General Approach to Charge Transfer Mechanisms

In order to develop such a broader view and a general qualitative understanding of charge transport, it is beneficial to consider the general one-electron Hamiltonian shown in (1). In this approach we follow the outline taken in [45]. This Hamiltonian assumes a low carrier density, and effects due to electron correlation or coulomb interaction are not considered. Despite these limitations, the following general one-electron Hamiltonian is useful to illustrate different limiting cases  

Jnm is the electronic interaction between site m and n in a perfectly ordered lattice and 8Jnm is its variation due to static disorder, and 

In (1), Hq yields the total energy of system in which the molecules and the lattice are excited, yet there are no interactions between molecules and the lattice. The transfer of an electron from site m to site n is given by //j. Polaronic effects, i.e., effects due to the interaction of the electronic excitation and the lattice, are given by H2 and H. hi H2, the energy of the site is reduced by the interaction with the lattice vibration. In H, the lattice vibration alters the transition probability amplitude from site m to n. The term lattice vibration may refer to inter-molecular or intra-molecular vibrations. Static disorder effects are considered in H4, which describes the changes to the site energy or transition probabihty amplitude by variations in the structure of the molecular sohd. 

If fluctuations in the intermolecular distances and orientations give rise to a large variation in the site energy and transition probability amplitude compared to the other terms, the static disorder dominates the charge transport. A charge carrier moves by uncorrelated hops in a broad density of states. Thermal activation is required to overcome the energy differences between different sites. 

These different modes of transport result in a dissimilar temperature dependence of the charge carrier mobility, and this often provides a convenient means to investigate which transport regime may apply. In this chapter, due attention is therefore given to experimental approaches that allow for an investigation of the transport mechanism, and concomitantly of the underlying electronic structure. 

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