Mobility, field dependence

The mobility model is based on the empirical fitting of the time-of-ffight data to obtain the observed mobility-field dependence [42, and references given therein]. In the mobility model the mobility p is assumed to vary with electric field F according to the formula... 

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

Experimental Hole Mobilities. The experimental values of hole mobihties in polymers are tabulated in Tables 1 and 2. The hole mobihty is field dependent. Whenever the experimental data have been fitted with equation 5, the parameters p.Q, O, and O, which give a complete description of the field dependence of the hole mobihty, are Hsted (Table 2). Otherwise, hole mobilities at selected fields are Hsted. All acronyms are defined in Figures 2 and 3. 

In the above consideration it has been tacitly assumed that the charge carrier mobility docs not depend on the electric field. This is a good approximation for molecular crystals yet not for disordered systems in which transport occurs via hopping. Abkowitz et al. [37] have solved that problem for a field dependence of ft of the form p-po (FIFU) and trap-free SCL conduction. Their treatment predicts... 

It is obvious, and verified by experiment [73], that above a critical trap concentration the mobility increases with concentration. This is due to the onset of intertrap transfer that alleviates thermal detrapping of a carrier as a necessary step for charge transport. The simulation results presented in Figure 12-22 are in accord with this notion. The data for p(c) at ,=0.195 eV, i.e. EJa—T), pass through a minimum at a trap concentration c—10. Location of the minimum on a concentration scale depends, of course, on , since the competition between thermal detrapping and inter-trap transport scales exponentially with ,. The field dependence of the mobility in a trap containing system characterized by an effective width aeff is similar to that of a trap-free system with the same width of the DOS. 

One result of the field-dependent mobility is that the space charge-limited current (SCLC, the maximum current that can How in the bulk of the sample) does no longer follow a simple V2H scaling [132] on the voltage Land sample thickness L. Muigatroyd [133] was able to show that, for a mobility as in Eq. (13.4), the monopolar SCLC current could be well approximated by ... 

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. 

Figure 12-16. Field dependence of die charge carrier mobility in an undiluted hopping system al various values of the disorder parameter a = a/kT (Kef. [67]).

There is abundant evidence that the above formalism provides a framework for explaining the majority of experimental facts including the temperature and field dependence of mobility albeit not in the entire field regime, notably (i) the temperature dependence of the slope parameter of lnxF172 plots, (ii) the prefaetor mobility, (iii) the influence of randomly positional dipoles on the width of the... 

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

The analytic theory outlined above provides valuable insight into the factors that determine the efficiency of OI.EDs. However, there is no completely analytical solution that includes diffusive transport of carriers, field-dependent mobilities, and specific injection mechanisms. Therefore, numerical simulations have been undertaken in order to provide quantitative solutions to the general case of the bipolar current problem for typical parameters of OLED materials [144—1481. Emphasis was given to the influence of charge injection and transport on OLED performance. 1. Campbell et at. [I47 found that, for Richardson-Dushman thermionic emission from a barrier height lower than 0.4 eV, the contact is able to supply... 

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)... 

The second short-channel effect is a drain field-dependent mobility, which occurs for source-drain fields above I05 V/cm, in agreement with similar phenom-... 

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]. 

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,... 

TABLE 10.2 Critical Field E and Nature of Field Dependence of Mobility in Various Nonpolar Liquids... 

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... 

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