Disorders gaussian model

Table 2 Results of data fits to the Gaussian disorder model of charge transport in EHO-...

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...

Figure 101 Calculated Poole-Frenkel plots according to the correlated disorder model for different values of o jkT (from top curve downward). The calculations according to the Gaussian disorder model with

A simple model, the Gaussian Disorder Model of Bassler and co-workers, has been very useful in rationalizing charge transport data on many amorphous molecular solids [59]. Its present version consists of the following assumptions. 

Despite the considerable success of Eq. (7) in consistently rationalizing mobility data in many systems, the Gaussian Disorder Model misses the mark in one major way. The field-strength [E) dependence predicted for a realistic value of d (3.0, approximately the smallest a ever encountered in practice) and various values of E is shown in Figure 39 [63a,b]. Only for strong fields (sometimes only above 10 V cm ) are the results adequately described as linear functions of whereas experimentally this linearity usually extends to the lowest values of E accessible (sometimes as low as lO V cm ) [60b, 63c,d]. It was initially proposed that the... 

Figure 39. Field-strength ( ) dependence of the mobility (p) predicted by the Gaussian Disorder Model. (Reprinted with permission from Ref [63b].)...

Although the general outlines of the Gaussian Disorder Model are probably correct, it is important to note some additional concerns. 

There is, at present, no realistic theoretical model of the effect of geometrical disorder. A proper model must take into account the complicated orientation dependence of the matrix element (K) [63g], as well as the distribution of positions and orientations of the CTM. The simple treatment adopted by the Gaussian Disorder Model predicts a dependence of the prefactor mobility (//q) on the geometrical disorder parameter Z, namely //q oc exp(i2 ) [63a], and this relationship has been used often to analyze experimental data. The comparison of TTA and TAPC at low concentrations disagrees with this prediction, and it appears to be untenable a priori anyway [60b, 63e]. A worthy challenge for future work will be to construct a model with enough realism to have predictive value. Recent reports indicate progress in this direction [641,o]. 

Although the standard Gaussian disorder model satisfactorily explains many experimental features, it displays a field dependence of the type Inp. a -/E only in a relatively narrow range and only at large fields E > 10 V/cm) [165]. In experiments,... 

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