Kinetic roughening of ion-sputtered Pd(001) surface: beyond the Kuramoto-Sivashinsky model

Nanoscale pattern formation produced by ion bombardment of a rotating target: The decisive role of the ion energy

We study the nanoscale patterns that form on the surface of a rotating sample of an elemental material that is bombarded with a broad noble gas ion beam for angles of incidence θ just above the critical angle for pattern formation θ_{c}. The pattern formation depends crucially on the ion energy E. In simulations carried out in the low-energy regime in which sputtering is negligible, we find disordered arrays of nanoscale mounds (nanodots) that coarsen in time. Disordered arrays of nanodots also form in the high-energy regime in which there is substantial sputtering, but no coarsening occurs close to the threshold angle. Finally, for values of E just above the sputter yield threshold, nanodot arrays with an extraordinary degree of hexagonal order emerge for a range of parameter values, even though there is a broad band of linearly unstable wavelengths. This finding might prove to be useful in applications in which highly ordered nanoscale patterns are needed.

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.

Nanoscale pattern formation on silicon surfaces bombarded with a krypton ion beam: experiments and simulations

The nanoscale patterns produced by bombardment of the (100) surface of silicon with a 2 keV Kr ion beam are investigated both experimentally and theoretically. In our experiments, we find that the patterns observed at high ion fluences depend sensitively on the angle of incidence Θ. For Θ values between 74° and 85°, we observe five decidedly different kinds of morphologies, including triangular nanostructures traversed by parallel-mode ripples, long parallel ridges decorated by short-wavelength ripples, and a remarkable mesh-like morphology. In contrast, only parallel-mode ripples are present for low ion fluences except for Θ = 85°. Our simulations show that triangular nanostructures that closely resemble those in our experiments emerge if a linearly dispersive term and a conserved Kuramoto-Sivashinsky nonlinearity are appended to the usual equation of motion. We find ridges traversed by ripples, on the other hand, in simulations of the Harrison-Pearson-Bradley equation (Harrisonet al2017Phys. Rev.E96032804). For Θ = 85°, the solid surface is apparently stable and simulations of an anisotropic Edwards-Wilkinson equation yield surfaces similar to those seen in our experiments. Explaining the other two kinds of patterns we find in our experiments remains a challenge for future theoretical work.

Theory of the nanoscale surface ripples produced by ion irradiation of a miscut (001) gallium arsenide surface

We develop a theory for the surface ripples produced by near-normal-incidence ion bombardment of a (001) GaAs surface with a small miscut along the [110] direction. We restrict our attention to the case in which the energy of the incident ions is below the sputter yield threshold and the sample temperature is just above the recrystallization temperature. Highly ordered, faceted ripples with their wave vector aligned with the [110] direction form when the ion beam is normally incident and there is no miscut. Two additional terms appear in the equation of motion when the beam is obliquely incident and/or there is a miscut: a linearly dispersive term and a nonlinearly dispersive term. The coefficients of these terms can become large as the threshold temperature for pattern formation is approached from above. In the absence of strong nonlinear dispersion, strong linear dispersion leads to ripples with a dramatically increased degree of order. These ripples are nearly sinusoidal even though they are on the surface of a single crystal. The exceptionally high degree of order is disrupted by nonlinear dispersion if the coefficient of that term is sufficiently large. However, by choosing the angle of ion incidence appropriately, the coefficient of the nonlinearly dispersive term can be made small. Ion bombardment will then produce highly ordered ripples. For a different range of parameter values, nucleation and growth of facets and spinodal decomposition can occur.

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.

Recent developments in ion beam-induced nanostructures on AIII-BV compound semiconductors

Ion-beam sputtering of two-component substrates constitutes an alternative route for the nanofabrication of 3D (three-dimensional) structures, such as quantum dots or nanowires with unique properties like a high degree of local ordering. To allow for feasibility in precision manufacturing, control and optimization it is necessary to completely understand all the phenomena behind the evolution of nanostructures. The formation and development during the ion irradiation of similar features has been extensively studied for almost a half of century, but only over the last few years have new results appeared, ones stimulating real progress within this field. In this paper we report on the growth of such 3D nanostructures after low energy ion-beam sputtering on specific materials belonging to the group of AIII-BV binary compound crystals. Special emphasis is given to the role of sample temperature (during irradiation or post-annealing) on the evolution of nanostructure patterns and their ordering. The formation of such systems will be explained as seen from a phenomenological perspective.

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.

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.

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.

Self-organized chains of nanodots induced by an off-normal incident beam

We propose a model to show that under off-normal bombardment of an incident ion beam, a solid surface may spontaneously form nanoscale dots lining up into chains perpendicular to the incident beam direction. These dots demonstrate a highly ordered hexagonal pattern. We attribute the self-organization behavior to surface instability under concurrent surface kinetics and to a shadow effect that causes the self-alignment of dots. The fundamental mechanism may be applicable to diverse systems, suggesting an effective approach for nanofabrication.

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

We report the experimental observation of interrupted coarsening for surface self-organized nanostructuring by ion erosion. Analysis of the target surface by atomic force microscopy allows us to describe quantitatively this intriguing type of pattern dynamics through a continuum equation put forward in different contexts across a wide range of length scales. The ensuing predictions can thus be consistently extended to other experimental conditions in our system. Our results illustrate the occurrence of nonequilibrium systems in which pattern formation, coarsening, and kinetic roughening appear, each of these behaviors being associated with its own spatiotemporal range.

