

For many solid targets, like semiconductors, that become amorphous under irradiation by energetic ions, the outermost surface layer displays formation of asymmetric nanoscale ripples in macroscopic timescales. In contrast to the well-known macroscopic case of an incompressible thin fluid film spreading down an incline, in which the morphological instability is controlled by gravity, here we prove that residual stress induced by the ions is responsible for pattern formation and accounts for its long-time dynamics, even in absence of sputtering effects. Using a continuum framework, we derive closed nonlinear evolution equations for the depth of the irradiated layer. This description includes novel terms associated with the spatial distribution of damage that builds up through sustained bombardment, thus extending to the nanoscale classic models of macroscopic fluidflow systems, and providing detailed information on the pressure and velocity fields within the irradiated layer. Numerical simulations reproduce the main dynamical features of surface nanopatterning under the assumed conditions, elucidating the ensuing nonlinear properties on ripple amplification and transport.

Highly ordered silicide ripple patterns induced by medium-energy ion irradiation

“…Ion-beam sputtering (IBS) has proven to be a powerful technique to produce nanopatterns on different surfaces in a short time and over relatively large areas [1]. In the last years, considerable advances have been made in the understanding of the fundamental mechanisms involved in IBS pattern formation and development [2][3][4][5][6][7][8][9][10][11]. From the experimental point of view, two main branches can be clearly distinguished: IBS patterning without and with simultaneous supply of foreign species (mainly metals) [2].…”

Order improvement of surface nanopatterns via substrate rocking under ion bombardment: Experiments and nonlinear models

“…Moreover, one can expect additional nonlinear effects, as e.g. those ensuing from refined descriptions of sputtering 42,43 and of surface-confined viscous flow, 4,31 to improve the quantitative description of IBS under substrate rocking for semiconductor targets.…”

“…in [4]). The most relevant nonlinearities induced by these relaxation processes have been recently elucidated, 31 indicating a highly complex interplay among various terms, all of which are conservative. Hence, we presently take the eaKS model as a minimal model representing the nonlinear competition between conservative effects, like ion-induced amorphization and viscous flow (via the conserved KPZ terms), and non-conservative effects, e.g.…”

Observation of ripples under different angles

“…The ion-beam induced nanopatterning effect was observed the first time by Cunningham 3 in the 1960's in Au at 70 • . Since then, many theories have been developed in order to explain the formation, focusing on erosion 4 , redistribution 5,6 and stress build-up [7][8][9][10] . The structures observed in experiments range from ordered nanodots in GaSb 11 and in Si 12 (with sample rotation) to parallel 13 and perpendicular to the ion-beam projection ripples 14 .…”