Observation and modeling of interrupted pattern coarsening: surface nanostructuring by ion erosion

Surface nanopatterning by ion beam irradiation: compositional effects

Surface nanopatterning induced by ion beam irradiation (IBI) has emerged as an effective nanostructuring technique since it induces patterns on large areas of a wide variety of materials, in short time, and at low cost. Nowadays, two main subfields can be distinguished within IBI nanopatterning depending on the irrelevant or relevant role played by the surface composition. In this review, we give an up-dated account of the progress reached when surface composition plays a relevant role, with a main focus on IBI surface patterning with simultaneous co-deposition of foreign atoms. In addition, we also review the advances in IBI of compound surfaces as well as IBI systems where the ion employed is not a noble gas species. In particular, for the IBI with concurrent metal co-deposition, we detail the chronological evolution of these studies because it helps us to clarify some contradictory early reports. We describe the main patterns obtained with this technique as a function of the foreign atom deposition pathway, also focusing in those systematic studies that have contributed to identify the main mechanisms leading to the surface pattern formation and development. Likewise, we explain the main theoretical models aimed at describing these nanopattern formation processes. Finally, we address two main special features of the patterns induced by this technique, namely, the enhanced pattern ordering and the possibility to produce both morphological and chemical patterns.

Parameter estimation for pattern formation induced by ion bombardment of solid surfaces using deep learning

The nanostructures produced by oblique-incidence broad beam ion bombardment of a solid surface are usually modelled by the anisotropic Kuramoto-Sivashinsky equation. This equation has five parameters, each of which depend on the target material and the ion species, energy, and angle of incidence. We have developed a deep learning model that uses a single image of the surface to estimate all five parameters in the equation of motion with root-mean-square errors that are under 3% of the parameter ranges used for training. This provides a tool that will allow experimentalists to quickly ascertain the parameters for a given sputtering experiment. It could also provide an independent check on other methods of estimating parameters such as atomistic simulations combined with the crater function formalism.

Model discovery for studies of surface morphological modifications based on Kuramoto-Sivashinsky dynamics

A wide range of observations in studies of surfaces exposed to ion beams can be explained and analyzed successfully by continuum models of the Kuramoto-Sivashinsky type. Despite certain progress in the theoretical understanding of the model parameters on the basis of atomistic models, much of the applications are based on phenomenological determination of several unknown quantities. In this work a numerical tool is discussed and investigated, which allows us to determine model coefficients and complex model structures from experimental findings. The method resembles known approaches in machine learning and data-driven reconstruction techniques. To keep the discussion on a fundamental level, numerical simulations are conducted by employing a scaled test model. The reconstruction technique is demonstrated for this model system and shows a high accuracy in recovering input parameters for situations without beam noise. As an application to an unknown system to be explored, the algorithm is then applied to a system with lognormal distributed ion bombardment. The impact of the beam fluctuations in the proposed model are discussed. Perspectives of the numerical algorithm for an analysis of experimental data are addressed.

Spatially Engraving Morphological Structure on a Polymeric Surface by Ion Beam Milling

Polymer surface patterning and modification at the micro/nano scale has been discovered with great impact in applications such as microfluidics and biomedical technologies. We propose a highly efficient fabricating strategy, to achieve a functional polymer surface, which has control over the surface roughness. The key development in this fabrication method is the polymer positive diffusion effect (PDE) for an ion-bombarded polymeric hybrid surface through focused ion beam (FIB) technology. The PDE is theoretically explored by introducing a positive diffusion term into the classic theory. The conductivity-induced PDE constant is discussed as functions of substrates conductivity, ion energy and flux. The theoretical results agree well with the experiential results on the conductivity-induced PDE, and thus yield good control over roughness and patterning milling depth on the fabricated surface. Moreover, we demonstrate a controllable surface wettability in hydrophobic and superhydrophobic surfaces (contact angles (CA) range from 108.3° to 150.8°) with different CA hysteresis values ranging from 31.4° to 8.3°.

Nanopatterning by ion beam sputtering in unconventional formats

Nanopatterning at solid surfaces by ion beam sputtering (IBS) has been practiced mostly for stationary substrates with an ion beam incident under a fixed sputter geometry. We have released such constraints in the sputter condition. We simultaneously apply two ion beams or sequentially vary the orientation of substrate with respect to an ion beam. We also periodically change either the azimuthal or polar angle of the substrate with respect to an ion beam during IBS. These unconventional ways of IBS can improve the order of the pattern, and produce novel and non trivial nano patterns that well serve as touch stones to refine the theoretical models and thus deepen our understanding of the patterning mechanisms by IBS.

A fast feedback controlled magnetic drive for the ASDEX Upgrade fast-ion loss detectors

A magnetically driven fast-ion loss detector system for the ASDEX Upgrade tokamak has been designed and will be presented here. The device is feedback controlled to adapt the detector head position to the heat load and physics requirements. Dynamic simulations have been performed taking into account effects such as friction, coil self-induction, and eddy currents. A real time positioning control algorithm to maximize the detector operational window has been developed. This algorithm considers dynamical behavior and mechanical resistance as well as measured and predicted thermal loads. The mechanical design and real time predictive algorithm presented here may be used for other reciprocating systems.

