Valence band modelling

Core-State model Valence-band model Experiment ... 

Figure 4-5. Density of states (DOS) for Ce203 calculated within the core-state model (a) and valence-band model (b). (Reproduced with permission from ref.5. Copy right 2000, The American Physical Society)...

Andreev, A. A. (1967). Parameters of the two valence bands model for SnTe from Hall effect measuring at high temperature. Fizika tverdogo tela, VoL 9, No. 5, (May, 1%7), pp. 1560-1561, ISSN 0367-3294. 

The systems discussed in this chapter give some examples using different theoretical models for the interpretation of, primarily, UPS valence band data, both for pristine and doped systems as well as for the initial stages of interface formation between metals and conjugated systems. Among the various methods used in the examples are the following semiempirical Hartree-Fock methods such as the Modified Neglect of Diatomic Overlap (MNDO) [31, 32) and Austin Model 1 (AMI) [33] the non-empirical Valence Effective Hamiltonian (VEH) pseudopotential method [3, 34J and ab initio Hartree-Fock techniques. 

Here, W is a cut-off of the order of the 7t-band width, introduced because the right-hand side of Eq. (3.13) is formally divergent. As in the discrete model, the spectrum of eigenstates of Hct for A(a)= Au has a gap between -Ao and +Alh separating the empty conduction band from the completely filled valence band. 

Valence band spectra provide information about the electronic and chemical structure of the system, since many of the valence electrons participate directly in chemical bonding. One way to evaluate experimental UPS spectra is by using a fingerprint method, i.e., a comparison with known standards. Another important approach is to utilize comparison with the results of appropriate model quantum-chemical calculations 4. The combination with quantum-chcmica) calculations allow for an assignment of the different features in the electronic structure in terms of atomic or molecular orbitals or in terms of band structure. The experimental valence band spectra in some of the examples included in this chapter arc inteqneted with the help of quantum-chemical calculations. A brief outline and some basic considerations on theoretical approaches are outlined in the next section. 

K). T is the measurement temperature and Tq is the "degeneracy temperature," equal to kEo, where k is the Boltzmann constant. According to a two-dimensional electron gas model for graphitic carbons (see ref. 2a), is the energy "shift" from the Fermi level (Ep), to the top of the valence band. Small values of To ( <344 K) and consequently of Eq signify a more perfect graphite... 

In the model presented above the forward dark current corresponds to an electron transfer via the conduction band. Using, however, a redox couple of a relatively positive standard potential the empty states of the redox system occur rather close to the valence band and the cathodic current could be due to an electron transfer via the valence band as illustrated in Fig. 3 b. In this case one still obtains the same i — U characteristic but the saturation current is now given by... 

The electronic conductivity of metal oxides varies from values typical for insulators up to those for semiconductors and metals. Simple classification of solid electronic conductors is possible in terms of the band model, i.e. according to the relative positions of the Fermi level and the conduction/valence bands (see Section 2.4.1). 

In order to understand the observed shift in oxidation potentials and the stabilization mechanism two possible explanations were forwarded by Kotz and Stucki [83], Either a direct electronic interaction of the two oxide components via formation of a common 4-band, involving possible charge transfer, gives rise to an electrode with new homogeneous properties or an indirect interaction between Ru and Ir sites and the electrolyte phase via surface dipoles creates improved surface properties. These two models will certainly be difficult to distinguish. As is demonstrated in Fig. 25, XPS valence band spectroscopy could give some evidence for the formation of a common 4-band in the mixed oxides prepared by reactive sputtering [83],... 

In order to explain the changing optical properties of AIROFs several models were proposed. The UPS investigations of the valence band of the emersed film support band theory models by Gottesfeld [94] and by Mozota and Conway [79, 88]. The assumption of nonstoichiometry and electron hopping in the model proposed by Burke et al. [87] is not necessary. Recent electroreflectance measurements on anodic iridium oxide films performed by Gutierrez et al. [95] showed a shift of optical absorption bands to lower photon energies with increasing anodic electrode potentials, which is probably due to a shift of the Fermi level with respect to the t2g band [67]. 

Fig. 8 a Valence band spectrum of Hf(Sio.5As0.5)As. b DOS curves obtained from LMTO band structure calculations on different ordered models for Hf(Sio.5Aso.5)As [119]. Reprinted with permission from [35], Copyright Elsevier... 

The stable configuration for the H—P pair is predicted by all of the quantum-mechanical calculations to have a hydrogen located at the silicon antibonding site (Si—AB). A model is shown in Fig. 7b, where a phosphorus lone pair lies along the (111) axis and is energetically in the valence band. Here, the theoretical predictions of the H vibrational frequency have been mixed, with the H—Si interaction and frequency overestimated by Hartree-Fock and Hartree-Fock-like methods and lower by local-density calculations. 

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