Morphology of ion-sputtered surfaces

Abstract

We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the continuum equation in terms of the physical parameters characterizing the sputtering process. We analyze the morphological features predicted by the continuum theory, comparing them with the experimentally reported morphologies. We show that for short time scales, where the effect of nonlinear terms is negligible, the continuum theory predicts ripple formation. We demonstrate that in addition to relaxation by thermal surface diffusion, the sputtering process can also contribute to the smoothing mechanisms shaping the surface morphology. We explicitly calculate an effective surface diffusion constant characterizing this smoothing effect, and show that it is responsible for the low temperature ripple formation observed in various experiments. At long time scales the nonlinear terms dominate the evolution of the surface morphology. The nonlinear terms lead to the stabilization of the ripple wavelength and we show that, depending on the experimental parameters such as angle of incidence and ion energy, different morphologies can be observed: asymptotically, sputter eroded surfaces could undergo kinetic roughening, or can display novel ordered structures with rotated ripples. Finally, we discuss in detail the existing experimental support for the proposed theory, and uncover novel features of the surface morphology and evolution, that could be directly tested experimentally.

Molecular dynamics of single-particle impacts predicts phase diagrams for large scale pattern formation

“…Displaced atoms that reach the surface with enough kinetic energy to leave are permanently sputtered away; all other displaced atoms come to rest within the solid or on the surface after phonon emission times of ~10 − 12 s. These processes contribute prompt erosive 14,15 and prompt redistributive 11,16,17 components of morphology evolution and are collectively denoted P [x].…”

Scaling laws in PZT thin films grown on Si(001) and Nb-Doped SrTiO3(001) substrates

“…[4,[7][8][9][10][11]. Initiated by advances in the statistical mechanics of various non-equilibrium systems, it has been observed that the roughness of many natural surfaces follows rather simple scaling laws, which can be quantified using scaling exponents.…”

Surfactant Sputtering: Theory of a new method of surface nanostructuring by ion beams

“…The model is completed by expressing the currents and current densities in terms of the surface geometry and the surfactant density. Expressions for the erosion currents in the absence of surfactants are available from the theory of Bradley and Harper [12] and its generalizations [13,14,15]. In addition, we take into account modifications of the sputtering yields so that the erosion currents of substrate and surfactant, J A and J B , respectively, are given by…”

“…J 0 denotes the flux of incident ions, Y A , Y B are the sputtering yields of the pure A and B system, respectively. We keep the first terms of the standard gradient expansion of the yield modification due to surface morphology [12,15],…”