The Nondispersive to Dispersive Transition

Time-of-flight photocurrent transierits for different values of o/kT. 

In the dispersive regime, the mobilities are thickness dependent. A further prediction is a change in the temperature dependence of the zero-field mobility 

The difference in I he temperature dependence in the nondispersive and dispersive regimes is thus due only to the difference in the constant in the exponential term. 

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Figure 19 The diagonal disorder parameter (alkTft at which the nondispersive to dispersive transition occurs versus thickness.

Figure 100 The thickness dependence of the nondispersive to dispersive transition temperature for vapor-deposited DEASP. The solid line has been calculated from Eq. (17), assuming o = 0.103 eV, as derived from the data in Fig. 99.

Ulanski et al. (1992) measured hole mobilities of PVK doped PC between 220 to 370 K. With decreasing temperature, the results show a transition from nondispersive to dispersive transport at 250 K. From the temperature dependence of the mobility in the nondispersive regime, the width of the DOS was determined as 0.116 eV. This yields a predicted nondispersive to dispersive transition of 305 K, considerably higher than the value determined experimentally. A comparison of thermally stimulated current, thermoluminescence, isothermal time-of-lflight, and thermally stimulated time-of-flight... 

Tc Nondispersive to dispersive transition temperature, in K Teff A parameter used to describe the temperature dependence of the mobility in the Gill formalism, in K... 

Since the early work of Scher and Montroll, there have been many studies of effects of positional disorder on charge transport in disordered solids (Poliak, 1977, 1977a Marshall, 1978, 1981. 1983 Mclnnes and Butcher, 1980 Schirmacher, 1981 Adler and Silver, 1982). These have lied to the general conclusion that while positional disorder can, under some conditions, give rise to dispersive transport, nondispersive transport is almost always attained after a carrier has executed a very few jumps. Hence, dispersive transport occurs over a small fraction of the thickness or at very low temperatures. This leads to the prediction that a transition from nondispersive to dispersive transport occurs within a single transit time or at increasing times with decreasing temperature. 

Yuh et al. (1987) investigated hole transport in TPD doped PC containing low concentrations of 5-(p-diethylaminophenyl)-l-phenyl-3-(p-diethylamino-styryl)-2-pyrazoline (DEASP). Time-of-flight photocurrent measurements showed a transition from nondispersive to dispersive and back to nondispersive behavior as the DEASP concentration increased from 0 to 1%. The results were described by Schmidlin s (1977) single-trap-controlled model. The attempt-to-escape frequency and trap depth were reported as 4 x 1012 s-1 and 0.56 eV. 

Borsenberger et al. (1995a) measured hole mobilities of TTA doped polymers with polymers with different dipole moments poly(styrene) (PS-1), poly(4-f-butylstyrene) (PS-2), poly(4-chlorostyrene) (PS-3), and bisphenol-A polycaibonate (PC). The dipole moments of PS-1 and PS-2 are near zero. For PC and PS-3, the values are 1.0 and 1.7 Debye. The dipole moment of TTA is 0.8 Debye. Figure 55 shows a series of photocurrent transients at different temperatures for 30% TTA doped PS-1 at 6.4 x 105 V/cm. W increases with decreasing temperature. For fields between 104 and a few multiples of 1CP v/cm, W increases with increasing field. Values of W were between 0.25 and 0.62. In all cases, W increases with decreasing TTA concentratioa Low-temperature transitions from nondispersive to dispersive transport, where the transients no longer show plateaus, were observed only at low concentrations. 

The results obtained by Berlin et al. concerning thermally activated diffusion along a one-dimensional system with energetic disorder lead to the condusion that at high temperature T > To, the transport is Gaussian. Nondispersive character of the transport was also found for low temperatures Ttransition rate l/( W). On the other hand for t >> 1/(W) the one-dimensional charge carrier transport possesses dispersive character. Therefore, the temperature To indicates the point at which transition from a nondispersive to dispersive transport takes place. ... 

In the long time limit Eq. (3.27) can be approximated by yrrA tL04 [114-]. This has been verified experimentally in a polyfluorene derivative [163], In this study the DF as well as the triplet concentration was monitored as a function of time and temperature to investigate the influence of dispersion on triplet-triplet annihilation. Since the attainment of dynamic equilibrium of triplet relaxation is temperature and time dependent it can by monitored via time resolved detection of DF. According to theory [164] and MC simulation [165] the time ts where the dispersive to nondispersive transition of relaxation occurs, is given by ... 

Figure 7.12 summarizes the transitions that occurred when TC was added to dispersed and nondispersed systems of MLO/water. In these emulsified particles, the confined W/O nanostructures were reversible structures, i.e., they existed in... 

Hole Transport in PMPS. In the experiments with layered structures (20) and visible excitation (to which PMPS is transparent), transient currents were observed only when the top electrode was negatively biased with respect to the substrate. The substrate was composed of a visible photoconductor (charge generation layer) overcoated aluminum ground plane. When the polymer top surface was directly (intrinsically) photoexcited with pulsed 337-nm excitation, current transit pulses were observed only when the top electrode was positively biased. Therefore, under the experimental conditions described, only hole transient transport could be directly observed. Transit pulses were nondispersive over a wide range of temperature. Figure 14 illustrates the relative increase in dispersion with decreasing temperature. In addition, no evidence for anomalous thickness dependence at the transit time was obtained, even at the lowest temperature. 

When charge transport fails to reach a steady state during the time available, the most likely reason is that the transit time is dominated by the time required to escape from the slowest site(s) that a carrier encounters as it crosses the sample. Furthermore, the distribution of release times is such that the carrier continues to encounter slower and slower sites as it crosses a sample. Transport under such conditions is called dispersive, and has been the subject of much study since a seminal paper by Scher and Montroll [73a-e]. The term dispersive alludes to the wide dispersion in release times and/or the fact that carriers that are injected simultaneously spread out, disperse, to an anomalous extent as they cross the sample. The literature has several examples of studies of this subject in amorphous molecular solids [66b, 73f-h]. Some materials undergo a transition from essentially dispersive transport at low temperatures to essentially nondispersive transport at higher temperatures, and this dispersive-to-nondispersive transition has been the subject of significant attention [73i-p]. 

If there exists only a unique maturation age r, then f a) = S a — r). Assuming that b w) = we we recover Nicholson s equation. Recently, a model consisting of two subpopulations, mature and immature, with an age-dependent disperser-nondisperser transition has been studied analytically and applied to the Neolithic transition in Europe. This model shows good agreement with observational data [292]. This example will be analyzed in detail in Chapter 7. 

In the case of ferroelectric ceramic powders dispersed in a polymer matrix, the ceramic inclusions are heterogeneous by themselves, exhibit high, nondispersive permittivities, and. usually, not very high conductivities. Such systems can be easily treated by the dielectric mixture formulas sununarized in Ref. 30. The only criterion is that the volume fraction of the inclusions is known and also something about their shape. The size distribution is not important. The dielectric dispersion of the competsite is determined by that of the nutrix, which can be measured separately. The usual effect of the high-permittivity. nondispersive, ceramic filler is to raise the permittivity level of the dispersion bands. Sometimes new MWS transitions are created, which ate not connected to molecular mobilities of the matrix. 

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