Zero-field mobility

Naito and Kanemitsu (1996) investigated the relationship between the prefactor mobilities, zero-field mobilities, and the glass transition temperatures of OX doped polyarylate (PA), PC, poly(methyl methacrylate) (PMMA), PS, poly(vinyl chloride) (PVC), polyethylene terephthalate) (PET), and poly(vinyl butyral) (PVB), DEH doped PC, 5(p-diethylaminophenyl)-l-phenyl-3-(/ -diethylaminostyryl)-2-pyrazoline (DEASP) doped PS, and DEASP doped PC. OX, DEH, and DEASP are highly polar molecules with similar dipole moments. By modifying the polymer, the glass transition temperature can be varied over... 

Polymer Method (for details see text) Mobility Zero field mobility... 

Figure 43. Comparison of the mobilities of holes in polystyrene doped with equivalent molar concentrations of TTA (above, 30 wt.%) and TAPC (below, 33 wt,%) at various field strengths and temperatures. Because the two triarylamine moieties in TAPC are linked, their arrangement should be somewhat different from that in TTA, yet the mobility behavior is nearly identical. At least in this example, differences in molecular packing do not lead to major differences in the mobility. Zero field values are extrapolations. (Reprinted with permission from Ref. [60b].)...

Figure 12-25. The temperature dependencies of die zero-field mobility for TTA and TTA doped wilh DTA, DAT, and TAA. The TTA concentration was 40%, ihe hinder material was polystyrene. The DTA, DAT and TAA to TTA concemialiinis were 1.11x10 5 niol/niol TIA (Ref. 7(> ).

We note a temperature dependence of the zero field mobility as exp[—( F()/F)2], a behavior which is indeed encountered in real organic semiconductors, and differs from both Millers-Abrahams fixed range and Moll s variable range hopping models. 

Table 10.2 lists the critical field Ec in various nonpolar liquids along with the approximate nature of field dependence of mobility when E > Eq. It is remarkable that the higher the zero-field mobility is, the smaller is the value of Ec, indicating the role of field-induced heating. Also note that in the sublinear case, Ec is larger in the case of molecular liquids than for liquefied rare gases,... 

Zero field drift mobility. After Schmidt (1988). 

Fig. 6 Zero field hole mobility of the bis-fluorene dendrimer of Fig. 5 as a function of lAT. The deviation of the ln t(F )cxl/r dependence below 215 K is a signature of the onset of transit time dispersion. From [49] with permission. Copyright (2008) by Elsevier...

Fig. 8 Temperature dependence of the zero field hole mobility in the low carrier density limit in a polyfluorene copolymer. The data are inferred from space-charge-limited current experiments and analyzed in terms of the extended Gaussian disorder model (see Sect. 4.1). From [90] with permission. Copyright (2008) by the American Institute of Physics...

Fig. 6.13. Superimposed zero field and pulsed field (81 V cm-1 peak amplitude) positron lifetime spectra. The pulsed field spectrum has been decomposed into heated components (broken line) and unheated components (crosses) to illustrate how the electric field splits up the positron ensemble. This is also illustrated by the inset, which shows, schematically, the energy distribution p(E,t) of the positron ensemble in the two-threshold model (see text). Reprinted from Physical Review Letters 56, Tawel and Canter, Observation of a positron mobility threshold in gaseous helium, 2322-2325, copyright 1986 by the American Physical Society.

If we consider a sample with shallow Gaussian traps and include PEE, the sample behaves as if there are no traps and the mobility is field dependent given by Eq. (3.56) far as the dependence of J on V is concerned. The zero field mobility and its temperature dependence are different in the two equations. If the traps are at a single energy level, <7t = 0 and the temperature variation of the mobility also becomes the same in the two cases. Eq. (3.58) represents both the models, it reduces to the existing shallow trap model (without PEE) when = 0 and to the existing field dependent mobility model when 6 = exp(-EtfkT). 

On average, a carrier located at can continue its motion only after thermal excitation. If all carriers were located at and a transport level existed at e = 0, the center of the DOS, the temperature dependence of the mobility should follow a non-Arrhenius dependence of the form exp[-(a/ 7)-2]. This temperature dependence has been recovered by both EMA studies and Monte Carlo simulations, although with a constant in the exponent of less than unity that accounts for the statistics of occupational energies. The predicted temperature dependence of the zero-field mobility is... 

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

In the lattice gas model, the hopping frequency of a carrier decreases exponentially with the hopping distance p as v = vQ exp(-2p/p0). Here, pQ is a wavefunction decay constant and vQ a frequency factor. From the Einstein relationship, the zero-field mobility is... 

The concentration dependence of the hole mobility of TPM-E doped PS was described by Magin et al. (1996). TPM-E is a moderately polar molecule with a dipole moment of 2.10 Debye. Figure 5 shows the temperature dependencies for 45% TPM-E. The results are similar to those reported for vapor-deposited TPM glasses and doped polymers described previously. The data in Fig. 5 yield n0 = 2.9 x 10-2 cm2/Vs and a = 0.111 eV. For purposes of comparison, Fig. 6 shows the zero-field data of Fig. 5 plotted versus T-l. From these results, it is clear that the temperature dependence cannot be described by an Arrhenius relationship over an extended range of temperatures. A further problem concerning the use of an Arrhenius relationship is the prefactor mobility. At 272 K, the data in Fig. 6 yields a prefactor mobility of 690 cm2/Vs, a value that is difficult to justify. For all concentrations, plots of ft versus (a/kT)2 were linear with slopes between... 

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