Electric-field Dependence

At low drift velocities, the mobilities are independent of F. This has been confirmed using the TOF method in many cases. An example is given in Fig. 8.36. 

The sublinear increase of vd(F) be interpreted with the aid of a model by Shockley [45], based on the inelastic scattering of charge carriers from longitudinal acoustic phonons. In this model, the assumption is made that the charge carriers scatter 

F = electric field. In the higher temperature range, /x is proportional to 7 n 0). After [20, 24]. 

The solid curves in Fig. 8.37 were computed with only one free parameter in Eq. (8.67), namely the longitudinal velocity of sound = 4 10 cm/s. /xq is not a fit parameter, since the zero-field mobility follows directly from the measurable slope of vd(F) for F 0 (see Fig. 8.37). The value for ce obtained in this way agrees surprisingly well with the independently-measured longitudinal sound velocity (compare Table 5.4) and is thus a good indication that the Shockley model for the electron-phonon coupling is also applicable to organic molecular crystals. 

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In plasma chromatography, molecular ions of the heavy organic material to be analy2ed are produced in an ionizer and pass by means of a shutter electrode into a drift region. The velocity of drift through an inert gas at approximately 101 kPa (1 atm) under the influence of an appHed electric field depends on the molecular weight of the sample. The various sonic species are separated and collected every few milliseconds on an electrode. The technique has been employed for studying upper atmosphere ion molecule reactions and for chemical analysis (100). 

Fig. 13. Electric-field dependence of the emission current obtained for a carefully aligned MWCNT film [38], Inset Fowler-Nordheim plot, where y is the field-enhancement factor.

Figure 11-5. Internal pholoemission response as a function of photon energy for (a) an AI/MEH-PPV/ Ca structure biased to collect elections and (b) for the same AtfMEII-PPV/Ca structure and a Cut MEH-PPV/Ca structure biased to collect holes. Inset in (a) shows the electric field dependence of the photorcspon.se ihicshold for the AI/MEH-PPV/Ca structure biased to collect electrons.

Figure 12-30. The electric field dependence of the hole mobility in McLPPP ut different lem-peralures.

Besides its temperature dependence, hopping transport is also characterized by an electric field-dependent mobility. This dependence becomes measurable at high field (namely, for a field in excess of ca. 10d V/cm). Such a behavior was first reported in 1970 in polyvinylcarbazole (PVK) [48. The phenomenon was explained through a Poole-ITenkel mechanism [49], in which the Coulomb potential near a charged localized level is modified by the applied field in such a way that the tunnel transfer rale between sites increases. The general dependence of the mobility is then given by Eq. (14.69)... 

It is important to realize that the migration in an electric field depends on the magnitude of the concentration of the charged species, whereas the diffusion process depends only on the concentration gradient, but not on the concentration itself. Accordingly, the mobility rather than the concentration of electrons and holes has to be small in practically useful solid electrolytes. This has been confirmed for several compounds which have been investigated in this regard so far [13]. 

The vibronic coupling features are evaluated in a perturbation treatment by taking acconnt of temperature and electric field dependence (5). 

In conclusion, the type of deformation induced by an electric field depends on the pH of the surrounding solution, the salt concentration, the position of the gel relative to the electrodes, and the shape of gel. 

Further, since both the zeta potential and the electric field depend on the ionic concentration and pH of the fluid (the tissue... 

The following explanation of the behavior of analytes during CE-SDS in the presence of sieving media is found in a monograph by Guttman 135 the electric force (Fe) that a particle experiences when placed in an electric field depends on the net charge (Q) of the particle and on the intensity of the electric field (E) ... 

Warta W, Karl N (1985) Hot holes in naphthalene high, electric-field-dependent mobilities. Phys Rev B 32 1172... 

Wang L, Fine D, Basu D, Dodabalapur A (2007) Electric-field-dependent charge transport in organic thin-fihn transistors. J Appl Phys 101 054515... 

Minari T, Nemoto T, Isoda S (2006) Temperature and electric-field dependence of the mobility of a single-grain pentacene field-effect transistor. J Appl Phys 99 034506... 

Veldman D, Ipek O, Meskers SCJ, Sweelssen J, Koetse MM, Veenstra SC, Kroon JM, van Bavel SS, Loos J, Janssen RAJ (2008) Compositional and electric field dependence of the dissociation of charge transfer excitons in alternating polyfluorene copolymer/fullerene blends. J Am Chem Soc 130 7721... 

Calculation of the electric field dependence of the escape probability for boundary conditions other than Eq. (11b) with 7 = 0 poses a serious theoretical problem. For the partially reflecting boundary condition imposed at a nonzero R, some analytical treatments were presented by Hong and Noolandi [11]. However, their theory was not developed to the level, where concrete results of (p(ro,F) for the partially diffusion-controlled geminate recombination could be obtained. Also, in the most general case, where the reaction is represented by a sink term, the analytical treatment is very complicated, and the only practical way to calculate the field dependence of the escape probability is to use numerical methods. 

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