14 and space group P4 2 /mnm. The unit cell consists of two metal atoms and four oxygen atoms. Each metal atom is situated amidst six oxygen atoms which approximately form the corners of a regular octahedron. Oxygen atoms are surrounded by three tin atoms which approximate the corners of an equilateral triangle. The lattice parameters are a5b 54.737 A, and c53.186 A. The ionic radii for O 22 and Sn 41 are 1.40 and 0.71 A, respectively. 1 The 6 unit cell atoms give a total of 18 branches for the vibrational modes in the first Brillouin zone. The mechanical representation of the normal vibration modes at the center of the Brillouin zone is given by 2,3 G5G 1 ~ A1g!1G 2 ~ A2g!1G 3 ~ B1g!1G 4 ~ B2g! 1G 5 ~ Eg!12G 1 ~ A2u!12G 4 ~ B1u!14G 5 ~ Eu!, ~1! using the Koster notation with the commonly used symmetry designations listed in parenthesis. The latter will be used throughout this article. Of these 18 modes, 2 are active in infrared ~the single A2u and the triply degenerate Eu), 4 are Raman active ~three nondegenerated modes, A1g , B1g , B2g , and a doubly degenerate Eg), and two are silent ( A2g , and B1u). One A2u and two Eu modes are acoustic. In the Raman active modes oxygen atoms vibrate while Sn atoms are at rest ~see Fig. 1 in Ref. 4!. The nondegenerate mode, A1g , B1g , and B2g , vibrate in the plane perpendicular to the c axis while the doubly degenerated E g mode vibrates in the direction of the c axis. The B 1g mode consists of rotation of the oxygen atoms around the c axis, with all six oxygen atoms of the octahedra participating in the vibration. In the A2g infrared active mode, Sn and oxygen atoms vibrate in the c axis direction, and in the Eu mode both Sn and O atoms vibrate in the plane perpendicular to the c axis. The silent modes correspond to vibrations of the Sn and O atoms in the direction of the c axis (B1u) or in the plane perpendicular to this direction ( A2g). According to the literature, the corresponding calculated or observed frequencies of the optical modes are presented in Table I. When the size of the SnO2 crystal is reduced, the infrared spectrum is modified because the interaction between electromagnetic radiation and the particles depends on the crystal’s size, shape, and state of aggregation. 8‐1 0 Experiments using Raman spectroscopy have also reported spectrum modification, at least partially. Low frequency bands have been observed previously in SnO2, 11 and several authors have reported the existence of bands not observed in single-crystal or polycrystalline SnO 2 which have been found to be closely related to grain size. 12‐15 However, some of these reports do not adequately explain the origin of the abnormal spectrum. The aim of this article is to present a complete Raman spectrum of SnO2 nanoparticles. The analysis comprises ~i! modification of the normal vibration modes active in Raman when the spectra are obtained from nanocrystals of SnO2 ~‘‘classical modes’’ !, ~ii! the disorder activated surface modes in the region around 475‐775 cm 21 , and ~iii! the appearance of the acoustic modes in the low-frequency region of the spectra.

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The complete Raman spectrum of nanometric SnO2 particles

Raman spectroscopy is widely used to study the vibrational and structural properties of single crystals. More recently, in the fields of chemistry, physics, and engineering, interest in the properties of small objects has arisen. Small objects include microcrystalline materials, artificially layered semiconductor structures, and colloidal suspensions. The reason for this recent interest is that these objects often display unique electronic properties which may find applications in devices. Since Raman spectroscopy is a convenient nondestructive tool, it is not surprising that it has been used to characterize such objects. In this review, we consider almost exclusively results obtained with semiconductors.

Raman spectroscopy of low-dimensional semiconductors

The interband absorption spectra of a system with Gaussian site diagonal disorder are calculated in the coherent potential approximation. The electron-hole vertex part due to interband stochastic correlation is taken into account. The relaxation of the k -selection rule and the effect of localization are studied through the calculation of the optical transition matrix elements. It is clarified that the band tail states contribute to an exponential absorption tail (the so-called Urbach tail) as a result of interplay between transfer energy and Gaussian-distributed site energies. Introduction of a negative interband correlation leads to a red shift of the absorption edge. This effect is discussed in connection with the photo-structural change observed in chalcogenide glasses.

