Designing steep, sharp patterns on uniformly ion-bombarded surfaces

TL;DR

This paper introduces a novel method for fabricating steep, sharp surface features by exploiting nonlinear dynamics of ion-bombarded surfaces, combining theory, simulation, and experiments to control pattern evolution efficiently.

Contribution

It develops a new theoretical framework for surface patterning using undercompressive shock solutions, enabling precise design of initial surfaces for desired patterns.

Findings

The evolution of steep surface features can be modeled as traveling wave curves.

The derived evolution equation accurately predicts experimental surface patterning.

The method allows efficient inverse design of initial surfaces for target patterns.

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 which 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 experimentally demonstrating the evolution of the initial surface into the target pattern.