The year 2016 was noteworthy for many reasons, and one of the most significant was the consensus that the semiconductor industry is near the end of semiconductor scaling, commonly known as Moore’s Law. For more than 50 years, scaling has referred to the phenomenon that the number of transistors per square inch of integrated circuit doubled every 18 months, leading to the modern explosion of goods and services powered by ever-smaller computer chips.
But, as University of Virginia Electrical and Computer Engineering Professor Avik Ghosh said, “We are running out of ideas on how to scale them down further.”
In other words, just as we approach breakthroughs in such fields as medical science and telecommunications, the pace of progress will slow unless researchers find an alternative to the materials currently used for semiconductors or new ways to do computing beyond Boolean ones and zeros produced by transistors.
Research that Ghosh is conducting with colleagues at Columbia University, Cornell University, the Japanese National Institute for Materials Science and IBM is a step in this direction. Physics World, the member magazine of the Institute of Physics, recognized the potential of recent work in his group by listing it among the top 10 breakthroughs for 2016.
In the 2-D World of Graphene, Electrons Behave Like Photons
Ghosh and his colleagues are exploring the characteristics of graphene, a material composed of carbon atoms linked together in a hexagonal lattice. Graphene is a two-dimensional material, just an atom thick, with a number of unusual properties that won it the 2010 Physics Nobel prize. The most talked about is its strength — graphene is 200 times stronger than the strongest steel — but for an electrical engineer, its most intriguing property is ease with which it conducts electricity. The measure of how fast electrons move in a material is called mobility. The electron mobility of silicon is approximately 1,400 centimeters square per volt second. The mobility of electrons in graphene on hexagonal boron nitride substrates is 100,000 at room temperature.
The challenge is that this electron flow cannot be manipulated using the same kind of on/off switching devices used in silicon. Graphene lacks something called a band gap, which means there is no way to turn off the flow of electrons. The current is always on. Chemists can engineer a band gap in graphene structurally, but the price is that the electrons slow considerably. “There are no obvious choices,” Ghosh said. “Either you have fast electrons that you cannot turn off, or you create a band gap and lose the advantages of graphene.”
Ghosh and his colleagues decided to approach the switching problem from another perspective. They knew that electrons in graphene move at a constant speed independent of any applied force, much like photons do in vacuum. This opens up the possibility of using varying electric fields from gate electrodes to redirect and collimate electron flow, much as lenses refract and polarizers align light. When light passes from one material to another at an angle, it changes directions, causing the distortion seen when a straw is placed in a glass of water. Conventional materials like glass have a positive index of refraction that quantifies the extent of bending. Pass light through metamaterials designed with a negative index of refraction, and it bends the opposite way.
A decade ago, scientists predicted that electrons passing through graphene could exhibit negative refraction. Ghosh and his fellow researchers were the first to find a convincing way to do so. The team created a p-n junction in the graphene by applying opposite voltages across two laterally separated gate electrodes, reducing the density of electrons in one area (creating a positively charged region) and increasing it in an adjacent area (a negative region). The difference in electron density is functionally equivalent to the difference in material density that causes light to refract. However, since applied voltages can be positive and negative, the sign change across a junction creates a device with a negative refractive index.
The team at Columbia used a technique called magnetic focusing to direct a sharply focused beam of electrons across the junction. As they tuned the magnetic field, they were able to map the trajectory of electrons on both sides of the p-n junction by collecting the electrons and measuring their voltage as the incident angle changed. They also determined that the junction focused the electron flow and allowed them to transmit along a narrow stream perpendicular to the junction. Ghosh’s group, which included former postdoctoral fellow K. M. Masum Habib and graduate student Mirza Elahi, developed detailed simulation techniques to model and validate the Columbia team’s measurements. This involved calculating the flow of electrons in graphene under various electric and magnetic fields and accounting for multiple bounces at edges and quantum tunneling at the junction. “The predictions we made based on our simulations matched the experimental results exactly,” Ghosh said.
The ability to steer and collimate electrons with a gate creates a possible path to a low-power, high-speed switch using electron optics, as proposed by Ghosh’s team earlier in a series of papers. The collimated electrons can be turned back with a second junction set at an angle to the first, much like a polarizer-analyzer pair can be used to cut off the intensity of light. For high-quality edges, this mechanism can turn off the electrons without compromising the mobility.
“While this device idea is still being tested, if successful it could mitigate some of the challenges with power in present-day digital electronics, and potentially impact high-speed analog RF electronics,” Ghosh said.
A Platform for Exploration
Ghosh’s expertise in simulation, combined with a background that spans physics, electrical engineering, materials science and quantum chemistry, makes him an excellent partner for experimentalists in nanoelectronics such as the Columbia team. “Because our simulation platform has enabled us to move out in different directions, we have gained a very broad perspective on the field of low-power devices, from electronics to nanomagnetics,” he said. “This is useful when working with colleagues who are focused on complicated experiments.”
Ghosh’s breadth also makes him the ideal person to write an overview of nanoelectronics that bridges the divide between fundamental knowledge in chemistry, materials science and physics and applications in areas like circuit design and computer science. Ghosh’s new book, Nanoelectronics: A Molecular View, published by World Scientific, targets senior undergraduates, graduate students and researchers interested in quantitative understanding and modeling of nanomaterial and device physics.
“The book is organized as a story about the journey of an electron in various materials and covers a variety of dramatic events that can happened to it along its path,” he said. “For me, this book has truly been a labor of love.”