Conceptual design of the ITER fast-ion loss detector

A conceptual design of a reciprocating fast-ion loss detector for ITER has been developed and is presented here. Fast-ion orbit simulations in a 3D magnetic equilibrium and up-to-date first wall have been carried out to revise the measurement requirements for the lost alpha monitor in ITER. In agreement with recent observations, the simulations presented here suggest that a pitch-angle resolution of ∼5° might be necessary to identify the loss mechanisms. Synthetic measurements including realistic lost alpha-particle as well as neutron and gamma fluxes predict scintillator signal-to-noise levels measurable with standard light acquisition systems with the detector aperture at ∼11 cm outside of the diagnostic first wall. At measurement position, heat load on detector head is comparable to that in present devices.

Designing steep, sharp patterns on uniformly ion-bombarded surfaces

We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion-bombarded surfaces. We show via theory, simulation, and experiment that the steepest parts of the surface evolve as one-dimensional curves that move in the normal direction at constant velocity. The curves are a special solution to the nonlinear equations that arises spontaneously whenever the initial patterning on the surface contains slopes larger than a critical value; mathematically they are traveling waves (shocks) that have the special property of being undercompressive. We derive the evolution equation for the curves by considering long-wavelength perturbations to the one-dimensional traveling wave, using the unusual boundary conditions required for an undercompressive shock, and we show this equation accurately describes the evolution of shapes on surfaces, both in simulations and in experiments. Because evolving a collection of one-dimensional curves is fast, this equation gives a computationally efficient and intuitive method for solving the inverse problem of finding the initial surface so the evolution leads to a desired target pattern. We illustrate this method by solving for the initial surface that will produce a lattice of diamonds connected by steep, sharp ridges, and we experimentally demonstrate the evolution of the initial surface into the target pattern.

Influence of metal co-deposition on silicon nanodot patterning dynamics during ion-beam sputtering

We address the impact of metal co-deposition in the nanodot patterning dynamics of Si(100) surfaces under normal-incidence 1 keV Ar(+) ion-beam sputtering (IBS). In particular, the effect of both the metal nature (Fe or Mo) and flux has been studied. Morphological and compositional evolution were followed by atomic force microscopy (AFM) and Rutherford backscattering spectrometry, respectively. For the same type of impurity, the dynamics is faster for a higher co-deposition flux, which also drives to larger asymptotic roughness and wavelength. Mo co-deposition yields rougher surfaces for a lower metal coverage than Fe and, remarkably, higher ordered patterns. X-ray photoelectron spectroscopy reveals the formation of silicide bonds even before pattern onset, stressing the relevant role of the affinity of the co-deposited metals for silicon. Further, current-sensing AFM performed at the initial and asymptotic stages indicates that the nanodot structures are metal-rich, resulting in coupled compositional and morphological patterns. These results are discussed in terms of phase segregation, morphology-driven local flux variations of impurities and silicide formation. This analysis reveals that the underlying (concurrent) mechanisms of pattern formation are complex since many processes can come into play with a different relative weight depending on the specific patterning conditions. From a practical point of view, it is shown that, by proper selection of the process parameters, IBS with metal co-deposition can be used to tune the dynamics and pattern properties and, interestingly, to produce highly ordered arrays.

Ageing dynamics of ion bombardment induced self-organization processes

Instabilities caused during the erosion of a surface by an ion beam can lead to the formation of self-organized patterns of nanostructures. Understanding the self-organization process requires not only the in-situ characterization of ensemble averaged properties but also probing the dynamics. This can be done with the use of coherent X-rays and analyzing the temporal correlations of the scattered intensity. Here, we show that the dynamics of a semiconductor surface nanopatterned by normal incidence ion beam sputtering are age-dependent and slow down with sputtering time. This work provides a novel insight into the erosion dynamics and opens new perspectives for the understanding of self-organization mechanisms.

Ion beam induced surface pattern formation and stable travelling wave solutions

The formation of ripple structures on ion bombarded semiconductor surfaces is examined theoretically. Previous models are discussed and a new nonlinear model is formulated, based on the infinitesimal local atomic relocation induced by elastic nuclear collisions in the early stages of collision cascades and an associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important, and it is shown that in this case certain 'magic' angles can occur at which the ripple patterns are most clearly defined. The results are in very good agreement with experimental observations.

Ion beam sputtered surface dynamics investigated with two-time correlation functions: a model study

Ion beam sputtering is a widely used technique to obtain patterned surfaces. Despite the wide use of this approach on different materials to create surface nanostructures, the theoretical model to explain the time evolution of the erosion process is still debated. We show, with the help of simulations, that two-time correlation functions can serve to assess the validity of different models. These functions can be measured experimentally with the x-ray photon correlation spectroscopy technique.

