Interstitial formation energy

Table II. Estimated Interstitial Formation Energies in Silicon...

The differences in the atom coordination around the interatomic cavities manifest themselves in the distribution of the interstitial formation energies. In LRC s as well as in crystals, the formation of dumbbell interstitial configurations is possible. The expressions for equilibrium concentrations of interstitials are similar to those given above for vacancies (6.19 and 20), with the difference, however, that one accounts in them for the difference of interstitial cavities and the possibility of dumbbell configuration formation. 

Fig. 9. Relative formation energies for different charge states of a H interstitial impurity in Si. The zero of energy is arbitrarily chosen as the energy of H° at T. This figure is not intended to display quantitative results but merely to provide a qualitative indication of the stability of different charge states. (Reprinted with permission from the American Physical Society, Van de Walle et al., 1989.)...

Calculations are now carried out routinely using a wide variety of programs, many of which are freely available. In particular, the charge on a defect can be included so that the formation energies, interactions, and relative importance of two defects such as a charged interstitial as against a neutral interstitial are now accessible. Similarly, computation is not restricted to intrinsic defects, and the energy of formation of... 

The formation energies of point defects in a pure metal are 1.0 eV (vacancies) and 1.1 eV (interstitials). The number of vacancies is ... 

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

While zinc interstitials are possible, the formation energy for these defects is higher than that of oxygen vacancies. As in the case of NiO, continuing theoretical studies are needed to clarify the location of holes and electrons in these phases. 

The (100) split-dumbbell defect in Fig. 8.5d, while having the lowest energy of all interstitial defects, still has a large formation energy (Ef = 2.2 eV) because of the large amount of distortion and ion-core repulsion required for its insertion into the close-packed Cu crystal. However, once the interstitial defect is present, it persists until it migrates to an interface or dislocation or annihilates with a vacancy. The... 

Self-Diffusion by the Interstitialcy Mechanism. If their formation energy is not too large, the equilibrium population of self-interstitials may be large enough to contribute to the self-diffusivity. In this case, the self-diffusivity is similar to that for self-diffusion via the vacancy mechanism (Eq. 8.19) with the vacancy formation and migration energies replaced by corresponding self-interstitial quantities. The... 

Calculations of the fractional interstitialcy components for B, P, As, and Sb are shown in Table I (33, 39-42). A significant spread in the values of/, is obtained. The value of / has been correlated with the amount of energy required to make a substitutional dopant atom become interstitial. Energies of interstitial formation in Si are shown in Table II. The larger the energy... 

FIGURE 2 Formation energy as a function of Fermi energy for Mg in different configurations (Ga-substitutional, N-substitutional and interstitial configuration). Also included are the native defects (nitrogen vacancies) and interstitial H. 

First-principles calculations have also been performed for formation energies of native defects in AIN [8,9], The main conclusions are similar to those for GaN self-interstitials and antisites are high in energy - with the exception of the A1 interstitial in cubic AIN, which is a triple donor and could act as a compensating centre in p-type material. 

FIGURE 3 Formation energy as a function of Fermi level for Mg, nitrogen vacancies, interstitial H and hydrogen-vacancy complexes in GaN [1,14],... 

The most obvious feature of this mechanism to test by our theoretical calculations concerns the energetics of APB formation. Thus atomistic calculations of the type discussed in Section 2 for the shear planes, showed that the <011> APB had a considerably lower formation energy than boundaries with other orientations. The result is in line with the proposed mechanism, as interstitial capture at the <011>... 

Figure 2 DFT formation energies as a function of temperature for the Tc interstitial (triangles), Tu interstitial (circles), Be interstitial (diamonds), and vacancy (squares), averaged over different replicas. Error bars denote the magnitude of the fluctuations due to proton disorder. Lines represent polynomial fits to the average results.

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