Trap-limited mobility

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]. 

Recently the concept of trap limited drift velocity providing the explanation for the observed saturation have gained much currency (12,13). This has been shown to be inapplicable in explaining these results (3) and % ould any way require trap limited mobilities to be > 20 m /V/s. This ultra high value finds no explanation in such trap limited transport theories and would indicate that the intrinsic mobility was even higher I... 

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.

Here (g)T = (e/m)Tf2/(r( + Tt) is called the ballistic mobility and (/t)H = + Tt) is the usual trap-controlled mobility. (q)F is the applicable mobility when the velocity autocorrelation time ( 1) is much less than the trapping time scale in the quasi-free state (fTf l). In the converse limit, (jj)t applies, that is—trapping effectively controls the mobility and a finite mobility results due to random trapping and detrapping even if the quasi-free mobility is infinite (see Eq. 10.8). 

Filter feeding The filtering or trapping of edible particles from seawater. This feeding mode is typical of many zooplankton and other marine organisms of limited mobility. 

A representative example for the information extracted from a TRMC experiment is the work of Prins et al. [141] on the electron and hole dynamics on isolated chains of solution-processable poly(thienylenevinylene) (PTV) derivatives in dilute solution. The mobility of both electrons and holes as well as the kinetics of their bimolecular recombination have been monitored by a 34-GHz microwave field. It was found that at room temperature both electrons and holes have high intrachain mobilities of fi = 0.23 0.04 cm A s and = 0.38 0.02 cm / V s V The electrons become trapped at defects or impurities within 4 ps while no trapping was observed for holes. The essential results are (1) that the trap-free mobilities of electrons and holes are comparable and (2) that the intra-chain hole mobility in PTV is about three orders of magnitude larger than the macroscopic hole mobility measured in PTV devices [142]. This proves that the mobilities inferred from ToF and FET experiments are limited by inter-chain hopping, in addition to possible trapping events. It also confirms the notion that there is no reason why electron and hole mobilities should be principally different. The fact... 

With mixed-valence compounds, charge transfer does not require creation of a polar state, and a criterion for localized versus itinerant electrons depends not on the intraatomic energy defined by U , but on the ability of the structure to trap a mobile charge carrier with a local lattice deformation. The two limiting descriptions for mobile charge carriers in mixed-valence compounds are therefore small-polaron theory and itinerant-electron theory. We shall find below that we must also distinguish mobile charge carriers of intennediate character. 

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... 

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). 

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,... 

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... 

The high quality of rubrene crystals has allowed detailed measurements of the transport characteristics, including the recent observation of the Hall effect [26]. Charge transport in rubrene single crystals, while trap-limited at low temperature, appears to occur via delocalized states over the 150-300 K temperature range with an (anisotropic) hole mobility of up to 20 cm /V s at room temperature [27,28]. 

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