Partially filled band

MetaUic behavior is observed for those soHds that have partially filled bands (Fig. lb), that is, for materials that have their Fermi level within a band. Since the energy bands are delocalized throughout the crystal, electrons in partially filled bands are free to move in the presence of an electric field, and large conductivity results. Conduction in metals shows a decrease in conductivity at higher temperatures, since scattering mechanisms (lattice phonons, etc) are frozen out at lower temperatures, but become more important as the temperature is raised. 

In real tran -polyacetylene, the structure is dimerized with two carbon atoms in the repeat unit. Thus the tt band is divided into occupied tt and unoccupied n bands. The bond-alternated structure of polyacetylene is characterishc of conjugated polymers. Consequently, since there are no partially filled bands, conjugated polymers are expected to be semiconductors, as pointed out earlier. However, for conducting polymers the interconnection of chemical and electronic structure is much more complex because of the relevance of non-linear excitations such as solitons (Heeger, 2001). 

In the absence of dynamic and static disorder, all partially filled band systems would exhibit coherent transport over long distances. With static and dynamic disorder, the modulation of the simple molecular orbital or band structure by nuclear effects entirely dominates transport. This is clear both in the Kubo linear response formulation of conductivity and in the Marcus-Hush-Jortner formulation of ET rates. The DNA systems are remarkable for the different kinds of disorder they exhibit in addition to the ordinary static and dynamic disorder expected in any soft material, DNA has the covalent disorder arising from the choice of A, T, G, or C at each substitution base site along the backbone. Additionally, DNA has the characteristic orientational and metric (helicoidal) disorder parameters arising from the fundamental motif of electron motion along the r-stack. 

Bulk crystalline radical ion salts and electron donor-electron acceptor charge transfer complexes have been shown to have room temperature d.c. conductivities up to 500 Scm-1 [457, 720, 721]. Tetrathiafiilvalene (TTF), tetraselenoful-valene (TST), and bis-ethyldithiotetrathiafulvalene (BEDT-TTF) have been the most commonly used electron donors, while tetracyano p-quinodimethane (TCNQ) and nickel 4,5-dimercapto-l,3-dithiol-2-thione Ni(dmit)2 have been the most commonly utilized electron acceptors (see Table 8). Metallic behavior in charge transfer complexes is believed to originate in the facile electron movements in the partially filled bands and in the interaction of the electrons with the vibrations of the atomic lattice (phonons). Lowering the temperature causes fewer lattice vibrations and increases the intermolecular orbital overlap and, hence, the conductivity. The good correlation obtained between the position of the maximum of the charge transfer absorption band (proportional to... 

The effect of an external electric field is to produce an acceleration of the electrons in the direction of the field, and this causes a shift of the Fermi surface. It is a necessary condition for the movement of electrons in the fc-space that there are allowed empty states at the Fermi surface hence electrical conductivity is dependent on partially filled bands. An insulating crystal is one in which the electron bands are either completely full or completely empty. If the energy gap between a completely filled band and an empty band is small, it is possible that thermal excitation of electrons from the filled to the empty band will result in a conducting crystal. Such substances are usually referred to as intrinsic semiconductors. A much larger class of semiconductors arises from impurities... 

On the terminology of the band model c- bonds form the completely filled low band, and rc-bonds make the partially filled band, which defines the electronic properties of the polyacetylene. 

Normally, ionic solids have very low conductivities. An ordinary crystal like sodium chloride must conduct by ion conduction since it does not have partially filled bands (metals) or accessible bands (semiconductors) for electronic conduction. The conductivities that do obtain usually relate to the detects discussed in the previous section. The migration of ions may be classified into three types. 

Recent band structure calculations have confirmed that the increase in electrical conductivity of doped polymer phthalocyanines is the result of both the existence of partially filled bands and the decrease of the M—M distance.104 They also confirm that the conduction process for the doped polymers changes from metal-centred (M = Cr, Mn, Fe and Co), to ligand and metal (M = Ni) and to ligand-centred (Cu and Zn) with increasing electronegativity of the metal atom along the first transition series. 

V Metals have electrons in a I 1 partially filled band or in a... 

