The new finding holds implications for the shape of other crystals used in the semiconductor industry, and might one day lead to templates for manufacturing tiny electronic parts, said William F. Saam, professor and chair of the Department of Physics at Ohio State University.
For instance, scientists could use this information to make patterns for wires that measure only a few nanometers (billionths of a meter) across, or even smaller semiconductors called quantum dots.
Saam and Vivek B. Shenoy, a former Ohio State graduate student and now an assistant professor at Brown University, derived equations which revealed a previously unknown series of phase transitions -- lines and points along the crystal surface that signal how atoms were forced to rearrange themselves to maintain stability.
The kind of stability in question is called thermal equilibrium, Saam explained, and most solid objects can only reach complete equilibrium after they've been held at a fixed temperature for a very long time. The results suggest that any crystal -- even a cut diamond -- would eventually lose its sharp edges given enough time.
Saam said that he was surprised by the findings, which He and Shenoy recently reported in the journal Surface Science. "Our results clearly illustrate that you cannot have sharp edges in any crystals that are at thermal equilibrium," he said. "The edges have to be round, and round in very special ways."
The Ohio State physicists examined data from experiments conducted in the mid-1990s, when scientists at the Massachusetts Institute of Technology (MIT) heated silicon crystals to temperatures higher than 1000 Kelvin (approximately 725 degrees C or 1340 degrees F). As the silicon cooled, particular surfaces organized themselves into series of parallel ridges, each smaller than a micron (one millionth of a meter) in size.
Saam was intrigued by the behavior of the silicon crystals, because the material had obviously undergone some kind of phase transition that rearranged atoms on the surface, he said.
To explain what a phase transition is, Saam offered an example. When water freezes into ice, it changes from a liquid phase into a solid phase. Materials such as silicon can undergo phase transitions, too, when the atoms adjust in order to maintain equilibrium with some internal or external force.
The MIT scientists concluded that their silicon crystals had changed shape because different surface phases existed together simultaneously along edges, but Saam disagreed.
"While it's true that different phases can co-exist -- a glass of ice water is a good example -- I just didn't think that's what was happening in this case," Saam said.
In a far-reaching extension of earlier work by a Russian scientist, he and Shenoy discovered a series of phase transitions associated with edge rounding. They derived equations to describe the physical forces at play on the surface of the crystal, noting that at any time, the steps on a silicon surface may attract or repel each other, depending on which forces are dominant.
"It looks like the process of reaching thermal equilibrium causes silicon to undergo not one transition, but a series of transitions from one facet to another as ridges organize and reorganize." Saam said.
The findings should hold true for any crystal structure that has reached thermal equilibrium. For a diamond left untouched at room temperature, the process would take centuries. Some such changes can still be seen in everyday life, however: a pane of glass in a very old window will thicken towards the bottom, because gravity pulls the atoms in the glass downward over time. The glass flows like a liquid, but because it flows very slowly, the change isn't visible to the naked eye. The MIT scientists fast-forwarded the process for silicon by heating the material and cooling it, Saam said.
In particular, he feels that scientists can apply his theories to materials other than silicon, for example gallium arsenide, platinum, and gold -- all elements that can play a significant role in the manufacturing of electrical components. By controlling certain forces, scientists could control the size of the ridges on the crystal, he said.
Next, Saam wants to extend these ideas to study another unusual silicon surface produced by the MIT scientists -- a surface of tiny, interlocking pyramids. While simple ridges could make good templates for nanowires, the valleys between pyramids could serve as cradles for quantum dots.
In the meantime, he hopes the MIT group and other experimental physicists will test the new phase transitions he and Shenoy identified.
The National Science Foundation sponsored this research.