Interband Absorption Spectra of Disordered Semiconductors in the Coherent Potential Approximation

Low-dimensional nanostructures of SnO{sub 2} thin films with the interesting features of the tetragonal rutile structure have been prepared by pulsed laser deposition. The microstructural evolution of nanocrystalline SnO{sub 2} thin films has been investigated using x-ray diffraction, transmission electron microscopy, high-resolution transmission electron microscopy, and Raman spectroscopy. Experimental results indicate that the as-prepared SnO{sub 2} thin films appear to be of polycrystalline state, have a large amount of defects, such as oxygen vacancies, vacancy clusters, and local lattice disorder at the interface and surface, and the appearance of a new Raman peak. It suggests that this new Raman peak is closely related to a surface layer of nonstoichiometic SnO{sub x} with different symmetries than SnO{sub 2}, or in other words, the new peak marks an additional characteristic of space symmetry of the grain agglomeration of nanocrystalline SnO{sub 2}. The study of the microstructural evolution of nanocrystalline SnO{sub 2} is significant for the understanding of the whole structure feature of nanomaterials and for the fabrication of new nanomaterials with favorable properties.

Insights into microstructural evolution from nanocrystalline Sn O 2 thin films prepared by pulsed laser deposition

A microscopic theory is presented to explain how the melting point in metallic small particles is dependent on size. The systems are described by an effective pair interaction of the Gaussian type, constructed to give the basic thermodynamic properties in the bulk metal at low temperatures. The thermodynamic melting temperature, at which the difference between the total Helmholtz free energy of a solid particle and that of a liquid particle of the same mass vanishes, is used as a criterion of the actual melting point in small particles. The variational principle based on the Gibbs-Bogoliubov inequality is used to calculate the Helmholtz free energies of both phases. Applications to the FCC metals Al, Pb and Ag are made and the calculated size dependences of the melting points are similar for all these metals. The result for Pb is in reasonable agreement with experimental data.

A theory of melting in metallic small particles

Self-Consistent Einstein Model and Theory of Anharmonic Surface Vibration. II Face-Centered Cubic Lattice

On the basis of a simple method by which quantitative disorder as well as topological disorder in amorphous solids can be treated systematically, we study the electronic density of states of tetrahedrally-bonded amorphous semiconductors such as amorphous silicon or germanium. We adopt the Weaire-Thorpe model and apply the coherent potential approximation to the random variations of the banding parameter V 1 and the bonding parameter V 2 of this model. It is possible to explain the disappearance of the dip between the two lower peaks of the valence band by introducing fluctuations in V 1 alone. This fact indicates that it is not always necessary to assume the existence of five-membered rings as a cause for the disappearance of the dip. We also discuss the effects of fluctuations in V 2 , missing atoms and broken bonds.

A Theoretical Approach to the Electronic Structure of Tetrahedrally-Bonded Amorphous Solids

Coherent potential approximation (CPA) is applied to evaluate the total density of states (DOS) and local density of states (LDS) for hydrogenated amorphous silicon (a-Si: H). Three configurations SiH, SiHHSi and SiHSi are considered for the silicon-hydrogen bonding states. Instead of calculating the electronic states of a-Si: H, the effect of hydrogenation is renormalized into an effective Si * –Si * bond so that the problem may be reduced to that of a-Si * with random effective bonds. The calculated Si * -LDS and DOS for three configurations are compared with other theory and experiments.

Toshio Hama

Papers

Self-Consistent Einstein Model and Theory of Anharmonic Surface Vibration. II Face-Centered Cubic Lattice

A Theoretical Approach to the Electronic Structure of Tetrahedrally-Bonded Amorphous Solids

A Simple Model of Hydrogenation in Tetrahedrally Bonded Disordered Semiconductors