Pattern formation in Ablated Surfaces

Using what we've learned about surface growth with gallium arsenide, we have started looking at what happens when you erode, or ablate, various surfaces. In particular, we are interested in the phenomenon of pattern formation when such ablation processes exhibit instabilities. In a recently published paper, we derive an equation which correctly predicts the formation of "suncups" such as those seen in the picture on the upper left.

Since snow is a granular medium, incident light penetrates the surface and gets scattered some distance before either being absorbed, or escaping the snow pack. Absorbed light heats and ultimately melts the snow, while escaped light gives the snow its bright white appearance. The proportion in which light is absorbed at various points on the snow surface is locally determined by its shape.

In ion sputtering, ions bombarding a target surface have sufficient kinetic energy to penetrate the surface and induce complex collision cascades within the bulk of the target material. This results in sputtering events in which the chemical bonds of the target are broken and material can be liberated from the surface entirely. Analogous to the case of snow, the shape of the target surface plays a key role in the local rate at which material is removed.

While the fundamental physics behind melting snow and sputtered targets is different, the symmetries are the same. Thus, striking similarities in the resulting patterns can be observed as in the pictures shown above. Interestingly, this allows us to describe processes which occur on vastly different length scales with the same mathematical model. Castro, Cuerno, et. al. are among the most recent to describe sputtered surfaces using the same equation as that which we have derived for snow.

The equation is similiar to the chaotic Kuramoto-Sivashinsky equation, but with an additional non-linear term. This new term slows the timescale of the dynamics and increases the characteristic length of the suncup-like pattern as shown in the numerical simulations below.