Raman Spectroscopy in Graphene Related Systems E-Book

Ado Jorio

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 717

Veröffentlichungsjahr: 2011

Beschreibung

Raman spectroscopy is the inelastic scattering of light by matter. Being highly sensitive to the physical and chemical properties of materials, as well as to environmental effects that change these properties, Raman spectroscopy is now evolving into one of the most important tools for nanoscience and nanotechnology. In contrast to usual microscopyrelated techniques, the advantages of using light for nanoscience relate to both experimental and fundamental aspects.

Leseprobe

Contents

Preface

Part One Materials Science and Raman Spectroscopy Background

1 The sp2 Nanocarbons: Prototypes for Nanoscience and Nanotechnology

1.1 Definition of sp2 Nanocarbon Systems

1.2 Short Survey from Discovery to Applications

1.3 Why sp2 Nanocarbons Are Prototypes for Nanoscience and Nanotechnology

1.4 Raman Spectroscopy Applied to sp2 Nanocarbons

2 Electrons in sp2 Nanocarbons

2.1 Basic Concepts: from the Electronic Levels in Atoms and Molecules to Solids

2.2 Electrons in Graphene: the Mother of sp2 Nanocarbons

2.3 Electrons in Single-Wall Carbon Nanotubes

2.4 Beyond the Simple Tight-Binding Approximation and Zone-Folding Procedure

3 Vibrations in sp2 Nanocarbons

3.1 Basic Concepts: from the Vibrational Levels in Molecules to Solids

3.2 Phonons in Graphene

3.3 Phonons in Nanoribbons

3.4 Phonons in Single-Wall Carbon Nanotubes

3.5 Beyond the Force Constant Model and Zone-Folding Procedure

4 Raman Spectroscopy: from Graphite to sp2 Nanocarbons

4.1 Light Absorption

4.2 Other Photophysical Phenomena

4.3 Raman Scattering Effect

4.4 General Overview of the sp2 Carbon Raman Spectra

5 Quantum Description of Raman Scattering

5.1 The Fermi Golden Rule

5.2 The Quantum Description of Raman Spectroscopy

5.3 Feynman Diagrams for Light Scattering

5.4 Interaction Hamiltonians

5.5 Absolute Raman Intensity and the Elaser Dependence

6 Symmetry Aspects and Selection Rules: Group Theory

6.1 The Basic Concepts of Group Theory

6.2 First-Order Raman Scattering Selection Rules

6.3 Symmetry Aspects of Graphene Systems

6.4 Symmetry Aspects of Carbon Nanotubes

Part Two Detailed Analysis of Raman Spectroscopy in Graphene Related Systems

7 The G-band and Time-Independent Perturbations

7.1 G-band in Graphene: Double Degeneracy and Strain

7.2 The G-band in Nanotubes: Curvature Effects on the Totally Symmetric Phonons

7.3 The Six G-band Phonons: Confinement Effect

7.4 Application of Strain to Nanotubes

7.5 Summary

8 The G-band and the Time-Dependent Perturbations

8.1 Adiabatic and Nonadiabatic Approximations

8.2 Use of Perturbation Theory for the Phonon Frequency Shift

8.3 Experimental Evidence of the Kohn Anomaly on the G-band of Graphene

8.4 Effect of the Kohn Anomaly on the G-band of M-SWNTs vs. S-SWNTs

8.5 Summary

9 Resonance Raman Scattering: Experimental Observations of the Radial Breathing Mode

9.1 The Diameter and Chiral Angle Dependence of the RBM Frequency

9.2 Intensity and the Resonance Raman Effect: Isolated SWNTs

9.3 Intensity and the Resonance Raman Effect: SWNT Bundles

9.4 Summary

10 Theory of Excitons in Carbon Nanotubes

10.1 The Extended Tight-Binding Method: σ–π Hybridization

10.2 Overview on the Excitonic Effect

10.3 Exciton Symmetry

10.4 Exciton Calculations for Carbon Nanotubes

10.5 Exciton Size Effect: the Importance of Dielectric Screening

10.6 Summary

11 Tight-Binding Method for Calculating Raman Spectra

11.1 General Considerations for Calculating Raman Spectra

11.2 The (n, m) Dependence of the RBM Intensity: Experiment

