Fundamental Aspects on Charge Hopping

The first reliable experimental evidence of HOMO hole-vibration coupling in organic semiconductor film was reported in 2002 [56]. As the HOMO band in UPS spectrum involves information on the coupling between the conduction hole and vibrations of the molecular ion, UPS measurements can offer key information that is necessary to unravel the fundamental mechanism in the carrier transport properties of organic devices. 

Charge hopping dominates the mobility in molecular systems with very narrow bandwidths and even in systems with larger bandwidths if the mean free path of the traveling charge is very small (the order of the intermolecular distance). Charge transfer processes and carrier dynamics of organic molecular solids have been studied in various fields and detailed theoretical descriptions can be found in several reviews [22-24, 57]. 

The hopping mobility (m) in the high-temperature regime can be approximated from the electron transfer rates by considering the Einstein relation for diffusive motion [20, 23], 

There are two Arei components, and A , corresponding to going to the ionized 

When the neutral state is in the vibrational ground state, the intensities of the vibrational progression resemble a Poisson distribution 

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