The Raman effect in crystals
TL;DR: A review of progress in the theoretical and experimental study of the Raman effect in crystals during the past ten years is given in this article, where the theory of those properties of long-wavelength lattice vibrations in both cubic and uniaxial crystals which can be studied by Raman scattering.
Abstract: A review is given of progress in the theoretical and experimental study of the Raman effect in crystals during the past ten years. Attention is given to the theory of those properties of long-wavelength lattice vibrations in both cubic and uniaxial crystals which can be studied by Raman scattering. In particular the phenomena observed in the Raman scattering from crystals which lack a centre of inversion are related to the theory. The angular variations of the scattering by any type of lattice vibration in a crystal having any symmetry can be easily calculated using a complete tabulation of the Raman tensor. Recent measurements of first-order lattice vibration spectra are listed. A discussion of Brillouin scattering is included. The relation of second-order Raman spectra to critical points in the lattice vibration density of states is discussed, and measurements of the second-order spectra of diamond and the alkali halides are reviewed. The theory and experimental results for Raman scattering by electroni...
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TL;DR: In this paper, the Raman spectra of anatase have been observed in both natural and synthetic crystals and the six Raman active fundamentals predicted by group theory are all observed and assigned.
Abstract: Raman spectra of anatase have been observed in natural and synthetic crystals. Both crystals show the same spectral features. The Raman band occurring at 516 cm−1 at room temperature is split into two peaks centred at 519 cm−1 and 513 cm−1 at low temperature (73 K). The six Raman active fundamentals predicted by group theory are all observed and assigned. The spectra are analyzed by a simple model considering only short-range forces and the calculated vibrational frequencies are in good agreement with the observed Raman frequencies.
1,922 citations
TL;DR: In this article, the second-order Raman spectrum of pyrolytic graphite has been studied and the dependence of the first-order graphite Raman spectra on crystallite size has been shown.
Abstract: First- and second-order Raman scattering from graphite has been studied. The second-order spectra of single crystals and of highly oriented pyrolytic graphite are continuous and exhibit several well-defined bands which can be attributed to features in the density of vibrational states as determined from current lattice-dynamics models. The density of states deduced from the lattice-dynamics model of Nicklow, Wakabayashi, and Smith provides the best replication of the second-order Raman spectrum, but is nevertheless somewhat deficient in this regard, and in need of improvement. The dependence of the first- and second-order graphite Raman spectra on crystallite size has also been studied for a series of samples with typical dimensions ${L}_{c}$ and ${L}_{a}$ as small as 30 \AA{}. With decreasing crystal size the features in the second-order spectrum broaden noticeably and additional broad features appear in both the first- and second-order spectra. The additional first- and second-order features are also attributed to structure in the vibrational density of states and arise from the wave-vector selection-rule relaxation that results from finite-crystal-size effects. Evidence is presented to demonstrate that the above described spectral features are intrinsic and not associated with impurity excitations.
1,907 citations
TL;DR: The essential Raman scattering processes of the entire first- and second-order modes in intrinsic graphene are described and the extensive capabilities of Raman spectroscopy for the investigation of the fundamental properties of graphene under external perturbations are described.
Abstract: Graphene-based materials exhibit remarkable electronic, optical, and mechanical properties, which has resulted in both high scientific interest and huge potential for a variety of applications. Furthermore, the family of graphene-based materials is growing because of developments in preparation methods. Raman spectroscopy is a versatile tool to identify and characterize the chemical and physical properties of these materials, both at the laboratory and mass-production scale. This technique is so important that most of the papers published concerning these materials contain at least one Raman spectrum. Thus, here, we systematically review the developments in Raman spectroscopy of graphene-based materials from both fundamental research and practical (i.e., device applications) perspectives. We describe the essential Raman scattering processes of the entire first- and second-order modes in intrinsic graphene. Furthermore, the shear, layer-breathing, G and 2D modes of multilayer graphene with different stacking orders are discussed. Techniques to determine the number of graphene layers, to probe resonance Raman spectra of monolayer and multilayer graphenes and to obtain Raman images of graphene-based materials are also presented. The extensive capabilities of Raman spectroscopy for the investigation of the fundamental properties of graphene under external perturbations are described, which have also been extended to other graphene-based materials, such as graphene quantum dots, carbon dots, graphene oxide, nanoribbons, chemical vapor deposition-grown and SiC epitaxially grown graphene flakes, composites, and graphene-based van der Waals heterostructures. These fundamental properties have been used to probe the states, effects, and mechanisms of graphene materials present in the related heterostructures and devices. We hope that this review will be beneficial in all the aspects of graphene investigations, from basic research to material synthesis and device applications.
1,184 citations
TL;DR: In this article, a series of tables are presented to facilitate rapid determination of the selection rules for vibrational transitions for nuclear site group analysis, where the number of infrared and Raman active modes of each symmetry may be obtained without detailed analysis of the symmetry elements in the crystallographic unit cell or the construction of tables.
Abstract: The group theoretical methods by which the symmetries of normal modes in crystals may be determined are outlined, and a series of tables are presented to facilitate rapid determination of the selection rules for vibrational transitions. Emphasis is placed on the method of nuclear site group analysis in which the number of infrared and Raman active modes of each symmetry may be obtained without detailed analysis of the symmetry elements in the crystallographic unit cell or the construction of tables. By using the tables presented here for most cases identification of the crystallographic space group is sufficient information to allow determination of the vibrational mode selection rules by inspection. Several examples are included in which crystals are analyzed by each of the methods.
1,064 citations
TL;DR: In this article, the theoretical background of Raman spectroscopy, with special attention to its sensitivity for mechanical stress, is discussed, and practical information is given for the application of this technique to stress measurements in silicon integrated circuits.
Abstract: Local mechanical stress is currently an important topic of concern in microelectronics processing. A technique that has become increasingly popular for local mechanical stress measurements is micro-Raman spectroscopy. In this paper, the theoretical background of Raman spectroscopy, with special attention to its sensitivity for mechanical stress, is discussed, and practical information is given for the application of this technique to stress measurements in silicon integrated circuits. An overview is given of some important applications of the technique, illustrated with examples from the literature: the first studies of the influence of external stress on the Si Raman modes are reviewed; the application of this technique to measure stress in silicon-on-insulator films is discussed; results of measurements of local stress in isolation structures and trenches are reviewed; and the use of micro-Raman spectroscopy to obtain more information on stress in metals, by measuring the stress in the surrounding Si substrate is explained.
923 citations
References
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Book•
01 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
8,520 citations
Book•
01 Jan 1954
TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.
Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.
7,756 citations
TL;DR: In this article, the interaction of light with non-conducting crystals has been studied in the context of crystal lattices and its applications in general theory and applications, such as semi-conductivity and superconductivity.
Abstract: 1. Crystal lattices. General theory 2. . Crystal lattices. Applications 3. Interaction of light with non-conducting crystals 4. Electrons in a perfect lattice 5. Cohesive forces in metals 6. Transport phenomena 7. Magnetic properties of metals 8. Ferromagnetism 9. Interaction of light with electrons in solids 10. Semi-conductors and luminescence 11. Superconductivity
3,538 citations
2,831 citations