From the outside, transistors seem so simple and straightforward. But inside, they’re actually a mess. If you could watch them working at the level of atoms, you’d see the electronic equivalent of a game of bumper cars. Electrons moving through even the best transistor channel can’t go in straight lines. Instead they’re buffeted continually by a host of imperfections and vibrations, which together put a strict limit on speed and generate a lot of heat in the process.
The good news is that it doesn’t have to be that way. By a quirk of quantum mechanics, electrons moving through atom-thick sheets of carbon—known as graphene—don’t suffer much at all from these sorts of collisions. Instead, they behave like massless particles, speeding along in straight lines for long distances just like photons do. And just like light, these electrons can be made to bend or bounce back when they move from one medium to another.
What can you do with this light-mimicking behavior? Well, here’s what we’d like to do: Replace the logic circuitry at the heart of every computer processor. Everyone today agrees that the days of the ever-shrinking CMOS transistor are numbered; the only disagreement is about what that number is. After 50 years of steady miniaturization, chipmakers have just about shrunk the device to its limits. The future gets hazy beyond 2020, but we know that to continue making faster, cheaper, and more energy efficient chips, we’ll need a new technology.
In the United States, the hunt for novel computing devices that can start replacing CMOS transistors in the coming decade has crystallized into a massive effort called the Nanoelectronics Research Initiative, which includes many of the world’s biggest chipmakers, state and federal agencies, and dozens of universities. Light-like graphene logic is just one of a half dozen or so possible successors to CMOS, but we think its combination of features makes it the heir apparent.
For one thing, graphene logic will be extraordinarily fast. Instead of manipulating information by turning the flow of current on and off through a transistor channel, graphene logic could perform calculations by bending, reflecting, focusing, and defocusing electrons moving at 1/300th the speed of light—about 10 times as fast as electrons in conventional silicon CMOS devices. Logic devices built from graphene will consume less power and take up far less real estate than CMOS or optical switches. And unlike any other technology being considered, graphene devices have the potential to simplify and speed up chips by creating truly reconfigurable logic. Such logic would be able to change its type on the fly: In response to electronic signals, an AND gate, for example, could be transformed into an OR gate and then back again. We have already shown that the fundamental physics of these graphene switches works just as theorists expected, and we are now on the verge of creating the very first reconfigurable devices.
As you might imagine, no ordinary semiconductor can be used to shuttle electrons around like beams of light. In the silicon CMOS transistors that make up today’s chips, electrons can barely move a few nanometers before they bounce off an impurity or are buffeted by acoustic waves generated by the crystal. Other semiconductor materials aren’t much better.
Photos: Ji Ung Lee, et al.
Gate Test: Laboratory experiments have shown that graphene’s resistance to the flow of current varies, depending on how it is angled when placed atop a pair of gates. The results suggest that the fraction of electrons that pass through the gate interface changes with the angle, just like light.
Click on the image to enlarge.
But graphene is different. First isolated in 2004, the material consists of a single sheet of carbon atoms arranged in a honeycomb-like lattice of hexagons. Roll it up and you’ve got a carbon nanotube. Stack it and you can make graphite. Material scientists still disagree about what they should call the stuff: Some say it’s a “zero bandgap semiconductor,” others simply refer to it as a semimetal. However you identify it, graphene is quite different from any other material we’re used to working with.
Graphene’s symmetrical, two-dimensional crystalline structure is responsible for most of its unique qualities. Electrons surrounding each carbon atom can take on only a limited set of energies; each electron occupies a level that corresponds to an allowed quantum state. Like all materials with a periodic arrangement of atoms, these allowed electrical states overlap in space and meld to form a new spectrum of allowed states—a band structure. In an ordinary semiconductor, electrons that are stuck to atoms are confined to the valence band, and those that are free to move around the lattice occupy the conduction band. But in graphene, these two bands actually touch, and they take on a highly unusual property.
If you calculate the energy of any free electron in graphene, you’ll find that, just as with the photon, its energy is directly proportional to its momentum. (A photon doesn’t have mass, but it has a momentum that arises from its wavelike, quantum-mechanical nature.) Because they are effectively massless, electrons in graphene always move at the maximum velocity possible, regardless of how energetic they are.
As a result, once they’ve been set in motion, electrons in graphene require no energy to keep going. What’s more, quantum mechanics prohibits one of the most basic outcomes of a collision—that of recoil. An electron in graphene isn’t allowed to completely reverse its direction of motion. This prohibition allows it to move virtually unimpeded through a graphene sheet and tunnel effortlessly through such barriers as p–n junctions.
While an electron or hole moving in silicon typically gets deflected after moving a few atom lengths at most, in graphene these charge carriers can travel in straight lines across tens of thousands of atoms at 10 times the speed they can in silicon. At room temperature, graphene’s electrical conductivity beats that of silver, the least resistive metal.
