Conduction band A partially filled

Conduction band A partially filled band or a band of vacant energy levels just higher in energy than a filled band a band within which, or into which, electrons must be promoted to allow electrical conduction to occur in a solid. 

Conduction band A partially filled or empty atomic energy band in which electrons are free to move easily, allowing the material to carry an electric current. 

FIGURE 21.10 Bands of MO energy levels for (a) a metallic conductor, (b) an electrical insulator, and (c) a semiconductor. A metallic conductor has a partially filled band. An electrical insulator has a completely filled valence band and a completely empty conduction band, which are separated in energy by a large band gap. In a semiconductor, the band gap is smaller. As a result, the conduction band is partially occupied with a few electrons, and the valence band is partially empty. Electrical conductivity in metals and semiconductors results from the presence of partially filled bands. 

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 ... 

Semiconductor—In an insulator at a temperature T = 0 all bands are either completely empty or completely filled, whereas in a metal, at least one band is partially filled. Insulators can be characterized by the band gap (energy gap) between the top of the -> valence band (highest filled band) and the bottom of the -> conduction band (lowest empty band). At T 4= 0 there is a nonvanishing probability that some electrons will be thermally excited from the valence bands into the conduction bands, leaving behind unoccupied states in the valence bands, which are called -> holes. These electrons and holes are then capable of participating in electronic conduction. Solids that are insulators at T = 0, but... 

A series of AgF+ salts (AgFMF4 with M = B, Au and AgFMF6 with M = As, Au, Ir, Ru, Sb, Bi) have been prepared. The first was AgFAsF6 [9] made by the interaction of AgF2 with AsF5 in aHF. They all have the weak, temperature independent paramagnetism indicative of a partially filled band and suggestive of metallic character [12]. In no case however has electrical conductivity of metallic type been demonstrated in any one of these solids. A wide variety of synthetic routes have been demonstrated for the preparation of (Ag—F)]]+ salts. 

In a semiconductor, as discussed in the previous section, localisation can also occur as the width of the allowed energy band is reduced, and this was defined in terms of a limiting mobility. The Anderson model shows that disorder can lead to localisation in metals as well as semiconductors. In metals, since conduction is due only to electrons within a partially filled band, the energy in the band tail that separates localised from delocalised electron states is termed the mobility edge. The onset of localisation in a metal occurs at a minimum conductivity. This can be seen as follows. For an electron at the Fermi energy its mean free path, l, is just the scattering time, r, multiplied by the electron velocity at the Fermi energy, vF. Then, from Equations (4.1) and (4.2) it follows that ... 

Current carried by delocalized electrons in bands Conductivity decreases with increasing temperature Substance with a partially filled conduction band (gap not relevant)... 

Conductors, such as the metals, are characterized by a partially filled band, so that the highest filled level and the lowest empty level are essentially at the same energy, the Fermi energy. Insulators have a large residual gap between the valence and conduction bands. Examples are ionic compounds, but also some covalent compounds such as diamond. Semiconductors have a small gap between the bands. Most of the covalent compounds in Table 5.3 fall into this class. 

We discuss the interaction of a partially filled electronic conduction band in a segregated donor-acceptor stack system with libra-tional modes of the solid. The orientational Peierls instability predicted by us earlier leads to the formation of chiral charge density waves, which interact and phase-lock below the metal-insulator transition via the Coulomb interaction. The effect of the resulting order on the physical properties of the system and the implications for the understanding of the recent neutron scattering data for the occurrence of several transitions in TTF-TCNQ will be discussed. 

Each band can be filled with electrons in a similar fashion to filling a plastic bottle with sand. If that bottle of sand is completely full, it is possible to tilt it or even turn it upside down and the grains of sand will not move. If the plastic bottle is not completely full (i.e., a partially filled band), then the grains of sand can easily move when the bottle is tilted. They are not localized in one position but delocalized across the top surface. In a similar way, electrons of a partially filled band are delocalized across the crystal and can conduct electricity. The energy of the highest filled levels is called the Fermi energy. 

A metallic conductor is a substance that has a partially filled band. It takes very little energy to move electrons from a filled level to an empty level in a band this results in high conductivity because there is no energy gap at the Fermi level. When the temperature of a metallic conductor is lowered, the conductivity increases because the thermal motion of the atoms in the crystal is slowed, allowing the electrons to move more easily. 

In conductors, the conduction band is partially occupied (Fig. 7.4). An electron close to the top of the filled part of this band (point A, Fig. 7.4) will be able to move to the empty part (part B) under the influence of any electric field other than zero. Thus, because of the lack of a forbidden gap, there is no threshold of electric field intensity below which electrons cannot move. Motion of the charge carriers and, consequently, conductivity are always possible for any voltage applied, no matter how small. 

Another point of interest is that not all but only about one electron per atom is free to carry the current. Only the electrons in levels near the top of the filled part of the partially filled band are free to move under the application of a field. As we saw in Section 28.4, to carry a current the electrons must be able to shift from one set of levels to another set vacant levels that are not very much different in energy must be available. Vacant levels are available only near the top of the filled part of a partially filled band and so only these electrons contribute to the conductivity. 

---