Portland, Ore. - Diamonds are forever, aren't they? Not according to a new interpretation of the crystalline structure of silicon wafers from researchers at Ohio State University.
Until now, scientists believed that crystalline facets met each other at atomically sharp edges. But new research at OSU suggests that the crystalline facets on the surface of silicon, gallium arsenide, glass and even diamond are all continually changing phases in a process of rounding off their edges by the force of thermal equilibrium.
To be sure, the process affects macroscopic characteristics only very slowly: It takes centuries for the sharp edges of diamond facets to visibly round, for example. But at the nanoscale the force acts instantly, determining the precise shapes of atomic-scale structures. By harnessing this force at the nanoscale, Ohio State University researchers hope to make it possible to prepattern nanowires and quantum dots onto future silicon wafers.
In chip fabrication, atomic precision accompanies many routine steps performed on silicon wafers. All the models, simulations and design specifications presuppose that crystalline edges are atomically precise. And above a micron they practically are, according to the OSU team-but not at the nanoscale.
"The common wisdom about crystalline surfaces is that different facets will intersect at atomically sharp edges," said professor William Saam, chairman of the department of physics at OSU.
Saam was assisted by a former student, Vivek Shenoy, who is now an assistant professor at Brown University. Their work was funded by the National Science Foundation.
"Then, 20 years ago, the physicist [Vladimir Aleksandrovich] Marchenko showed that in fact, sharp edges in crystals could not exist, because they cost too much energy-from a mathematical analysis of the thermodynamics," said Saam.
The forces of thermodynamic equilibrium compel all complex systems, including crystalline lattices, to relax to their lowest-energy state. Previously, theory maintained that simultaneous equilibrium states coexisted-one for each facet meeting at a crystalline edge-thereby enabling atomically precise edges. But Marchenko pointed out that thermodynamic equilibrium will force the edge to round off.
Marchenko in his 1981 research study didn't elaborate on exactly how this rounding off of the crystalline edges would occur, but Saam's and Shenoy's mathematical derivations now predict an almost constant shifting among phases-reminiscent of the way crystalline glass continually flows to the bottom of very old windows, making the panes thicker at the bottom than at the top.
"Shenoy and I have carried Marchenko's work much further, by deriving in detail how, if a sharp edge doesn't exist, what the rounded portion actually looks like," said Saam.
The pair's most scientifically provocative claim is to posit the existence of hitherto undiscovered phases at silicon and other crystalline edges including gallium arsenide, platinum and gold-a claim that will likely be put to the test in experiments in the near future. "We have pointed out the existence of new phases and new phase transitions between them-in a nutshell that's what we've done," said Saam.
The current theory that scientists and engineers use to interpret their observations of crystalline surfaces basically ignores Marchenko's predictions, and instead posits that only two simultaneous phases coexist at thermodynamic equilibrium to form atomically sharp edges. Saam and Shenoy predict that engineers will instead discover that direct observation of nanoscale silicon edges will reveal multiple intermediary phases rounding the edges in a way that cannot be explained with the traditional two-phases-coexisting doctrine.
"Our analysis leads to the prediction of new phases which have not been predicted before," said Saam. "Contemporary wisdom would say that you have two phases coexisting at an edge, whereas in fact the edge is not there, which leads to a continuum of phases. That all of these are equilibrium phases was not realized before. There are lots of equilibrium phases in between."
The most detailed observation to date of crystalline edges at the atomic scale was done by Massachusetts Institute of Technology scientists in the 1990s. The MIT group heated silicon wafers to over 1,000 degrees Kelvin (approximately 725 degrees C or 1,340 degrees F) to simulate the effects of aging. They observed, where atomically sharp edges should be, what are now called "Marchenko grooves"-a series of parallel ridges rounding off the sharp edges.
The MIT researchers were investigating surfaces, not just the edges, and they interpreted the Marchenko grooves using the traditional two-phases-coexisting doctrine of atomically sharp edges. According to Saam, the MIT group interpreted the observed Marchenko grooves-the curved-edged trenches that appear to defy the two-phases-coexisting doctrine with visible rounding-as bunches of two-phase steps (one phase at an angle and the other made up of stepped tiers that only appeared smoothly curved).
Saam and Shovey counter that stepped surfaces usually appear rough, but that switching to a new understanding of Marchenko grooves predicts a continuous range of curves that appear smooth because they are smooth.
If their interpretation proves out, then it could lead to future technology candidates for nanowires and other atomic-scale devices for 21st-century chips, according to Saam. "Marchenko grooves can be at a scale of anything from a micron down to just a few nanometers and can be made from many different materials including silicon, gallium arsenide-even carbon nanotubes," he said. By understanding the origin of Marchenko grooves, Saam and Shovey hope to enable nanowires to be fabricated from them.
A second, even more promising potential outcome arises from Saam's and Shenoy's observation of pyramid structures (which were also observed by the seminal MIT study). "These pyramidal shapes can populate a field, so you are utilizing three directions instead of two," said Saam. "They could provide a template that is visually suggestive of the idea that quantum dots could be grown in the pits in between the pyramids."
By prepatterning wafers with arrays of quantum dots, nanowires and even more exotic molecular-size devices, future chips could make use of nanoscale complexity underneath while using more easily fabricated layers on top. Today, nanoscale carbon-nanotube transistors have been demonstrated but they had to be hunted for one by one on the wafer, because they cannot be fabricated in regular arrays. Saam hopes that his contribution to understanding silicon surfaces will enable such arrays to be prepatterned onto wafers in the future.
"We have provided a basic understanding of the physics of this phenomenon, and what the phases and phase transitions involved are in all the crystals around it," Saam said. "Our hope is that with time our ideas will lead to better wafer designs." He added, "But these are things for the future and I would not attempt to predict how that will go. But I do think that most engineers will find it quite surprising that you won't have atomically sharp edges at the nanoscale."
Saam hopes to pique interest among research scientists and engineers so that his predictions can be put to the test by directly imaging the edges of silicon structures. "The best thing you could do for me is to interest some engineers in doing these crystal-shape experiments," said Saam. "The technology is there to test my predictions with silicon-this kind of detailed look at the shape of a crystal below a micron has already been done for gold and lead, and somebody should do it for silicon."
In the meantime, Saam plans to apply his theoretical framework to explaining the conditions that lead to the formation of nanoscale fields of pyramids. The idea is to have a theory in place that engineers could use to create and control their placement on wafers.