Coupling of morphology to surface transport in ion-beam-irradiated surfaces: normal incidence and rotating targets

Continuum models have proved their applicability to describe nanopatterns produced by ion-beam sputtering of amorphous or amorphizable targets at low and medium energies. Here we pursue the recently introduced 'hydrodynamic approach' in the cases of bombardment at normal incidence, or of oblique incidence onto rotating targets, known to lead to self-organized arrangements of nanodots. Our approach stresses the dynamical roles of material (defect) transport at the target surface and of local redeposition. By applying results previously derived for arbitrary angles of incidence, we derive effective evolution equations for these geometries of incidence, which are then numerically studied. Moreover, we show that within our model these equations are identical (albeit with different coefficients) in both cases, provided surface tension is isotropic in the target. We thus account for the common dynamics for both types of incidence conditions, namely formation of dots with short-range order and long-wavelength disorder, and an intermediate coarsening of dot features that improves the local order of the patterns. We provide for the first time approximate analytical predictions for the dependence of stationary dot features (amplitude and wavelength) on phenomenological parameters, that improve upon previous linear estimates. Finally, our theoretical results are discussed in terms of experimental data.

Nanopatterning by multiple-ion-beam sputtering

We conducted a systematic study on nanopatterning by multiple-ion-beam sputtering, focusing on the superposition of the simple patterns formed by individual ion beams. When Au(001) is simultaneously sputtered by two ion beams at grazing incidence, both nanodot and nanohole patterns are obtained. If a rippled surface is subsequently sputtered at normal incidence, a nanobead pattern is obtained. All of the obtained patterns consist of the nanopatterns formed by individual ion beams; however, the superposition of nanopatterns is not realized in its ideal form. We also discuss the microscopic mechanism of pattern formation by multiple-ion-beam sputtering, and consider the questions and possibilities remaining to be explored.

Ion beam sputtering induced nanostructuring of polycrystalline metal films

The development of fine scale nanostructures in polycrystalline metal films by off-normal ion beam sputtering (IBS) follows similar mechanisms to those in random targets, i.e. the pattern results from the interplay of curvature-dependent-roughening and various smoothing processes. By grazing angle IBS of the deposited metal films it is possible to fabricate metallic nanoripples, nanowires, and nanorods onto semiconductor or insulator substrates without using a template. It has been found that the rms roughness of the as-deposited film is substantially reduced under ion bombardment before the development of nanoscale patterns. The structural anisotropy of the sputtered morphology can have a great influence on the local physical properties of the underlying material. In this paper, we shall review the experimental results on the formation and characteristics of the IBS ripples on polycrystalline metal films prepared by the physical vapor deposition (PVD) technique.

Ion erosion induced nanogrooves: temporal evolution and azimuth dependence

Ion sputtering at grazing incidence of the Cu(001) surface leads to the formation of a regular pattern of nanogrooves with a well defined separation distance between the grooves. The grooves are only two atomic layers deep for a low ion flux and their height remains the same independent of sputter time. The average separation distance of the nanogrooves is at least 5 nm and can be increased beyond 40 nm, depending on substrate temperature, fluence, the ion's mass and energy. Anneal experiments of a nanogroove pattern also show an increase in average nanogroove separation with anneal time. The increase of the average nanogroove separation with time is larger for nanogrooves created along a ⟨100⟩ azimuth compared to the ⟨110⟩ azimuth. The ⟨100⟩ oriented step edges show a high density of kinks, suggesting that detachment from kinks is the rate limiting step in the process that governs the periodicity. Also both adatoms and vacancies are involved in this process, while the grazing incident ion beam continuously creates new nanogrooves. The creation of new nanogrooves and the movement observed during annealing are used as ingredients for a description of the temporal behaviour of the average nanogroove periodicity.

From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley-Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.

Propulsion of ripples on glass by ion bombardment

The propulsion of surface ripples on SiO(2) by an ion beam was investigated by in situ electron microscopy. The observed propagation of the ripples contradicts existing models for ion-beam-induced ripple development. A new model based on the Navier-Stokes relations for viscous flow in a thin layer is introduced. It includes inhomogeneous viscous flow, driven by spatial variations in the deposition of the energy of the ion beam. The model explains the observed reversed propagation. The hitherto unknown propulsion mechanism is important for understanding nanoscale pattern formation by ion bombardment.

Nonlinear ripple dynamics on amorphous surfaces patterned by ion beam sputtering

Erosion by ion-beam sputtering (IBS) of amorphous targets at off-normal incidence frequently produces a (nanometric) rippled surface pattern, strongly resembling macroscopic ripples on aeolian sand dunes. A suitable generalization of continuum descriptions of the latter allows us to describe theoretically for the first time the main nonlinear features of ripple dynamics by IBS, namely, wavelength coarsening and nonuniform translation velocity, that agree with similar results in experiments and discrete models. These properties are seen to be the anisotropic counterparts of in-plane ordering and (interrupted) pattern coarsening in IBS experiments on rotating substrates and at normal incidence.

Self-organized ordering of nanostructures produced by ion-beam sputtering

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.