We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. We find that transitions may take place between various scaling behaviors when experimental parameters, such as the angle of incidence of the incoming ions or their average penetration depth, are varied.

We report on the production of ordered assemblies of silicon nanostructures by means of irradiation of a Si (100) substrate with 1.2 keV Ar+ ions at normal incidence. Atomic force and high-resolution transmission electron microscopies show that the silicon structures are crystalline, display homogeneous height, and spontaneously arrange into short-range hexagonal ordering. Under prolonged irradiation (up to 16 h) all dot characteristics remain largely unchanged and a small corrugation develops at long wavelengths. We interpret the formation of the dots as a result of an instability due to the sputtering yield dependence on the local surface curvature.

We study the self-organized ordering of nanostructures produced by ion-beam sputtering of targets amorphizing under irradiation. By introducing a model akin to models of pattern formation in aeolian sand dunes, we extend consistently the current continuum theory of erosion by IBS. We obtain new nonlinear effects responsible for the in-plane ordering of the structures, whose strength correlates with the degree of ordering found in experiments. Our results highlight the importance of redeposition and surface viscous flow to this nanopattern formation process.

We study kinetically rough surfaces which display anomalous scaling in local properties such as the roughness or the height-difference correlation function. By studying the power spectrum of the surface and its relation to the height-difference correlation, we distinguish two independent causes for anomalous scaling. One is superroughening (global roughness exponent larger than or equal to 1), even if the spectrum behaves nonanomalously. Another cause is what we term an intrinsically anomalous spectrum, in whose scaling an independent exponent exists, which induces different scaling properties for small and large length scales. We show that in this case the surface does not need to be superrough in order to display anomalous scaling. The scaling relations we propose for the structure factor and height-difference correlation for intrinsically anomalous surfaces are shown to hold for a random diffusion equation, independently of the value of the global roughness exponent below or above one.

In recent years Ion Beam Sputtering (IBS) has revealed itself as a powerful technique to induce surface nanopatterns with a large number of potential applications. These structures are produced in rather short processing times and over relatively large areas, for a wide range of materials, such as metals, insulators, and semiconductors. In particular, silicon has become a paradigmatic system due to its technological relevance, as well as to its mono-elemental nature, wide availability, and production with extreme flatness. Thus, this review focuses on the IBS nanopatterning of silicon surfaces from the experimental and the theoretical points of view. First, the main experimental results and applications are described under the light of the recently established evidence on the key role played by simultaneous impurity incorporation during irradiation, which has opened a new scenario for an improved understanding of the phenomenon. Second, the progress and state-of-art of the theoretical descriptions of the IBS nanopatterning process for this type of targets are discussed. We summarize the historical approach to IBS through simulation techniques, with an emphasis on recent information from Molecular Dynamics methods, and provide a brief overview of the earlier and most recent continuum models for pure and compound systems.This work has been partially supported by the Spanish Ministries of Science and Innovation (grants Nos. FIS2009-12964-C05-01, FIS2009-12964-C05-03, FIS2009-12964-C05-04, and BES-2010-036179) and of Economy and Competitiveness (grants Nos. FIS2012-38866-C05-01 and FIS2012-38866-C05-05, FIS2012-32349 and FIS2013-47949-C2-2). A.R.C. also acknowledges funding from SFRH/BPD/74095/2010 (Portugal) and from Juan de la Cierva program (Spain) under contract No. JCI-2012-14509.Publicad