Conduction-band level

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

Figure 4 Conduction band levels and excitation levels of infinite periodic hydrogen chains by using different approximations of the polarization propagator. The left part refers to the crystalline orbital energy differences, namely, the Hartree-Fock excitation energies the right part refers to the random phase approximation results obtained by using 41 k-points in half the first Brillouin zone.

Fig. 5.14 Inoue et al. carried out a systematic study of the photocatalytic reduction of CO2 by different semiconductor powders in aqueous suspensions. Shown here is the energy correlation between semiconductor catalysts and redox couples in water, as presented in their paper. In principle, the solution species with more positive redox potential with respect to the conduction band level of the semiconductor is preferably reduced at the electrode. Photoexcited electrons in the more negative conduction band certainly have greater ability to reduce CO2 in the solution. (Reproduced from [240])...

Semiconductor electrodes seem to be attractive and promising materials for carbon dioxide reduction to highly reduced products such as methanol and methane, in contrast to many metal electrodes at which formic acid or CO is the major reduction product. This potential utility of semiconductor materials is due to their band structure (especially the conduction band level, where multielectron transfer may be achieved)76 and chemical properties (e.g., C02 is well known to adsorb onto metal oxides and/ or noble metal-doped metal oxides to become more active states77-81). Recently, several reports dealing with C02 reduction at n-type semiconductors in the dark have appeared, as described below. 

Respectively, electrons in reducing reactants are weakly bound thus, redox couples with a negative standard potential vs. SHE are positioned in the upper part of the diagram, that is, in the vicinity of the conduction band level in the semiconductor electrode. 

Transitions to some levels in the conduction band are more likely than transitions to others. This is because transitions between valence band and conduction band levels, like those between atomic energy levels are governed by selection rules. The spin selection rule still holds when promoted to the conduction band the electron... 

Recently, the electron-transfer kinetics in the DSSC, shown as a schematic diagram in Fig. 10, have been under intensive investigation. Time-resolved laser spectroscopy measurements are used to study one of the most important primary processes—electron injection from dye photosensitizers into the conduction band of semiconductors [30-47]. The electron-transfer rate from the dye photosensitizer into the semiconductor depends on the configuration of the adsorbed dye photosensitizers on the semiconductor surface and the energy gap between the LUMO level of the dye photosensitizers and the conduction-band level of the semiconductor. For example, the rate constant for electron injection, kini, is given by Fermi s golden rule expression ... 

Organic dyes having appropriate HOMO and LUMO levels to the redox potential of iodine and the conduction-band level of the semiconductor, respectively, could be utilized as well. As described in Section I, organic dyes such as 9-phenylxan-thene dyes have been used as photosensitizers in the early research. Generally, organic dyes have several advantages as photosensitizers ... 

Two factors combine to lend a greater diversity in the stereochemistries exhibited by bivalent germanium, tin and lead compounds, the increased radius of Mn compared with that of Mw and the presence of a non-bonding pair of electrons. When the non-bonding pair of electrons occupies the isotropic valence level s orbital, as in, for example, the complex cations Pb[SC(NH2)2]6+ and Pb[antipyrine]6+, or when they are donated to conductance band levels, as in the binary tin and lead selenides or tellurides or the perovskite ternary phases CsMX3 (M = Sn, Pb X = Cl, Br, I), then the metal coordination is regular. However, in the majority of compounds an apparent vacancy in the coordination sphere of the metal is observed, which is usually ascribed to the presence of the non-bonding pair of electrons in a hybrid orbital and cited as evidence for a stereochemically active lone pair . 

The semiconductor nanocrystallites work as electron acceptors from the photoexcited dye molecules, and the electron transfer as sensitization is influenced by electrostatic and chemical interactions between semiconductor surface and adsorbed dye molecules, e.g., correlation between oxidation potential of excited state of the adsorbed dye and potential of the conduction band level of the semiconductor, energetic and geometric overlapping integral between LUMO of dye molecule and the density of state distribution of the conduction band of semiconductor, and geometrical and molecular orbital change of the dye on the... 

At equilibrium, the Fermi energy is the same on both sides of the interface. But since this energy is not, in general, the same in the bulk of the materials before contact, relative to vacuum level, the positions of the valence- and conduction-band levels in the semiconductor must adjust band bending occurs. The two most probable cases are sketched in Fig. 23, for a p-type semiconductor, since CPs are generally so. 

A final interesting feature of the conduction bands, which we can discuss in the context of the F,-only bands, is the gap Eq between the nondegeneratc conduction-band level at F and the valence-band maximum at F. A formula for this gap was obtained from the full LCAO theory in Eq. (3-43), which is repeated... 

Eq. (6-18), we gave the energy difference between the conduction band levels at F as 2Bi -h 2B. For homopolar semiconductors it takes the simple form... 

Similarly, the shift in the triply degenerate conduction-band levels are the negative of this and expressions for the shifts in any other band of interest are derivable from the formulae for the energy. 

This was defensible in the inert-gas solids (though we noted that the gap was slightly reduced in those solids), but in the ionic crystal the nonmctallic ion electronic levels are greatly raised and the important excited levels (for exciton levels as well as for lower conduction-band levels) are dominated by the states on metallic ions see Fig. 14-1. Pantelides noted in fact that a critical study of the analysis of experiments in terms of the independent-ion model did not support the model. The model appeared to work for the alkali halides, but this was by fitting 16 experimental numbers with 8 adjustable parameters and the systematic variation made this fitting possible. Little success was had with other compounds. 

Eqs. (6-1) through (6-6), in terms of interatomic matrix elements defined in Eq. (3-26). We shall utilize the bands at points of highest symmetry, These are the s-like levels at F with energy a,+ 4K5 , the p-like levels at F with energy fip (4Fpp 4- 8Kpp )/3, and the two valence-band levels at X. We do not use the conduction-band levels at X, which are in poor agreement with the true bands. (This was shown in Fig. 3-8.) When we set the first six levels mentioned equal to their nearly-free-elcctron counterparts, the six equations may be solved to obtain the four interatomic matrix elements and the term values e, and fip. 

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