Mechanisms of Electrical Conductivity in Carbon Nanotubes and Graphene

Mechanisms of Electrical Conductivity in Carbon Nanotubes and Graphene

Rafael Vargas-Bernal (Instituto Tecnológico Superior de Irapuato, Mexico)
DOI: 10.4018/978-1-5225-7359-3.ch008
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There is enormous interest in carbon nanomaterials due to their exceptional physical properties, from the perspective of science and engineering of materials applied to the electronics industry. Significant progress has been made towards understanding the mechanisms of electrical conductivity of carbon nanotubes and graphene. However, scientists around the world continue studying these mechanisms to exploit them fully in different electronic applications with a high technological impact. This chapter discusses the mechanisms of electrical conductivity of both nanomaterials, analyzes the present implications, and projects its importance for future generations of electronic devices. In particular, it is important to note that different mechanisms may be identified when these nanomaterials are used individually, when they are incorporated as fillers in composite materials or hybrid materials, or even when they are doped or functionalized. Finally, other electrical variables with important role in electrical conductivity of these materials are also explored.
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Electrical conduction can be defined as the movement of electrical carriers through a transmission medium. A transmission medium is a material substance that transmits or guides through of itself electromagnetic waves. This movement of carriers generates an electrical current in response to an electrical field. Moreover, in each type of material, different mechanisms of electrical conduction are presented. For example, electrons are electrical carriers in metals, and the Ohm’s law is the mathematical relationship used to determine the mathematical expression between the electrical current (I) and the applied potential difference (V) between a pair of ends of the material (Bird, 2014):

(1) where R and G are electrical resistance and electrical conductance, respectively. Thus, one or more electrons from each atom can move freely within the metal, since they are loosely bound to the atom in the higher level of the valence band. These electrons are incorporated to the conduction band as electrical carriers due to the potential difference, and therefore, an electrical current is generated. An electrical current is a flow of electrical charge carried out regularly by moving electrons through a medium.

Electrical conductivity (σ) also called specific conductance can be defined as the ability of a material for conducting an electrical current. In three-dimensional conductor materials, the electrical conductance can be mathematically expressed as:

(2) where A is the cross-sectional area, L is the length, W is the width, t is the thickness, and, ρ and σ are electrical resistivity and electrical conductivity of the material, respectively. Two different types of electrical conductivities can be found in materials: surface conductivity and bulk conductivity. Surface conductivity or sheet conductance quantifies the electrical conductance of thin films with uniform thickness nominally. This represents the rate between the electrical conductivity of the material, and the thickness of the thin film. Therefore, it is mathematically expressed as:
(3) whose units are square per Ohm or Siemen square or denoted by sq/Ω or □/Ω or S·sq or S·□, which is dimensionally equal to an Siemen. Bulk conductance, specific electrical conductance, or volume conductivity (σ) is expressed in units of Siemens per meter (S/m).

Key Terms in this Chapter

Ballistic Conduction: or Ballistic Transport : The transport of electrons in a medium having negligible electrical resistivity or the highest electrical conductivity.

Electrical Conductivity: The physical property that quantifies how strongly a given material opposes the flow of electrical current. A low resistivity indicates a material that readily allows the movement of electrical charge.

Diffusive Transport: The movement of electrons from a region of high concentration to a region of low concentration where variables such as pressure or temperature are involved.

Electronic Device: Device that accomplishes its purpose controlling the flow of electrons applied to digital electronics, analog electronics, microelectronics, optoelectronics, or integrated circuits.

Carbon Nanomaterials: Nanostructures of carbon such as fullerenes, carbon nanotubes, nanofibers and graphene with unique physicochemical properties with multiple technological applications.

Interconnect: A path of material that connects two elements or components in an integrated circuit, through which electrical current is transported.

Graphene: A two-dimensional, crystalline allotrope of carbon whose atoms are densely packed in a regular sp 2 -bonded atomic-scale chicken wire (hexagonal) pattern composed by a one-atom thick layer of graphite.

Band Gap: An energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors.

Quantum Tunneling or Tunneling: A quantum mechanical phenomenon, where an electron tunnels through a band gap, which it classically could not surmount.

Carbon Nanotubes: Allotropes of carbon with a cylindrical nanostructure of length-to-diameter of up to 132,000,000:1, which have unusual properties and valuable for nanotechnology, electronics, optics and other fields of materials science and technology.

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