Independence of interrupted coarsening on initial system order: ion-beam nanopatterning of amorphous versus crystalline silicon targets

Interrupted coarsening (IC) has recently been identified as an important feature for the dynamics of the typical length-scale in pattern-forming systems on surfaces. In practice, it can be beneficial to improve pattern ordering since it combines a certain degree of defect suppression with a limited increase in the typical pattern wavelength. However, little is known about its robustness with respect to changes in the preparation of the initial system for cases with potential applications. Working in the context of nano-scale pattern formation by ion-beam sputtering (IBS), we prove that IC properties do not depend on sample preparation. Specifically, interface dynamics under IBS is quantitatively compared on virgin amorphous and crystalline silicon surfaces, using 1 keV Ar(+) ions at normal incidence where nanodot pattern formation is triggered by concurrent co-deposition of Fe atoms during processing. Atomic force microscopy shows that dot patterns with similar spatial order and dynamics are obtained in both cases, underscoring the key dynamical role of the amorphous surface layer produced by irradiation. Both systems have been quantitatively described by an effective interface equation. We employ a new procedure based on the linear growth of the initial surface correlations to accurately estimate the equation coefficients. Such a method improves the predictive power of the interface equation with respect to previous studies and leads to a better description of the experimental pattern and its dynamical features.

Nonlinear wavelength selection in surface faceting under electromigration

We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as t(1/2). For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening before reaching a continuous family of stable nonequilibrium steady states.

One-dimensional pattern of Au nanodots by ion-beam sputtering: formation and mechanism

Highly ordered one-dimensional arrays of nanodots, or nanobeads, are fabricated by forming nanoripples and nanodots in sequence, entirely by ion-beam sputtering (IBS) of Au(001). This demonstrates the capability of IBS for the fabrication of sophisticated nanostructures via hierarchical self-assembly. The intricate nanobead pattern ideally serves to identify the governing mechanisms for the pattern formation: nonlinear effects, especially local redeposition and surface-confined transport, are essential both for the formation and the preservation of the one-dimensional order of the nanobead pattern.

Nonlinear sand bedform dynamics in a viscous flow

We investigate theoretically the nonlinear evolution of a sand bedform sheared by a laminar viscous flow. On the basis of the hydrodynamic equations coupled with a sediment transport law, we derive a closed nonlinear and nonlocal equation for the spatiotemporal evolution of the bedform profile in the case of an unbounded flow. The numerical resolution of this equation shows that the bedform coarsens indefinitely in the course of time. During the coarsening process, the wavelength scales as the cube of the vertical extension w as a result of the nonlinear interactions. Interestingly, in the case of a bounded flow, we argue that coarsening is interrupted when the flow perturbation induced by the bedform extends over the whole flow depth h, and we predict that the final wavelength λ{f} and vertical extension w{f} should scale respectively as (γ/ν)h³ and h (where ν is the fluid viscosity and γ the flow shear rate).

Ion-Induced Nanoscale Ripple Patterns on Si Surfaces: Theory and Experiment

Nanopatterning of solid surfaces by low-energy ion bombardment has received considerable interest in recent years. This interest was partially motivated by promising applications of nanopatterned substrates in the production of functional surfaces. Especially nanoscale ripple patterns on Si surfaces have attracted attention both from a fundamental and an application related point of view. This paper summarizes the theoretical basics of ion-induced pattern formation and compares the predictions of various continuum models to experimental observations with special emphasis on the morphology development of Si surfaces during sub-keV ion sputtering.

Spontaneous pattern formation induced by ion bombardment of binary compounds

A theory is developed that explains the genesis of the strikingly regular hexagonal arrays of nanoscale mounds that can form when a flat surface of a binary compound is subjected to normal-incidence ion bombardment. We find that the species with the higher sputter yield is concentrated at the peaks of the nanodots and that hysteretic switching between the flat and the hexagonally ordered state can occur as the sample temperature is varied. Surface ripples are predicted to emerge for a certain range of the parameters.

Surface pattern formation and scaling described by conserved lattice gases

We extend our 2+1 -dimensional discrete growth model [Odor, Phys. Rev. E 79, 021125 (2009)] with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence. By mapping the slopes onto particles, two-dimensional nonequilibrium binary lattice model emerges, in which the (smoothing or roughening) surface diffusion can be described by attracting or repelling motion of oriented dimers. The binary representation allows simulations on very large size and time scales. We provide numerical evidence for Mullins-Herring or molecular-beam epitaxy class scaling of the surface width. The competition of inverse Mullins-Herring diffusion with a smoothing deposition, which corresponds to a Kardar-Parisi-Zhang (KPZ) process, generates different patterns: dots or ripples. We analyze numerically the scaling and wavelength growth behavior in these models. In particular, we confirm by large size simulations that the KPZ type of scaling is stable against the addition of this surface diffusion, hence this is the asymptotic behavior of the Kuramoto-Sivashinsky equation as conjectured by field theory in two dimensions, but has been debated numerically. If very strong, normal surface diffusion is added to a KPZ process, we observe smooth surfaces with logarithmic growth, which can describe the mean-field behavior of the strong-coupling KPZ class. We show that ripple coarsening occurs if parallel surface currents are present, otherwise logarithmic behavior emerges.