An Electron Runs through It

Surprising rivulets and ripples complicate the microchip picture

Most paintings or prints lose their definition the closer you get to them. That doesn’t happen when you put your nose near the arresting prints of Harvard University physicist Eric J. Heller. The closer you approach Heller’s prints, which resemble swaying seaweed, rippling silks, and Georgia O’Keeffe flowers, the more refined the images get. By the standard artistic metrics of form, color, and composition, these are stunning artworks. Yet each one tells a scientific tale as well: Heller’s prints depict the subtle interplay between some microchip electrons and the crystalline landscape in which they move.

IN A DIFFERENT VEIN. This and the two richly branching images below show artistic renderings of simulated electron-flow paths in thin sheets of electrons. “Transport II,” Heller
ROUGH TERRAIN. A topographic-type plot of energy variation across a patch of a two-dimensional electron gas shows uneveness that shapes electron paths. G. Finkelstein, et al./Science
“Transport III” (Detail). Heller
“Transport XI” (Detail). Heller

Within a stack of various semiconductor materials are infinitesimally thin zones where one semiconductor layer ends and another begins. Each zone can harbor a sheet of electrons. Physicists refer to such sheets as electron gases. Cool to cryogenic temperatures a chip made of precisely deposited gallium arsenide and aluminum gallium arsenide, for example, and a curious branching of the flow of electrons in the sheet becomes detectable.

That’s the physical phenomenon that Heller models in computers and portrays with his prints, which now go for hundreds of dollars or more.

While investigating electron gases over more than 40 years, researchers made stunning discoveries that netted two Nobel prizes. “Aside from the fact that all our computers are based on devices with electrons in buried layers,” says Raymond C. Ashoori of the Massachusetts Institute of Technology (MIT), “there’s magic to be found [in those layers]. The physics is really extraordinary.”

Not until the past few years have scientists found ways to image the physics going on in these electronic environments. Those images depict both the intricate trajectories of flowing electrons and the roller-coaster topography responsible for those trajectories.

The visualizations already have shattered some assumptions about electron behavior, such as the idea that electrons flow uniformly. As ordinary transistors become exceedingly tiny in the next couple of decades, the images could take on much more significance.

“What we see [now] at low temperatures in larger devices will eventually be seen at higher temperatures in smaller devices,” predicts Charles G. Smith of Cambridge University in England.

Such electron behaviors “could be gremlins in future devices,” adds Stanford University physicist Mark A. Topinka, “or maybe they could be exploited.” Whether they prove detrimental or valuable may depend on what new forms transistors and other electronic devices take as chip makers shrink them ever smaller.

Buried treasure

When electrons are confined to cold, cramped quarters, as two-dimensional electron gases in chilled semiconductor stacks are, their quantum natures loom large.

For example, by carefully monitoring electric currents, resistances, magnetic fields, and other properties of supercold microstructures, physicists made two Nobel prize–winning discoveries. In 1980, they uncovered what’s known as the quantum Hall effect and then, 2 years later, the so-called fractional quantum Hall effect.

In other experiments, physicists have corralled electrons within regions of two-dimensional electron gases, called quantum dots, that behave as artificial atoms (SN: 4/11/98, p. 236). Some of these investigations have had practical payoffs, such as new types of lasers.

Researchers whose work has incorporated ways of depicting what electron gases look like have had aesthetic payoffs as well. One of those groups includes Harvard teams of theorists and experimentalists led by Heller and Robert M. Westervelt, respectively.

The experimentalists developed an electron-watching technique that relies on an atomic-force microscope (AFM). With that instrument, scientists usually visualize a sample’s surface atoms by dragging a sharp tip over the surface and monitoring the force between the surface and the tip, which can be as fine as a single atom.

To make measurements of electronic flow, some researchers have forced an electron gas to pass through a narrow, electrically defined gap, before permitting the electrons to spread out again. In 2000, Smith and his Cambridge University colleagues reported using an AFM to visualize expected undulations in electron flow within such a channel. The next year, Westervelt and his colleagues unveiled a different AFM technique that enabled them to move beyond the channel.

By using the AFM tip to make local measurements outside the channel, while simultaneously using coarser electrodes to monitor the overall current through the material, Westervelt and his coworkers imaged flow across the two-dimensional gas with remarkable precision.

“No one expected the images to be that sharp and that great,” says Heller. Following those experiments, Heller simulated the electron flows with computers, producing images of rich, delicate branching patterns that go far beyond what can be seen in actual chips. Call it scientifically informed art.

“I have a compulsion every once in a while,” Heller admits. “I have to do something [artistic]. This happens to me only in my most scientifically creative periods.”

In his art pieces, Heller embellishes the computer-generated branching patterns with color, shading, and other effects by means of image-manipulation software.

He has also worked with geometric forms from his research in quantum mechanics, crystallization, and molecular collisions. The dramatic, organic look of electron trajectories, however, is giving Heller a new visual lexicon that is resonating with the scientifically oriented public. A 163-centimeter-by-122-cm print of one of his electron branching patterns hangs in the great rotunda of the National Academy of Sciences in Washington, D.C. Shows of his images have been presented this year at the Exposition Center of the University of Montreal and the Lawrence Hall of Science at the University of California, Berkeley.

