Electrons and Electron Holes

The charged defects that most readily come to mind are electrons. In a crystal containing defects, some fraction of the electrons may be free to move through the matrix. These are denoted by the symbol e. The superscript represents the effective negative 

The counterparts to electrons in semiconducting solids are holes, represented by the symbol h. Each hole will bear an effective positive charge, qe, of +1, which is represented by the superscript to emphasize that it is considered relative to the surrounding structure. The concentration of holes that are free to carry current through a crystal is often given the symbol p in semiconductor physics. 

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Brus L E 1984 Electron-electron and electron-hole Interactions In small semiconductor crystallites the size dependence of the lowest excited electronic state J. Chem. Phys. 80 4403-9... 

The relatively high mobilities of conducting electrons and electron holes contribute appreciably to electrical conductivity. In some cases, metallic levels of conductivity result ia others, the electronic contribution is extremely small. In all cases the electrical conductivity can be iaterpreted ia terms of carrier concentration and carrier mobiUties. Including all modes of conduction, the electronic and ionic conductivity is given by the general equation ... 

Brus, L. E. (1984). Electron-electron and Electron-Hole Interactions in Small Semiconductor... 

By analogy with similar materials in which free electrons and electron holes are formed, NiO is called a p-type compound having vacant site Schottky defects, and ZnO is an n-type compound having interstitial Frenkel defects. The concentrations of these defects and their relation to the oxygen pressure in the surrounding atmosphere can be calculated, for a dilute solution of defects by the application of a mass action equation. The two reactions shown above are represented by the equations... 

Typical photodiode detectors consist of a p layer which is made of an electron deficient material an n layer which is electron abundant and a depletion region, the p-n junction, located between the two layers. At equilibrium, when no light or current is applied to the system, the p-n junction is in electrostatic equilibrium and the alignment of electrons and electron holes on the two sides of thejunction region creates a contact potential voltage. As incident light strikes the surface of the diode, the... 

In addition to stress, the other important influence on solid state kinetics (again differing from fluids) stems from the periodicity found within crystals. Crystallography defines positions in a crystal, which may be occupied by atoms (molecules) or not. If they are not occupied, they are called vacancies. In this way, a new species is defined which has attributes of the other familiar chemical species of which the crystal is composed. In normal unoccupied sublattices (properly defined interstitial lattices), the fraction of vacant sites is close to one. The motion of the atomic structure elements and the vacant lattice sites of the crystal are complementary (as is the motion of electrons and electron holes in the valence band of a semiconducting crystal). 

We have seen that it is possible to control electron (and electron hole) concentrations by the chemical potential of a component of the crystalline compound within a finite range of homogeneity. This observation leads to an effect that is known as... 

These equations result from the intimate mixing of electron-electron and electron-hole channels (the Parquet summation). This is of crucial importance in one dimension. The f-matrix or random-phase approximations are incapable of doing this and are fundamentally wrong in one dimension. Notice also that g4 is absent because it does not alone contribute any logarithmic term. It leads only to charge and spin velocity corrections. It is normally neglected in the RG treatments (see Refs. 15 and 39 for a discussion of this). It will only be taken into account for the uniform susceptibility in part d. 

When the conductor is at T < T, any further evolution of the solid will be dominated by the two-dimensional Fermi surface, in which the phenomenon of nesting is all important. Figure 7b illustrates this peculiar property of the Fermi surface, where part of the Fermi surface, say at k < 0, can superimpose on the other part when translated by wave vector Q0. The response functions at this wave vector is dominant. In two dimensions, the mixing between electron-electron and electron-hole channels (see Section IV.B.3.b) does not occur. The RPA structure emerges. At Q = Q0, one has, putting W" = V" - g",... 

Figures Conductivities of oxygen ions, electrons and electron holes in ZrggYg,Ojg as a function of oxygen partial pressure at different temperatures (adopted from ref 52). The ionic domains and typical p(02)-ranges of fuel cell operation are also shown...

The net charge distribution p(x, x) = ne (x, x) — n, i(x, x) can 0e used for computing the energy functional of the electron-electron and electron-hole interactions in the tunnel gap. The potential energy of the induced charges as a function of the dot location is proportional to the integral... 

The oxygen vacancies formed at elevated temperatures and low oxygen partial pressure are assumed to be doubly ionized. The thermally activated charge disproportionation reaction given by Eq. (10.51) reflects the localized nature of electronic species and may be treated as equivalent to the generation of electrons and electron holes by ionization across a pseudo band gap cf. Eq. (10.27)). The associated free enthalpy of reaction may be taken equal to the effective band gap energy. 

Based on the rigid band theory, the electronic theory considered the metal as a collective source of electrons and electron holes, characterized... 

Under equilibrium conditions the electrical conductivity of many oxide phases, e.g., CugO, FeO, CoO, NiO, or ZnO at elevated temperatures is a function of the oxygen partial pressure in the ambient gas phase 12). The oxygen partial pressure determines the metal excess or deficit in the metal oxide and thereby the concentration of electrical carriers especially excess electrons and electron holes. Thus, after proper calibration, the steady-state oxygen activity ao(st) may be deduced from measurements of the conductance of a metal oxide foil used as catalyst while an oxygen transfer reaction, e.g., CO2 + H2 = CO -)- HjO or 2N2O = 2N2 + O2 proceeds at the surface of the metal oxide 13). 

To suppress the electron and electron-hole recombination and continuously supply valence-band electron holes for an oxidative process, a sacrificial electron acceptor must be used to scavenge the electron in the conduction band [15,20], Oxygen is usually used in photocatalytic oxidation because of its ability to capture conduction-band electrons from most semiconductors [8]. The oxygen radical anion formed after the quenching of an electron is an additional oxidant, which is useful for oxidative waste degradation, but may be a source of side reactions in organic synthesis. To reduce such side reactions, the use of other electron acceptors such as methyl viologen and N2O has been reported [74]. 

With a low-intensity light source, the number of electrons and electron holes available on the semiconductor particles increases linearly with the increase of photon flux. With a high-intensity light source, however, the number of electrons and electron holes available on the semiconductor particles increases with the square root of photon flux because of electron-electron-hole recombination and the dynamic shortage of organic substrates to scavenge electrons and/or electron holes [81-83]. Therefore, the quantum yield of a reaction catalyzed by semiconductor particles generally decreases with the increase... 

FIGURE 1.1. Schematics of the electron-hole generation in a photocatalyst particle and some of the mechanisms involved a) Ray promotes the formation of the electron-hole and electron, b) electron-hole is used in the formation of the OH groups promoting oxidation processes, c) the electron is utilized in a number of reduction processes, d) electron and electron-hole can recombine contributing to process inefficiency. 

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