Point defects insulators

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

The compound will be stoichiometric, with an exact composition of MX10ooo when the number of metal vacancies is equal to the number of nonmetal vacancies. At the same time, the number of electrons and holes will be equal. In an inorganic compound, which is an insulator or poor semiconductor with a fairly large band-gap, the number of point defects is greater than the number of intrinsic electrons or holes. To illustrate the procedure, suppose that the values for the equilibrium constants describing Schottky disorder, Ks, and intrinsic electron and hole numbers, Kc, are... 

S2.3 Point Defects and Energy Bands in Semiconductors and Insulators... 

A point defect in an insulator or semiconductor is represented on band diagrams as an energy level. These energy levels can lie within the conduction or valence bands, but those of most consequence for electronic and optical properties are those that lie in the band gap. The effects of these impurities on the electronic properties of the solid will... 

Next let us discuss the electronic defects associated with point defects in semiconductive or insulating compounds, which lead to non-stoichiometry. Consider a NiO crystal, which has a NaCl-type structure, as NiO can be regarded as an ionic crystal, the valence states of Ni and O are Ni and O , respectively. We assume that the non-stoichiometry originates only from metal vacancies. Generation of metal defects in NiO may be expressed by a chemical reaction similar to eqn (1.119), i.e. 

Concentration equilibrium among A , A , A , and h is discussed on the assumption that these equations can be treated as chemical equilibrium ones. (Similarly, D", D, (donor levels), and e are regarded as chemical species, see Fig. 1.24(c).) We have a reasonable reason for regarding these species as chemical species. As is well known, the electrical properties of metals and alloys are independent of the concentration of point defects or imperfections existing in their crystals, because the number of electrons or holes in metals or alloys is roughly equal to that of the constituent atoms. For the case of semiconductors or insulators, however, the number of electrons or holes is much lower than that of the constituent atoms and is closely correlated to the concentration of defects. In the latter case, electrons and holes can be considered as kinds of chemical species, for a reason similar to that discussed above for the case of point defects. Let us consider the chemical potential, which is most characteristic of chemical species. Electrochemical potential of electrons is written as... 

Thus, lattice defects such as point defects and carriers (electrons and holes) in semiconductors and insulators can be treated as chemical species, and the mass action law can be applied to the concentration equilibrium among these species. Without detailed calculations based on statistical thermodynamics, the mass action law gives us an important result about the equilibrium concentration of lattice defects, electrons, and holes (see Section 1.4.5). 

In the present chapter we focus on the optical spectra of the transitional metal ion impurities, as the point defects in insulating crystals. The reasons are because the JT effect is most often encountered in the transitional metal complexes, and very common in the octahedral complexes. We shall make use of the configuration coordinate approach [12], which enables one to apply much of the theory developed for molecules to the case of an isolated impurity in a crystal. 

J.-M. Spaeth, H. Overhof, Point Defects in Semiconductors and Insulators (Springer,... 

The TSC method was first developed by Bucci and Fieschi in 1964 (15). The technique was initially used to characterize point defects in simple crystals. Later, it was applied to a wide variety of samples, including inorganic materials (insulators as halide crystals, polycrystals, or amorphous materials semiconductors in crystalline or amorphous state), or organic materials (small molecules in noncrystalline or crystalline states, amorphous or semicrystalline synthetic macromolecules, and natural macromolecules) (12-14). 

Of particular interest are those surfaces where AFM has provided complementary information or revealed surface stmcture which could not be obtained by STM. One obvious application is the imaging of insulators such as NaCl(OOl) [120]. In this case it was possible to observe point defects and thermally activated atomic jump processes, although it was not possible to assign the observed maxima to anion or cation. 

Depending on material and treatment, the surface can be an insulator, a semiconductor or a conductor. Technically produced surfaces are flat or curved. A distinction is made between flatness, waviness and roughness. The surfaces contain defects on an atomic and on a macroscopic scale. Such atomic defects are point defects,... 

Band structure details of insulators can be determined from their UV/VIS spectra. Defects in the crystal produce electronic levels within the gap between the conduction and the valence bands. Spectroscopic measurements at low temperature allow the investigation of the phonon structure of a crystal. Absorptions due to lattice or point defects can be used to describe the optical and electronic properties of the insulator. For example, Cr in AI2O3 crystals leads to an intense color change of the crystal. Many so-caUed color centers are based on lattice defects caused by intercalation of atoms in the crystal lattice. 

CL Cathode Luminescence Insulators, semiconductors Electrons 5-50 keV Photons 0.1-5 eV 1 nm-2 pn 1 or 2 nm Energy levels of impurities and point defects 30... 

Point defects are particularly important in ceramics because of the role they can play in determining the properties of a material. The entire semiconductor industry is possible because of minute concentrations of point defects that are added to Si the dopants determine if the Si is n-type, p-type, or semi-insulating they determine the electrical properties. Solid-oxide fuel cells work because of the large concentrations of oxygen vacancies present the vacancies provide fast ion conduction pathways. CZ is cubic because of the presence of point defects that stabilize the cubic structure. 

Meng BS, Klein BDB, Booske JH, Cooper RF (1996) Microwave absorption in insulating dielectric ionic crystals including the role of point defects. Phys Rev B 53 12777-12785... 

Factors affecting the potential measurements are broken test leads, corroded contact points, and defective insulation of test leads. An improperly calibrated RE can also be an important source of errors. The existence of vegetation or of other metals may introduce errors of over 100 mV. 

Wright, J.C., 1985, Laser Spectroscopy of Point Defect Equilibria in Insulators Transitions of Insulators to Superionic State, in Proc. Int. Conf. on Defects in Insulating Crystals, Cryst. Lattice Defects and Amorphous Mat., Vol. 12, ed. F. Liithi (Gordon and Breach, New York) pp. 505. 

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