Graphene in High-Frequency Electronics
This two-dimensional form of carbon has properties not seen in any other substance
A transistor made with graphene looks very much like a conventional FET, in that it has a region covered by an insulator under a gate electrode that controls the flow of electrons or holes from source to drain. However, the physical properties of graphene are very different from other semiconductors, and the mechanism of current control is altered, so the electrical properties of a graphene FET diverge quite a lot from conventional FETs.
The most important of these different properties is that graphene does not have a bandgap, an energy range in most nonmetals where electron states cannot exist. In other words, for graphene, as its electrons travel in orbitals around their carbon atoms, there is no energy difference between the conduction band (where electrons are free to move around and form bonds) and the valence band (where electrons are tightly bound to their atoms). Because of this property, some call graphene a gapless semiconductor and some call it a semi-metal. In semiconductor FETs, the bandgap allows the channel to be turned on or off—preventing or allowing a flow of electricity—by applying a voltage to the gate. Without a bandgap, graphene always conducts, but the amount of conduction is controlled by the number of charge carriers in the material. Thus, the current can be modulated, but it cannot be completely stopped. In silicon FETs, the ratio of the on current to the off current might be 1:104 or 1:105, but the ratio for graphene FETs may be smaller than 1:10. Also, in silicon FETs, a state called pinch-off occurs when part of the channel is effectively off, leading to a high resistance to current. High output resistance is required for transistors to amplify the input signal at the gate, which is needed for almost all practical circuits. But the absence of a bandgap in graphene means there is no pinch-off in its channel region, so achieving high output resistance is difficult.
Because silicon FETs can be turned off, they can be used for digital computers for which there are only two states allowed: on or off, current flowing or current blocked. In standard silicon-manufacturing technology, most of the transistors are off most of the time. With millions of transistors in an integrated circuit, this means the current flow is controllable. If the off-state of such transistors only resulted in a small reduction of current, then the circuits would require enormous amounts of power to keep them going, and we would never have home computers or portable electronic devices, because they would heat up and deplete their batteries very quickly. However, analog and radio frequency circuits, which modulate the amplitude of signals rather than turn them on or off digitally, are essentially always conducting. Silicon FETs can be used for digital or analog circuits, but graphene FETs are better suited—at the moment—just for analog circuits.
There are some other interesting differences between graphene and semiconductors. Because it is a purely two-dimensional material, it has no body, no bulk. All current flows on its surface. As a result, anything contacting graphene might affect its current flow by scattering it off the atoms of the contacting material. Additionally, in semiconductors the level of gate voltage required to turn the transistor on has been controlled by adding small amounts of other materials, in a process called doping. But doping in graphene is only possible through surface contact, which again is hard to control during manufacturing.
Finally, current sometimes flows equally well in both directions through a graphene FET. In silicon and other semiconductors with a bandgap, current is predominantly via either electrons or holes, as determined by the fabrication of the transistor. But graphene allows almost equal conduction of electrons and holes, so it is an ambipolar device. (However, when the graphene is made from silicon carbide, it becomes unipolar.) So far, this property is regarded as a nuisance, but there might be some unique applications resulting from this quirk. There have been demonstrations of frequency multipliers and dual-mode amplifiers (both used with communications signals) that make use of this peculiar property.
The result of these different behaviors can be seen in traditional direct-current (DC) electrical characteristics of the graphene FETs. The transfer characteristic relates the output current through the drain to the input voltage on the gate, from which transconductance is derived. Qualitatively this measurement shows how “strong” the device is: A stronger device delivers more current for a given input voltage than a weaker device. The output characteristic relates the drain current to the drain voltage, from which the output resistance is computed. Both transconductance and output resistance of any transistor need to be known to design analog circuits.
Yet in spite of the very different physics and resulting DC electrical behavior, it has been shown that graphene FETs behave very much like their semiconductor counterparts when they are operated at high frequency, under alternating-current (AC) conditions. This comparison is made by measuring each system’s frequency response, its output signal strength when it is given a particular input signal.
The primary means of estimating frequency response is through the cutoff frequency. A universally used metric for describing the frequency response of FETs, cutoff frequency is a fundamental property indicating how quickly a signal can travel from the gate to the drain of the device, and all new device technologies are measured against both existing ones and projections of expected cutoff frequencies in the future.
This metric is derived from other measurements that describe the frequency dependence of the small-signal AC current gain of a transistor when the output is short-circuited. An AC voltage is applied to the gate at various frequencies, resulting in an AC input current. The measured output current (also AC) is divided by the input current, as a function of frequency. In the case of FETs, this only makes sense for AC measurements, as no DC current can flow through the insulating gate. If a FET is well behaved, this current gain should decrease as the inverse of the frequency. The point at which it falls to a value of 1 is the cutoff frequency.
Some of our earliest work with graphene FETs, which were actually made from tiny flakes of the material, showed the right AC behavior. The current gain drops with frequency, so “cutoff frequency” is a meaningful term. Additionally, cutoff frequency was shown to be proportional to the transconductance divided by gate capacitance, and cutoff frequency increased as the channel length was reduced. These three traits showed that in high-frequency operation, graphene FETs act a lot like semiconductor FETs, which nurtured the idea that graphene transistors could potentially be used in similar circuits. In a few short years, we have seen cutoff frequency increase from a few gigahertz to over 300 gigahertz, almost catching up with the most sophisticated semiconductor devices.
Frequency response depends inversely on the length of the gate, and proportionally to the transconductance, which is loosely proportional to mobility. Thus, to make faster devices, we can either reduce the gate length or use higher mobility materials. The work with graphene has consistently shown the advantage of its mobility. Compared to silicon FETs, graphene FETs have always had higher cutoff frequencies at the same gate length.