11.3 Simple Tight-Binding Calculation for the Electronic Structure

11.4 Extended Tight-Binding Calculation for Electronic Structures

11.5 Tight-Binding Calculation for Phonons

11.6 Calculation of the Electron–Photon Matrix Element

11.7 Calculation of the Electron–Phonon Interaction

11.8 Extension to Exciton States

11.9 Matrix Elements for the Resonance Raman Process

11.10 Calculating the Resonance Window Width

11.11 Summary

12 Dispersive G’-band and Higher-Order Processes: the Double Resonance Process

12.1 General Aspects of Higher-Order Raman Processes

12.2 The Double Resonance Process in Graphene

12.3 Generalizing the Double Resonance Process to Other Raman Modes

12.4 The Double Resonance Process in Carbon Nanotubes

12.5 Summary

13 Disorder Effects in the Raman Spectra of sp2 Carbons

13.1 Quantum Modeling of the Elastic Scattering Event

13.2 The Frequency of the Defect-Induced Peaks: the Double Resonance Process

13.3 Quantifying Disorder in Graphene and Nanographite from Raman Intensity Analysis

13.4 Defect-Induced Selection Rules: Dependence on Edge Atomic Structure

13.5 Specificities of Disorder in the Raman Spectra of Carbon Nanotubes

13.6 Local Effects Revealed by Near-Field Measurements

13.7 Summary

14 Summary of Raman Spectroscopy on sp2 Nanocarbons

14.1 Mode Assignments, Electron, and Phonon Dispersions

14.2 The G-band

14.3 The Radial Breathing Mode (RBM)

14.4 G’-band

14.5 D-band

14.6 Perspectives

References

Index

The Authors

Ado Joriois a Professor in the Physics Dept. of the Federal University of Minas Gerais, Brazil, where he also earned his PhD, in 1999. His Post-doctoral research was done at MIT, USA, where his collaboration with the Dresselhaus group and with Professor Saito started. He has authored and co-authored several book chapters and books on carbon science and has been active in science policy in Latin America.Mildred Dresselhausreceived her Ph.D. at the University of Chicago in 1958 and started research on carbon science in 1960 with Gene Dresselhaus while working at the MIT Lincoln Laboratory. She has been an MIT professor since 1967, and started working with Riichiro Saito in 1991 and with Ado Jorio since 2000.Riichiro Saitoreceived PhD degree from the University of Tokyo in 1985. After being a Research Associate at the University of Tokyo in 1985 and an Associate Professor at the University of Electro-Communication in Tokyo in 1990, he became Professor at Tohoku University in Sendai since 2003.Gene F. Dresselhausreceived his PhD degree from the University on California, Berkeley under the supervision of Charles Kittel. He has actively worked on a variety of problems in condensed matter physics. He has taught courses in condensed matter physics at the University of Chicago and at Cornell University. He currently holds a Research appointment at MIT and jointly leads a research group at the MIT Center for Materials Science and Engineering which studies graphite intercalation compounds, fullerenes, graphene, and carbon nanotubes. He has Co-authored or Co-edited six books on Carbon Science.

The Authors

Prof. Ado JorioDepartamento de FísicaUniversidade Federal de Minas GeraisAv. Antonio Carlos, 6627, CP 70230.123-970 Belo Horizonte, MGBrazil

Prof. Riichiro SaitoTohoku UniversityDept. of Physics6-3 Aoba, Aramaki, Aoba-kuSendai 980-8578Japan

Prof. Mildred S. DresselhausDr. Gene DresselhausMITRoom 13-300577 Massachusetts Ave.Cambridge, MA 02139-4307USA

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A. J. and R. S. dedicate this book to the 80th birthday of Professor Gene Dresselhaus (born Nov. 7, 1929) and Professor Mildred S. Dresselhaus (born Nov. 11, 1930).

