Dragoman Daniela. - 2D Nanoelectronics: Physics and Devices of Atomically Thin Materials

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Springer International Publishing AG 2017

Mircea Dragoman and Daniela Dragoman 2D Nanoelectronics NanoScience and Technology 10.1007/978-3-319-48437-2_1

1. 2D Carbon-Based Nanoelectronics

Mircea Dragoman 1

(1)

National Research and Development Institute in Microtechnologies, Bucharest, Romania

(2)

Faculty of Physics, University of Bucharest, Bucharest, Romania

Mircea Dragoman (Corresponding author)

Email:

Daniela Dragoman

Email:

Abstract

This chapter is dealing with the physics and applications of graphene in nanoelectronics, sensors and optoelectronics. Therefore, the physical properties of graphene presented in this chapter, as well as the specific phenomena encountered in this material, are directly linked to the electronic or optoelectronic devices.

1.1 Physical Properties of 2D Carbon-Based Materials

More than 10 years after the discovery of graphene (Novoselov et al. ), which is a single sheet of carbon atoms with a thickness of 0.34 nm arranged into a hexagonal structure, the main physical phenomena in this material seem to be well understood, although some debates are still present even today.

Graphene distinguishes itself by its uncommon physical properties, which are at the origin of unprecedented mechanical or electrical physical parameters that surpass similar characteristics of any other materials, including semiconductors. Why? The answer to this question is the subject of this section.

Graphene is formed from carbon atoms in the sp 2 hybridization state, each atom being covalently bonded to three others. Thus, graphene crystallizes in a honeycomb lattice consisting of two interpenetrated triangular sublattices, which can be visualised in Fig. are identical, the labels A and B being introduced only for visualisation purposes and for understanding the sublattices interplay.

Fig. 1.1

Atomic honeycomb structure of graphene and its interpenetrated triangular sublattices

Graphene is at the origin of other carbon-based materials. For instance, graphite is formed from many graphene monolayers stacked as a pile, while carbon buckyballs are produced when graphene is wrapped as a sphere. On the other hand, when rolled-up, graphene forms the carbon nanotube, which is a key material for nanoelectronic devices working from few hundred of megahertz up to X rays.

Figure .

Fig. 1.2

The conduction in graphene via hybridization of p z atomic orbitals

Because each of the two interpenetrating triangular sublattices of the honeycomb lattice contributes to the wavefunction of charge carriers in graphene, the wavefunction is in this case a spinor rather than a scalar, as in common semiconductor materials.

The tight-binding approximation, considering only interactions between nearest neighbors, gives an energy dispersion relation of the form (Castro-Neto et al. ):

(1.1)

where a = 0.142 nm represents the distance between two C atoms and t = 2.75 eV is the nearest-neighbor hopping energy. A rigorous deduction of ( it follows that graphene monolayer is a zero-bandgap semiconductor.

Fig. 1.3

Dispersion relation in graphene ( left ), and its contour plot ( right )

Near the Dirac points, i.e. at low energy values, the dispersion relation is:

(1.2)

where is the Fermi velocity and , with the wavevector of charge carriers relative to Dirac points. This linear dispersion relation is the hallmark of graphene monolayer and implies that the effective mass of charge carriers vanishes near Dirac points, unlike in common semiconductors. Another difference from common semiconductors is that the transport properties in graphene are the same for electron or hole states, since the dispersion relation is completely symmetric around the Dirac point.

In the approximation, the Dirac equation for the graphene monolayer is written as (Wu et al. ):

(1.3a)

(1.3b)

where with

(1.4)

and and represent the spinorial wavefunctions around the K and K points, respectively.

The eigenvalues and eigenvectors are obtained from () (considering the potential energy as

(1.5)

and

(1.6a)

respectively, where

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