Shocks in Ion Sputtering Sharpen Steep Surface Features

Simple dynamical model that leads to sputter cone formation

We introduce a model for sputter cone formation that includes only the angular dependence of the sputter yield and a fourth-order smoothing effect like surface diffusion. In one dimension, a sputter cone is a particular kind of shock wave that is known as an undercompressive shock. Simulations of our model show that a wide variety of initial conditions lead to the formation of sputter cones and that the opening angle of the cones does not depend on the detailed form of the initial condition. In two dimensions, a sputter cone is a higher-dimensional analog of an undercompressive shock. For two particularly simple choices of parameters, a sputter cone is a four-sided pyramid with rounded edges that is produced by the superposition of two orthogonal, one-dimensional undercompressive shocks.

Sawtooth structure formation under nonlinear-regime ion bombardment

Linear-regime Ar⁺ bombardment of Si produces symmetrical ripple structures at ion incidence angles above 45° measured off-normal (Madi 2009 J. Phys.: Condens. Matter 21). In the nonlinear regime, new behaviors emerge. In this paper, we present experimental results of ion bombardment that continues into the nonlinear regime until pattern saturation at multiple ion incidence angles, showing the evolution of their grazing incidence small-angle x-ray scattering (GISAXS) spectra as well as atomic force microscopy topographs of the final, saturated structures. Asymmetric structures emerge parallel to the direction of the projected ion beam on the sample surface, constituting a height asymmetry not found in the linear regime. We then present simulations of surface height evolution under ion bombardment using a nonlinear partial differential equation developed by Pearson and Bradley (2015 J. Phys.: Condens. Matter 27 015010). We present simulated GISAXS spectra from these simulations, as well as simulated scattering from a sawtooth structure using the FitGISAXS software package (Babonneau 2010 J. Appl. Crystallogr. 43 929-36), and compare the simulated spectra to those observed experimentally. We find that these simulations reproduce many features of the sawtooth structures, as well as the nearly-flat final GISAXS spectra observed experimentally perpendicular to the sawtooth structures. However, the model fails to reproduce the final GISAXS spectra observed parallel to the sawtooth structures.

Emergence and detailed structure of terraced surfaces produced by oblique-incidence ion sputtering

We study the nanoscale terraced topographies that arise when a solid surface is bombarded with a broad ion beam that has a relatively high angle of incidence θ. We find that the surface is not completely flat between the regions in which the surface slope changes rapidly with position: Instead, small-amplitude ripples propagate along the surface. Our analytical work on these ripples yields their propagation velocity as well as the scaling behavior of their amplitude. Our simulations establish that the surfaces exhibit interrupted coarsening, i.e., the characteristic width and height of the surface disturbance grow for a time but ultimately asymptote to finite values as the fully terraced state develops. In addition, as θ is reduced, the surface can undergo a transition from a terraced morphology that changes little with time as it propagates over the surface to an unterraced state that appears to exhibit spatiotemporal chaos. For different ranges of the parameters, our equation of motion produces unterraced topographies that are remarkably similar to those seen in various experiments, including pyramidal structures that are elongated along the projected beam direction and isolated lenticular depressions.

Effect of Crystal Orientation on Self-Assembly Nanocones Formed on Tungsten Surface Induced by Helium Ion Irradiation and Annealing

The self-assembly nanocone structures on the surface of polycrystalline tungsten were created by He⁺ ion irradiation and then annealing, and the resulting topography and morphology were characterized using atomic force microscopy and scanning electron microscopy. The cross-sectional samples of the self-assembly nanocones were prepared using an in situ-focused ion beam and then observed using transmission electron microscopy. The self-assembly nanocones were induced by the combined effect of He⁺ ion irradiation, the annealing process and the chromium impurity. The distribution characteristics, density and morphology of the nanocones exhibited a distinct difference relating to the crystal orientations. The highest density of the nanocones was observed on the grain surface with a (1 1 1) orientation, with the opposite for that with a (0 0 1) orientation and a medium value on the (1 0 1)-oriented grain. The size of the self-assembly nanocones increased with increasing the annealing time which met a power-law relationship. Irradiation-induced defects acted as the nucleation locations of the protrusions which attracted the migration of the tiny amount of chromium atoms. Under the action of temperature, the protrusions finally evolved into the nanocones.

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.

