Defect electron

A second kind of electronic defect involves the electron. Let us suppose that the second plane of the cubic lattice has a vacancy instead of a substitutional impurity of differing valency. This makes it possible for the lattice to capture and localize an extraneous electron at the vacancy site. This is shown in the following diagram. The captured electron then endows the solid structure with special optical properties since it ean absorb photon energy. The strueture thus becomes optically active. That is, it absorbs light within a well-defined band and is called a "color-center" since it imparts a specific color to the crystal. 

The alkali halides cire noted for their propensity to form color-centers. It has been found that the peak of the band changes as the size of the cation in the alkali halides increases. There appears to be an inverse relation between the size of the cation (actually, the polarizability of the cation) and the peak energy of the absorption band. These are the two types of electronic defects that are found in ciystcds, namely positive "holes" and negative "electrons", and their presence in the structure is related to the fact that the lattice tends to become charge-compensated, depending upon the type of defect present. 

In the heterogeneous solid, a different mechanism concerning charge dominates. If there are associated vacancies, a different type of electronic defect, called the "M-center", prevails. In this case, a mechanism similcu to that already given for F-centers operates, except that two (2) electrons occupy neighboring sites in the crystal. The defect equation for formation of the M-center is ... 

This type of electronic defect, found only in heterogeneous solids, consists of two associated, negatively-charged anion vacancies, one on each plcme as shown. 

RBa2Cu307 ceramics (R is a rare-earth metal or yttrium) EFG tensor, comparison with point charge calculation, spatial distribution of electron defects in the lattice... 

Since the number of phonons increases with temperature, the electron-phonon and phonon-phonon scattering are temperature dependent. The number of defects is temperature independent and correspondingly, the mean free path for phonon defect and electron defect scattering does not depend on temperature. 

The description theoretical study of defects frequently refers to some computation of defect electronic structure i.e., a solution of the Schrodin-ger equation (Pantelides, 1978 Bachelet, 1986). The goal of such calculations is normally to complement or guide the corresponding experimental study so that the defect is either properly identified or otherwise better understood. Frequently, the experimental study suffices to identify the basic structure of the defect this is particularly true when the system is EPR (electron paramagnetic resonance) active. However, if the computational method properly simulates the defect, we are provided with a wealth of additional information that can be used to reveal some of the more basic and general features of many-electron defect systems and defect reactions. 

N. M. Johnson, Electronic Defects in CW Transient Thermal Processed Silicon... 

In addition to the defects listed above, which may be termed structural defects, there are also electronic defects. The first of these are electrons that are in excess of those required for chemical bonding and that, in certain circumstances, constitute charged defects that can carry current. In addition, current in some materials is carried by particles... 

As well as these intrinsic structural defect populations, electronic defects (excess electrons and holes) will always be found. These are also intrinsic defects and are present even in the purest material. When the equilibria among defects are considered, it is necessary to include both structural and electronic defects. 

Reactions involving the creation, destruction, and elimination of defects can appear mysterious. In such cases it is useful to break the reaction down into hypothetical steps that can be represented by partial equations, rather akin to the half-reactions used to simplify redox reactions in chemistry. The complete defect formation equation is found by adding the partial equations together. The mles described above can be interpreted more flexibly in these partial equations but must be rigorously obeyed in the final equation. Finally, it is necessary to mention that a defect formation equation can often be written in terms of just structural (i.e., ionic) defects such as interstitials and vacancies or in terms of just electronic defects, electrons, and holes. Which of these alternatives is preferred will depend upon the physical properties of the solid. An insulator such as MgO is likely to utilize structural defects to compensate for the changes taking place, whereas a semiconducting transition-metal oxide with several easily accessible valence states is likely to prefer electronic compensation. 

A straightforward method is to incorporate ahovalent impurity ions into the crystal. These impurities can, in principle, be compensated structurally, by the incorporation of interstitials or vacancies, or by electronic defects, holes, or electrons. The possibility of electronic compensation can be excluded by working with insulating solids that contain ions with a fixed valence. 

If the total conductivity of a material is made up of contributions from cations, anions, electrons, and holes, equations such as (6.1), for ionic conductivity, must be extended to include the electronic defects ... 

Creation and Elimination of Electronic Defects These are the normal intrinsic electrons and holes present in a semiconductor. Electrons can combine with holes to be eliminated from the crystal thus ... 

The four equations [(7.9)-(7.12)] are simplified using chemical and physical intuition. Two examples are given. In the first (Sections 7.63-7.6.6) the case where ionic point defects are more important than electrons and holes is considered, and in the following sections (Sections 7.7.1-7.7.5) the reverse case, where electronic defects are more important than vacancies, is described. 

Because it is assumed that Ks is a lot greater than Ke it is reasonable to ignore the minority electronic defects and approximate the electroneutrality Eq. (7.12) by the relation ... 

It is important that the complete diagram displays prominently information about the assumptions made. Thus, the assumption that Schottky defect formation was preferred to the formation of electronic defects is explicitly stated in the form Ks > Ke (Fig. 7.9e). As Frenkel defect formation has been ignored altogether, it is also possible to write Ks > Ke > > Kt , where A p represents the equilibrium constant for the formation of Frenkel defects in MX. 

BROUWER DIAGRAMS ELECTRONIC DEFECTS 7.6.1 Electronic Defects... 

The equations involving defect formation will be identical to Eqs. (7.7-7.10). However, the values for the equilibrium constants chosen in Section 7.5.3 are now reversed to give greater concentrations of electronic defects at the stoichiometric point ... 

Figure 7.10 Brouwer diagram for a phase MX in which electronic defects are the main point defect type (a) initial points on the diagram, (b) variation of defect concentrations in the near-stoichiometric region, (c) extension to show variation of defect concentrations in the high partial pressure region, (d) extension to show variation of defect concentrations in the low partial pressure region, and (e) the complete diagram.

In general, there is little problem in extending the concepts just outlined to more complex materials. The procedure is to write down the equations specifying the various equilibria point defect formation, electronic defect formation, the oxidation reaction, and the reduction reaction. These four equations, only three of which are independent, are augmented by the electroneutrality equation. Two examples will be sketched for the oxides Cr2C>3 and Ba2In2Os. 

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