Mobility electric field dependence

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]. 

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

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... 

Fig. 28. Electric field dependence of the solvated electron drift mobility in liquid ethane at various temperatures (K). After Doldissen et al. [348].

Baird et al. [350]). In the following analysis, the functional forms, p(E), which have been proposed (see below) to represent the field-dependence of the drift mobility are used for electric fields up to 1010Vm 1. The diffusion coefficient of ions is related to the drift mobility. Mozumder [349] suggested that the escape probability of an ion-pair should be influenced by the electric field-dependence of both the drift mobility and diffusion coefficient. Baird et al. [350] pointed out that the Nernst— Einstein relationship is not strictly appropriate when the mobility is field-dependent instead, the diffusion coefficient is a tensor D [351]. Choosing one orthogonal coordinate to lie in the direction of the electric field forces the tensor to be diagonal, with two components perpendicular and one parallel to the electric field. 

The other source of an effective electric field dependence of the diffusion coefficient is due to hydrodynamic repulsion. As the ions approach (or recede from) one another, the intervening solvent has to be squeezed out of (or flow into) the intervening space. The faster the ions move, the more rapidly does the solvent have to move. A Coulomb interaction will markedly increase the rate of approach of ions of opposite charge and so the hydrodynamic repulsion is correspondingly larger. It is necessary to include such an effect in an analysis of escape probabilities. Again, the force is directed parallel to the electric field and so the hydro-dynamic repulsion is also directed parallel to the electric field. Perpendicular to the electric field, there is no hydrodynamic repulsion. Hence, like the complication of the electric field-dependent drift mobility, hydro-dynamic repulsion leads to a tensorial diffusion coefficient, D, which is similarly diagonal, with components... 

Consequently, while the effect of an electric field dependence of both drift mobility and diffusion coefficient and also hydrodynamic repulsion decreases, the recombination probability, dielectric saturation and relaxation effects increase the recombination probability. 

Hong and Noolandi [72], Berg [278], and Pedersen and Sibani [359] have also noted the connection between the survival probability and homogeneous density distribution. Finally, the escape probability of an ion pair formed with a separation, r0, with an arbitrary monotonically decreasing potential energy of interaction and with electric field-dependent mobility and diffusion coefficient ions was found by Baird et al. [350] to be (see also Tachiya [357])... 

The electric field dependence of the hole mobility in a series of PVK TNF films of varying composition is shown in Fig. 5(b)17. The carrier drift mobilities are extremely low and strongly dependent on the electric field. Similar electric field dependence was observed for electron drift mobilities. The mobilities obey the empirical relation... 

Figure 93 Transient photocurrent signals (i) for 8 pm thick Alq3 layers sandwiched between the ITO anode and A1 cathode. Light pulses entered the samples through the ITO anode. The change from the dispersive transport for Alq3 as-received from the supplier (circles) to the non-dispersive transport with purified (squares) Alq3 samples. It can be seen in both linear (a) and double logarithmic (b) plots. In the inset of part (a) electric field dependence of mobility is shown, in part (b) the TOF transient for as-received Alq3 exposed to ambient is added (diamonds). After Ref. 423. Copyright 2003 American Institute of Physics, with permission.

Numerous measurements over a large range of electric fields and temperatures have established that, in many materials, the carrier mobility can be described by a universal law bearing the Poole-Frenkel like form of the electric field dependence... 

Figure 104 Electric field dependence of TOF-measured electron mobility in thin films of Alq3 the data of Ref. 336 ( ), Ref. 425 ( ), and Ref. 341 (o).

Figure 7 (left) The electric field dependence of the time-ofiflight hole mobility for poly(9.9-dioctylfluorene) films. The open circles are data for a film prepared by spin coating. The filled circles are for a sample spin coated on a rubbed polyimide orientation layer, annealed in the nematic phase and then quenched to form a glassy film. 

---