Point defect examples

Point defects and complexes exliibit metastability when more than one configuration can be realized in a given charge state. For example, neutral interstitial hydrogen is metastable in many semiconductors one configuration has H at a relaxed bond-centred site, bound to the crystal, and the other has H atomic-like at the tetrahedral interstitial site. 

If tlie level(s) associated witli tlie defect are deep, tliey become electron-hole recombination centres. The result is a (sometimes dramatic) reduction in carrier lifetimes. Such an effect is often associated witli tlie presence of transition metal impurities or certain extended defects in tlie material. For example, substitutional Au is used to make fast switches in Si. Many point defects have deep levels in tlie gap, such as vacancies or transition metals. In addition, complexes, precipitates and extended defects are often associated witli recombination centres. The presence of grain boundaries, dislocation tangles and metallic precipitates in poly-Si photovoltaic devices are major factors which reduce tlieir efficiency. 

In addition to the configuration, electronic stmcture and thennal stability of point defects, it is essential to know how they diffuse. A variety of mechanisms have been identified. The simplest one involves the diffusion of an impurity tlirough the interstitial sites. For example, copper in Si diffuses by hopping from one tetrahedral interstitial site to the next via a saddle point at the hexagonal interstitial site. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

An effect which is frequently encountered in oxide catalysts is that of promoters on the activity. An example of this is the small addition of lidrium oxide, Li20 which promotes, or increases, the catalytic activity of dre alkaline earth oxide BaO. Although little is known about the exact role of lithium on the surface structure of BaO, it would seem plausible that this effect is due to the introduction of more oxygen vacancies on the surface. This effect is well known in the chemistry of solid oxides. For example, the addition of lithium oxide to nickel oxide, in which a solid solution is formed, causes an increase in the concentration of dre major point defect which is the Ni + ion. Since the valency of dre cation in dre alkaline earth oxides can only take the value two the incorporation of lithium oxide in solid solution can only lead to oxygen vacaircy formation. Schematic equations for the two processes are... 

Dick and Styrus [63] report real-time resistivity measurements on shoek-loaded silver foils. The inferred vaeaney eoneentration is 1.5 x 10 per atomie site for samples shoek loaded to 10 GPa. The eombined effect of point-defect generation and reeombination to form vaeaney clusters, for example, can be influential on pulse-duration effeets such reload, release, and recovery. This topie has not yet reeeived the degree of experimental study that it deserves. 

Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

Several points are worth noting about these formulae. Firstly, the concentrations follow an Arrhenius law except for the constitutional def t, however in no case is the activation energy a single point defect formation energy. Secondly, in a quantitative calculation the activation energy should include a temperature dependence of the formation energies and their formation entropies. The latter will appear as a preexponential factor, for example, the first equation becomes... 

One type of point defect that cannot be entirely eliminated from a solid compound is the substituted ion or impurity defect. For example, suppose a large crystal contains 1 mole of NaCl that is 99.99 mole percent pure and that the 0.01% impurity is KBr. As a fraction, there is 0.0001 mole of both K+ and Br ions, which is 6.02 X 1019 ions of each type present in the 1 mole of NaCl Although the level of purity of the NaCl is high, there is an enormous number of impurity ions that occupy sites in the lattice. Even if the NaCl were 99.9999 mole percent pure, there would still be 6.02 X 1017 impurity cations and anions in a mole of crystal. In other words, there is a defect, known as a substituted ion or impurity defect, at each point in the crystal where some ion other than Na+ or Cl- resides. Because K+ is larger than Na+ and Br is larger than Cl-, the lattice will experience some strain and distortion at the sites where the larger cations and anions reside. These strain points are frequently reactive sites in a crystal. 

Structural Imperfections. In many respects HREM has had a greater impact upon our knowledge of the nature of the atomic reorganization at crystalline imperfections than any other single technique. One of the very first contributions of HREM as a new analytical and structural tool was described in the paper by Iijimia (42) in 1971 on 2 10 29 v -ewe< down to its b - axis. Structural faults, arising from subtle fluctuations in composition, could be clearly seen in the block-structure (based on NbO octahedra) which is a feature of this ternary oxide system. More than a decade later similar materials are yielding to active scrutiny by HREM, and Horiuchi (43), for example, has shown how point defects may be directly viewed... 

It is known that hydrogen incorporated into Si subsequently exposed to ionizing radiation inhibits the formation of induced secondary point defect (Pearton and Tavendale, 1982a). For example, in both Si and Ge a number of electron or y irradiation induced defect states appear to be vacancy-related, and exposure of the Si or Ge to a hydrogen plasma (or implantation of hydrogen into the sample) prior to irradiation induces a degree of... 

No material is completely pure, and some foreign atoms will invariably be present. If these are undesirable or accidental, they are termed impurities, but if they have been added deliberately, to change the properties of the material on purpose, they are called dopant atoms. Impurities can form point defects when present in low concentrations, the simplest of which are analogs of vacancies and interstitials. For example, an impurity atom A in a crystal of a metal M can occupy atom sites normally occupied by the parent atoms, to form substitutional point defects, written AM, or can occupy interstitial sites, to form interstitial point defects, written Aj (Fig. 1.4). The doping of aluminum into silicon creates substitutional point defects as the aluminum atoms occupy sites normally filled by silicon atoms. In compounds, the impurities can affect one or all sublattices. For instance, natural sodium chloride often contains... 

Such changes in the defect population can be critical in device manufacture and operation. For example, a thin him of an oxide such as SiO laid down in a vacuum may have a large population of anion vacancy point defects present. Similarly, a him deposited by sputtering in an inert atmosphere may incorporate both vacancies and inert gas interstitial atoms into the structure. When these hlms are subsequently exposed to different conditions, for example, moist air at high temperatures, changes in the point defect population will result in dimensional changes that can cause the him to buckle or tear. 

These examples indicate that it is necessary to keep the possible effect of point defects on bulk and mechanical properties in mind. Although less definitive than electronic and optical properties, they may make the difference in the success or failure of device operation. 

The treatment assumes that the point defects do not interact with each other. This is not a very good assumption because point defect interactions are important, and it is possible to take such interactions into account in more general formulas. For example, high-purity silicon carbide, SiC, appears to have important populations of carbon and silicon vacancies, and Vsj, which are equivalent to Schottky defects, together with a large population of divacancy pairs. 

The simplest way to account for composition variation is to include point defect populations into the crystal. This can involve substitution, the incorporation of unbalanced populations of vacancies or by the addition of extra interstitial atoms. This approach has a great advantage in that it allows a crystallographic model to be easily constructed and the formalism of defect reaction equations employed to analyze the situation (Section 1.11). The following sections give examples of this behavior. 

In the previous sections composition variation has been attributed more or less to point defects and extensions of the point defect concept. In this section structures that can be considered to be built from slabs of one or more parent structures are described. They are frequently found in mineral specimens, and the piecemeal way in which early examples were discovered has led to a number of more or less synonymic terms for their description, including intergrowth phases, composite structures, polysynthetic twinned phases, polysomatic phases, and tropochemical cell-twinned phases. In general, they are all considered to be modular structures. 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

The random-walk model of diffusion needs to be modified if it is to accurately represent the mechanism of the diffusion. One important change regards the number of point defects present. It has already been pointed out that vacancy diffusion in, for example, a metal crystal cannot occur without an existing population of vacancies. Because of this the random-walk jump probability must be modified to take vacancy numbers into account. In this case, the probability that a vacancy is available to a diffusing atom can be approximated by the number of vacant sites present in the crystal, d], expressed as a fraction, that is... 

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