Principles of Raman Scattering in Carbon Nanotubes

Principles of Raman Scattering in Carbon Nanotubes

K. A. Shah (Govt. Degree College for Women, Anantnag, India) and M. A. Shah (Department of Physics, National Institute of Technology, Srinagar, India)
DOI: 10.4018/978-1-4666-5824-0.ch006
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Carbon nanotubes have attracted the scientific community throughout the world, and in the past decade, a lot of work has been reported related with synthesis, characterization, and applications of carbon nanotubes. This chapter is written for readers who are not familiar with the basic principles of Raman spectroscopy in carbon nanotubes. The structure of carbon nanotubes, types of the carbon nanotubes, Brillouin zone of carbon nanotubes, and band structure of carbon nanotubes are discussed at length, which will serve as foundation for the study of Raman scattering in carbon nanotubes. The Density of States (DOS) of single walled carbon nanotubes are illustrated by an example which will encourage readers to calculate the DOS of any type of carbon nanotube. The Raman modes of vibration are discussed, and Raman spectroscopic analysis is presented by considering the typical spectra of single-walled carbon nanotubes.
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Structure Of Carbon Nanotube (Cnt)

Carbon nanotubes are tubular carbon molecules provided with very particular properties. Their structure is similar to fullerenes, but while fullerene’s molecules form a spherical shape, nanotubes are cylindrical structures with the ends covered by half of a fullerene molecule. Nanotube diameter is of the order of few nanometers, while their length is of the order of several millimeters. The physical properties make them potentially useful in nanometer scale electronic and mechanical applications. They show unusual strength, unique electrical properties and extremely high thermal conductivity. The chemical bonding between carbon atoms inside nanotubes is always of sp2 type. Nanotubes align themselves into ropes held together by the van der walls force and can merge together under high pressure. Nanotubes can be excellent conductors as well as semiconductors, depending on their structure. The thermal conductivity of carbon nanotubes is also high in the axial direction. The particular properties of carbon naotubes make them of great interest for potential use in biotechnology, since they can be opened and filled with other molecules. The structure, electrical conductance and transport properties of carbon nanotubes has been discussed at length by Saito, Dresselhaus, and Dresselhaus (1998).

The structure of carbon naotubes has been explored by high resolution TEM and STM, yielding direct confirmation that the nanotubes are cylinders derived from honeycomb lattice (graphene sheet). As stated earlier the structure of a SWNT can be conceptualized by wrapping a one-atom-thick layer of graphite called graphene into a seamless cylinder. The way the graphene sheet is wrapped is represented by a pair of indices (n, m) called the chiral vector (Ch) as shown in Figure 1. The intersection of the vector OB (which is normal to Ch) with the first lattice point determines the fundamental one dimensional (1D) translation vector T. The unit cell of the one dimensional lattice is the rectangle defined by the vectors Ch and T (Figure 1). The cylinder connecting the two hemispherical caps ofthe carbon nanotube (see Figure 1) is formed by superimposing the two ends of the vector Ch and the cylinder joint is made along the two lines OB and AB’ in Figure 1. The vectors OB and AB` are both perpendicular to the vector Ch at each end of Ch .

Key Terms in this Chapter

Density of States: The Density of States (DOS) of a system can be defined as the number of states per interval of energy at each energy level that are available to be occupied by electrons. For a system a high DOS at a specific energy level means that there are many states available for occupation and zero DOS means that no state can be occupied at that energy level.

Carbon Nanotubes: Carbon nanotube can be thought as a rolled sheet of graphene in the form of cylinder with diameter of the order of a nanometre varying from 0.5 to 3nm. The carbon nanotubes can be metallic or semiconducting depending upon the value of two integers n and m. They have unique electrical, mechanical, thermal, optical and magnetic properties.

Brillouin Zone: The Brillouin zone is defined as the set of points in k-space that can be reached from the origin without crossing any Bragg plane. Equivalently it can be defined as the Wigner-Seitz Cell of the reciprocal lattice. In case of single walled carbon nanotubes the first Brillouin zone is given by irreducible set of equidistant lines whose length and spacing are dependent on the values of two integers n and m.

Raman Spectroscopy: Raman scattering is the inelastic scattering of light that provides the chemical and structural information of a liquid or crystal. A Raman spectrum is a plot of the intensity of Raman scattered radiation as a function of its frequency difference from the incident radiation. This difference in frequency is called Raman shift. Raman spectroscopy is widely used for studying carbon nanotube - length and diameter, whether nanotubes are single- walled or multi-walled, isolated or bundle, conduction type of semiconducting or metallic and even chirality.

Band Structure: Band structure describes the ranges of energy that an electron within a solid may have or ranges of energy that it may not have. It provides electronic levels in crystal structure which are characterized by a Bloch vector k and a band index n. The band theory can be used to explain many electrical, optical, magnetic, and physical properties of crystals.

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