Defect recombination

The recombination of electrons and holes is a rather complicated process. We have to distinguish between (a) the direct recombination of electrons and holes, occurring in particular at high concentrations of charge carriers (b) recombination via defect states which depends, among other factors, on the densities and capture cross-sections of the defects (recombination centers) located in the bulk of the solid or on its surface. 

The second part of Eqn. (1.23) is obtained from Eqn. (1.22). From the requirement of eleetroneutrality and the definition of a (linearized) defect recombination zone of width R, Eqns. (1.22) and (1.23) yield... 

If we denote the point defect injected by the applied field into the wrong sublattice of AX by i (e.g A ), and the conjugate defect that carries the flux in AX by j (e.g., V ), then the steady state condition for both fluxes (i, j) in the defect recombination zone r is... 

We conclude that a crystal which is continuously irradiated with particles of sufficient kinetic energy and in which no further reactions (e.g., phase formations) take place becomes more and more supersaturated with point defects. Recombination starts if the defects can move fast enough by thermal activation. A steady state is reached when the rates of defect production and annihilation (by recombination) are equal. In the homogeneous crystal, the change in local defect concentration (cd) over time is given by (see Section 5.3.3)... 

The conclusion itself suggests that from the point of view of formal chemical kinetics both energy transfer and the Frenkel defect recombination with... 

Fig. 3.2. Two principal mechanisms of defect recombination in solids, (a) Complementary defect annihilation, r is the clear-cut (black sphere) radius, (b) distant tunnelling recombination due to overlap of wave functions of defects. Two principal kinds of hole centres - H and Vk...

Another, alternative mechanism of defect recombination is spontaneous electron tunnelling from an electron centre to its hole partner (or in terms of... 

Defect diffusion traditionally is treated as a process in continuum medium. However, discreteness of the crystalline lattice becomes important in particular situations, e.g., when defect recombination occurs in several hops (nearest neighbour recombination) [3, 4] or even for nearest-site hops of defects if their recombination is controlled by the tunnelling whose probability greatly changes on a scale of lattice constant [45, 46],... 

Let us consider first the case of low temperatures and immobile defects (,static reaction). In this situation electron tunnelling is the only channel of defect recombination and concentration decay. Depending on the defect relative spatial distribution, two recombination regimes can arise. 

To describe quantitatively the diffusion-controlled tunnelling process, let us start from equation (4.1.23). Restricting ourselves to the tunnelling mechanism of defect recombination only (without annihilation), the boundary condition should be imposed on Y(r,t) in equation (4.1.23) at r = 0 meaning no particle flux through the coordinate origin. Another kind of boundary conditions widely used in radiation physics is the so-called radiation boundary condition (which however is not well justified theoretically) [33, 38]. The idea is to solve equation (4.1.23) in the interval r > R with the partial reflection of the particle flux from the sphere of radius R ... 

To consider defect recombination controlled by the anisotropic potential, equation (3.1.4), it was suggested [76] to rewrite the quasi-steady-state equation (4.2.22) in a form... 

Figure 7.13 shows similar dependence for a fixed dose rate but varying the temperature (F centre mobility). As it is expected from equation (7.2.14), the higher the temperature, the more intensive defect recombination is and thus the lower the saturation concentration. Curve 3 in Fig. 7.13(b) confirms once more that T 100°C is the optimal aggregation temperature for a given dose rate of 1017 cm-3 s-1 whereas at higher temperatures a portion of F2 centres decreases. 

A wide range of condensed matter properties including viscosity, ionic conductivity and mass transport belong to the class of thermally activated processes and are treated in terms of diffusion. Its theory seems to be quite well developed now [1-5] and was applied successfully to the study of radiation defects [6-8], dilute alloys and processes in highly defective solids [9-11]. Mobile particles or defects in solids inavoidably interact and thus participate in a series of diffusion-controlled reactions [12-18]. Three basic bimolecular reactions in solids and liquids are dissimilar particle (defect) recombination (annihilation), A + B —> 0 energy transfer from donors A to unsaturable sinks B, A + B —> B and exciton annihilation, A + A —> 0. 

The cross-section for charged-defect recombination will likely be larger than that for neutral-defect recombination. In addition, dopant ions will likely provide additional recombination sites when the dopant is paired with a point defect. 

Tsai TH, Chen SL, Xiao X, Chiang YH, et al. 2006. Gene therapy of focal cerebral ischemia using defective recombinant adeno-associated virus vectors. Front Biosci. 11 2061-2070. 

Schmitz, G., Assmann, G., Rail, S. C., Jr., and Mahley, R. W., Tangier disease Defective recombination of a specific Tangier apolipoprotein A-I isoform (pro-apo A-I) with high density lipoproteins. Proc. Natl. Acad. Sci. U.S.A. 80, 6081-6085 (1983). 

Fig. 8.21. Illustration of the competition between band tail radiative recombination and defect recombination either by tunneling (solid line) or by thermal excitation to the band edge (dashed line).

At temperatures above 100 K, the defect recombination mechanism changes gradually from tunneling to direct capture of a mobile electron or hole at a defect. The capture rate defines the capture cross-section such that the free carrier lifetime is given by... 

The defect recombination is predominantly, but not completely, non-radiative. The quenching of the band tail luminescence at high temperature or at high defect density is accompanied by the onset of a weak luminescence transition at lower energy. Some typical luminescence spectra are shown in Fig. 8.25 for doped and high defect density undoped material. The peak energy at low temperature is... 

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