To facilitate growing sales of his prints, his wife, Sharl Heller, has set up an online gallery (


Before the Harvard team’s experiments, no one expected such variegated flow patterns in a very cold, two-dimensional electron gas. That’s because most researchers studying those gases use such perfect crystals that electrons move ballistically, that is, they travel extraordinary distances—tens to hundreds of micrometers—before colliding with one another or with atoms in the material.

Westervelt and his colleagues had expected their AFM-imaging process to depict, at most, several uniform, featureless swaths of electric current. Instead, the images revealed that electrons were traveling curvy, branching paths. Some of those paths were thicker than others, indicating that electrons preferred particular routes through the semiconductor.

“When we first got the experimental images, we really didn’t understand them at all,” recalls Brian J. LeRoy, now at Delft University of Technology in the Netherlands.

When experimentalists are baffled by their results, they often go to theorists to get help making sense of their findings. Westervelt and his coworkers had only to stroll to Heller’s office in a nearby building. Upon first seeing the images, “I was astonished at their structure and beauty,” Heller recalls. However, he also immediately recognized what was going on.

“For him, it was instantaneous,” Westervelt recalls.

Certain electrically charged atoms, or ions, that the team had embedded a short distance above the electron gas were affecting the electron’s motions, Heller surmised. Electric fields from those ions and from some other features in that overlying layer were extending into the electron gas, making themselves felt as forces whose strength and direction differed across the gas.

Speaking of those ions from an electron’s perspective, Heller notes that “you fly over ballistically, but they deflect you a little bit.” Together, those deflections steer the electrons into patterns known to mathematicians and physicists as caustics. In Heller’s hands, these emerge in images looking like folds in fabric and swaying seaweed.

In complementary work, Ashoori’s team has created what look like topographic maps. The MIT scientists do this using a cousin of the AFM known a scanning tunneling microscope. The peaks and valleys depicted on those maps indicate the presence of electron-deflecting forces, and the steepness of their slopes indicates the forces’ strengths.

“[Westervelt’s group] is looking at rivers flowing in the landscape, and we’re making a topographic map of the landscape,” Ashoori says.

Wavy gravy

Some more-recent electron imaging may result in practical payoffs in electronics and computing.

When the Harvard scientists uncovered the dramatic branching of electron flow in cold semiconductors, they also observed another intriguing pattern in their pictures: tiny ripples seemingly superimposed on the branches.

As quantum mechanics predicts, electrons are as much waves as they are particles. In the branching measurements, it seems, waves bouncing back to the channel were interfering with other waves, creating patterns of crests and troughs from constructive and destructive interference.

Westervelt and his colleagues have put those ripples to scientific use. The researchers have deposited electrode patches on their chips’ surfaces in such a way that they impose what amount to electrostatic mirrors on electron gases. With these, the scientists intensify electronic-interference patterns within the electron gases. This opens the way to making measurements of the varying energies and densities of electrons throughout the gas, Westervelt says.

Such measurements may prove valuable to makers of so-called high electron-mobility transistors, which are used today in cell phones and other high-frequency equipment. Those transistors are made from semiconductor wafers processed to incorporate electronic architectures akin to two-dimensional electron gases. “Knowing the density fluctuations would presumably help the folks who grow these wafers to do better,” Topinka says. Harvard’s Ania C. Bleszynski presented the new work at a physics meeting in July in Santa Barbara, Calif.

In other studies, the Harvard team and a group led by Klaus Ensslin of the Swiss Federal Institute of Technology Zürich (ETHZ) have each independently obtained images of quantum dots occupied by single electrons. ETHZ and Harvard groups present quantum-dot visualizations in the Nov. 19 Physical Review Letters and an upcoming Nano Letters, respectively.

The researchers aim to eventually visualize the electron’s intrinsic quantum-wave shape. With such data, scientists may learn to use those boxed-up electrons as basic components, or qubits, of quantum computers—machines expected to exploit quantum physics to vastly outperform current computers in certain calculations (SN: 2/22/03, p.124: Knotty Calculations).

Graphic scientist

Electron gases, caustics, atomic force microscopes—all of these may seem far away from common experience. But they’re not, says Heller.

At night, mixing of cold and warm air creates short-lived air pockets of varying densities that act as weak lenses, gently bending starlight much as donor ions skew particle trajectories in electron gases. For observers on the ground, this ever-changing distribution of lenses produces the twinkling of stars.

Also, regions of different density in the ocean make it possible for some sounds to travel for many miles along focused paths, perhaps facilitating communications between widely separated whales. What’s more, caustics at the ocean surface may give rise to the behemoth, ship-gobbling ocean swells known as rogue waves, adds Heller, who is currently developing a rogue-wave theory “having to do with what I learned from this electron branching.”

What’s for certain already is that these branching patterns, in the hands of Heller and his image processors, yield beautiful and compelling compositions that people are willing to pay for. There’s a universality to those patterns that Heller says reflects exciting commonalities across categories ranging from electronics to aesthetics. Says Heller, “The ‘looks-like-something-I’ve-seen-before’ reaction is exactly what I want.”

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