Interband-transition

Logothetidis S, Aiouani M, Garriga M and Cardona M 1990 interband transitions in Ai Ga. As aiioys Phys. Rev. 

VEELS spectra are limited in practice to tbe relatively narrow energy range of about 30 eV over wbicb plasmons or interband transitions can occur. In contrast to AES, XPS, or even CEELS, where excitations can occur over hundreds of eV, the probability of spectral overlap is much higher for VEELS. It is fortunate that most... 

Sometimes it is possible to distinguish surface and bulk plasmons by lowering Eq so that the bulk plasmon will decrease in intensity more rapidly than the surface plasmon. However both surface states and interband transitions can show the same behavior. 

H. RAETHERin Exeitations of Plasmons and Interband Transitions by Electrons, Springer-Verlag, Berlin-Heidelberg-New York, 1980. 

Linear absorption measurements can therefore give the first indication of possible alloy formation. Nevertheless, in systems containing transition metals (Pd-Ag, Co-Ni,. ..) such a simple technique is no longer effective as interband transitions completely mask the SPR peak, resulting in a structurless absorption, which hinders any unambiguous identification of the alloy. In such cases, one has to rely on structural techniques like TEM (selected-area electron diffraction, SAED and energy-dispersive X-ray spectroscopy, EDS) or EXAFS (extended X-ray absorption fine structure) to establish alloy formation. 

Although the conductivity of polyacetylene is generally discussed in terms of solitons, the question of the precise nature of the major charge-carriers continues to be a subject of debate, with conflicting evidence from different experiments. Spectro-electrochemical studies provide evidence that the charge in doped polyacetylene is stored in soliton-like species (although this is not the only possible interpretation [142, 143]), with absorptions in the optical spectra corresponding to transitions to states located at mid-gap [24,89, 119]. The intensity of the interband transitions... 

The background dielectric constant e for the metal arises from the polarizability of the ion cores and the contribution of interband transitions.11 For mercury and other simple metals, with a large band gap and relatively unpolarizable ion cores, one expects a background dielectric constant close to unity. With e = 1 and n°° = 8.17 x 1022 cm-3 (mercury), the capacitance per unit area is... 

The most fundamental transition that can take place is the transfer of an electron from the valence band to the conduction band. This creates a mobile electron and a mobile hole, both of which can often be treated as defects. Transitions of this type, and the reverse, when an electron in the conduction band drops to the valence band, eliminating a hole in the process and liberating energy, are called interband transitions. Apart from the electrons and holes themselves, interband transitions do not involve defects. All other transitions do. 

The simple energy-gap scheme of Figure 4.6 seems to indicate that transitions in solids should be broader than in atoms, but still centered on defined energies. However, interband transitions usually display a complicated spectral shape. This is due to the typical band structure of solids, because of the dependence of the band energy E on the wave vector k ( k =2nl a, a being an interatomic distance) of electrons in the crystal. 

This important selection rnle indicates that interband transitions mnst preserve the wave vector. Transitions that preserve the wave vector (snch as those marked by vertical arrows in Figure 4.8(a)) are called direct transitions, and they are easily observed in materials where the top point in the valence band has the same wave vector as the bottom point in the conduction band. These materials are called direct-gap materials. 

Figure 4.8 Interband transitions in solids with band-gap energy Eg-, (a) A direct band gap. Two direct transitions are indicated by arrows, (b) An indirect band gap. Two indirect band-gap transitions are indicated by arrows. The transitions at photon energies lower than Eg require absorption of phonons. The transitions at photon energies higher than Eg involve emission of phonons.

The simple free electron model (the Drude model) developed in Section 4.4 for metals successfully explains some general properties, such as the filter action for UV radiation and their high reflectivity in the visible. However, in spite of the fact that metals are generally good mirrors, we perceive visually that gold has a yellowish color and copper has a reddish aspect, while silver does not present any particular color that is it has a similarly high reflectivity across the whole visible spectrum. In order to account for some of these spectral differences, we have to discuss the nature of interband transitions in metals. 

This behavior results from the appearance of a new interband transition corresponding to formation of intradendrimer Cu clusters. The measured onset of this transitions at 590 nm agrees with the reported value [121], and the nearly exponential shape is characteristic of a band-like electronic structure, strongly suggesting that the reduced Cu does not exist as isolated atoms, but rather as clusters [122]. The presence of metal clusters is also supported by loss of signal in the EPR spectrum [123] following reduction of the dendrimer Cu + composite. 

The approach for preparing dendrimer-encapsulated Pt metal particles is similar to that used for preparation of the Cu composites chemical reduction of an aqueous solution of G4-OH(Pt +)n yields dendrimer-encapsulated Pt nanoparticles (G4-OH(Ptn)). A spectrum of G4-OH(Pt6o) is shown in Fig. 12 a it displays a much higher absorbance than G4-OH(Pt +)6o throughout the wavelength range displayed. This change results from the interband transition of the encapsulated zero-valent Pt metal particles. 

Spectra of G4-OH(Pt)n, n= 12, 40, and 60, obtained between 280 nm and 700 nm and normalized to A = 1 at A = 450 nm, are shown in Fig. 12 b all of these spectra display the interband transition of Pt nanoparticles. Control experiments clearly demonstrate that the Pt clusters are sequestered within the G4-OH dendrimer. For example, BH4 reduction of the previously described G4-NH2(Pt +)n emulsions results in immediate precipitation of large Pt clusters. Importantly, the dendrimer-encapsulated particles do not agglomerate for up to 150 days and they redissolve in solvent after repeated solvation/drying cycles. 

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