Theory of terraced topographies produced by oblique-incidence ion bombardment of solid surfaces

When a solid surface is bombarded with a broad ion beam at a relatively large angle of incidence, the surface often develops a terraced form. We introduce a model that includes an improved approximation to the sputter yield and that produces a terraced surface morphology at long times for a wide range of parameter values. Numerical integrations of our equation of motion reveal that the terraces coarsen as time passes, just as observed experimentally. We also show that the terrace propagation direction can reverse as the amplitude of the surface disturbance grows. This highlights the important role higher order nonlinearities play in determining the propagation velocity at high fluences.

Three-dimensional micro/nano-scale structure fabricated by combination of non-volatile polymerizable RTIL and FIB irradiation

Room-temperature ionic liquid (RTIL) has been widely investigated as a nonvolatile solvent as well as a unique liquid material because of its interesting features, e.g., negligible vapor pressure and high thermal stability. Here we report that a non-volatile polymerizable RTIL is a useful starting material for the fabrication of micro/nano-scale polymer structures with a focused-ion-beam (FIB) system operated under high-vacuum condition. Gallium-ion beam irradiation to the polymerizable 1-allyl-3-ethylimidazolium bis((trifluoromethane)sulfonyl)amide RTIL layer spread on a Si wafer induced a polymerization reaction without difficulty. What is interesting to note is that we have succeeded in provoking the polymerization reaction anywhere on the Si wafer substrate by using FIB irradiation with a raster scanning mode. By this finding, two- and three-dimensional micro/nano-scale polymer structure fabrications were possible at the resolution of 500,000 dpi. Even intricate three-dimensional micro/nano-figures with overhang and hollow moieties could be constructed at the resolution of approximately 100 nm.

Nanopore fabrication in amorphous Si: Viscous flow model and comparison to experiment

Nanopores fabricated in free-standing amorphous silicon thin films were observed to close under 3 keV argon ion irradiation. The closing rate, measured in situ, exhibited a memory effect: at the same instantaneous radius, pores that started larger close more slowly. An ion-stimulated viscous flow model is developed and solved in both a simple analytical approximation for the small-deformation limit and in a finite element solution for large deformations. The finite-element solution exhibits surprising changes in cross-section morphology, which may be extremely valuable for single biomolecule detection, and are untested experimentally. The finite-element solution reproduces the shape of the measured nanopore radius versus fluence behavior and the sign and magnitude of the measured memory effect. We discuss aspects of the experimental data not reproduced by the model, and successes and failures of the competing adatom diffusion model.

Application of surface chemical analysis tools for characterization of nanoparticles

The important role that surface chemical analysis methods can and should play in the characterization of nanoparticles is described. The types of information that can be obtained from analysis of nanoparticles using Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), time-of-flight secondary-ion mass spectrometry (TOF-SIMS), low-energy ion scattering (LEIS), and scanning-probe microscopy (SPM), including scanning tunneling microscopy (STM) and atomic force microscopy (AFM), are briefly summarized. Examples describing the characterization of engineered nanoparticles are provided. Specific analysis considerations and issues associated with using surface-analysis methods for the characterization of nanoparticles are discussed and summarized, with the impact that shape instability, environmentally induced changes, deliberate and accidental coating, etc., have on nanoparticle properties.

Dual-beam focused ion beam/electron microscopy processing and metrology of redeposition during ion-surface 3D interactions, from micromachining to self-organized picostructures

Focused ion beam (FIB) tools have become a mainstay for processing and metrology of small structures. In order to expand the understanding of an ion impinging a surface (Sigmund sputtering theory) to our processing of small structures, the significance of 3D boundary conditions must be realized. We consider ion erosion for patterning/lithography, and optimize yields using the angle of incidence and chemical enhancement, but we find that the critical 3D parameters are aspect ratio and redeposition. We consider focused ion beam sputtering for micromachining small holes through membranes, but we find that the critical 3D considerations are implantation and redeposition. We consider ion beam self-assembly of nanostructures, but we find that control of the redeposition by ion and/or electron beams enables the growth of nanostructures and picostructures.

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.

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.

Highly ordered Ga nanodroplets on a GaAs surface formed by a focused ion beam

The morphological evolution of a GaAs surface induced by a focused ion beam (FIB) has been investigated by in situ electron microscopy. Under off-normal bombardment without sample rotation, Ga droplets with sizes from 70 to 25 nm in diameter on the GaAs surface can self-assemble into a highly ordered hexagonal pattern instead of Ostwald ripening or coalescence. The mechanism relies on a balance between anisotropic loss of atoms on the surface of droplets due to sputtering and an anisotropic supply of atoms on the substrate surface due to preferential sputtering of As. The ratio of wavelength to the droplet diameter predicted by this model is in excellent agreement with experimental observations.