Electrons interband transitions

Finally, in Sect. E the optical and magnetic properties are considered. It is found experimentally that some Zintl phases are colored and in ternary systems the color changes continuously as a function of the composition. This change can be correlated to a shift in a maximum of the imaginary part 2 of the dielectric constant e, and 2 can be interpreted by electronic interband transitions ) The magnetic susceptibility and Knight shift are discussed on the basis of spin polarized band structure calculations . Spin and orbital contributions are also considered. 

The results for Pb [145], however, caused debates [107]. This electrode is not the best candidate for probing the plasma free electron properties. Single electron interband transitions for Pb Ue in the low frequency part ( 2 eV) of the spectrum. On the other hand, the data on potential dependent elec-troreflectance [144] were reported at one relatively low frequency (1.96 eV) where an interference between single electron and... 

Mee Mgg is difference in dipole moments of the excited and ground states, Mge is the transition matrix between these states, and A e is the HOMO-LUMO gap (electronic interband transition energy). 

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. 

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. 

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 different pumping methods, such as the commonly used current injection or optical pumping electron beam pumping and avalanche breakdown have been studied in detail (for further refs, see and information has been obtained regarding the excitation probabilities of the different interband transitions. The very short laser pulses (less than 10 sec) obtained enable rapid processes and their time dependence to be studied. 

This behavior differs completely from the discrete one-electron absorptions of low-nuclearity metal cluster molecules [17]. Instead, it resembles the 5d - 6s,6p interband transition of colloidal gold. This demonstrates clearly that the AU55 cluster has electronic energy levels which are closely spaced in a developing band structure, quite similar to colloidal gold. On the other hand, these electrons do not seem to show a collective behavior which would give rise to the plasma resonance. 

The second and perhaps most probable explanation is damping and broadening of the resonance, due to size dependent, single electron 5d- 6p,6s interband transitions. Their explanation is that the discrete level structure of the Au 55 cluster acts as an effective decay channel. In reducing the plasmon lifetime, it would also strongly increase the bandwidth of the resonance, washing out the resonance peak. 

Intrinsic luminescence where an electron is excited from the valence band to the conduction band, so-called interband transition. Recombination of this electron with a hole in the valence band generates a photon, the energy of which corresponds to the energy difference of the band gap (Fig. 2.6a) ... 

These equations are identical with the high-frequency limit (9.13) of the Lorentz model this indicates that at high frequencies all nonconductors behave like metals. The interband transitions that give rise to structure in optical properties at lower frequencies become mere perturbations on the free-electron type of behavior of the electrons under the action of an electromagnetic field of sufficiently high frequency. 

The alkali metals, with only one free electron per atom, have lower plasmon energies than those of divalent free-electron metals such as Mg and A1 because the plasma frequency decreases with decreasing electron density. Thus, surface plasmon energies for alkali metals are in or near the visible, whereas they are in the far ultraviolet for Mg, Al, and Pb. Surface plasmon energies of the divalent metals Ag, Au, and Cu are shifted toward and into the visible because of interband transitions (see Fig. 12.9d) this is also the cause of the large values of c" for Au and Cu. 

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