Raman spectroscopy of carbon nanotubes
Introduction
Carbon nanotubes have proven to be a unique system for the study of Raman spectra in one-dimensional systems, and at the same time Raman spectroscopy has provided an exceedingly powerful tool for the characterization of single-wall carbon nanotubes. The unique optical and spectroscopic properties observed in single-wall carbon nanotubes (SWNTs) are largely due to the one-dimensional (1D) confinement of electronic and phonon states, resulting in the so-called van Hove singularities (vHSs) in the nanotube density of states (DOS) [1], [2]. These singularities in the DOS, and correspondingly in the electronic joint density of states (JDOS), are of great relevance for a variety of optical phenomena. Whenever the energy of incident photons matches a vHS in the JDOS of the valence and conduction bands (subject to selection rules for optical transitions), one expects to find resonant enhancement of the corresponding photophysical process. Owing to the diverging character of vHSs in these 1D systems, such an enhancement can be extremely confined in energy (meV), appearing almost like transitions in a molecular system. In combination with the unique 1D electronic structure, the resonantly enhanced Raman scattering intensity allows one to obtain detailed information about the vibrational properties of nanotubes, even at the isolated individual SWNT level [3].
The contents of this review are as follows. Section 2 provides the background for discussing the Raman effect in carbon nanotubes, summarizing the nanotube geometrical structure, as well as the electronic and vibrational (phonon) structure. Section 3 presents the different aspects of the Raman scattering processes, such as first- and second-order scattering, resonant and non-resonant scattering, Stokes or anti-Stokes scattering, intravalley or intervalley scattering, other elementary excitations and the parameters for Raman measurements. Section 4 discusses resonance Raman intensity calculations, including the formulation of the Raman intensity, selection rules for the Raman scattering, electron–photon matrix elements and electron–phonon matrix elements. Section 5 presents a brief description of sample preparation and the experimental set up. Sections 6 and 7 summarize Raman scattering experimental results, respectively for first- and for second-order Raman features. In Section 6 the radial breathing modes (RBMs), the assignment that defines the uniqueness of each SWNT, and the G-band (tangential modes) are discussed. In Section 7, the D-band (disorder-induced feature) and the -band (D-band overtone) are given, as well as other double resonance features and the effects on the Raman spectra of interactions of SWNTs with their surroundings. Finally in Section 8 we mention MWNTs, and Section 9 presents concluding remarks, summarizing past achievements in the field and pointing to promising directions for future developments.
Section snippets
Structure and notation
This section provides a brief introduction to the unusual structural properties of single-wall carbon nanotubes, that emphasizes their unique 1D attributes and sets them apart from other materials systems. A SWNT can be described as a single layer of a graphite crystal that is rolled up into a seamless cylinder, one atom thick, usually with a small number (perhaps 10–40) of carbon atoms along the circumference and a long length (microns) along the cylinder axis [4]. Each SWNT is specified by
Classification of Raman scattering processes
In the Raman spectra of graphite and SWNTs, there are many features that can be identified with specific phonon modes and with specific Raman scattering processes that contribute to each feature. The Raman spectra of graphite and SWNTs can provide us with much information about the exceptional 1D properties of carbon materials, such as their phonon structure and their electronic structure, as well as information about sample imperfections (defects). Since mechanical properties, elastic
Resonance Raman intensity calculations
In this section, we discuss how to calculate the resonance Raman intensity. As discussed in Section 3, all Raman scattering events are a combination of two electron–photon interactions (absorption and emission) and either one or more electron–phonon interactions (phonon scattering), depending on whether the feature is associated with a one-phonon or a multi-phonon Raman process, respectively. In the case of a second-order one-phonon process, we must explicitly consider the electron-defect
Raman spectroscopy experiments for carbon nanotubes
In this section we present an overview of Raman spectroscopy experiments for carbon nanotubes. In general, contributions to the Raman signal from resonance Raman processes are very much larger than contributions from non-resonance processes. This is especially the case for SWNTs, where the resonance condition for a vHS energy position of a given nanotube is satisfied only within a small region of laser energy excitation, such as . Thus, when we observe an isolated nanotube
The radial breathing mode
The radial breathing mode (RBM) can be used to study the nanotube diameter () through its frequency (), to probe the electronic structure through its intensity () and to perform an assignment of a single isolated SWNT from analysis of both and , as discussed below.
Overview of double resonance spectral features
Although generally of weaker intensity than the first-order Raman features presented in Section 6, the second-order Raman spectra (either two-phonon or defect-induced) provide a large amount of important information about carbon nanotube electronic and vibrational properties that cannot be obtained by probing the first-order features. This is the central focus of the present section. Such an abundance of new information becomes accessible because the selection rules for the second-order
Multi-wall carbon nanotubes—MWNTs
Because of the large diameter of the outer tubes for typical multi-wall carbon nanotubes (MWNTs) and because MWNTs contain an ensemble of carbon nanotubes with diameters ranging from small to very large, most of the characteristic differences that distinguish the Raman spectra in SWNTs from the spectra for graphite are not so evident in MWNTs. For example, the RBM Raman feature associated with a small diameter inner tube (less than 2 nm) can sometimes be observed when a good resonance condition
Summary and future directions
In this article we review the resonance Raman spectroscopy (RRS) of SWNTs and show how to use RRS to characterize SWNT samples using the many features observed in the rich RRS spectra. In particular, we show how the electronic and phonon properties of SWNTs can be investigated by using the strict resonance9 conditions for many
Acknowledgements
A.J acknowledges financial support by PRPq-UFMG, and the Instituto de Nanociências (Millennium Institute Program), CNPq, Brazil. R.S. acknowledges a Grant-in-Aid (No. 13440091) from the Ministry of Education, Japan. G.D and M.S.D. acknowledge support under NSF Grants DMR 04-05538, and INT 00-00408.
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