Preface

Raman spectroscopy is the inelastic scattering of light by matter. Being highly sensitive to the physical and chemical properties of materials, as well as to environmental effects that change these properties, Raman spectroscopy is now evolving into one of the most important tools for nanoscience and nanotechnology. In contrast to usual microscopy-related techniques, the advantages of using light for nanoscience relate both to experimental and fundamental aspects. Experimentally, the techniques are widely available, relatively simple to perform, possible to carry out at room temperature and under ambient pressure, and require relatively simple or no special sample preparation. Fundamentally, optical techniques (normally using infrared and visible wavelengths) are nondestructive and noninvasive because they use the photon, a massless and chargeless particle, as a probe.

For understanding Raman spectroscopy, a combination of experiments and theory is important because some concepts of basic solid state physics are needed for explaining the behavior of the Raman spectra as a function of many experimental parameters, such as light polarization, the energy of the photon, temperature, pressure and changes in the environment. In this book, starting from some known example of physics and chemistry, we will explain how to use the basic concepts of molecular and solid state physics, together with optics to understand Raman scattering. Graphene, nanographite and carbon nanotubes (sp2 carbons) are selected as the materials to be studied, due to their importance to nanoscience and nanotechnology, and because the Raman technique has been extremely successful in advancing our knowledge about these nanomaterials. It is possible to observe Raman scattering from one single sheet of sp2-hybridized carbon atoms, the two-dimensional (2D) graphene sheet, as well as from a narrow strip of a graphene sheet rolled-up into a 1 nm diameter cylinder to form the one-dimensional (1D) single-wall carbon nanotube. These observations are possible simply by shining light on the nanostructure focused through a commonly available microscope. This book therefore focuses on the basic concepts of both Raman spectroscopy and sp2 carbon nanomaterials, together with their interaction. The similarities and differences in the Raman spectra for different sp2carbon nanomaterials, such as graphene and carbon nanotubes, provide a deep understanding of the Raman scattering capabilities that are emphasized in this book.

There is a general feeling that Raman spectroscopy is too complicated for a nonspecialist. Often, common users of Raman spectroscopy as a characterization tool for their samples only touch the surface of the capabilities of the Raman technique. This book is aimed to be sufficiently pedagogic and also detailed to help the general nanoscience and nanotechnology user of Raman spectroscopy to better utilize their instrumentation to yield more detailed information about their nanostructures than before. Our challenge was writing a book that would build from the most basic concept, the Schrödinger equation for the hydrogen atom, going up to the highest level use and application of Raman spectroscopy to study nanocarbons in general.

The book was initially structured for use in a course for graduate students in the Federal University of Minas Gerais (UFMG), Brazil, and it is organized in two parts. The first part gives the basic concepts of Raman spectroscopy and nanocarbons, addressing why we choose nanocarbons as prototype materials for writing this Raman book. The text is suitable for physicists, chemists, material scientists, and engineers, building a link between their languages, a link that is necessary for the future development of nanoscience. The second part gives a detailed treatment of the Raman spectroscopy of nanocarbons, addressing both fundamental material science and the use of Raman spectroscopy towards material applications. Again nanostructured sp2-hybridized carbon materials are model systems, both due to the common interest that physicists, chemists, material scientists, and engineers have in these systems and because these systems are pertinent to the length scales where these fields converge. By giving more details, the second part gives examples of the large amount of physics one can learn from studying nanocarbons.

