Hydrodynamic approach to surface pattern formation by ion beams

Abstract

On the proper timescale, amorphous solids can flow. Solid flow can be observed macroscopically in glaciers or lead pipes, but it can also be artificially enhanced by creating defects. Ion Beam Sputtering (IBS) is a technique in which ions with energies in the 0.1 to 10 keV range impact against a solid target inducing defect creation and dynamics, and eroding its surface leading to formation of ordered nanostructures. Despite its technological interest, a basic understanding of nanopattern formation processes occurring under IBS of amorphizable targets has not been clearly established, recent experiments on Si having largely questioned knowledge accumulated during the last two decades. A number of interfacial equations have been proposed in the past to describe these phenomena, typically by adding together different contributions coming from surface diffusion, ion sputtering or mass redistribution, etc. in a non-systematic way. Here, we exploit the general idea of solids flowing due to ion impacts in order to establish a general framework into which different mechanisms (such as viscous flow, stress, diffusion, or sputtering) can be incorporated, under generic physical conservation laws. As opposed to formulating phenomenological interfacial equations, this approach allows to assess systematically the relevance and interplay of different physical mechanisms influencing surface pattern formation by IBS.

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

“…The solid flow description 19 of IBS is based on the fact that, as a consequence of the impact of the ions and the subsequent release of energy within the target, defects are created inside the material. These events occur in a few picoseconds after the impact.…”

“…19, that stem from the assumption that the main driving field in the process is the ion-induced residual stress that builds up in the flowing layer. Particular care has been taken to perform the experiments under wellcontrolled conditions that allow their meaningful comparison with the theoretical predictions.…”

“…To date, two main non-BH-type mechanisms have been proposed to explain formation or absence of patterns in IBS of monoelemental semiconductors, namely, mass redistribution [13][14][15][16] and ion-induced solid flow. [17][18][19] The former employs results from molecular dynamics (MD) simulations in order to rephrase the Carter-Vishnyakov effect 12 as the influence on the surface morphology of mass (rather than momentum) transfer induced by the beam. The solid flow model proceeds, rather, through a continuum description of the surface flow that is driven by the confined stress due to the accumulated damage on the surface amorphous layer produced by irradiation.…”

“…The solid flow model proceeds, rather, through a continuum description of the surface flow that is driven by the confined stress due to the accumulated damage on the surface amorphous layer produced by irradiation. Available models for flow include both Newtonian [17][18][19] and viscoelastic 20,21 constitutive laws. Remarkably both the mass redistribution and the viscous flow descriptions agree with experiments with respect to, e.g., the value of θ c and the dependence of the pattern wavelength on θ .…”

Surface instability and pattern formation by ion-induced erosion and mass redistribution

“…In the BH model, curvature-dependent sputtering depends linearly on the locally deposited energy approximated by Sigmund's ellipsoidal energy deposition [9]. Other continuum models which were developed to describe pattern formation on surfaces consider plastic flow in a viscoelastic continuum under ion induced stress [10][11][12] or hydrodynamic behaviour of an amorphous surface layer exposed to ion irradiation [13][14][15][16]. A recent experimental study on the lateral ripple propagation velocity for Si irradiated with 10 keV Xe ions reveals good agreement with the prediction by the BH model, indicating that curvature-dependent sputter erosion must play a significant role for ripple for pattern formation [17].…”