Physicists at Lawrence Berkeley National Laboratory have, for the first time, directly imaged how electrons interact with individual defects in a two-dimensional semiconductor, capturing the transition of electrons from an ordered Wigner solid into a liquid-like state at atomic resolution. The study, published in Nature in June, examined devices built on molybdenum diselenide, a 2D material already central to next-generation transistor and sensor research.

The results carry direct weight for device engineering. In conventional silicon electronics, atoms sit in three-dimensional lattices and electrons mostly move independently through the material — what physicists call a Fermi liquid. Confine electrons to a single atomic layer, and their mutual repulsion can dominate instead. Under those conditions they freeze into a Wigner solid: an immobile, orderly arrangement that behaves collectively rather than as independent particles.

Because electrons in 2D materials have almost no room to route around imperfections, defects shape device behavior far more strongly than in bulk silicon. Until now, researchers could not see that interaction directly. "Some of the conclusions in these previous experiments were ambiguous because the researchers could not actually see the electrons and the defects at the same time," says Mike Crommie, a senior faculty scientist in Berkeley Lab's Materials Sciences Division and professor of physics at UC Berkeley. "They were inferring the behavior based on electrical conductivity."

Building an imageable device

The barrier was structural. Resolving features on the scale of single atoms inside a working semiconductor device is extremely difficult. The team, co-led by Crommie and Feng Wang, also a faculty senior scientist at Berkeley Lab and UC Berkeley physics professor, spent years engineering a stack that a scanning tunneling microscope could read: molybdenum diselenide sandwiched between a graphite top layer and a boron-nitride-coated silicon wafer below. The microscope's metal tip scans the semiconductor through tiny holes etched into the graphite.

The researchers imaged samples with varying defect densities and, after each scan, tuned the electron density in the device to drive the material between its Wigner solid and Fermi liquid states. The differences were dramatic. With many defects, electrons locked into an unexpectedly stable Wigner solid with highly irregular, disordered patterns. With fewer defects, they formed orderly triangular, crystal-like arrangements that melted into the Fermi liquid state far more readily.

"It was exciting to see the Wigner solid melt into liquid-like waves splashing up against defects," Crommie says. "Some defects acted like large potholes, while others acted like tiny speed bumps."

Simulations close the loop

Verifying that these images reflected real physics, not microscope artifacts, required theory that did not exist. No method in the literature could simulate strongly interacting electrons around random defects in a 2D semiconductor at the necessary scale. A Flatiron Institute team — Shiwei Zhang, Research Fellow Conor Smith, former Research Fellow Yubo Yang (now at Hofstra University) and Research Scientist Miguel Morales — augmented Quantum Monte Carlo simulation with neural networks to compute the electron-defect interactions from first principles.

"The methodological advances by incorporating neural networks added a new element that got us over the hump," says Zhang, a senior research scientist at the Simons Foundation's Flatiron Institute. The simulated patterns closely matched the microscope images. "This remarkable agreement confirmed the accuracy of both our theoretical simulation tool and our imaging technique," Crommie says.

Additional collaborators came from UC Berkeley, the University of New Mexico, Hofstra University, Arizona State University and Japan's National Institute for Materials Science. Funding came from the U.S. Department of Energy's Office of Science, the DoD Vannevar Bush Faculty Fellowship, the National Science Foundation and the Flatiron Institute.

Why it matters for manufacturing

For process engineers, the message is that defect placement and defect type — not just defect count — will grow in importance as devices shrink toward their physical limits. "The semiconductors in today's smartphones and computers don't contain Wigner solids, but they may in the future as devices become more advanced," Crommie says. "Our methods can help researchers and manufacturers understand what electrons will do under these conditions, informing the design of increasingly miniaturized devices with advanced capabilities."

The combined imaging-plus-simulation methodology is transferable to other 2D semiconductors with strongly interacting electrons, and the team is now extending the work in two directions: electron behavior confined to narrow channels within devices, and electron behavior in near-defect-free 2D materials.