Mechanisms of defect recombination

An initial distribution function within geminate pairs directly defines their stability. In terms of the black sphere model, dissimilar defects (v, i) disappear instantly when approaching to within, or when just created by irradiation at the critical relative distance ro (called also clear-cut radius) - see 

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

From pair kinetics toward the many-reactant problem 

Tunnelling recombination of primary F, H pairs can result either in closely spaced v+,i pairs (the so-called a, I centres) which annihilate immediately due to Coulomb interaction and a consequently large instability radius. However some i ions occur in crowdion configurations, and leave vacancy moving away up to 4-5 oq even at 4 K [31]. The distinctive feature of tunnelling recombination is its temperature independence, which makes it one of the major low-temperature secondary processes in insulating solids with defects. 

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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...

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 ... 

It should be stressed once more that the accumulation curve n(t) (or U(t)), especially at high doses, cannot be described by a simple equation (7.1.53) which is often used for interpreting the real experimental data (e.g., [19, 20]). Despite there is the only recombination mechanism, the A + B —> 0 accumulation kinetics at long t due to many-particle effects is no longer exponential function of time (dose). Therefore, successful expansion of the experimental accumulation curve U = U(t) in several exponentials (stages) does not mean that several different mechanisms of defect creation are necessarily involved (as sometimes they suggest, e.g., [39, 40]). 

While most of the research in metastable defect formation has focussed on light-induced defects, there has recently been growing interest in thermally generated defects. Smith and Wagner (1985 Smith et al., 1986) extended the proposed Staebler-Wronski mechanism of electron-hole recombination via band tail states, resulting in the formation of dangling... 

We note in conclusion that taking account of correlation of defects in genetic pairs, formation of pairs of new defects (e.g., owing to the tunnelling mechanism of recombination), and of radiation-induced disclocation loops, etc., substantially complicate the development of rigorous and universal theory of the kinetics of defect accumulation. The temperature dependence of the efficiency of defect accumulation contains substantial information on the correlation within genetic pairs and on the nature of their interaction [119, 124] and is also of great theoretical importance. 

The analysis conducted in this Chapter dealing with different theoretical approaches to the kinetics of accumulation of the Frenkel defects in irradiated solids (the bimolecular A + B —> 0 reaction with a permanent particle source) with account taken of many-particle effects has shown that all the theories confirm the effect of low-temperature radiation-stimulated aggregation of similar neutral defects and its substantial influence on the spatial distribution of defects and their concentration at saturation in the region of large radiation doses. The aggregation effect must be taken into account in a quantitative analysis of the experimental curves of the low-temperature kinetics of accumulation of the Frenkel defects in crystals of the most varied nature - from metals to wide-gap insulators it is universal, and does not depend on the micro-mechanism of recombination of dissimilar defects - whether by annihilation of atom-vacancy pairs (in metals) or tunnelling recombination (charge transfer) in insulators. 

The rapid thermalization of carriers in extended states ensures that virtually all of the recombination occurs after the carriers are trapped into the band tail states. The two dominant recombination mechanisms in a-Si H are radiative transitions between band tail states and non-radiative transitions from the band edge to defect states. These two processes are described in this section and the following one. The radiative band tail mechanism tends to dominate at low temperature and the non-radiative processes dominate above about 100 K. The change with temperature results from the different characteristics of the transitions. The radiative transition rate is low, but there is a large density of band tail states at which recombination can occur. In contrast, the defect density is low but there is a high non-radiative transition rate for a band tail carrier near the defect. Band tail carriers are immobile at low temperatures, so that the recombination is... 

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 light output of a LED is given by the injection current and the radiative efficiency and is governed by two primary loss mechanisms. A large fraction of the recombination at room temperature is by non-radiative transitions at defects (see Section 8.3.5). The thermal quenching of the photoluminescence is lower in the alloys than in... 

When the light is switched off, the photoconduction will decay as the carrier population gradually returns to equilibrium. By studying photoconduction kinetics it is often possible to determine the dominant mechanism of carrier loss neutralisation at electrodes, recombination of electrons with holes, or trapping at defects or impurity centres. 

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