Read about the challenges of working with something 80,000 times smaller than the width of a human hair.

From cancer therapy to mass storage devices, science is coming up with tiny structures that will play a big role in the future. Mark Bradley, physics professor at the Colorado State University, studies these structures and focuses on patterns at the nanoscale in particular. One of these patterns has been puzzling him and his colleagues for the longest time, until he recently turned online to find the solution. Read our interview with him below.

ResearchGate: One nanometer

is 80,000 times smaller than the width of a human hair. What can we do with something so tiny?

Mark Bradley: There are lots of different reasons why you would want to make nanostructures. We’re already familiar with what happens at scales of everyday life where things are of visible size, but a lot of things change fundamentally when you get down to the nanoscale.

Ideally you could make anything you like at the nanoscale. To start off, you make simple repetitive structures which can have uses, for example in storage. You can make arrays of tiny dots for magnetic storage that is used in computers. The dots are very tiny and perfectly organized and this gives you a means of making storage that has very high memory capacity.

RG: How do you make nanostructures?

Bradley: That’s actually one of the fundamental problems in nanotechnology and there are two different approaches to solve it. There’s the top-down approach: for example, you can take a finely focused electron beam and write patterns on a solid surface with it. This will eject atoms from the surface. The problem is that it is really expensive and time consuming to write patterns over a large area in this way. Then there’s the bottom-up approach: you provide a gross external stimulus to the system and then it organizes itself into tiny patterns.

RG: Which approach do you follow?

Bradley: What I work on is a particular type of bottom-up approach. Here, you take a solid surface which is flat on an atomic level and you bombard it with a broad ion beam. You have all those ions that are impacting the solid, all coming in at the same angle relative to its surface. Now every time an ion arrives it can kick one or more atoms off the surface of a solid. That’s a process called “sputtering.”

Ions are raining down all over the place, kicking atoms out of the surface and eroding it. At first blush you’d think that the surface would simply remain flat. In fact, when the ion beam hits obliquely, what often happens is that the surface develops tiny ripples. If you focus close in on the surface, it looks like the surface of windswept sand.

RG: A miniature desert made by an ion beam?

Bradley: Yes, except that the wavelength of these ripples is incredibly small. What we mean when we say “wavelength” is the distance between two consecutive peaks in the wave. It can be as small as ten nanometers — that’s ten billionths of a meter!

You can do the ion bombardment over a broad area of the solid surface. People can even do it over one meter by one meter areas with special equipment – this is huge for nanotechnology. When you do this for a relatively short time, nanoscale ripples form continuously everywhere.

RG: What happens if you continue shooting the ions?

Bradley: In many cases if you bombard for a long time the ripples develop what we call a “terraced form.” So instead of having an undulating appearance like the sand dunes I’ve mentioned before, a cross section of the ripples has a sawtooth form.

RG: Why does that happen?

Bradley: That’s the question. It’s been experimentally observed many, many times, but there hasn’t been any understanding of why that would happen. So my student Dan Pearson and I modified the existing theory and made an improved approximation. We showed that if you sputter the surface with ions and wait long enough, the ripples actually go from being smoothly undulating to developing a sawtooth, terraced form.

But we had a problem. We’re not applied mathematicians, we’re physicists, and the equation that we got that governs the behavior of the surface – well – it was unusual, and we were not quite sure what to do with it.

RG: How did you solve this problem?

Bradley: I posted three questions in total on ResearchGate asking for recommendations on how we ought to proceed in analyzing this equation. I think by now one of them has had between two and three thousand views, but I’m not sure. We got a lot of answers, many of which were very helpful.

The first question I asked made us realize that we weren’t quite looking at things precisely enough. Then I posed a more carefully formulated question and we got a deluge of answers. We discovered that all sorts of applied mathematicians were interested in our problem and that they were willing to play around with it. They gave us lots of good advice.

The people who are on hand here in our math department are not experts on this particular type of equation. But there are experts around. In the old days you could write them and then hope that they would respond, right? But now with ResearchGate we can do a scattershot approach. I would compare it to when we first got email, just now we can reach many more people at the same time.

Image of nanoscale ripples in "terraced form" courtesy of Qiangmin Wei

Featured image courtesy of Engineering at Cambridge

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