Charge hopping sites

A textbook example for the successful application of the model of Arkhipov et al. is the work of van Woudenbergh et al. [173]. More recently, Agrawal et al. [106] compared injection limited currents and space-charge-limited currents in a copper-phthalocyanine sandwich cell with TTO and Al electrodes. An analysis of experimental data yields consistent values for the width of the DOS distribution as well as for inter-site separation [174]. These studies support the model of thermally activated injection into a Gaussian DOS distribution of hopping sites and confirm the notion that disorder facilitates injection because it lowers the injection barrier, although the transport velocity decreases with increasing disorder. 

Charge hopping Electron or hole transport between equivalent sites. 

Unlike the Poole-Frenkel effect, the dipole trap argument does not require high concentrations of charged traps. Further, the problem of small distances between the hopping sites relative to the position of the potential energy maxima, which is a major limitation of Poole-Frenkel arguments, is avoided. The model predicts field and temperature dependencies that are similar to the disorder formalism. The dipole trap model and the disorder formalism both lead to activation energies that are temperature dependent. 

Figure 38. Schematic of an amorphous molecular solid with both energetic and geometrical disorder. Each randomly oriented hopping site (CTM) is represented by a disk with the number of concentric rulings representing the energy of a charge carrier. (Site A is relatively shallow site B is very deep.) Electric field direction is E. See the text for a detailed explanation.

Figure 5. The amorphous structure of an organic matrix leads to a Gaussian density of states for the HOMO of the donor transport matrix. Some of the donors will have a relatively small oxidation potential (in the shaded region) and these sites are likely to experience a potential barrier inhibiting charge hopping to adjacent sites of higher oxidation potential. A hole may in this way become an immobilized cation.

The fundamental difference between disorder and polaron models is related to the difference in energy of hopping sites due to disorder and the change in molecular conformation upon addition or removal of a charge at a given site. In the disorder... 

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