Concentration, species defect

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... 

Semiconductive elements Si and Ge (Group IVB or 13 in the periodic table) have become very important electronic materials since development of a purification method. The electronic properties of semiconductive elements of high purity can be controlled by the species and concentration of defects and impurity elements. On the other hand, in the case of semiconductive compounds, that is, III-V and II-VI compounds, we have to consider not only control of the purity of constituent elements but also the nonstoichiometry, both of which have much influence on the electronic properties. In this sense, control of the electrical properties of semiconductive compounds is more difficult than that of semiconductive elements. 

Both categories of transport discussed above involve the motion of defects relative to an otherwise ordered array of ions, so the transport is referred to as defect transport. The concentrations of such defects (as contrasted with the total atom concentrations within the oxide lattice) are the important quantities for mass transport, charge transport, and space—charge effects, so it is the species defect concentration which appears in the diffusion equation. Likewise, the diffusion coefficients... 

Cs denotes the concentration of defects at the surface and Q the concentration of the defects in the bulk. The two previous reactions, which are consecutive, produce intermediate species whose variation of concentration Cs is dependent on... 

Chemical reactions for defects can be formulated and treated using the mass-action law. As for other chemical reactions, equilibrium constants can be defined in terms of the activities of the defects and other species. Under the normal constrictions we can approximate activities with concentrations of defects and partial pressures of gases. The equilibrium constants can also be expressed in... 

As discussed in Section 7.2.3, radiation can induce segregation of alloy elements at defect sinks such as grain boundaries [101]. Typically, RIS is a result of inverse Kirkendall (IK) effects in which the evolution of defect concentration field drives the evolution of alloy composition field. ID rate theory modeling [44,101] is widely used to describe the coupled evolution between defect flux and composition flux. These rate theory models considered both vacancy-mediated and interstitial-mediated solute transport, as well as point defect recombination and defect loss to dislocations. At steady state, the solute segregation direction depends on the relative diffiisivity of different species-defect coupled diffusion. In austenitic Fe-Cr-Ni alloys, the vacancy-mediated solute diffusion alone is sufficient in describing the RIS trend and the interstitial-mediated solute diffusion is usually assumed to have a neutral contribution to RIS [44]. However, in Fe-Cr F/M alloys, both interstitial- and vacancy-mediated diffusion should be considered [102]. 

Consider a compound semiconductor AB. Species B is volatile and exists as a dimer, Bj, in the vapor phase. Describe how the concentration of defects varies over a wide range of B2 partial pressure. For the sake of this analysis, consider only atomic defects of B and assume that they either are neutral or singly ionized. 

We consider an AB alloy which consists of an equal number of A and B sites. For the subsequent analysis, every site is uniquely associated with either an A or a B sublattive. The following is trivially generalised to A iBn alloys. The alloy is not quite stoichiometric, and has the composition A Bj.x, where for the validity of the independent defect approximation we must suppose x to be within a few percent of 0.5. Each site of each sublattice can be occupied by its own atom, an atom of the other kind (an antisite defect) or a vacancy. There are therefore six species for which we define the concentrations on each sublattice ... 

The type of disorder may be determined by conductivity measurements of electronic and ionic defects as a function of the activity of the neutral mobile component [3]. The data are commonly plotted as Brouwer diagrams of the logarithm of the concentration of all species as a function of the logarithm of the activity of the neutral mobile component. The slope is fitted to the assumption of a specific defect-type model. 

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