Even though the Raman effect was first observed in the early 1920s, we believe this book is the starting point for lots of new scientific perspectives that the “nano” generation is making possible. We hope the reader will be interested in Raman spectroscopy and will accept the challenges that many researchers are now trying to solve in applying this technique to study nanostructures. Problem sets are included at the end of each chapter, designed to provide a better understanding of the concepts presented in this book and to reinforce the learning process. We appreciate if the readers are willing to solve our problems and send the solutions to the authors to post on the web. The answers by the readers and students using this book can be posted on the following web page: http://flex.phys.tohoku.ac.jp/book10/index.xhtml.

Finally, we strongly acknowledge all students and collaborators who have contributed to the development of this book.

Ado Jorio, Belo Horizonte, MG, BrazilRiichiro Saito, Sendai,JapanGene Dresselhaus and Mildred S. Dresselhaus,Cambridge, MA, USA

September, 2010

Part One Materials Science and Raman Spectroscopy Background

2

Electrons in sp2 Nanocarbons

Usually Raman spectra only involve phonons explicitly, being independent of the laser energy used to excite the Raman spectra and the electronic transitions in the material (to the extent that the electron–phonon interaction is weak). Furthermore, the usual Raman scattering signal is weak. However, the scattering efficiency gets much larger and the Raman signal much stronger when the laser energy matches the energy between optically allowed electronic transitions in the material. This intensity enhancement process is called resonance Raman scattering (RRS) [91]. Under the RRS regime, the resonance Raman intensity is further enhanced by the large density of electronic states (DOS) available for the optical transitions. This large density of states is especially important for one-dimensional systems, which have singularities in their density of states at the energy onset of an allowed optical transitions.

This chapter has the goal of reviewing the important concepts needed for understanding the Raman spectroscopy of sp2 nanocarbons, making a link between molecular and solid state science. Due to the peculiar π-electron structure (delocalized pz orbitals, as discussed in Sections 1.3 and 2.2.2), the Raman spectroscopic response in sp2 nanocarbons depends strongly on their electronic structure due to the ubiquitous resonance processes that dominate their inelastic scattering of light. For this reason, it is important to review the electronic properties of these systems.

We start by reviewing the basic concepts relevant to the electronic energy levels of isolated molecules and what happens when these molecules are assembled in the solid state. In Section 2.1 we present the one-electron system for the hydrogen atom and then move to more and more complex systems, discussing the formation of molecular orbitals and finally building the transition to solid state systems in Section 2.1.5, and to nanocarbon systems in particular (Sections 2.2 and 2.3). Here both the molecular orbital theory (bonding and antibonding states) and the valence bonding theory (hybridization) are introduced and, while the discussion of the intermixing may not be fully rigorous, it is useful for gaining an understanding of carbon systems. In Section 2.2.1 we present the crystal structure of graphene, which is followed by the tight-binding model for the -band electronic structure for monolayer graphene in Section 2.2.2. The -bands extend over an energy range that goes from the Fermi point up to the ultra-violet, and the -bands are thus responsible for all transport and optical phenomena. In Section 2.2.3 the -bands are reviewed to yield the electronic structure for graphene which contains both and -bands. In flat graphene the -bands are not important for optical phenomena. However, when curvature is present, like in the case of carbon nanotubes, - hybridization can occur, with consequences on the optical response. The remaining sections of this chapter extend the picture to few-layer graphene and then to many-layer graphene in Section 2.2.4 and to quantum confinement phenomena occurring in nanoribbons (Section 2.2.5). The effect of quantum confinement on the electronic structure of nanotubes is next discussed in Section 2.3. The structure of carbon nanotubes is introduced in Section 2.3.1 followed by a discussion of the zone-folding procedure (Section 2.3.2) and the density of electronic states (Section 2.3.3), which is important to understand Raman spectroscopy in these materials, as discussed in Section 2.3.4. This chapter ends with a short discussion in Section 2.4 of the physics beyond the simple tight-binding and zone-folding approximations. This final section comes here just as a brief introduction to concepts that will be developed in later chapters.