Defects equilibration

Note that the balances of matter, sites, and charge are obeyed. According to standard kinetics, we formulate the rate equation of this defect equilibration process and denote, for simplicity sake, Ag by i, VAg by V and AgAg by Ag. Let us designate the frequency of a site exchange between a vacancy and an ion on a different sublattice as v. According to a bimolecular rate equation, the time derivative of the concentration is... 

When the point defect relaxation is diffusion controlled, we can use Eqn. (5.89) to determine k. After setting rAB = aAX (= unit cell dimension), it is found that at even moderate temperatures (= 100°C), x is on the order of a millisecond or less. This r is many orders of magnitude shorter than relaxation times for nonstoichiometric compounds where the point defect pairs equilibrate at external surfaces (Section 5.3.2). In other words, intrinsic defects equilibrate much faster than extrinsic defects if, during the defect equilibration, the number of lattice sites is conserved. 

The Kirkendall effect in metals shows that during interdiffusion, the relaxation time for local defect equilibration is often sufficiently short (compared to the characteristic time of macroscopic component transport) to justify the assumption of local point defect equilibrium. In those cases, the (isothermal, isobaric) transport coefficients (e.g., Dh bj) are functions only of composition. Those quantitative methods introduced in Section 4.3.3 which have been worked out for multicomponent diffusion can then be applied. 

In order to clarify the meaning of D in the case of incomplete (local) defect equilibration, let us consider a linear diffusion geometry and assume that the equilibration of the defects with the external oxygen buffer occurs only at one end of the sample. The fluxes of the components can then be expressed as... 

D thus depends on a, which, according to Eqn. (5.131), is determined by the assumptions which govern the equilibration of oxygen (d//G = 0) or the vacancies (d v = 0). In other words, the interdiffusion coefficient D depends directly on the mode and extent of the point defect equilibration. 

So far it has been assumed that the defect electronic states form a narrow band at E. When there is a broad distribution of energy levels, the defect equilibration favors those with the lowest formation energy, which are the states lowest in the gap (see Eq. (6.40)). The effect of the distribution is particularly significant in comparing the defect states in differently doped materials, because the contribution of the gap state to the formation energy depends on the charge state (Bar-... 

The data show that the effect of adsorbed molecules is more complicated than is described above, as there are fast and slow processes with opposite conductance changes (see Fig. 9.13(a)). One possible explanation is that the band bending induces defect states, through the defect equilibration process described in Chapter 6. This might explain the slow decrease of the conductance after the initial... 

The metastability phenomena influence the performance of the active matrix arrays. Defect creation in the channel causes a threshold voltage shift when a TFT is held on for an extended time and results in a slow drift of the on-current. Fortunately the rate of defect creation is low at room temperature and represents a minor problem. There is a larger effect on the characteristics of the high voltage TFTs. Resistors fabricated from n a-Si H change their resistance slowly because of defect equilibration and can affect the gain of amplifier circuits. 

If the temperature of a potassium chloride crystal is suddenly decreased, then the number of Schottky defects present will be greater than the new equilibrium value. That is, the crystal is supersaturated with respect to defects. Equilibration is then achieved by the reaction ... 

The last two examples show that inter diffusion processes and chemical diffusion coefficients can vary widely, depending upon the transport numbers of the ionic and electronic defects. A theoretical calculation is only possible if it is assumed that defect equilibrium is maintained. Whether the assumption of local defect equilibrium is applicable to an individual case will depend upon the relaxation time for the defect equilibration process. That is, it will depend upon the density of defect sources and sinks. In most cases, therefore, it will depend upon the density of dislocations and of low- and high-angle grain boundaries. 

Two characteristic times are employed (a) Tj, defined as the longest of the relaxation times for defect equilibration, proportional to and (b) Tr, defined as the renewal time for chain conformation, proportional to M. This latter time is the time to form a new isotropic tube. For polystyrene of M = 650,000 g/mol at 117°C, they found that... 

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