NCSA NEWS

The steps between

By Kathleen Ricker, NCSA

Story posted May 9, 2007

Below the nanometer level, flaws in the surfaces of crystalline silicon yield unexplored worlds ripe for colonization with data.

Silicon, in various forms, is the second most abundant element on Earth. It's found mostly as part of a compound in the form of sand and rock. To achieve the high-purity semiconductor form of silicon on which the global electronics industry is based, silicon rods are immersed in a silicon-containing compound gas at extremely high temperatures. The resultant chemical reaction deposits silicon from the gas onto the rods, producing a crystal with the same atomic structure as a diamond.

It's this form of silicon in which Cristian Ciobanu, an assistant professor of mechanical engineering and materials science at the Colorado School of Mines, is most interested. What happens, he wants to know, when you make cuts in the surface of a solid chunk of silicon that do not follow the "grain" of the solid? One might first imagine a flat edge along the cut, which is what would happen in wood or in steel at a macroscopic scale. But that's not what it looks like at the atomic level, says Ciobanu, because when the atoms on the surface are disrupted by the (mis)cut, they will try to rearrange themselves to form as stable a structure as possible. Ciobanu wants to discover what kinds of structures those might be.

He is interested in the problem of how atoms on a silicon surface reconfigure their structure primarily because it's interesting and difficult, he says, but emphasizes that it is a problem that also has practical applications. On some silicon surfaces, he explains, miscuts form steps and terraces that are very straight and evenly spaced over large areas of the silicon substrate at distances of around one nanometer. The steps can then be used as tracks for writing and storing information at a factor a million times denser than the storage capacity of a conventional CD-ROM.

A question of balance

Apples stacked in a supermarket display will hold the shape if stacked correctly, says Ciobanu, thanks to gravity. If half the apples in the front layer are removed carefully, the remaining apples, assisted by gravity, will reorganize to form a flat terrace followed by a step to another flat layer just behind it.

But the apples require close proximity to bond with each other or interact with each other. In contrast, when silicon atoms rearrange themselves, what happens to them depends not only on their immediate neighbors but also on other nonadjacent silicon atoms both within their layer and some layers deep. "A lot of atoms have to be happy," says Ciobanu, "not just the ones at the surface."

To achieve a stable structure, silicon atoms on the surface tend to bond so that each one has four neighbors -- the number of neighbors they have in bulk (subsurface layers). Theoretically, one could look for surface and step structures by trying to increase the number of neighbors of each atom -- or in the language of chemistry, by reducing the number of dangling bonds (broken covalent bonds) at the surface. But lowering the number of dangling bonds per surface area too far would result in lengthening and distorting the new surface bonds and stressing the surface.

Thus, the stable surface structure has to be achieved through a balance between reducing the density of dangling bonds and the stress generated by this reduction process. The physical quantity that incorporates both stress and chemical bonding is the surface energy, or the excess energy that the atoms have, per unit area, with respect to their bulk form. When the bulk is disrupted, the reconstruction of the atomic structure of the surface is determined by lowering this surface energy. Disrupting a surface means creating a step whose atomic structure can be found by lowering the step formation energy (excess energy with respect to the surface). Furthermore, disrupting a step creates a kink in it, the structure of which can be found by lowering the kink formation energy. Figure 1 illustrates the surface, step, and kink in relationship to one another.

Recently Ciobanu used NCSA supercomputing resources to study the atomic structure of surfaces; he is now studying the structure of steps on surfaces. In the latter case, the problem is that even when the surface structure is known, the positions of the steps on that surface -- specifically, the location at which the step disrupts the atomic pattern (the reconstruction) on the terrace -- are not known beforehand. Neither is known, a priori, how wide the step is, or exactly how many atoms the step region has. To deal with these complex structural issues, Ciobanu and his student, Ryan Briggs, have adapted a genetic algorithm for solving the atomic structure of steps on silicon surfaces, while at the same time finding the width of the step and its location (Figure 2).

Evolution of a step structure

Ciobanu is using NCSA's Tungsten cluster to run genetic algorithms to determine the way the silicon atoms are arranged at the steps that form between known surface structures (terraces). The genetic algorithm optimization begins with a given number of step structures in which the step-zone atoms are positioned randomly. This "gene pool," or Generation Zero, is then continuously optimized by cross-over operations (such as that shown in Figure 2b) in which two "parent" structures are picked arbitrarily and mixed to create a new structure, the "child." If the child is "fit," that is, if it has a sufficiently low surface energy without being identical to an existing structure, then it is included in the pool. With the addition of a new child, the worst structure (corresponding to the highest step formation energy) is discarded from the pool. Repeated application of the cross-over operation leads to a decrease in the formation energies (or to an increased fitness) of all the step structures in the pool, and as the genetic algorithm progresses, both the best and the average formation energies also decrease (Figure 3).

Interestingly, if the selected step zone (Figure 2a) is wide enough, the step can negotiate its best location with respect to the terraces around it. At the same time, the number of atoms in the steps and their location are being optimized, which is an important and versatile improvement in an otherwise well-known algorithm. As a result of this algorithm, Ciobanu has succeeded in accumulating a large number of simulated step structures that could prove useful in the future for applications such as increased data storage capacity, and applications used by experimental groups such as those at the University of Illinois and the Naval Research Laboratory who work on the Si(114) surfaces (the terraces chosen by Ciobanu for his study). "It's not too far-fetched," says Ciobanu, "to speculate that one day some of our simulations could be confirmed by experiments or could be useful in interpreting experimental data."

Ciobanu's calculations require a great deal of computing power because in order to find the best step structures he must evolve the algorithm through thousands of cross-over operations, only discarding unfit structures after their step formation energy has been computed. CSM, one of the older schools in Colorado, is a public research university devoted to engineering and applied science. In the past, the school has not had to provide extensive computational facilities for research. However, that could soon change, stimulated by the successful usage of national high-end computing facilities such as those provided by NCSA and other supercomputing centers. CSM is presently making investments to acquire high-performance computational facilities on campus, to keep up with the increasingly demanding research done by its faculty.

"By providing rapid and substantial allocations of computing time and reliable support for Tungsten," says Ciobanu, "NCSA has been of tremendous help in my research."

This research is supported by the Colorado School of Mines.

Team members
Cristian Ciobanu
Ryan Briggs

For further information: http://www.mines.edu/~ciobanu/