Resonating valence band model

The essential parameters of the model are Ufi/W and the occupied width of the f band, /J.+ W. The latter can be estimated directly from the off-resonance valence band photoemission spectra, which have been measured by Lang et al. (1981). This yields a rough estimate of the energy separation of the two peaks to be 2 to 3 eV... 

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

The corresponding quantum mechanical expression of s op in Equation (4.19) is similar except for the quantity Nj, which is replaced by Nfj. However, the physical meaning of some terms are quite different coj represents the frequency corresponding to a transition between two electronic states of the atom separated by an energy Ticoj, and fj is a dimensionless quantity (called the oscillator strength and formally defined in the next chapter, in Section 5.3) related to the quantum probability for this transition, satisfying Jfj fj = l- At this point, it is important to mention that the multiple resonant frequencies coj could be related to multiple valence band to conduction band singularities (transitions), or to transitions due to optical centers. This model does not differentiate between these possible processes it only relates the multiple resonances to different resonance frequencies. 

It is worthwhile to mention the ample use of screening final states models in understanding core levels as well as valence band spectra of the oxides. The two-hole models, for instance, which have been described here, are certainly of relevance. Interpretational difference exists, for instance, on the attribution of the 10 eV valence band peak (encountered in other actinide dioxides as well), whether due to the non-screened 5f final state, or to a 2p-type characteristics of the ligand, or simply to surface stoichiometry effects. Although resonance experiments seem to exclude the first interpretation, it remains a question as to what extent a resonance behaviour other than expected within an atomic picture is exhibited by a 5 f contribution in the valence band region, and to what extent a possible d contribution may modify it. In fact, it has been shown that, for less localized states (as, e.g., the 3d states in transition metals) the resonant enhancement of the response is less pronounced than expected. 

The resonance Raman spectrum of rans-[ (bpy)2Ru(CN) 2(/ -CN)]2+ under near-resonance conditions with the MMCT band showed enhancement of the bridging cyanide stretching as expected for this type of electronic transition (109). Analysis of the IR spectrum supports the valence-localized model in contrast to a previous study (110). 

For bulk semiconductors at room temperature, the mechanism for the resonant nonlinearity can be described by the band-filling model [82,87]. This is shown schematically in Figure 16b for a direct gap semiconductor such as CdS. Absorption of photons across the band gap, g, generates electrons and holes which fill up the conduction and valence band, respectively, due to the Pauli exclusion principle. If one takes a snap shot of the absorption spectrum before the electrons and holes can relax, one finds that the effective band gap, , increases (Figure 166), since transitions to the filled states are forbidden. The bleaching efficiency per photon absorbed can be derived as... 

NEXAFS provides the first clear experimental evidence of the difference in the formation of the Al/DP-PPV, Ca/DP-PPV and Au/DP-PPV interfaces. We report that A1 does not induce the formation of new unoccupied states in DP-PPV, whereas Ca and Au cause the creation of new intra-gap states as well as a higher lying resonance in DP-PPV. Valence band photoelectron spectroscopy of model... 

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