One of the first things you might think to do with this material is to use it to make fast transistors. And indeed, researchers have done just that. With the support of the United States’ Defense Advanced Research Projects Agency, colleagues of ours at IBM have shown that graphene can be used to build speedy radio frequency switches on silicon wafers. Since the work began in 2008, graphene transistors have been built that can amplify signals over a wide range, up to frequencies of 280 gigahertz. Researchers expect to be able to create switches capable of handling 500-GHz signals by 2013.
These transistors are great for radio frequency circuits such as RF amplifiers or mixers. But the technology isn’t well suited for making logic devices. For one thing, graphene isn’t really a semiconductor. Because graphene in its natural state has no bandgap, a vanishingly small amount of energy is needed to knock an electron free of its valence band. So graphene switches are always in some conductive state. Current can be made to move back and forth, but it can’t easily be turned on and off, meaning there’s no easy way to represent bits.
Engineers have some tricks that can be used to create an artificial bandgap. They can, for example, pattern graphene into very thin ribbons or apply an electric field across two layers of graphene stacked one on top of the other. But while these sorts of approaches do create a bandgap, they have the side effect of reducing electron speed. In nanoribbons, for example, electrons have a tendency to get scattered by the edges of the ribbon. And neither technique is far enough along to create speedy transistors with high enough on-off ratios and low enough leakage current to compete with present-day chips.
If we toss out the idea of making transistors, we can take advantage of graphene’s best properties and, if we’re fortunate, end up with a new technology that can keep the world on a Moore’s Law–like progression toward cheaper, lower power and better-performing processors.
Given the fact that we’re contemplating treating electrons just like light, you might ask why we don’t simply build logic from photonic systems. Optical devices like lasers have long been an attractive way to make speedy computing circuitry. Instead of transistors, the systems use a combination of amplifiers, modulators, emitters, detectors, and waveguides to manipulate photons and perform computations.
But optoelectronic circuits themselves aren’t a practical option for next-generation logic. The components can’t get any smaller than the wavelength of light they’re manipulating, which for optical circuits means feature sizes on the order of one micrometer, dozens of times the size of today’s CMOS devices. The light sources needed also draw a lot of power, making them impractical for microprocessor chips.
Graphene offers a good compromise—electrons in a graphene switch will move much faster than they can in ordinary transistors, and at the same time, the devices themselves will take up much less space and consume far less energy than a photonic system.
As with a CMOS transistor, the basic unit for manipulating electrons in reconfigurable graphene logic is a simple straight p–n junction. These can be created by making a four-layer stack. At the very bottom, embedded into the substrate, two patches—or gates—made of conductive material are built. An insulating layer of oxide is placed on top, and then a rectangle of graphene is placed on top of that. Electrodes placed on top of the graphene, at either end of the rectangle, are used to supply a reference current to the device.
By applying a positive voltage on one gate, you can pull electrons from the nearest electrode into the graphene, creating an n-doped material. Applying a negative voltage to the other gate will draw holes from the other electrode into the graphene, creating a p-doped material. The resulting p–n junction isn’t like the kind you’ll find in a normal diode or transistor; it won’t rectify current by allowing it to go in only one direction. Charge carriers pass freely across the barrier. But the junction does have the unique property of being angle dependent. The chance that an electron will get transmitted or reflected at the junction depends on its angle of approach.
In 2007, theorist Vadim Cheianov of Lancaster University, in the United Kingdom, and two colleagues suggested this angle-dependent behavior could have an important application in electronics. The group showed that if electrons are injected from a single point on one side of a perfectly straight graphene p–n junction, the particles spread out, refract when they hit the junction, and then refocus to a point on the other side.
It may not sound too profound, but this sort of behavior isn’t really seen in the natural world—you can’t focus light with a flat lens. But graphene bends a stream of electrons differently than the way most materials bend light: It has the electronic equivalent of what’s referred to in optics as a negative index of refraction. An electron traveling through an n-doped region of graphene effectively takes on negative energy when it moves into a p-doped region, and conservation of momentum demands that it be bent in this counterintuitive way. So far, the only way to manipulate electromagnetic radiation in this fashion is to use artificial materials, which are often constructed by manipulating metal wires. It turns out that graphene is a natural electronic analogue to these metamaterials.
Beyond focusing and defocusing electrons, graphene’s refractive properties can also cause the total internal reflection of electrons. The material can be set up to accomplish this trick by taking advantage of the same angle dependence in a graphene p–n junction. For example, if the gates beneath a sheet of graphene are properly spaced, electrons sent toward a junction at a shallow angle—say, 45 degrees or less—won’t be able to pass through the boundary; they will all be reflected. To let the electrons pass through the junction unimpeded, you simply reverse the voltage on one of the gates, creating a uniform n–n or a p–p device.
Inspired by these remarkable capabilities, a number of Nanoelectronics Research Initiative researchers, including teams at our two institutions—IBM and the University at Albany, State University of New York—have been investigating how this refractive behavior can be used to manipulate electron flow and make logic switches.
At the start, most of our research was theoretical. We realized that to make proper logic, we had to come up with designs that could actually perform logic operations, and we had to get a better understanding of how competitive they might be against state-of-the-art CMOS.
