Designing steep, sharp patterns on uniformly ion-bombarded surfaces

Abstract

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 onedimensional 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 onedimensional 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.ion bombardment | steep structure design | simulations | FIB | shock wave F abricating steep, sharp features with desired morphologies on surfaces is a major challenge of materials science. Certain methods are available by direct engraving, such as focused ion beam (FIB) or lithography (1-4), but these require enormous time and energy. A promising method to efficiently make patterns on a large scale by exploiting dynamics is to erode a surface with uniform ion bombardment (5-9). A flat surface can become unstable and develop features such as quantum dots or hexagonal patterns (10-17). Such spontaneous pattern growth could spawn high-throughput methods to manufacture periodic metamaterials such as optical antenna arrays (18) and the split ring resonators used in negative refractive index materials and optical cloaking (19).However, because linear instabilities are neither small enough nor amenable enough to control, interest has recently turned to the potential for nonlinear dynamics to create even steeper, sharper features (20). Large-amplitude, steep structures are of interest for 3D engineering applications such as micromechanics, microprocessor integration, data storage, and photonic band gap waveguides. They are also of interest in atom probe tomography, which uses samples frequently created by FIB ion irradiation (21) and which is strongly influenced by the geometry of the steep-walled final samples (22). Experiments and simulations have shown that knife-edge-like ridges, varying on scales at least an order of magnitude smaller than those accessible to linear instabilities, can arise ...

Ion-induced nanopatterning of silicon: Toward a predictive model

“…7to even higher order. As the focus here is on linear theories, we refer readers to two other reviews that cover this specific line of inquiry, 32,72 as well as more recent work specifically exploring the behavior of nearly vertical, shock-like features on otherwise flat surfaces, 5,[73][74][75] and sawtooth-like structures featuring alternating facets of different slopes. [76][77][78][79] Of particular interest in our context, however, we note that this approach also yielded additional linear terms at third and fourth orders.…”

Stress-driven nonlinear dynamics of ion-induced surface nanopatterns

“…4 for conditions (e) and (f) in Table I. Undercompressive shocks have been previously reported in the description of IBS systems via kinetic (rather than hydrodynamic) continuum models [30,[73][74][75][76][77]. The connection between such undercompressive shocks and sawtooth morphologies has been specifically addressed in Refs.…”

Sawtooth structure formation under nonlinear-regime ion bombardment

“…When collecting GISAXS data, samples are first bombarded in situ under vacuum to remove the native oxide layer and to amorphize and smoothen the surface layer. All samples are bombarded at incidence angles corresponding to pattern amplification, because bombardment of high-amplitude structures at those incidence angles leads to steep feature formation rather than smoothening [28]. Data are collected at selected ion fluences throughout bombardment by the PILATUS area detector.…”