Band conductivity

Metals conduct electricity through conduction bands. Conduction bands arise from the application of Molecular Orbital theory to multi-atom systems. (See Chapter 10.) The bonding molecular orbitals and, sometimes, other molecular... 

With insulators or semiconductors, the valence band is completely filled and is separated from the next highest allowable energy band (conduction band) by a gap (or forbidden band). In order for valence electrons to be raised into the conduction band, they must be given a sizable amount of energy. With insulators this gap corresponds to several electron volts. For semiconductors the gap is sufficiently small so that a significant number of electrons can acquire the necessary additional energy by thermal means at room temperature. 

Fig. 2-12. Electron energy band formation of silicon crystals from atomic frontier orbitals number of silicon atoms in crystal r = distance between atoms rg = stable atom-atom distance in crystals, sp B8 = bonding band (valence band) of sp hybrid orbitals sp ABB = antibonding band (conduction band) of sp hybrid orbitals.

Electrical conductivity measurements on silicate melts indicate an essentially ionic conductivity of unipolar type (Bockris et al., 1952a,b Bockris and Mellors, 1956 Waffe and Weill, 1975). Charge transfer is operated by cations, whereas anionic groups are essentially stationary. Transference of electronic charges (conductivity of h- and n-types) is observed only in melts enriched in transition elements, where band conduction and electron hopping phenomena are favored. We may thus state that silicate melts, like other fused salts, are ionic liquids. 

That is, it appears that normal band conduction, with lattice-phonon, ionized-impurity, and possibly space-change (or localized-potential) (Podor,... 

Both of the potassium and polybromide intercalation compounds are good conductors of electricity. In the potassium inlercalam. the electrons in the conduction band can carry the current directly, as in a metal. In the compounds of graphite with polybromide. holes in the valence band conduct by the mechanism discussed previously for semiconductors (Chapter 7). 

The metallic lustre of the elemental substances formed by the heavier Group 14 elements in the diamond structure can be interpreted in terms of the valence band/conduction band picture. The spectrum of excited states which can arise from promotion of an electron from the valence band to the conduction band covers the whole of the visible region, leading to opaqueness and specular reflectance. In the case of diamond itself, the lowest electronic excited state lies well into the ultraviolet. 

It should be noted that more complex molecules than CO (e.g., methanol) produce many kinds of intermediates in the course of the catalytic oxidation, and they will chemisorb to form surface states. If the energy of the surface states formed by chemisorption of these intermediates are shallow enough from the delocalized band (conduction band and valence band) edges in the... 

At ultrahigh pressure and low temperature, such as 250 GPa and 77 K, solid molecular hydrogen transforms to a metallic phase, in which the atoms are held together by the metallic bond, which arises from a band-overlap mechanism. Under such extreme conditions, the H2 molecules are converted into a linear chain of hydrogen atoms (or a three-dimensional network). This polymeric H structure with a partially filled band (conduction band) is expected to exhibit metallic behavior. Schematically, the band-overlap mechanism may be represented in the following manner ... 

Thus it follows that the temperature dependence of conductivity is similar to that for band conduction (Eq. (2.37)), but for different reasons. 

Because the room temperature hopping mobility is low (< 10-5 m2 V-1 s-1) in contrast to that typical for band conduction ( 10-1 m2 V-1 s 1), hopping conductors are sometimes referred to as low-mobility semiconductors . Another important distinction between band and hopping conductors is the very different doping levels encountered. Whereas doping levels for silicon are usually in the parts per million range, in the case of hopping conductors they are more typically parts per hundred. 

In the case of intrinsic band conduction the experimental activation energy SA is identified with half the band gap (Eq. (2.37)) in the case of extrinsic or impurity semiconductivity, SA is either half the gap between the donor level and the bottom of the conduction band or half the gap between the acceptor level and the top of the valence band, depending upon whether the material is n or p type. In such cases the temperature dependence is determined by the concentration of electronic carriers in the appropriate band, and not by electron or hole mobility. 

In ceramics containing transition metal ions the possibility of hopping arises, where the electron transfer is visualized as occurring between ions of the same element in different oxidation states. The concentration of charge carriers remains fixed, determined by the doping level and the relative concentrations in the different oxidation states, and it is the temperature-activated mobility, which is very much lower than in band conduction, that determines a. 

The literature abounds with reports of thermal activation energies for shallow donors in GaN, obtained from Hall effect measurements over a range of temperatures, above and below room temperature, though their interpretation is rendered problematic by a number of complicating factors. At low temperatures there is clear evidence for impurity band conduction (see, for example, [31]) which severely limits the temperature range over which data may usefully be fitted to the standard equation for free carrier density n in terms of the donor density ND and compensating acceptor density NA ... 

Although Fe304 is cited as the classical example of this effect, it should be noted that the transition temperature is about four times smaller than is predicted from electrostatic considerations. Also the room-temperature Hall mobilities of the charge carriers are 0.5 cm2/V-sec (719), which might be thought to represent narrow-band conductivity. (In Fe304 there arc 3.5 t2g electrons per B-site cation, so that if R < Rc, and upper H-site t2g band, which is split from a lower t2g band by intraatomic exchange via the localized eg electrons, would be one-sixth filled.) However, intermediate mobil-... 

Now let the bands interact. The bands repel each other as they did in the H problem of Exercise 6.3. They mix in such a way that the lower band (valence band) will have dominant H character and the higher band (conduction band) dominant Li character. At k= ir/d, there is no interaction by symmetry. Unlike in the regular H problem these two orbitals are no longer degenerate and their linear combinations are not... 

Figure 7.4. (a) A schematic DOS curve showing localized states below a critical energy, fj, in the conduction band. Conduction electrons are localized unless the Fermi energy is above E. (6) In weakly disordered metals, a pseudogap, forms over which states are localized around the Fermi energy, owing to an overlap between the valence band and conduction band tails. 

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