One of the first designs we explored was the simple binary switch. You could build such a switch with just a square of graphene. If you draw an imaginary diagonal across the square, you create two triangles of graphene. Under each of these triangles you place a triangular wedge of conducting material—such as copper or heavily doped silicon—that can be either positively or negatively charged. These buried wedges act as gates, altering the electronic properties of the graphene above them. If both wedges have the same charge, the switch is on, and an electron coming from one side of the graphene square can move in a straight line from one side of the square to the other. But if opposite biases are applied, the two graphene regions will become oppositely doped, and nearly all the electrons will be reflected at the interface. Now the switch is off.
This simple device can be arranged in series to create a range of logic functions, including NOT, OR, and AND. According to our simulations, these devices should pass 1000 to 100 000 times as much current when they’re on as when they’re off, on par with CMOS and about 1000 times as good as graphene transistors. Because electrons move faster through the graphene, our calculations also suggest that logic made in this way could be 57 percent faster than CMOS, when power and area are held constant.
Raw speed is one thing, but these sorts of devices could also do things that traditional transistors can’t do. With three buried gates and three electrodes for input and output, we reckon graphene switches can be made to perform a range of fairly complex logic functions by creating multiplexer devices. A multiplexer is usually used in communications applications to combine multiple inputs to make a single output signal. But the device’s ability to handle multiple data streams also makes it a powerful way to make programmable logic.
In this case, the three buried gates and two electrodes on either side of the rectangular multiplexer device can all act as inputs. An electrode at the center of the device delivers the output. Electrons coming from electrodes on either end of the device may reach the electrode at the center, but only if the three gates beneath the device have the right voltages to allow the electrons through. This basic device can be reconfigured to support as many as eight different logic functions—everything from the simple inversion of a signal to more sophisticated constructions such as NOT (A and NOT B). By changing the voltage of the gates, the multiplexer can be made to switch between these functions in an instant.
That’s a big departure from the way today’s chips work. In CMOS circuits, a p-type transistor can’t be converted to an n-type transistor or vice versa. As a result, you need more transistors to perform some of the more sophisticated logic operations. It takes at least eight transistors, for example, to perform an XOR function, an operation that could easily be accomplished with a single graphene multiplexer. That means less area on the chip and less power consumed. Considered another way, reconfigurable graphene logic can perform nearly three times as many calculations per second as a CMOS circuit, given the same amount of area and power.
That wouldn’t be too impressive if reconfigurable graphene logic remained in the realm of theory. But research into these devices has already begun to make its way from simulation to the laboratory.
In our preliminary studies of simple p–n junctions fabricated in the lab, we’ve shown that oppositely doped regions of graphene can be used to bend the paths of electrons. Varying the angle of a p–n junction with respect to an incoming beam of electrons can significantly alter the resistance of the device. This is an early proof of principle that we can create devices that can divert electrons.
We might also be able to create the electronic equivalent of an optical fiber. Early last year, a team at Harvard reported they had created a channel for electrons by applying different voltages to gates that were placed parallel to a graphene sheet. In their system, the electrons hit the sides of the graphene channel at glancing angles and experienced significant internal reflection.
The work suggests we could use graphene not only to make switches but also to guide electrons from one logic device to the next. These steering devices would be built the same way that logic devices are in a graphene sheet; the only difference between them would be the way voltages are applied to gates beneath the graphene sheet.
For now the biggest hurdle to bringing these new sorts of integrated circuits into production is the purity of the material. Electrons in today’s graphene can move up to a micrometer before getting scattered by imperfections, such as corrugations in the surface of the material or grain boundaries between adjacent crystal patches. But electrons will likely need to be able to travel for 100 micrometers or even millimeters in graphene in order for it to be a viable logic material.
Fortunately, graphene fabrication has only been getting better since the material was first isolated. One of the first techniques used to make graphene was to push graphite across the surface of a silicon wafer, a process that could produce only imperfect, microscopic flakes. Now we have more precise methods that can produce fairly pure graphene on a large scale.
We can heat silicon carbide wafers, for example, to evaporate the silicon on the surface, leaving behind a layer of graphene. We can make even purer graphene sheets by growing the material using chemical vapor deposition and then using a layer of polymer to transfer the graphene to a wafer. This technique has met with great success. In December, a team at IBM used it to create the first graphene-based RF devices and amplifier circuits built on a 200-millimeter wafer, the biggest graphene layer with fully functional circuits that’s been shown so far.
We have very good reason to anticipate that graphene quality will only continue to improve. With luck, we might see graphene-based reconfigurable logic prototypes within the next five years. For building logic capable of replacing CMOS circuits, it won’t be a moment too soon.
About the Authors
Chun-Yung Sung supervises graphene and other research at IBM’s T.J. Watson Research Center, in Yorktown Heights, N.Y. Ji Ung Lee is a professor of nanoscale engineering at the University at Albany, State University of New York. Both have been astounded by how far graphene has come since it was first isolated in 2004. “With any luck, this material will take logic beyond silicon, well into the nanoscale,” says Sung.
