Point-Defect Production

Fick s second law states the conservation of the diffusing species i no i is produced (or annihilated) in the diffusion zone by chemical reaction. If, however, production (annihilation) occurs, we have to add a (local) reaction term r, to the generalized version of Fick s second law c, = —Vjj + fj. In Section 1.3.1, we introduced the kinetics of point defect production if regular SE s are thermally activated to become irregular SE s (i.e., point defects). These concepts and rate equations can immediately be used to formulate electron-hole formation and annihilation... 

Point defect production as a result of implantation damage of the kind shown in Figure 20 gives rise to anomalous B diffusion during subsequent annealing. A summary of recent models that explain these effects follows... 

An important distinction between the alkali azides and ionic materials, such as the halides, is the susceptibility of the azides to point-defect production by UV radiation. There has been little research concerned with understanding how UV radiation produces individual point defects in the azides. Clearly the presence of the molecular anion, NJ, is important, and many of the defects are dissociation products of the azide ion. However, just the presence of a molecular anion is not sufficient. Cyanates, for example, do not have defects produced in them by UV light even though the NCO is isoelectronic with N3 [35]. It is important to consider the detailed electronic structure of the azide ion as well as the electronic structure of the lattice. Such factors as the energy of the first excited state with respect to the ground state, the proximity of an unbound state of the NJ to the lower excited state, the electron affinity and the ionization potential, as well as the band structures of individual azides, are important. 

They are the operating quality costs of prevention and appraisal that are considered to be controllable quality costs. Add that in year 2000 the IRS decided to let companies deduct ISO 9000 costs as a business expense. Also there are the internal and external failure costs. As the controllable cost of prevention and appraisal increases, the uncontrollable cost of internal and external failure decreases. At some point the cost of prevention and appraising defective product exceeds the cost of correcting for the product failure. This point is the optimum operating quality cost. 

Despite the fact that not all details of the photographic process are completely understood, the overall mechanism for the production of the latent image is well known. Silver chloride, AgBr, crystallizes with the sodium chloride structure. While Schottky defects are the major structural point defect type present in most crystals with this structure, it is found that the silver halides, including AgBr, favor Frenkel defects (Fig. 2.5). 

Solid-solid reactions are as a rule exothermic, and the driving force of the reaction is the difference between the free energies of formation of the products and the reactants. A quantitative understanding of the mechanism of solid-solid reactions is possible only if reactions are studied under well-defined conditions, keeping the number of variables to a minimum. This requires single-crystal reactants and careful control of the chemical potential of the components. In addition, a knowledge of point-defect equilibria in the product phase would be useful. 

In physical and chemical metallurgy, the Kirkendall effect, which is closely related to point defect relaxation during interdiffusion, has been studied extensively. It can be quantitatively defined as the internal rate of production or annihilation of vacan-... 

We have to evaluate the diffusion coefficient or any other transport coefficient with the help of point defect thermodynamics. This can easily be done for reaction products in which one type of point defect disorder predominates. Since we have shown in Chapter 2 that the concentration of ideally diluted point defects depends on the chemical potential of component k as d lncdefec, = n-dp, we obtain quite generally... 

By a change of temperature or pressure, it is often possible to cross the phase limits of a homogeneous crystal. It supersaturates with respect to one or several of its components, and the supersaturated components eventually precipitate. This is an additive reaction. It occurs either externally at the surfaces, or in the crystal bulk by nucleation and growth. Reactions of this kind from initially homogeneous and supersaturated solid solutions will be discussed in Chapter 12 on phase transformations. Internal reactions in the sense of the present chapter occur after crystal A has been brought into contact with reactant B, and the product AB forms isothermally in the interior of A or B. Point defect fluxes are responsible for the matter transport during internal reactions, and local equilibrium is often established throughout. 

AC/ is known as the overpotential in the electrode kinetics of electrochemistry. Let us summarize the essence of this modeling. If we know the applied driving forces, the mobilities of the SE s in the various sublattices, and the defect relaxation times, we can derive the fluxes of the building elements across the interfaces. We see that the interface resistivity Rb - AC//(F-y0) stems, in essence, from the relaxation processes of the SE s (point defects). Rb depends on the relaxation time rR of the (chemical) processes that occur when building elements are driven across the boundary. In accordance with Eqn. (10.33), the flux j0 can be understood as the integral of the relaxation (recombination, production) rate /)(/)), taken over the width fR. 

We conclude that a crystal which is continuously irradiated with particles of sufficient kinetic energy and in which no further reactions (e.g., phase formations) take place becomes more and more supersaturated with point defects. Recombination starts if the defects can move fast enough by thermal activation. A steady state is reached when the rates of defect production and annihilation (by recombination) are equal. In the homogeneous crystal, the change in local defect concentration (cd) over time is given by (see Section 5.3.3)... 

Excess Point Defects and Low-Thermal-Budget Annealing. Submicrometer VLSI (very-large-scale integration) technologies require low thermal budgets (the product of dopant diffusivity and diffusion time) to limit the diffusional motion of dopants. Two options exist to reduce the thermal... 

In this type of selective electrode, the membrane is an ionic solid which must have a small solubility product in order to avoid dissolution of the membrane and to ensure a response that is stable with time. Conduction through the membrane is principally ionic and is due to point defects in the crystal lattice, relying on the fact that no crystal is perfect. 

In an ideal situation dislocation lines would penetrate the whole crystal. In reality they mostly extend from one grain boundary to another one or they are pinned by impurities. If the lines form a closed circle inside the crystal, they are called loops. Summarizing, one may say that dislocations can arise from vacancy clusters as well as from interstitial clusters due to their pressure on the lattice. Very often they are the final products of an annealing procedure. Dislocations already existing interact with point defects and impurities acting as traps or sinks. 

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