# Electron “Leapfrog” Could Lead to Low-Power Nanoscale Devices

Remember leapfrog? Not the electronic tablets currently in Santa’s bag, but the outdoor, no-equipment-required game where your friends crouch down in a line and you vault over each person until you reach the front? It turns out that electrons play a variation of this game too.

 A game of leapfrog. Image Credit: Chicago’s North Shore Convention and Visitors Bureau (CC BY 2.0)

In a paper that will soon be published in Physical Review Letters, a team of Canadian scientists have discovered the physical process behind an intriguing and useful property of some circuits called negative differential resistance.

The resistance of an electrical circuit describes how electrons flow through the circuit. Just as water flows easily through a newly installed pipe but a clogged pipe reduces its flow, electrons flow more easily through a circuit with low resistance.

The relationship V=IR may ring a bell for some readers, in which V is voltage, I is current (the flow of electrons), and R is resistance. The voltage of a circuit describes the difference in electric charge between two points on a circuit. To take the plumbing analogy a little further, voltage is a lot like water pressure. When you decrease the voltage in a circuit, the current also decreases.

However, in some special cases V=IR doesn’t hold and the opposite occurs—a decrease in voltage leads to an increase in current. This is what is meant by negative differential resistance (NDR). It can lead to very effective electronic oscillators and amplifiers, among other devices.

The opportunities keep researchers looking for physical process that produce NDR. They have seen hints of it on the nanoscale and the molecular scale, but still have a long way to go before they can incorporate NDR in devices of those scales. The problem is that the physics behind many observed NDRs at the nanoscale is not very well understood. Scientists and engineers have used it to their advantage after conditions resulting in NDR were discovered, but we can’t fully capitalize on the possibilities until we understand the physics behind it and can design devices with that in mind.

One possible application is in ultra-low power nanoscale devices, the research focus of the lab of Professor Robert Wolkow at University of Alberta, Canada. They aim to develop fast, low-power electronics on the atomic scale.

Recent work suggests that using a scanning tunneling microscope (STM) to probe an atomic arrangement that leads to NDR can shed light on the physics at play. For the first time, the team applied a new kind of time-stamped STM technique to this arrangement and measured the passage of electrons through a single silicon atom down to the nanosecond. In other words, they directly measured the transit time of an electron through an atom to less than a billionth of a second.

The experiment was designed so that electrons could travel through an atom alone or while the atom was already occupied by an electron. The results show that if the atom was already occupied by an electron, the incoming electron “leapfrogged” over the first one, going through the atom much faster than it could if it was alone.

What does this have to do with NDR? A mathematical model of this process that closely matches their results suggests that, when the voltage in the circuit goes up, the electrons are pulled off the atom toward the other terminal in succession. When the voltage goes down, the electron already in the atom lingers and a second comes in and leapfrogs (or reflects off) to the other side. Since the second electron travels faster through the atom, the current goes up and you get NDR.

If leapfrog isn’t your game, this golf illustration might be useful. Putting a ball involves both aim and speed. Even if you hit the ball in exactly the right direction, it must slow down enough in the region of the hole to drop in. In this experiment, when the atom was already occupied by an electron and another electron came along, the incoming electron acted like a ball that didn’t slow down enough drop into place—instead it reflected off of the “hole,” traveling through the atom more quickly than expected.

This may not be a child’s game of leapfrog, but it’s fun to imagine electrons gleefully vaulting over one another, picking up speed as they go. On a serious note, now that we have a working predictive model for NDR, scientists are better equipped to investigate whether this type of atomic arrangement can be scaled up and used in practical devices. Perhaps that will lead to some gleeful leaping too.

Kendra Redmond