4-band model

Fournier R and Salahub D R 1990 Chemisorption and magnetization A bond order-rigid band model Surf. Sol. 238 330-40... 

Fig. 6. Band model for the charge mode detector biased to deep depletion. The charge, integrates in the potential well defined by the insulator and...

Fig. 8. The photodiode detector (a) band model where the photon generates electron—hole pairs that are separated by the built-in potential setting up a photocurrent (b) physical model for a planar diode. The passivation is typically Si02 for Si diodes, an In oxide for InSb diodes, and CdTe for HgCdTe...

Fig. 8. (a) Energy levels for the band model of silver haUde crystals. The band bending at the surface (-) is exaggerated. The extent of bending is at... 

At high temperature, the conductivity was found to increase linearly with temperature and the observed high-temperature MR was positive. In fact, by fitting the data using a simple two-band model] 17] the authors obtained the theoretical curve in Fig. 4 (a). The fitting parameters showed that the ratio Op/ct, where Op and are the partial conductivities of holes and electrons, respectively, decreases with increasing tern-... 

Fig. 4. (a) Magnetic field dependence of the high- and low-temperature MR, respectively. The solid lines are calculated using a simple two-band model for (a) and the 2D weak localization theory for (b) (after Song et o/.[16]). 

Fig. 5. Electrical resistance as a function of the temperature at the indicated magnetic fields for a single microbundle of carbon nanotubes. The solid line is a fit using the two-band model for graphite (see inset) with an overlap A = 3.7 meV and a Fermi level right in the middle of the overlap (after Langer et at. l9 ).

Next we turn to our canonical band results. To do so we have used a generalized canonical band model that includes spin-polarization. Hence we introduce a spin dependent shift,... 

Figure 2. The structural energy difference (a) and the magnetic moment (b) as a function of the occupation of the canonical d-band n corresponding to the Fe-Co alloy. The same lines as in Fig. 1 are used for the different structures. In (b) the concentration dependence of the Stoner exchange integral Id used for the spin-polarized canonical d-band model calculations is shown as a thin dashed line with the solid circles. The value of Id for pure Fe and Co, calculated from LSDA and scaled to canonical units, are also shown in (b) as solid squares.

In a previous work we showed that we could reproduce qualitativlely the LMTO-CPA results for the Fe-Co system within a simple spin polarized canonical band model. The structural properties of the Fe-Co alloy can thus be explained from the filling of the d-band. In that work we presented the results in canonical units and we could of course not do any quantitative comparisons. To proceed that work we have here done calculations based on the virtual crystal approximation (VGA). In this approximation each atom in the alloy has the same surrounding neighbours, it is thus not possible to distinguish between random and ordered alloys, but one may analyze the energy difference between different crystal structures. 

To summarize we have reproduced the intricate structural properties of the Fe-Co, Fe-Ni and the Fe-Cu alloys by means of LMTO-ASA-CPA theory. We conclude that the phase diagram of especially the Fe-Ni alloys is heavily influenced by short range order effects. The general trend of a bcc-fcc phase transition at lower Fe concentrations is in accordance with simple band Ailing effects from canonical band theory. Due to this the structural stability of the Fe-Co alloys may be understood from VGA and canonical band calculations, since the common band model is appropriate below the Fermi energy for this system. However, for the Fe-Ni and the Fe-Cu system this simple picture breaks down. 

In this work, we present calculated SFE using the LKKR-CPA method for Al-Cu and Al-Mg which are of interest from the point of view of superplasticity. We use the SFE to validate the rigid band model which allows a deeper insight into the electronic structure and its implication on the nature of inter-atomic potentials. 

Figure 3 Compositional dependence of the stacking fault energy calculated from the rigid-band model (solid line) compared with the more accurate results from the LKKR-CPA calculation (dashed line) for the Al-Cu alloy system.

