Point defects formation properties

S.3 Theoretical Computation of Point-Defect Formation Properties... 

The possible point-defect structures, migration properties,. . . are so numerous in intermetallic compounds that experiment alone cannot solve the problem. Unfortunately, theory here is still in its infancy. For example, the commonly used Miedema and bond-breaking semiempirical models to estimate point-defect formation energies are quite contradictory. It is only recently, since the 1980s, that more sophisticated theoretical methods have been developed and seem to be able to predict point-defect structures and properties with some accuracy. Great progress can be expected from the combined use of Monte-Carlo and molecular-dynamics simulations (Rey-Losada et al., 1993). 

As discussed in the next chapters, point defect formation does not only depend on the bonding properties but also on the vibrational properties. Point defect concentrations in many substances are comparable close to the melting point. 

We will be considering primarily inorganic solids but must keep in mind that the same principles also apply to organic solids. Therefore, we intend to examine the nature of point defects in terms of their thermodynamics, equilibria and the energy required for their formation. It will be seen that point defects follow the same physical chemistry laws that apply to inorgcuiic compounds and physical properties in general. 

Point defect populations profoundly affect both the physical and chemical properties of materials. In order to describe these consequences a simple and self-consistent set of symbols is required. The most widely employed system is the Kroger-Vink notation. Using this formalism, it is possible to incorporate defect formation into chemical equations and hence use the powerful methods of chemical thermodynamics to treat defect equilibria. 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

Typical point defects present at the Si02 surface are the so called E centres, holes trapped at oxygen vacancies, and Si dangling bonds. These latter defects are particularly important when present at the Si/SiOz interface because they markedly affect the electrical properties of electronic devices. These defects, which are also known as Pb centres, have been widely investigated in the past. Recently however, the microscopic origin of these defects has been unravelled by means of a sophisticated UHV-ESR system by Futako et al, 178 who elucidated the formation processes of interface dangling bonds (Pb centres) during the initial oxidation of a clean Si(lll) surface. After oxidation of one or two Si layer(s), the... 

Point defects are an important part of the work in this paper. There are many reasons for the formation of point defects in minerals and their presence can exert important perturbations on the properties of the material (4). Point defects are formed because of the thermally driven intrinsic disorder in a lattice, the addition of aliovalent impurities or dopants, the presence of metal-nonmetal nonstoichiometry, and the creation of nonideal cation ratios. The first three source of defects are well-known from binary compounds but the last is unique to ternary compounds. Ternary compounds are much more complex than the binary compounds but they also have gained a great deal of attention because of the variety of important behavior they exhibit including now the presence of superconductivity at high temperatures. The point defects can be measured by introducing probe ions into the lattice. 

If cations or anions in a lattice are replaced by others that have a different valence, or alternatively if interstitial atoms or ions are added to the stmcture without compensating populations of vacancies, the composition of the crystal must change. Variable populations of such defects will lead to composition ranges of the solid phase and to additional electronic or optical properties. At low concentrations, these defects can be conveniently considered as point defects distributed at random throughout the structure. As the number of defects increases, interactions will lead to the formation of clusters or extended defects. 

Catalytic applications of ceria and ceria-based mixed oxides depend primarily upon the nature and concentration of the defects present in the material. Although experimental techniques are available for the study of these defects, the characterization of their physical properties at the atomic level is often very difficult. The most important point defects in ceria are oxygen vacancies, reduced Ce centers and dopant impurities. The formation energy of such defects and the energetics of their mutual interactions within the bulk oxide have been the subject of several computational studies. 

Quantum-chemical simulation in a cluster approach has shotvn that introduction of hydrogen in silicon nanoclusters leads to initial stages of silicon layers amorphization, whereas oxygen atoms play a role of the stabilizing factor forming initial stmctures of silicon oxide from amorphized silicon layers. The experiments have demonstrated that H, He and Ar ion-beam treatments have a qualitatively similar impact on the electrical properties of Si wafers and are caused by the formation of point defects by ions (independing of ion type) and the creation of donors in the under-surface wafer region (only in a caseof H -treatment at elevated temperatures). 

Because ion-beam treatment effect on the electrical properties of the wafers is independent of the treatment temperature and ion type, one of the mechanisms of this influence is the formation of point defects. This can lead to (i) the positive charge creation in the surface oxide layer [2] (ii) transfer of boron atoms into the electrically inactive interstitial positions by the ion-beam generated Sii atoms... 

Until recently very little was understood as to the factors which determine whether point or extended defects are formed in a non-stoicheiometric phase, although interesting empirical correlations between shear-plane formation and both dielectric and lattice dynamical properties of the defective solid had been noted. Theoretical techniques have, however, provided valuable insight into this problem and into the related one of the relative stabilities of extended and point defect structures. The role of these techniques is emphasized in this article. 

---