Weak bond model

If the weak bonding model is valid for high angle grain boundaries (>20°) it follows that diffusion in amorphous preparations of a given material should also show this measure of enhanced diffusion, when compared widr die crystalline material. 

Distributions of formation energies - the weak bond model... 

The weak bond model assumes that the terms in the square bracket in Eq. (6.39) are negligible, so that... 

The weak bond model is useful because the distribution of formation energies can be evaluated from the known valence band and defect density of states distributions. Fig. 6.12 illustrates the distribution of formation energies, N iU). The shape is that of the valence band edge given in Fig. 3.16 and the position of the chemical potential of the defects coincides with the energy of the neutral defect gap state. Fig. 6.12 also shows that in equilibrium virtually all the band tail states which are deeper than convert into defects, while a temperatiue-dependent fraction of the states above convert. 

Fig. 6.12. The distribution of formation energies according to the weak bond model. The shape is proportional to the valence band density of states.

A different weak bond model results when hydrogen is involved in the defect creation process. Consider a model in which hydrogen is released from a Si—H bond and breaks a weak Si—Si bond, by attaching to one of the silicon atoms. The model is illustrated in Fig. 6.13, and is described by the reaction. 

The two weak bond models predict different defect densities, the... 

Fig. 6.13. Illustration of the hydrogen-mediated weak bond model in which a hydrogen atom moves from a Si—H bond and breaks a weak bond, ieaving two defects (Dh and D ) (Street and Winer 1989).

The useful feature of the weak bond model is that it provides a first-principles calculation relating the defect density to measurable quantities, Ty and E. Further development of the model is needed, as the assumptions are yet to be confirmed, and a detailed analysis of doped a-Si H using the model has not been reported. The weak bond model provides a framework for understanding how the defect density varies with growth conditions and alloying, aspects of which are discussed next. 

The defect density in the weak bond model (e.g. Eqns. (6.43) or... 

Fig. 6.14. Predicted temperature dependence of the equilibrium defect density for four different weak bond models, the details of which are deseribed in the text (Street and Winer 1989).

The weak bond model assumes a non-equilibrium distribution of weak bonds arising from the disorder of the a-Si H network. It has been proposed that the shapes of the band tails are themselves a consequence of thermal equilibrium of the structure (Bar-Yam, Adler and Joannopoulos 1986). The formation energy of a tail state is assumed proportional to the difference in the one-electron energies, so that the energy, required to create a band tail state of energy Ey from the valence band mobility edge is... 

Zhao, Y. W., Chang, L., and Kim, S. H., "A Mathematical Model for Chemical-Mechanical Polishing Based on Formation and Removal of Weakly Bonded Molecular Species, Wear, Vol. 254,2003, pp. 332-339. 

Recently, Vayner and coworkers [239] have revisited the model proposed by Augustine et al. [34] which is based on the assumption that the QN can make a nucleophilic attack to an activated carbonyl. According to this model the two possible zwitterionic intermediates that can thus be formed have different energies, which leads to the selective formation of one of the two intermediates, and, therefore, to e.s. after hydrogenolysis by surface hydrogen. This model nevertheless does not explain the e.d. of nonbasic modifiers, such as the one reported by Marinas and coworkers [240], which have no quinuclidine moiety and no nitrogen atom, and thus no possibility to form zwitterionic intermediates. Furthermore, in situ spectroscopic evidence for hydrogen bond formation between the quinuclidine moiety of cinchonidine and the ketopantolactone has been provided recently [241], which supports the hypothesis of the role of weak bond formation rather than the formation of intermediates such as those proposed by Vayner and coworkers. 

Figure 2. RRKM calculations of the kinetic shift for model hydrocarbon ion dissociations as a function of ion size. Calculations are shown both for a fairly weakly bonded ion (1.86 eV) and a fairly strongly bonded one (3.10 eV), and in each case both the conventional and the intrinsic kinetic shifts are plotted.

The weak and highly polar Cl—F bond in FCIO can be rationalized in terms of either a (p—7T )a bond (see Section II, C) or a simple valence bond model (66) resulting in a resonance hybrid of the following canonical forms FCIO2 F + C102. It has been discussed in detail by Parent and Gerry (220), by Carter et al. (43), and in Section II, C of this review. 

Chuvylkin et al. (54) have used this approach to discuss EPR signals arising from weak R02 surface complexes in a number of systems where the g tensor does not fit the pattern expected [Eq. (6) and Fig. 3] from the ionic model. This is not discussed quantitatively, but they conclude that the appearance of covalently bonded oxygen is impossible without a favorable orientation of appropriate electronic orbitals. A similar covalent bonding approach has been considered theoretically for the chemisorption of oxygen on silicon surfaces (55). Examples of weakly bonded oxygen are given in Section IV,E. 

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