Conduction band in solids

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. 

Formation of bands in solids by assembly of isolated atoms into a lattice (modified from Bard, 1980). When the band gap Eg kT or when the conduction and valence band overlap, the material is a good conductor of electricity (metals). Under these circumstances, there exist in the solid filled and vacant electronic energy levels at virtually the same energy, so that an electron can move from one level to another with only a small energy of activation. For larger values of Eg, thermal excitation or excitation by absorption of light may transfer an electron from the valence band to the conduction band. There the electron is capable of moving freely to vacant levels. The electron in the conduction band leaves behind a hole in the valence band. 

Silicon is an indirect band gap solid with an available non-radiative pathway from the conduction band to the valence band. In photo voltaic cells, electrons are promoted from the valence band to the conduction band and are then used to do electrical work. The promoted electrons do not return directly to the valence band either by emitting energy or by a non-radiative pathway. In LEDs, the return of the electrons to the valence band by emitting light is important. This return has a low probability because of the indirect band gap and the electrons use the non-radiative pathway instead. Promotion to the conduction band in the solar cell will also be of low probability, but no competing non-radiative route is available. 

Titanium dioxide is a light-sensitive semiconductor, and absorbs electromagnetic radiation in the near UV region. The energy difference between the valence and the conductivity bands in the solid state is 3.05 eV for rutile and 3.29 eV for anatase, corresponding to an absorption band at <415 nm for rutile and <385 nm for anatase. 

Analysis of Hall-effect data has been one of the most widely used techniques for studying conduction mechanisms in solids, especially semiconductors. For the single-carrier case, one readily obtains carrier concentrations and mobilities, and it is usually of interest to study these as functions of temperature. This can supply information on the predominant charge-carrier scattering mechanisms and on activation energies, i.e., the energies necessary to excite carriers from impurity levels into the conduction band. Where two or more carriers are present, the analysis becomes more complex, but much more information can be obtained from sludies of the temperature and magnetic held dependencies. 

Figure 28.1 The electronic structure of a solid can be described in terms of a band model in which bonding electrons are primarily found in a low-energy valence band, while conduction is typically associated with antibonding or nonbonding high-energy orbitals known as the conduction band. In the case of a semiconductor (left), these two bands are separated by a quantum-mechanical forbidden zone, the band gap. Excitation of electrons from the valence band to the conduction band gives rise to the bulk optical and electronic properties of the semiconductor. In the case of a metal (right), the conduction band and valence band overlap, giving rise to a continuum of states.

Fig. 4. Hartree-Fock free atom 4s valence electron orbital for potassium (solid line) and the 4s-like orbital, obeying the Wigner-Seitz boundary condition, appropriate to the bottom of the conduction bands in metallic potassium (dashed line). Both orbitals are normalized, for the metal, integration is limited to the Wigner-Seitz sphere of radius rws...

Figure 2 shows the energy-level diagram of the molecular orbitals of the 1-D silicon clusters (SiH2)nH2 with silicon 3d orbitals. The levels shown by broken lines are unoccupied. These unoccupied levels correspond to the conduction band in crystalline silicon. The occupied levels shown by solid lines around — 17 to —13eV and —11 to —9eV are the valence orbitals mainly localized on silicon 3s and 3p orbitals, respectively. The unoccupied levels are the... 

The net photocurrent and the quantum yield are a function of a number of competing processes " as shown in Fig. 1.22. For an n-type semiconductor, the externally measurable current i is the difference between the photocurrent and the forward current of electrons. The electron current is decreased to zero under certain anodic bias. While the flux of holes to the surface is exclusively controlled by the solid-state properties, all the other reaction steps depend on the surface properties of the semiconductor. The holes arriving at the surface can either (i) transfer to an electron donor in the solution, (ii) be trapped at the surface states, or (iii) recombine with electrons in the conduction band in the depletion region or at the surface. Process (iii) does not generate current in the external circuit, whereas process (ii) produces only transient current charging up the surface states. Only process (i) produces steady photocurrent. The measured photocurrent /ph can therefore be different from the flux of holes to the surface due to these processes. 

Nomura S. and Kobayashi T. (1991), Nonparabolicity of the conduction-band in CdSe and CdS cSei c semiconductor microcrystallites . Solid State Comm. 78, 677-680. 

Band theory should be treated with some caution. The presence of bands in solid state structures is well supported by X-ray emission and absorption data where energy is emitted (or absorbed) over a range relating to the band structure. However, even in this simple case, band theory fails to explain why MnO is insulating. In the argument used above, MnO has electron vacancies in the t2g and should be conducting. 

One factor affecting the dielectric strength is the electronic structure of the polymer, and in particular its band gap. In quantum mechanics [29], each electron in a molecule can only occupy one of a discrete set of allowed energy levels. In solids, the overlaps between different repeating units of the material (for example, the repeat units in quasi-one-dimensional systems such as polymer chains [29-31]) cause these discrete energy levels to broaden into bands. The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. (In terms which are equivalent but more familiar to chemists, the band gap is... 

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. 

The energy gap, generally measured in electron volts (eV), between the top of the valence band and the bottom of the conduction band in a crystalline solid. See Conduction band, Energy band, Valence band. 

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