Valence band orbitals

Phosphorus and arsenic have nearly identical electronegativities, so in GaP Asi. , the dominant effect is the smaller atomic radius of P relative to As. Substituting P atoms for As atoms shrinks the dimensions of the semiconductor lattice. This leads to greater overlap of the valence orbitals, increased stability of the bonding orbitals (valence band), and an increased band gap. 

HOMO = highest occupied molecular orbital (valence band)... 

The material becomes semiconducting if electrons are injected into the unoccupied antibonding orbitals (conduction band) or are removed from the occupied bonding orbitals (valence band). At a surface, bonds between Si atoms are broken. Within the idealized hybridization scheme, the surface atom has a free sp% orbital... 

Conductive polymers are turned into semiconductors through delocalization of the n electrons, and the n bonding orbital (valence band) and n orbital (conduction band) are separated by the energy gap. Eg. It is these n electrons that are involved in the electrochemical reaction when conductive polymers are used as electrodes. The a electrons of carbon atoms that form the structure of the polymer are almost completely independent of the reaction. It is thought that approximately 6% of the a electrons can be involved in the oxidation and reduction of a conductive polymer, and still maintain a stable reversible reaction. 

Both anatase and mtile are broad band gap semiconductors iu which a fiUed valence band, derived from the O 2p orbitals, is separated from an empty conduction band, derived from the Ti >d orbitals, by a band gap of ca 3 eV. Consequendy the electrical conductivity depends critically on the presence of impurities and defects such as oxygen vacancies (7). For very pure thin films, prepared by vacuum evaporation of titanium metal and then oxidation, conductivities of 10 S/cm have been reported. For both siugle-crystal and ceramic samples, the electrical conductivity depends on both the state of reduction of the and on dopant levels. At 300 K, a maximum conductivity of 1 S/cm has been reported at an oxygen deficiency of... 

In most metals the electron behaves as a particle having approximately the same mass as the electron in free space. In the Group IV semiconductors, dris is usually not the case, and the effective mass of electrons can be substantially different from that of the electron in free space. The electronic sUmcture of Si and Ge utilizes hybrid orbitals for all of the valence elecU ons and all electron spins are paired within this structure. Electrons may be drermally separated from the elecU on population in dris bond structure, which is given the name the valence band, and become conduction elecU ons, creating at dre same time... 

Because each lithium atom has one valence electron and each molecular orbital can hold two electrons, it follows that the lower half of the valence band (shown in color in Figure 5) is filled with electrons. The upper half of the band is empty. Electrons near the top of the filled MOs can readily jump to empty MOs only an infinitesimal distance above them. This is what happens when an electrical field is applied to the crystal the movement of electrons through delocalized MOs accounts for the electrical conductivity of lithium metal. 

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. 

Conjugated polymers are generally poor conductors unless they have been doped (oxidized or reduced) to generate mobile charge carriers. This can be explained by the schematic band diagrams shown in Fig. I.23 Polymerization causes the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the monomer to split into n and n bands. In solid-state terminology these are the valence and conduction bands, respectively. In the neutral forms shown in Structures 1-4, the valence band is filled, the conduction band is empty, and the band gap (Eg) is typically 2-3 eV.24 There is therefore little intrinsic conductivity. 

Bonding in solids may be described in terms of bands of molecular orbitals. In metals, the conduction bands are incompletely filled orbitals that allow electrons to flow. In insulators, the valence bands are full and the large band gap prevents the promotion of electrons to empty orbitals. 

Fig. 9.10 CASTER densities of states for LigZn2Ge3. Nonbonding electron density distribution over selected bunches of crystal orbitals in the valence-band dispersion (a) six orbitals between -2.4 and -0.7 eV, (b) four orbitals ranging from -3.3 to -1.9 eV.

However, in oxides, e.g. that of aluminium, AI2O3, the sp band of the aluminium hybridizes with the p orbitals of the oxygen to form a new band below the Fermi level, which leaves a gap of 7 eV to the antibonding part of the band. The lower part is the valence band, the upper part the conduction band, and the separation between them is the band gap. This material is an insulator, as it will be hard for an electron to become excited to the conduction band so that it can move through the oxides. 

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