By Chris Lee

Spurned electrons throw light on electronic noise at very small length scales.

Normally, noise is something we scientists try to avoid. In the most advanced physics experiments, the goal is usually to measure something new. If you ever ask the experimenters why it took them so long to do a measurement, the most common answer is “finding a way to defeat the noise.”

Sometimes, though, the noise becomes more interesting than the signal, telling us new things about the physical system we are studying. The study of noise is not new, of course, but with our increasingly precise control of quantum systems, we can study it in ever finer detail.

In this case, researchers studied Johnson noise, otherwise known as white noise. In a metal, there is a sea of electrons that is free to travel around in constant motion—the fact that the temperature is above absolute zero is enough to keep electrons in motion. Because of this motion, the density of electrons varies slightly from place to place at any given time. These fluctuations create small attractive and repulsive forces that drive electrons to attempt to neutralize the fields. In doing so, they create new density fluctuations and fields in an endlessly repeating cycle.

If you could freeze the electrons and examine the density as a function of position along a wire, you would find that the density fluctuations occur at huge range of length scales. That is, there are density waves with lengths that are very long—the length of the wire, in fact—and there are density fluctuations with shorter wavelengths. The result is tiny electrical currents that have frequency components that occur at all time scales. You cannot escape this white noise—it’s everywhere.

All of this hides the motion of individual electrons, though. An electron sitting in this sea will feel a force and start to move in a particular direction. However, the metallic crystal isn’t perfect, so it hits an imperfection in the crystal—an imperfection might be a missing atom, or it could be the boundary of the crystal or a range of other deviations from the regularity of the crystal structure. When an electron hits an imperfection, it stops dead (contributing to those density fluctuations we discussed early) before starting to drift off again in whatever direction the local electric fields tell it to go.

This behavior means that when you look at a current flowing through a wire, it looks more like water diffusing through sand than water flowing through a pipe.

Using diamonds to see current

How could you possibly observe this behavior in detail? Using impure diamonds, as it turns out. I’ve discussed nitrogen vacancies in diamond in the past. Essentially, a carbon atom likes to be surrounded by four other carbon atoms. Nitrogen, on the other hand, only likes to have three atoms around it. If nitrogen is substituted for one of the carbon atoms, it cruelly rejects one of its neighbors. The electron proffered by the carbon atom is left stranded between a cold and uninviting nitrogen atom and a carbon atom that would sooner be rid of it. The nature of these surroundings gives the electron a very well-defined energy level structure, creating what is called an NV- center.

What makes the NV- center special is that the excited state has quite a high energy, so you need to use green light to drive the electron into it. Even better, both the excited state and the ground state have a couple of additional energy levels associated with the spin orientation of the electron. The energy difference among these levels is very low. The probability of the ground state electron being in any one of them depends very much on the surrounding magnetic field, which makes it very sensitive to stray electrical currents (which generate a magnetic field).

This provides a convenient way to measure tiny electrical currents: first use an optical light source to drive the NV- center into a specific state. After a short time, probe the NV- center to see if it is still in that state. In that intervening time, the stray current will sometimes cause the NV- center to change state, telling you something about the local environment at that time. After many repeated measurements, you end up with a picture of the currents flowing in the vicinity of the NV- center.

The vast majority of all diamonds contain some nitrogen. In most yellow diamonds the nitrogen atoms have grouped themselves in very specific ways. This happens during and right after the diamond is formed. These nitrogen arrangements absorb light in the blue region of the spectrum producing a yellow color. Yellow diamonds can contain an orange, green or brown modifying color states NCDIA

Watching the current flow

To put this into practice, the researchers created a diamond that had individual NV- centers lying just under the diamond’s surface (5-25nm below the surface). They next coated the top of the diamond with silver to provide a local source of stray currents. They were then able to measure the noise currents (or, more specifically, the magnetic field associated with the noise current) for a range of temperatures. These measurements, though, cannot be understood all by themselves, because they are very local, while the current is also determined by the bulk properties of the silver.

When these measurements were coupled to measurements of the bulk conductivity of the film, it was possible to determine that, as expected, the electrons behaved like they were diffusing through the metal. That is, the electrons were bouncing around in the metal, and a lot of that bouncing was happening at the boundaries between silver crystals.

In a second experiment, the researchers used a silver film that consisted of just a single crystal. For bulk measurements, the diffusion model still fits the observations—the silver atoms are vibrating, creating places for electrons to scatter. But on the scale of the NV- center, the diffusion model fails (at least at low temperature). Instead, a large fraction of the electrons pass over the NV- center without scattering at all.

These sorts of measurements are very useful. Since the NV- center is not in contact with the conductor, it provides a cleaner measurement technique, avoiding problems associated with making electrical connections at very small scales. Understanding noise and current flow at smaller and smaller length scales may also have technological relevance for designing and fabricating semiconductor circuits.

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