Recombination via traps

Many (17), and Wang and Wallis (18), it is explicitly assumed that in adapting the Shockley-Read model (19) of recombination via traps to the surface the volume and surface portions of die conduction bands are in good thermodynamic equilibrium. Garrett (20) has shown, however, that in the case where the region of space charge is much wider than the mean free path of the carriers, the barrier may become the limiting factor. 

This is the so-called Shockley-Read equation describing recombination via traps. It also plays an important role in the description of recombination processes via surface states, as discussed in Chapter 2. In the above equation one may also replace n and pt by the relations... 

A considerable interest in strongly luminescing thiol-capped II-VI semiconductor nanocrystals (NCs) is stimulated by their potential applications in bio-imaging and labelling, photovoltaics, LEDs, FRET-based devices, nanophotonic structures, etc. Recently, thiol-capped ZnSe NCs have been reported to be successfully synthesized [1,2]. As-prepared ZnSe NCs demonstrate a weak whitish-blue photoluminescence (PL) related mainly to radiative recombination via trap states. However, the PL quantum yield can be significantly increased by a post-preparative photochemical treatment of the NCs [1]. 

Equation (12) is all the information we need to modify the cmituiuity equatimis to take trapping, detrapping and recombination via traps into account. However, what is still missing is the influence of the trap levels on the space charge and subsequently the Poissmi equation. 

The recombination rate Rp has been discussed above there are two main routes [2] (a) direct VB/CB transition and (b) recombination via localised states within the bandgap. The first is important in small bandgap semiconductors, but its importance decreases with increasing energy. The second is likely to be the dominant process for higher bandgap materials since it facilitates energy transfer to the lattice. The trap equilibria have already... 

The features of all these models are (1) general recombination via intermediate energy traps is allowed inside and outside the depletion region and (2) the concentration of holes is not allowed to build up to the point at which the potential distribution is affected. 

An explanation for the observed effects can be based on the assumption that carboxyl groups in protonated form may be a good photoelectron acceptor. This may be associated with the known easier electrochemical reduction of organic acids at low pH [8]. Excited electron-hole pairs in ZnSe core may recombine in few possible ways. First, a direct recombination results in the appearance of excitonic emission band at A,=408 nm. The second possible pathway is the energy transfer to Mn ion followed by Mn emission at A.=590 nm. At the neutral and acidic pH an additional recombination channel may be realized via trapping of photoelectrons by carboxyl groups (prior to the energy transfer to Mn ions)... 

Less vigorous approaches to describe surface recombination were taken by Kelly and Memming,158 Rajeshwar,134 and Peter et al.159,160 These authors considered the possibility of charge transfer via surface states. Thus, as shown in Fig. 20, the minority carriers which are trapped by surface states would either recombine with majority carriers (surface recombination via surface states) or transfer to the electrolyte (charge transfer via surface states or surface state mediated charge transfer). There are many experimental results which support the surface state mediated charge transfer under illumination134,158-161 and in the dark.162-164... 

The recombination current via traps in the transition region will be considered next, and this requires the second term in (6.15), As there are now six recombination coefficients, let us suppose for simplicity that... 

Fig. 8.2 The transition region recombination current density via traps according to equation (8.11). Key to the curve...

The distribution of localized states that we usually take into account needs to be discretized in energy to calculate the contribution of the trapped charge to the space charge and to calculate the recombination via these traps. We usually discretize the states with at least 20 levels to make sure our result is not influenced by the discretization. A typical number of gridpoints for the discretization in the spatial dimension is 200. 

Rapid e / h recombination, the reverse of equation 3, necessitates that D andM be pre-adsorbed prior to light excitation of the Ti02 photocatalyst. In the case of a hydrated and hydroxylated Ti02 anatase surface, hole trapping by interfacial electron transfer occurs via equation 6 to give surface-bound OH radicals (43,44). The necessity for pre-adsorbed D andM for efficient charge carrier trapping calls attention to the importance of adsorption—desorption equihbria in... 

Hole trapping by electron donors bound to the surfaces of the semiconductor particles competes with the e - h+b recombination, allowing e b to react with molecular 02 via Eq. (10.23). Fig. 10.10 shows that the quantum yield, peroxide formation increases with increasing concentration of the electron donor. 

The surface-state model, in which the luminescent recombination occurs via surface states, was proposed to explain certain properties of the PL from PS, for example long decay times or sensitivity of the PL on chemical environment. In the frame of this model the long decay times are a consequence of trapping of free carriers in localized states a few hundred meV below the bandgap of the confined crystallite. The sensitivity of the PL to the chemical environment is interpreted as formation of a trap or change of a trap level by a molecule bonding to the surface of a PS crystallite. The surface-state model suffers from the fact that most known traps, e.g. the Pb center, quench the PL [Me9], while the kinds of surface state proposed to cause the PL could not be identified. 

The EE and phE mechanisms for neat polymers proposed by ourselves and others all involve the consequences of breaking bonds during fracture. Zakresvskii et al. (24) have attributed EE from the deformation of polymers to free radical formation, arising from bond scission. We (1) as well as Bondareva et al. (251 hypothesized that the EE produced by the electron bombardment of polymers is due to the formation of reactive species (e.g., free radicals) which recombine and eject a nearby trapped electron, via a non-radiative process. In addition, during the most intense part of the emissions (during fracture), there are likely shorter-lived excitations (e.g., excitons) which decay in a first order fashion with submicrosecond lifetimes. The detailed mechanisms of how bond scissions create these various states during fracture and the physics of subsequent reaction-induced electron ejection need additional insight. 

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