The way that charge carriers (electron and holes) move through quantum capacitors made from 2D materials and van der Waals heterostructures can be tuned by applying an electrostatic field to the gate electrode in these devices. Over the last few years, this field effect has been used to make a wide range of metal-oxide-semiconductor (MOS) electronics, including field-effect transistors (FETs) and floating-gate memory devices.

To better understand the field effect and so improve these devices further, a team led by Elton Santos of the Queen’s University, Belfast, and Chih-Jen Shih of ETH Zurich, has developed a new multiscale theoretical model for a metal-oxide-graphene semiconductor quantum capacitor (MOGS) QC. The model combines first-principles electronic structure calculations and the “Poisson-Boltzmann” equation to model how the field effect penetrates though graphene in the (MOGS) QC.

Accumulation of charge at the semiconductor/graphene interface

“By using graphene as a model system, we first develop a macroscopic model to describe how charge distributes in graphene and the semiconductor layers when we apply a gate voltage to the metal electrode in the device,” explains Shih. “We find that, depending on the voltage applied, the space charge density in the semiconductor layers changes in a nonlinear way. This leads to an accumulation of charge (or inversion layer) at the semiconductor/graphene interface.”

The researchers backed up their results using ab initio calculations using density functional theory, including van der Waals interactions, which are important in nanoscale materials.

Ranking 2D compounds' transparency to an electric field

Next, Santos and colleagues formulated an index or parameter that quantifies how transparent a monolayer 2D material is to an electric field. “We found that that the transparency is determined by the combined effect of 2D material quantum capacitance and classical semiconductor capacitance,” says Santos. “By then calculating the quantum capacitance for a variety of 2D materials using accurate ‘hybrid functionals’, we can therefore rank a variety of 2D compounds according to their transparency to an electric field.”

Here is the ranking they calculated: graphene > silicene > germane > tungsten sulphide (WS2) > tungsten telluride (WTe2) > tungsten selenide (WSe2) > molybdenum sulphide (MoS2) > molybdenum selenide (MoSe2) > molybdenum telluride (MoTe2). In these material the main charge carrier is the electron.

Reducing the need for expensive lab work and test trials

“The fact that monolayer 2D materials are transparent to an electrostatic field implies that we can apply the field to a two-terminal device by using a 2D material as one terminal,” Shih and Santos tell “For example, a Schottky diode can become a vertical transistor by using a graphene terminal and placing a gate electrode before it. In the future, we could even enhance the performance of other two-terminal devices, such as solar cells and light-emitting diodes, using applied fields (from a simple electrical battery, for instance).”

The model, developed by the UK-Swiss team, considers an interface formed between a layer of 2D material and a bulk semiconductor. In principle, the approach could readily be extended to a stack of multiple 2D materials or new types of van der Waals heterostructures. “This will allow us to design and predict the behaviour of cutting-edge devices made from these materials, before they are actually fabricated – something that will significantly help in the development of a range of future applications,” say Shih and Santos. “In this way, we will be able to search for the right combinations of different 2D crystals while reducing the need for expensive lab work and test trials.”

The work is detailed in Nano Letters DOI: 10.1021/acs.nanolett.6b01876.