Edge Dislocations in Silicon
By Mark Mostoller, Ted Kaplan, and Matt Chisholm


Mark Mostoller (left), Matt Chisholm, and Ted Kaplan show their models of a “dreidl,” which has a closed symmetric structure of five-fold and seven-fold rings that resembles a child’s dreidl, or Hanukkah top. Silicon and germanium can have dreidl structures. Photograph by Tom Cerniglio.

In the past half century, the world has been transformed by an electronic revolution that is based largely on silicon technology. Semiconductor devices using this technology have become smaller and smaller, yet far more powerful, over time. Defects have a profound effect on device performance. The controlled introduction of substitutional impurities (dopants) like boron and phosphorous in silicon, for example, is what makes transistors work. In this country, only a few incongruously important groups like the air traffic controllers at O’Hare airport in Chicago have lagged this revolution and still use electronic equipment with vacuum tubes.

Dislocations are line defects that are generally thought to be bad actors because among other things, they tend to suck in the dopants that make devices perform. The same negative view is held of planar defects like grain boundaries, which can be viewed as arrays of dislocations. In the worst case, if all the dopants so carefully introduced were to segregate to dislocations, the device would fail to work at all. Any electrical activity associated with dislocations was thought to be due to such impurity segregation or to the presence of so-called dangling bonds.To explain the latter requires a short refresher course on the crystal structure of silicon.

drawing Fig. 1. The diamond-cubic crystal of silicon, with atoms on the cube corners and faces in red, and those inside in blue; each blue atom has four neighbors, and each lies in six-fold rings.

Silicon crystallizes in the diamond cubic structure (shown in Fig. 1), which is responsible for the hardness of the diamond form of carbon. Notice two things about the structure. First, each atom has four neighbors at the corners of a tetrahedron around it. Second, if you pick, say, a blue atom and follow nearest-neighbor bonds until you return to the same atom, the atoms are members of six-fold rings. If, in some defect structure, a silicon atom has fewer than four neighbors, it is said to have dangling bonds.

drawing Fig. 2. Looking down the core of an (a/2) <110> edge dislocation in Si (left), with atoms in the core marked in yellow, and the dreidl (right) that forms at the intersections of the dislocation grid in Ge/Si(001) bicrystals.

It is important to determine the atomic and electronic structure of dislocations in semiconductors because they can have such profound effects on electrical and mechanical properties. Our work began with a microscope in ORNL’s Solid State Division. By using a technique called Z-contrast imaging, we can now look at materials with atomic-scale resolution. Matt Chisholm had been using this technique to investigate bicrystals of germanium on silicon [Ge/Si(001)]. He observed a 4% lattice mismatch between germanium and silicon; for this system, a regular square grid of edge dislocations formed at the interface, 100 apart. The microscope images showed that the cores of the dislocations had the structure shown in Fig. 2, in which five-fold and seven-fold rings are stacked together. We confirmed this observation by doing large-scale simulations in systems of roughly 20,000 atoms, using classical interatomic forces that give a good description of pure silicon and germanium. At the intersections on the grid, we found a closed symmetric structure (also shown in Fig. 2), which we called the “dreidl” after the child’s Hanukkah top that it resembles. Again, we see a structure that consists of linked five-fold and seven-fold rings. This discovery was reported with the headline “Atomic Dreidls” in the February 10, 1994, issue of the weekly AIP Physics News Update of the American Institute of Physics. The simulations showed that in both the individual dislocations and their intersections, all atoms retain their tetrahedral coordination, albeit with changes in bond lengths and angles. There are no dangling bonds.

In 1993, we were joined by postdoctoral scientists Feng Liu and Victor Milman, who both had experience in first principles calculations of material structure and properties. (Liu is now at the University of Wisconsin at Madison, and Milman is with Molecular Simulations in Cambridge, U.K.) Milman was among the first to get his code working on the new Intel Paragon machines, which occasioned a certain amount of muttering and lamentation on his part. We were interested in the electronic properties that these defects in Ge/Si(001) might have; but systems of 20,000 atoms are too large, even with a Paragon, to perform electronic structure calculations. Instead, we chose a simpler system of dislocation dipoles in silicon, in which all of the dislocations run along the same direction, but whose cores alternate between five-fold on top of seven-fold rings and seven-fold on top of five-fold rings.

“This finding suggests that dislocations themselves, with no dangling bonds and without segregated impurities, may be electrically or optically active.”

drawing Fig. 3. Shift in energy of the highest occupied electronic state into the bulk band gap for edge dislocation dipoles in Si as a function of system size.

Using a combination of first-principles, classical, and tight-binding calculations running on the XPS/35, workstations, and a Cray YMP, respectively, we treated supercells of from 64 to 576 atoms. The 576-atom sample is among the largest systems for which such first-principles calculations have been done, and this turned out to have important results. As the system size grows and the separation of the dipoles increases, the strain becomes more concentrated in the dislocation cores. So despite the absence of dangling bonds, electronic states localized at the cores rise about 0.2 eV into the band gap, as shown in Fig. 3. (Semiconductors and insulators have an energy band gap between the highest occupied electronic states and the lowest unoccupied levels, whereas metals have no gap.) This finding suggests that dislocations themselves, with no dangling bonds and without segregated impurities, may be electrically or optically active. Previous work by others on similar systems was done for smaller samples. They had found no such deep gap states for dislocations in pure silicon. Now we know why.

Further information

  • Mark Mostoller, M. F. Chisholm, and Theodore Kaplan, “New Extended Point Defect Structure in Diamond Cubic Crystals,” Phys. Rev. Lett. 72, 1494 (1994).

  • Feng Liu, Mark Mostoller, V. Milman, M. F. Chisholm, and Theodore Kaplan, “Electronic and Elastic Properties of Edge Dislocations in Si,” Phys. Rev. B 51, 17192 (1995).


MARK MOSTOLLER was born in Somerset, Pennsylvania, and grew up in Pittsburgh. He received his Ph.D. degree in applied physics from Harvard University. He was a staff member in ORNL’s Solid State Division from 1969 to spring 1997. He has worked on lattice vibrations, random alloys, electronic and vibrational properties at surfaces and interfaces, and numerical simulations of the structure and properties of materials. He received Lockheed Martin technical achievement awards in 1990, 1992, and 1996.

TED KAPLAN is a theoretical physicist in ORNL’s Computer Science and Mathematics Division. Born in New York City, he received both his undergraduate and Ph.D. degrees from the Massachusetts Institute of Technology. He has been at ORNL since 1972, when he joined the Solid State Division. His research has included the theory of random alloys, fractal interfaces, chaos, rapid solidification, and thin film growth. Most recently, he has worked on large-scale numerical simulations of the properties of materials. He received a Lockheed Martin publication award in 1996.

MATT CHISHOLM is a materials scientist in the Solid State Division. Born in Sayre, Pennsylvania, he received his B.S. degree from Northwestern University. After 4 years at Reynolds Metals Company, where he worked on aluminum alloys for cans, cars, and aircraft, he obtained his Ph.D. degree from Carnegie-Mellon University. Subsequently, he worked for IBM before joining the ORNL staff in 1988. His primary research interest is the determination of the structures of defects in crystalline materials. His primary research tools are the unique direct imaging electron microscopes in the Solid State Division.


Where to?

Next article | Contents | Search | Mail | Review Home Page | ORNL Home Page