Defect recombination mechanisms

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... 

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... 

The parameter cro depends on the recombination mechanism (radiative vs. non-radiative) and is typically of the order 107 or 1015 s-1, respectively [21] (see, however, Zamaraev et al. [27], who observed cro up to 1021 s 1). The other recombination parameter, r0, is nothing but half the Bohr radius of the wave-function of an electron centre and is, for example, about 0.5 A for F and Ag° centres and 1 A for shallower Tl° centre in KC1. For paramagnetic defects this parameter could be found by means of EPR and ENDOR [28-30]. 

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]). 

As it has been said above, accumulation of radiation-induced (Frenkel) defects takes place in all kinds of solids irrespective which of the two basic recombination mechanisms - annihilation or tunnelling recombination - occurs [9, 11, 13, 17-20, 39, 42, 99-107]. In a good approximation this process could be considered as the A + B —> 0 reaction with the particle input. In many cases strong arguments exist for the clustering of radiation-induced... 

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... 

Defects provide the dominant recombination path when their density is above about 10 cm" or when the temperature is higher than about 100 K. The recombination mechanism depends on the temperature and on the mobility of the carrier. The low temperature mechanism is discussed first. 

The charge-induced defect creation mechanism is too slow to be significant at low temperature and the electronic recombination effects reestablish themselves. Low temperature measurements (0-100 K) have been performed using an IR probe beam to modulate the excess carrier density that is in the band tail states (Hundhausen, Ley and Carius... 

The carrier lifetime is longer in the nipi structures than for bulk a-Si H, but the excess carrier lifetimes decrease below a few minutes when the temperature is raised above 50 K. It is concluded that the tunneling recombination mechanism is present at low temperatures, but is obscured by the defect creation mechanism at elevated temperatures. 

For Si, in order for an electron at the bottom of the CB to recombine with a hole from the top of the VB, the momentum of the electron must shift from k h to ky, (Figure 4.5b). However, this is not allowed by the Law of Conservation of Momentum. Instead, an indirect recombination mechanism must take place, wherein the electron is captured by an interstitial defect with energy E, which facilitates its relaxation to the top of the VB. This process is accompanied by the emission of phonons, or lattice vibrations rather than light emission. 

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... 

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