Object of the investigation: Semiconductor organic polymers

Organic polymers are polymeric systems consisted of long carbon chains.

In the 1977  researchers found that the conductivity of certain polymers could be changed over the full range from insulator to metal by chemical doping. Them found that conjugated polymers can conduct.

An ideal conjugated polymer can be viewed as an extended regular chain of carbon atoms that have alternating single and double bonds. 

Fig.1 Examples of different conjugated polymers

The p-electrons associated with the double bonds are delocalized along the carbon chain, because they are relatively weakly bound to the carbon atoms. It allows to electrons run along polymer chain such it happens in 1 dimensional ideal crystal. 

Fig.2 Transport in the ideal polymer chain (schematically) 

 However, it is very difficult to synthesize long chain molecules without introducing any defects. The long chains of polymer aspire to bend or twist.

Fig.3 Examples of different polymer chains distortions

Geometrical and chemical defects play an all-important role!

Consequently, the polymer chain can be seen as a sequence of relatively short conjugated segments of varying length. In this “molecular” picture, excitations and/or charge are localized on such segments (we will call those segment as a sites). Because of the variation in conjugation lengths, the energy levels are distributed. Charge transport in such systems, being the result of interchain (intersite) hopping, has been studied in great detail during the last decade.

Fig.4  Transport in the conjugated polymer chain (schematically)

So, accepted picture for description of charge carriers transport is hopping transport between the elementary sites possessing energetic and positional disorder, that can be associated with region of conjugations of chaotically folded polymer chain.

Diffusion in the presence of disorder is an ever enlarging field due to a wealth of new phenomena and processes that are being unraveled. While the mechanism for the diffusion process itself is rather simple, in the presence of disorder if is much more difficult to treat because one now has a combination of two stochastic processes, strongly dependent on each other. The details of their coupling is not clear, but one must into account the fact that disorder can appear in a wide variety of different forms.

Hopping was assumed to be controlled by jumps rates of Miller-Abrahams:

, where - tunneling rate, R_ij- distance between sites, a-lattice unit size, E_i-site energy, k- Boltzman's constant, T-temperature, F-electrical field, (x_i-x_j)- displacement along field

More about semiconductor polymer:
Dr. Nir Tessler home page: http://www.ee.technion.ac.il/people/nir/lab.html (animation of the organic semiconductor devices)