Our modern world runs on a vast array of semiconductor devices such as diodes, transistors, and integrated circuits. They power multitudes of electronics equipment, computers and smartphones, and many others. At the fundamental level, these devices work by controlling the flow of electrons in a semiconductor to process or store information or perform energy conversion. A critical task in semiconductor research and development is to characterize and engineer the electronic properties of these materials to meet the requirements of a given application.

One big question is central to this effort: How can we figure out what is really happening inside a semiconductor? For nearly two centuries, the answer has unfolded step by step. And in a new paper published in Science Advances, IBM Research has demonstrated the next step in advanced characterization of electronic materials. To understand the significance of it, we need to look back at where we started.

The simplest and oldest characterization test for electronic materials is based on Ohm’s law: applying an electric field or a voltage to a material and measuring the resulting current. This method, first formulated by Georg Simon Ohm in 1827, reveals the material’s ability to conduct electricity: its conductivity.1 In 1879, Edwin Hall introduced a second excitation, applying a magnetic field to a material. He discovered that the flow of charges is deflected by the magnetic field and produces a measurable voltage, a phenomenon known as the Hall effect.2 This technique enables us to extract three key pieces of information about the electronic charges flowing through the material: the ‘carrier type’ i.e. whether the charge carrier is an electron or its absence, called a ‘hole’; how fast these charges move (carrier mobility); and how many charge carriers are in the material (carrier density). These two techniques, Ohm’s law and the Hall effect, form the essential foundations of electronic material characterization as shown in Figure 1.

Advances in understanding of electronics transport in solid.

From a conceptual standpoint, these characterization efforts rely on applying a stimulus or excitation and measuring a response. The greater variety of excitations we use, the more information we can get. In addition to electric and magnetic field excitation, the Hall effect can be expanded by introducing a third excitation — light or photon excitation. Illuminating a semiconductor creates excess electrons and ‘holes,’ allowing researchers to probe their transport properties simultaneously. In 2019, an IBM-led team in collaboration with the Korea Advanced Institute of Science and Technology (KAIST) made a major breakthrough with the discovery of a new equation and technique that enabled simultaneous measurement of electron and hole properties including their mobilities, density, and recombination lifetime. The new technique, reported in Nature, is called the ‘Carrier-Resolved Photo-Hall’ (CRPH) effect.3 It opened the door to additional insights into materials and paved the way for the next exciting discovery.

A new discovery, an ancient idea

Beyond the photo-Hall effect, there remains a fourth stimulus: heat or A phonon is a quasiparticle that represents vibrational energy and can also be used to describe heat transfer when classical heat transfer models don’t apply.phonon excitation, which are lattice vibrations that we can measure as temperature. By controlling the temperature of a material, we can extend the CRPH technique to probe the defect states in semiconductors. Measuring and engineering the defects or trap states in semiconductors is critical for the function of many semiconductor devices, from CMOS logic and memory to LEDs and solar cells.

In the new Science Advances paper, an IBM-led team reported a breakthrough in understanding the photo-Hall effect in the presence of traps.4 The experiment is undoubtedly complex, involving all four excitations mentioned above. However, when the data is analyzed in terms of a new quantity called ‘photo-Hall conductivity’ vs. conductivity alone, the result collapses into a hyperbola, an astonishingly simple and elegant equation where the key trap parameters can be easily deduced as shown in Figure 2.

As light intensity increases, the hyperbola curve reaches a peak and then turns around approaching an asymptote. The peak position of the hyperbola indicates saturation of traps, indicating trap density. The “sharpness” of the hyperbola allows us to extract the trap energy, and the slope of the asymptotes yields the ratio of electron-to-hole mobility. With further calculations, we can extract a complete set of information including more than 20 parameters describing the material and charge carrier properties from this single measurement technique.

Conic sections and their applications: the planetary motion and now, the electron transport in solid.

This hyperbola is part of a family of curves famously known as conic sections, one of the oldest ideas in mathematics that traces its roots back to 300BCE in ancient Greece, as shown in Figure 2. The conic sections have also played a very important role in physics, including as the key idea in the discovery of Kepler’s first law. In the 17th century, Kepler showed that the planetary orbits are ellipses with the sun at one focus. His example offers some lessons for this research.

First, Kepler’s discovery was enabled by precision experimental measurements — the most precise planetary data that had been taken at the time — that allowed him to uncover the geometry that explained planetary motion. Similarly, in this latest study, the ability to detect traps and resolve electron and hole mobility from photo-Hall data demanded a large set of precision measurements, which were enabled by another recent IBM invention: the parallel dipole line (PDL) Hall system.3 The PDL system is a unique rotating magnet setup that allows compact and high-sensitivity photo-Hall measurement. Second, the complex phenomena under study (planetary motions and electron transport in solid) fortuitously can be cast into simple geometric problems: ellipse and hyperbola respectively. The geometric description of the problems becomes the key to extracting various information from the system in a simple way.

IBM has a long history of advancing the fundamentals of semiconductor science and technology, including breakthroughs in materials characterization with the invention of the scanning tunneling microscope (STM), and the atomic force microscope (AFM), as well as theoretical advances such as Dennard’s scaling law, which has guided decades of logic technology development since its establishment in 1974. The discovery of carrier- and trap-resolved photo-Hall and its photo-Hall conics equation continue this lineage, with the potential to help accelerate the development of a wide array of semiconductor applications. The new technique has been intensively used within IBM to investigate many new semiconductor materials beyond silicon for next-generation logic, AI systems, photovoltaics, and more.

Beyond its immediate practical application, this discovery marks a fascinating milestone in our long journey that started with Ohm’s law in 1827. Now, two centuries later, we have made a leap in understanding that the complex dynamics of electrons in solids, in the presence of electric, magnetic, photon, and phonon excitations, can be cast as a simple geometric problem — a conic section. This new idea gives us the unprecedented ability to unlock multitudes of charge carrier and material information in semiconductors.