Electron mobility field dependence

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

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]. 

In liquid Ne, evidence has been found for a high-mobility species, which may be a delocalized electron, that converts to a low-mobility species in several tens of nanoseconds (Sakai et al, 1992). Field dependence of the low-mobility species is supralinear, but the lifetime of the high-mobility species increases with the field strength and decreases with temperature from -2 to -100 ns. 

Schmidt (1976) has given a classical model for the field dependence of quasi-free electron mobility that predicts p(E) in the high-field limit. At any... 

Table 10.4 lists the values of trap density and binding energy obtained in the quasi-ballistic model for different hydrocarbon liquids by matching the calculated mobility with experimental determination at one temperature. The experimental data have been taken from Allen (1976) and Tabata et ah, (1991). In all cases, the computed activation energy slightly exceeds the experimental value, and typically for n-hexane, 0/Eac = 0.89. Some other details of calculation will be found in Mozumder (1995a). It is noteworthy that in low-mobility liquids ballistic motion predominates. Its effect on the mobility in n-hexane is 1.74 times greater than that of diffusive trap-controlled motion. As yet, there has been no calculation of the field dependence of electron mobility in the quasi-ballistic model. 

Equation (3) implies that the field dependence of the mobility can become negative if a < E in (3a) or if E > 1.5 in (3b). This is a signature of positional disorder. The reason is the following. Suppose that a migrating charge carrier encounters a site from which the next jump in field direction is blocked because of poor electronic coupling. Under this condition the carrier may find it easier to circumvent that blockade. If the detour involves jumps against the field direction it... 

The density dependence of Vg in Kr was determined by field ionization of CH3I [62] and (0113)28 [63]. Whereas previous studies found a minimum in Vg at a density of 12 X 10 cm [66], the new study indicates that the minimum is at 14.4 x 10 cm (see Fig. 3). This is very close to the density of 14.1 x 10 cm at which the electron mobility reaches a maximum in krypton [67], a result that is consistent with the deformation potential model [68] which predicts the mobility maximum to occur at a density where Vg is a minimum. The use of (0113)28 permitted similar measurements of Vg in Xe because of its lower ionization potential. The results for Xe are also shown in Fig. 3 by the lower line. 

An interesting example of a diffusion-controlled reaction is electron attachment to SFg. Early studies showed that in -alkanes, k increases linearly with over a wide range of mobilities from 10 to 1 cm /Vs [119]. Another study of the effect of electric field E) showed that in ethane and propane, k is independent of E up to approximately 90 kV/cm, but increases at higher fields [105]. This field is also the onset of the supralinear field dependence of the electron mobility [120]. Thus over a wide range of temperature and electric field, the rate of attachment to SFg remains linearly dependent on the mobility of the electron, as required by Eq. (15). 

Computer simulation has also been used to calculate the external electric field effect on the geminate recombination in high-mobility systems [22]. For the mean free time x exceeding -0.05, the field dependence of the escape probability was found to significantly deviate from that obtained from the diffusion theory. Furthermore, the slope-to-intercept ratio of the field dependence of the escape probability was found to decrease with increasing x. Unlike in the diffusion-controlled geminate recombination, this ratio is no longer independent of the initial electron-ion separation [cf. Eq. (24)]. 

An estimate of the electron-ion recombination rate constant in high-mobility systems based on an empirical model of energy dissipation processes was provided by Warman [38]. He related the rate constant to the field dependence of the electron mobility, and proposed... 

The diffusion coefficients of the ion are usually estimated from their mobilities (or conductances), which can be measured independently. Diffusion coefficients (or mobilities) vary over very large ranges for the solvated electron in different solvents (neopentane, D 2 x 10 4 m2 s 1 and n 7 x 10 3 m2 V-1 s 1 hexane, D 2 x 10 7 m2 s 1 and ju 8x 10 6 m2 V-1 s 1) [320]. There is considerable evidence that the mobility of electrons is not constant, but on the contrary, the mobility depends on the applied electric field, increasing approximately proportionately with electric field at high fields in solvents where n is small and decreasing with electric field in solvents where n is large. If the solvated electron mobility depends on the electric field, then the diffusion coefficient may also depend on the electric field. The implications of these complications are discussed in Sect. 2.2 and in Chap. 8, Sect. 2.7. 

Doldissen et al. [348] found that the solvated electron mobility may be increased (or decreased) fourfold at fields 107Vm 1 compared with the mobility at low fields (<105 Vm 1). Such electric fields are small compared with those mutual fields when ions approach to within 2 nm or less of each other (>2xl08 Vm 1). No measurements of drift mobilities have been possible at such electric fields. It is not possible to state that the field dependence extends to these large electric fields, though the trend of the experimental results at moderately large electric fields is often extrapolated to large electric fields (Mozumder [349] and... 

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

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