What’s A Mott FET?

The unique physics of two-dimensional semiconductors offers the potential for new kinds of switches that could extend the usefulness of conventional MOSFETs into a variety of new areas.

A MOSFET applies a voltage to one side of the gate capacitor. The resulting electric field in the channel shifts the band structure and facilitates or impedes the flow of carriers. So as devices shrink, the gate capacitance shrinks, as well.

The problem is that fast switching speeds require short channels and high carrier densities. That makes it more difficult to create a sharp ON/OFF transition, leading to high OFF-state leakage currents. Two-dimensional semiconductors are interesting for MOSFETs in part because they offer reduced interface scattering and improved channel mobility.

The limitations of the MOSFET structure are well-known and have helped motivate the last several decades of device research. Gate-all-around transistors, for example, seek to improve control of the channel by applying an electric field from all sides. Tunnel FETs (TFETs), meanwhile, depend on tunneling through an energy barrier.

Several new device concepts depend on new switching mechanisms. For instance, the flow of carriers can be changed via the polarization of a ferroelectric material or a structural phase change. One of the more intriguing variations on this theme is based on the Mott transition from a metallic to an insulating state.

Electrons in a good conductor are de-localized, detached from their atomic cores and free to drift under the influence of an applied electric field. In the absence of an external field, their movement depends on the balance between kinetic energy and Coulombic attraction and repulsion between each other and the atomic lattice.

Temperature plays an important role here. At lower temperatures, electrons have less kinetic energy, and other forces become correspondingly more important. Reducing physical degrees of freedom, for instance, by confining the carriers in a one-dimensional or two-dimensional material, or in a structure like a quantum well, further constrains the ability of electrons to respond to Coulombic forces.

What is a Mott insulator?
If the kinetic energy is low enough, or if scattering within the lattice is strong enough, the carriers may be unable to overcome the repulsion between electrons. Unable to move, they become localized, trapped in the lower part of the conduction band. (Or, more precisely, they are trapped in the lower of two Hubbard bands into which the conduction band has split.) This is a Mott insulator, and the transition between the metallic and insulating states is a Mott transition.

Correlated electron states such as the Mott transition arise in theoretical discussions of the behavior of carriers at zero Kelvin. Practical applications of such structure are obviously limited, but Mott insulator behavior has been seen in a variety of materials — notably transition metal oxides — at ambient and higher temperatures.

When the transition from insulator to metal occurs, carriers trapped in the lower part of the conduction band are again free to move throughout the material, giving as much as 4:1 increase in carrier concentration. In addition to temperature, the transition can be triggered by an increase in carrier density, such as an electrolytic layer or a charge applied to a capacitor. These structures are collectively described as MottFETs.

Band engineering with graphene
So what does all this have to do with graphene? As Guorui Chen, a post-doctoral researcher at UC Berkeley, explained, the assembly of van der Waals heterostructures from freestanding two-dimensional layers allows separate optimization of each layer in a stack. Interlayer and electrostatic coupling then can be used to manipulate the electrical properties of the component layers.

Chen’s group stacked trilayer graphene between monolayers of hexagonal boron nitride, forming dual-gate devices with a gold electrode on top and a silicon substrate on the bottom. Because of the different lattice spacings of graphene and hBN, these structures formed a superlattice with periodicity, depending on the twist angle

Sweeping the top gate voltage produced two prominent resistance peaks, which the authors attributed to the half-filled electron states characteristic of Mott insulators. Varying both the top and the bottom gate voltage allowed independent control of the electrical field strength and the charge concentration. This approach to superlattice engineering should be applicable to many two-dimensional materials, including transition metal dichalcogenides like MoS₂.

At this time, such structures lie in the realm of experimental physics, not practical devices. But the history of the semiconductor industry is a story of repeated redefinitions of “practical” and “impractical” approaches. The transistor itself began as a surface science experiment, and the industry now makes billions of “impossible” devices every day.

As device engineers peer into their crystal balls, Mott FETs offer one possible solution to the challenges of extreme scaling.

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