Layer by Layer Forever

Joachim Jacobsen and I studied the question of whether in principle it is possible to grow flat surfaces indefinitely. One very often wants to add many layers of atoms to a surface: either growing exotic new layered materials for use in disk drive heads, or depositing wires and devices on computer chips, ... Usually, one would like the surface to stay flat as it grows: ideally, we'd like one layer of atoms to complete itself before the next one starts.

On the right, you see a picture of a surface which is starting along a bad path. Light colors represent atoms in high layers (isolated atoms and clumps we call islands), and dark colors represent atoms in lower layers (vacancies and pits). Most of the surface is pretty flat, but there is a big dark-grey pit! This pit represents a region of the surface which has lagged behind by a whole monolayer: pits like these will eventually lead the surface to become rough.

Experimentalists have various ways to test whether their surfaces are growing layer by layer (flat), or 3D (rough). One way is by using STM to directly image the layers; another way is to scatter something off the surface and look for oscillations in the ``Anti-phase intensity''.
If a layer completes and forms a perfectly flat surface, you get anti-phase intensity of one; if the surface is rough (or flat but half-covered with a new layer), the antiphase intensity goes to zero. The dashed line in the picture on the left shows the anti-phase intensity for our computer model. (We're growing on a platiunum (111) surface at 130K at one layer per second, using KMC with EMT potentials.) It goes away quickly.

The spiky, solid line is our proposed new method for growing surfaces. We suggest using pulsed sputtering. If we sputter (remove atoms) from the surface just after a complete layer has been laid down, the extra atoms and islands can be removed without digging new pits: this smooths the surface. The spikes show how the surface gets smoother (bigger antiphase intensity) each time we sputter: the smaller inset graph shows that it stays smooth even after a hundred layers (at least on the computer!). It also shows that a rough surface can be made smooth by using our pulsed sputtering method.

It's important to pick the right time to sputter. The big pit in the top picture formed even though we did pulsed sputtering. Our surface stayed flat for forty layers before the pit formed. Can we time things so as to make layer-by-layer growth last forever?

The reason that we lasted for forty layers is that small pits tend to shrink: only big pits grow. We tested this by starting with pits of various sizes, and watching them grow or shrink. Averaging over many runs we get the picture on the right. By timing our pulses after every 1.15 layers, we find that a pit has to make it to ~350 atoms big before it'll keep growing. We then change our timing to try to make pits of all sizes shrink.
This graph shows our theory curve, for how big a pit needs to be before it will grow and mess up our surface (the critical pit size Rc). If we start sputtering each time we deposit 1.15 layers of atoms (0.15 on the horizontal axis), we see that it needs to have a radius around 10 (around the same as the ~350 atoms we saw above). By estimating the growth parameters and developing a theory for the fluctuations in island size, we are able to predict that growing at 0.24 (about one and a quarter layers deposited, then 1/4 layer sputtered away) we could grow layer-by-layer forever!

More information:

This research was paid for by THE US GOVERNMENT through the Cornell Center for Materials Research and the Cornell Theory Center.
Last modified: September 12, 1998

James P. Sethna,

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).