Figure 21.8 shows that an electrical potential can shift electrons from one set of energy levels to the other only if the band is partially filled. If the band is completely filled, there are no available vacant energy levels to which electrons can be excited, and therefore the two sets of levels must remain equally populated, even in the presence of an electrical potential. This means that an electrical potential can t accelerate the electrons in a completely filled band. Materials that have only completely filled bands are therefore electrical insulators. By contrast, materials that have partially filled bands are metals. 

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. 

The MOs of a semiconductor are similar to those of an insulator, but the band gap in a semiconductor is smaller (Figure 21.10). As a result, a few electrons have enough thermal energy to jump the gap and occupy the higher-energy conduction band. The conduction band is thus partially filled, and the valence band is partially empty because it now contains a few unoccupied MOs. When an electrical potential is applied to a semiconductor, it conducts a small amount of current because the potential can accelerate the electrons in the partially filled bands. Table 21.3 shows how the electrical properties of the group 4A elements vary with the size of the band gap. 

Doping a semiconductor / V I enhances its electrical conductivity by increasing the population of electrons and/or positive holes in the partially filled bands. 

Materials with partially filled bands are metallic conductors, and materials with only completely filled bands are electrical insulators. Explain why the population of the bands affects the conductivity. 

The electrical properties of any material are a result of the material s electronic structure. The presumption that CPs form bands through extensive molecular obital overlap leads to the assumption that their electronic properties can be explained by band theory. With such an approach, the bands and their electronic population are the chief determinants of whether or not a material is conductive. Here, materials are classified as one of three types shown in Scheme 2, being metals, semiconductors, or insulators. Metals are materials that possess partially-filled bands, and this characteristic is the key factor leading to the conductive nature of this class of materials. Semiconductors, on the other hand, have filled (valence bands) and unfilled (conduction bands) bands that are separated by a range of forbidden energies (known as the band gap ). The conduction band can be populated, at the expense of the valence band, by exciting electrons (thermally and/or photochemically) across this band gap. Insulators possess a band structure similar to semiconductors except here the band gap is much larger and inaccessible under the environmental conditions employed. 

The 1 1 solid adduct of tetrathiafulvalene (TTF) and tetracyanoquin-odimethane (TCNQ) is the first-discovered molecular metal, which consists of alternate stacks each composed of molecules of the same type (Fig. 4.1.3). A charge transfer of 0.69 electron per molecule from the HOMO (mainly S atom s lone pair in character) of TTF to the LUMO of TCNQ results in two partially filled bands, which account for the electrical conductivity of TTF TCNQ. 

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 ... 

In order to discuss the valence electronic state and chemical bonding of lithium vanadium oxide we made calculations using cluster models. The density of states (DOS) and the partial density of states (PDOS) of Li1.1V0.9O2 are obtained by this study as shown in Figure 3.4. The filled band located from —8 to —3 eV is mainly composed of O 2p orbital. The partially filled band located around —2 to 4 eV is mainly composed of V 3d orbital. Unoccupied band located above 5 eV is... 

Wilson ((>85) has pointed out that if a Brillouin zone is full, the electrons occupying the states of this zone can make no contribution to the electric current. This fact follows from the definition of the zone as a region enclosing all reduced wave vectors. Imagine all electrons of Figure 6 shifted Akx by an external field. The electrons in states within Akx of the zone boundary are reflected to the opposite zone boundary, so that the zone remains filled and there is no transfer of charge. This observation permits a sharp distinction between metallic conductors, semiconductors, and insulators. Because of the high density of states in a band, a crystal with partially filled bands is a metallic conductor. If all occupied zones (or bands) are filled, the crystal is a semiconductor if Ef kT, is an insulator if kT. 

From equation 46 it is possible to derive a necessary condition for semiconductor or insulator properties The Fermi level may lie within an energy gap if the number of electrons per atom (only atoms whose orbitals participate in band formation are counted) is nj i 2(21 + l)/v, where l is the angular momentum of the atomic orbitals participating in partially filled bands, v is the number of atoms per primitive unit cell, and n is an integer. (Perturbation mixtures from higher states do not change the number of states in the band.) Thus if s and p states are admixed (id and / electrons neglected), a compound may be a semiconductor or insulator if the number of electrons per atom is... 

---