Polarons molecular ‘nearly small’ polaron

An attractive model, specifically designed for the case of molecular semiconductors is that of the molecular nearly small polaron (MP) developed by SiUnsh [23]. Initially, the model was developed to resolve the contradiction between a power law temperature dependence of the mobiUty (Eq. 12) reported in naphthalene and pery-lene, which is typical of band theory, and a mean free path of the order of the lattice constant, which would lead to hopping transport. As no transport theory was able to give a satisfactory quantitative description of the experimental facts, a phenomenological approach was adopted. In the model, the carrier is considered as a polaron-type particle resulting of interactions of the carrier with vibrations of the lattice. 

The electron polaron corresponds to the nearly free electron of the conventional band model, whereas the lattice polaron is more or less the above discussed small polaron. By using the Heisenberg uncertainty principle, the interaction time r may be evaluated from the overlap integral 7 as r = H/J. In a molecular crystal, the overlap integral J is of the order of 0.01 eV. r is also connected to the mobility through Eq. (22). 

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