Traps limited

Figure 9-28. Trap-limited current (low ills (solid lines) lo the experimental (symbols) l/V characteristics of two typical devices with a 200 nin and 600 nm thick hole-transport layer and Alq3. Inset shows l/V curves for various different Alq3-lhicknesses. Reproduced front Ref. 82. ...

Figures 12-12 and 12-13 document that trap-free SCL-conduction can, in fact, also be observed in the case of electron transport. Data in Figure 12-12 were obtained for a single layer of polystyrene with a CF -substituted vinylquateiphenyl chain copolymer, sandwiched between an ITO anode and a calcium cathode and given that oxidation and reduction potentials of the material majority curriers can only be electrons. Data analysis in terms of Eq. (12.5) yields an electron mobility of 8xl0 ycm2 V 1 s . The rather low value is due to the dilution of the charge carrying moiety. The obvious reason why in this case no trap-limited SCL conduction is observed is that the ClVquatciphenyl. substituent is not susceptible to chemical oxidation.

On the experimental front, Burrows and Forrest 155] have measured the electric field and thickness dependence of the current and radiance from bilayer devices with various HTLs and Alqs as the ETL. The data were analyzed in temis of trap-limited transport in the Alq t layer, with the assumption that the voltage drop across the HTL is negligible. However, this assumption was challenged by Vestweber and Riess [ I56 and Giebcler et al. 1157], who demonstrated that HTL plays an important role in determining the efficiency of bilayer OLEDs. 

An important question concerning energy trapping is whether its kinetics are limited substantially by (a) exciton diffusion from the antenna to RCs or (b) electron transfer reactions which occur within the RC itself. The former is known as the diffusion limited model while the latter is trap limited. For many years PSII was considered to be diffusion limited, due mainly to the extensive kinetic modelling studies of Butler and coworkers [232,233] in which this hypothesis was assumed. More recently this point of view has been strongly contested by Holzwarth and coworkers [230,234,235] who have convincingly analyzed the main open RC PSII fluorescence decay components (200-300 ps, 500-600 ps for PSII with outer plus inner antenna) in terms of exciton dynamics within a system of first order rate processes. A similar analysis has also been presented to explain the two PSII photovoltage rise components (300 ps, 500 ps)... 

In the case of material with a significant concentration of localized states, it is possible to assnme that transport of a carrier over any macroscopic distance will involve motion in states confined to a single energy. Here it is necessary to note that a particn-larly important departnre from this limiting situation is (according to Rose [4]) a trap-limited band motion. In this case, transport of carrier via extended states is repeatedly interrnpted by trapping in localized states. The macroscopic drift mobility for such a carrier is reduced from the value for free carriers, by taking into acconnt the proportion of time spent in traps. Under steady-state conditions, we may write... 

For the simplest case of a single set of localized states sitnated at a particular energy Ei, the trap-limited drift mobility of carriers moving in extended states at is readily compnted from equation (3.3). If the effective density of extended states at Ep is Np and the trap concentration is N, then we may write... 

It follows that in the trapping limit an arbitrary initial state will have a component that is trapped and does not decay ... 

The expression for the depression of the lowest level of a manifold of levels for general r in the shallow-trap limit is... 

TABLE I. Intensity Distribution in the Shallow-trap limit. Upright Band, m = 6... 

TABLE II. Intensity Distribution in the Deep-trap Limit. 

Several catalysts on the market today contain special vanadium traps or vanadium scavengers in order to protect the active ingredients against poisoning and/or destruction by Vanadium. These "Metal Traps" limit the mobility of the vanadium pentoxide compounds under FCC conditions (2, 10). The nickel problem needs to be approached differently and more recently, progress has been made towards reducing the dehydrogenation activity of nickel dispersed on FCC catalysts (11). 

The most general theory valid at the arbitrary diffusion coefficients, DA, DB, and D(, also corrects only the concentration dependence in the denominator of Eq. (3.712), but in full accordance with both the target and trap limits [255]. 

Mist traps limit the amount of the aerosols of mechanical pump oils from leaving the pump and drifting into the room containing the pump. These traps are different from the other traps in that they go on the exhaust of the mechanical pump and do not protect the pump or the system, only the operators. 

The hydrogen diffusion coefficient is not constant, but decreases with time (Street et al. 1987b). The data in Fig. 2.22 show a power law decrease in p-type a-Si H of the form r , with a 0.2 at the measurement temperature of 2(X) C. The time dependence is associated with a distribution of traps originating from the disorder. A similar effect is found in the trap-limited motion of electrons and holes and is analyzed in Section 3.2.1. The time dependence of is reflected in the kinetics of structural relaxation discussed in Section 6.3.1. 

To explain the trap-limited transport it is useful to consider the model of a single trapping level of density, Nj., at energy E. below the conducting states, as illustrated in Fig. 3.10. The drift mobility is the free carrier mobility reduced by the fraction of time that the carrier spends in the traps, so that,... 

Fig. 3.10. Illustration of trap-limited transport of carriers for a discrete or distributed trap level.

With the experimental results in mind we retium to the analysis of the trap-limited transport. The time-dependent decrease in the apparent mobility is obviously consistent with our earlier argument that the average trapping time will increase with the number of trapping events for an exponential band tail. Scher and Montroll (1975) were the first to point out this property of a very broad distribution of release times and to associate the effect with transport in disordered semiconductors. They analyzed the random walk of carriers with such a distribution and... 

It is natural to look for a connection between the time-dependent hydrogen diffusion and the similar dispersive motion of electrons and holes in a band tail. Section 3.2.1 shows that the trap-limited carrier mobility has as a power law time dependence with a dispersion... 

In some cases the drift of carriers may be seriously interrupted by capture at trapping sites in the solid. If the traps are energetically shallow, i.e. the depth of the potential well is comparable with thermal energies (kT), the carriers will soon escape again, and the only effect will be to reduce the apparent mobility. The trap-limited mobility fiT will be given by... 

BD concentrations of 0 and 1 %, the transit time increases by a factor of ca. 3000. The corresponding mobility, referred to as the trap-limited mobility, decreases by the same factor, roughly in inverse proportion to the impurity concentration. The decrease is actually somewhat faster, proportional to (concentration), probably indicating that true steady state has not yet been achieved [53a]. While the outlines of the effect of a charge-trapping impurity seem simple, the details are not [74i]. The literature has several examples of recent work on this subject [44c, 46d, 53a, 65g,i, 74J-0]. 

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