Primary Photoexcitations in Conjugated Polymers Molecular Exciton versus Semiconductor Band Model (Ed. N.S. Sariciftci) World Scientific, Singapore 1997. 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

Wilson JA (1977) A Generalized Configuration - Dependent Band Model for Lanthanide Compounds and Conditions for Interconfiguration Fluctuations. 32 57-91 Wilson MR (1999) Atomistic Simulations of Liquid Crystals. 94 41-64 Winkler H, see Trautwein AX (1991) 78 1-96... 

Noteworthy also is the extensive compilation of early data on layered MX2 given by Wilson and Yoffe [37], who worked out a group-by-group correlation of transmission spectra of the compounds to available electrical and structural data and produced band models in accord with a molecular orbital approach. 

We have shown the least complicated one which turns out to be the simple cubic lattice. Such bands are called "Brilluoin" zones and, as we have said, are the allowed energy bands of electrons in any given crystalline latttice. A number of metals and simple compounds have heen studied and their Brilluoin structure determined. However, when one gives a representation of the energy bands in a solid, a "band-model is usually presented. The following diagram shows three band models ... 

In this diagram, we show the band model structure at the juncture of two metals, each of which has its own Fermi Level. The Fermi Level is the energy level of the electrons contained in the metal. That is- when metal atoms (each... 

The key parameters of the electronic structure of these surfaces are summarized in Table 9.3. The calculated rf-band vacancy of Pt shows no appreciable increase. Instead, there is a shght charge transfer from Co to Pt, which may be attributable to the difference in electronegativity of Pt and Co, in apparent contradiction with the substantial increase in Pt band vacancy previously reported [Mukerjee et al., 1995]. What does change systematically across these surfaces is the J-band center (s ) of Pt, which, as Fig. 9.12 demonstrates, systematically affects the reactivity of the surfaces. This correlation is consistent with the previous successes [Greeley et al., 2002 Mavrikakis et al., 1998] of the bimetallic surfaces and the effect of strain. Compressive strain lowers s, which, in turn, leads to weaker adsorbate-surface interaction, whereas expansive strain has the opposite effect. 

Hammer-Nprskov d-band model, 70, 272-273, 327 Heme-copper oxidase, 610 High Throughput Synthesis of Nanoparticles, 572-574 Hydrogen (underpotential) adsorption, 60-63,254, 471-484, 526 Hydrogen evolution reaction (HER), 31, 79-87... 

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). 

Although the band model explains well various electronic properties of metal oxides, there are also systems where it fails, presumably because of neglecting electronic correlations within the solid. Therefore, J. B. Good-enough presented alternative criteria derived from the crystal structure, symmetry of orbitals and type of chemical bonding between metal and oxygen. This semiempirical model elucidates and predicts electrical properties of simple oxides and also of more complicated oxidic materials, such as bronzes, spinels, perowskites, etc. 

Fig. 4. Energy level diagrams showing possible electronic configurations for positively-charged polaron (a) and bipolaron (b) defects and (c) a schematic bipolaron band model. The negatively-charged polaron would carry three electrons and the bipolaron four. Also shown is the neutral polaron-exciton (d) which would decay to restore the chain structure.

Figure 5. Schematic of energy band model of the rutile form of TiOz (4)...

It has also to be remembered that the band model is a theory of the bulk properties of the metal (magnetism, electrical conductivity, specific heat, etc.), whereas chemisorption and catalysis depend upon the formation of bonds between surface metal atoms and the adsorbed species. Hence, modern theories of chemisorption have tended to concentrate on the formation of bonds with localized orbitals on surface metal atoms. Recently, the directional properties of the orbitals emerging at the surface, as discussed by Dowden (102) and Bond (103) on the basis of the Good-enough model, have been used to interpret the chemisorption behavior of different crystal faces (104, 105). A more elaborate theoretical treatment of the chemisorption process by Grimley (106) envisages the formation of a surface compound with localized metal orbitals, and in this case a weak interaction is allowed with the electrons in the metal. 

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