A New Close-Up View of Electrons Inside Semiconductors

Thanks to a powerful new approach, physicists have directly observed with unprecedented detail how electrons interact with defects in advanced semiconductor devices. This work included an innovative computer simulation tool that enabled accurate theoretical modeling and interpretations of the experimental observations.

Together, the experimental and computational results “open the door to the discovery of never-before-seen electron behaviors that can be used for new semiconductor capabilities,” says Mike Crommie, a senior faculty scientist in Berkeley Lab’s Materials Sciences Division and professor of physics at the University of California, Berkeley. “This will be important for the future development of semiconductor devices at the ultimate limits of miniaturization.”

The study, published in Nature in June, provides new insights into cutting-edge ultrathin devices known as two-dimensional (2D) semiconductors that exhibit unusual electron states.

“Our study yielded valuable insights into why electrons in 2D semiconductors behave the way they do,” says Crommie, who co-authored the study.

“This is such a beautiful example of the synergistic power of seamless integration of experiment and theory at the frontier to advance quantum science,” says study co-author Shiwei Zhang, a senior research scientist at the Simons Foundation’s Flatiron Institute.

Other research team members include Feng Wang, a faculty senior scientist in Berkeley Lab’s Materials Sciences Division and a professor in UC Berkeley’s Department of Physics, and scientists from the University of California, the Flatiron Institute, the University of New Mexico, Hofstra University, Arizona State University and the National Institute for Materials Science in Japan.

Ultrathin Physics

Conventional silicon-based semiconductor devices such as transistors, computer chips and sensors are made of materials in which atoms are arranged in three-dimensional structures. In recent years, device developers have increasingly explored using 2D semiconductors, materials made of a single layer — or a few layers — of atoms. Their ultrathin structure alters electron behavior, potentially enabling new capabilities in future semiconductor devices.

The Berkeley Lab–led research team investigated 2D materials in which the electrons are in an unusual state known as a Wigner solid. In ordinary semiconductor devices, electrons typically behave like independent particles moving through the material. Their interactions with one another have a relatively minor influence on their behavior — and on the device’s overall operation.

“Physicists call this conventional state a Fermi liquid because the electrons move around like waves in the ocean,” says Crommie.

Under certain conditions, electrons can enter a Wigner solid state in which they separate from one another and become immobile. Physicists describe such a system as ‘strongly interacting’ because the electrons’ mutual repulsion becomes the dominant factor shaping their behavior. Rather than moving independently, electrons in Wigner solids organize themselves into a relatively orderly pattern and behave collectively.

The researchers wanted to better understand how defects affect electron behavior in 2D semiconductors. Because electrons in 2D materials are confined to a thin layer, defects can significantly influence their behavior. Unlike electrons in thicker three-dimensional materials, electrons in a 2D material have much less space to move around defects.

In the study, the researchers imaged electrons in a 2D semiconductor device as they transitioned from a Wigner solid to a Fermi liquid. By combining their imaging with advanced simulations, they evaluated how defects influence electron behavior across these different states.

“Our objective was to uncover new electron behavior,” says Crommie. “New electron behavior can lead to exciting opportunities to develop advanced devices with useful new properties and capabilities.”

Influential Defects

Historically, it has not been possible for scientists to directly image how electrons and defects interact in strongly interacting 2D semiconductor systems. It is extremely difficult to design semiconductor devices that can be imaged with sufficient resolution to resolve features on the scale of individual atoms. As a result, researchers have often resorted to a less direct approach to understanding electron-defect interactions: connecting wires to semiconductor devices and measuring how easily electricity flows through them.

“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 Crommie. “They were inferring the behavior based on electrical conductivity.”

To address the imaging challenge, the team used a scanning tunneling microscope. This instrument hovers a tiny metal tip just above a material’s surface and measures the electrical current as the tip scans across it. To achieve the highest possible structural and electronic resolution, the research team spent years carefully developing a device that sandwiches the 2D semiconductor material of interest — in this case, molybdenum diselenide — between a graphite layer on top and a silicon wafer with a boron nitride layer on the bottom. The metal tip scans the molybdenum diselenide through tiny holes cut into the graphite.

The team used this setup to image semiconductor samples with different defect densities. After each image was taken, they adjusted the density of electrons in their 2D device to visualize the material’s transition from a Wigner solid to a Fermi liquid.

The images the researchers obtained revealed that electron behavior in their devices varied dramatically based on the number of defects in the 2D semiconductor material. When many defects were present, the electrons became locked into an unexpectedly stable Wigner solid state exhibiting highly irregular, disordered patterns. With fewer defects present, the electrons arranged themselves into much more orderly, triangular, crystal-like patterns that transitioned more readily to the Fermi liquid state.

Crommie describes the moment when he first viewed the images and realized he was seeing something fundamentally new. “It was exciting to see the Wigner solid melt into liquid-like waves splashing up against defects,” he says. “We could see how electrons respond to defects in very different ways. Some defects acted like large potholes, while others acted like tiny speed bumps.”

Agreeing With Theory

To explain the defect-electron interactions observed in these images and confirm that the images were not artifacts of the microscope’s operation, the team needed to compare them with a theoretical model. The challenge was that there was no existing theory in the scientific literature for accurately simulating images of 2D semiconductor systems with strongly interacting electrons and random defects. It is difficult to perform the complex calculations needed to predict the behavior of large collections of electrons under these conditions.

A research team at the Flatiron Institute took on this challenge. The team consisted of Zhang, Research Fellow Conor Smith, former Research Fellow Yubo Yang (now an assistant professor at Hofstra University) and Research Scientist Miguel Morales. They augmented a sophisticated computer simulation technique called Quantum Monte Carlo with neural networks to calculate, based on the laws of quantum mechanics, how strongly electrons in a 2D semiconductor interact with defects.

“The methodological advances by incorporating neural networks added a new element that got us over the hump,” Zhang says.

The simulated electron behavior closely matched the patterns observed in the microscope images.

“This remarkable agreement confirmed the accuracy of both our theoretical simulation tool and our imaging technique,” says Crommie. “It also helped us better understand the physics underlying the behaviors we observed in our images.”

Crommie adds that the results suggest that controlling both the placement and the types of defects will likely become a much more important consideration as device developers push digital electronics, sensors and other semiconductor devices to ever smaller dimensions.

Other researchers and device developers can apply the team’s methodology — an integrated combination of imaging and theoretical simulations — to understand the electronic behavior of other 2D semiconductors, particularly those with strongly interacting electrons.

“The semiconductors in today’s smartphones and computers don’t contain Wigner solids, but they may in the future as devices become more advanced,” says Crommie. “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 team is extending its results by exploring how electron behavior is affected when electrons are confined to tiny channels in semiconductor devices. Another goal is to investigate how electrons behave in 2D semiconductors with fewer defects.

This research was supported by the U.S. Department of Energy’s Office of Science, Basic Energy Sciences; the U.S. Department of Defense’s Vannevar Bush Faculty Fellowship; the National Science Foundation; and the Flatiron Institute (a division of the Simons Foundation).