Spray on integrated circuits

MOSFETs are probably the most ubiquitous device in modern electronic circuits.
A major effort is underway to develop commercially viable organic devices that can exploit the ease and low-cost processing associated with polymers.

This week at the weekly science meeting of the Centre for Organic Photonics and Electronics (COPE) we are going to discuss a paper about enhancement of carrier mobilities in organic field effect transistors (OFETs).

From current-voltage (I-V)characteristics the paper extracts mobilities, threshold voltages, and the density of trap states. Since it was not clear to me how one gets such quantities from the data I went on a search and found this widely cited 1998 review by Horowitz. It was helpful because he gives equations which can be used to extract these parameters from I-V characteristics. However, he gives no derivations or references for the derivation and so I am still in the dark about the assumptions and range of validity of the equations. Hopefully, someone will comment on this posting and illuminate it for me. One concern and question I have is: to what extent the equations require a semiconductor band picture for their validity? Or are they just a consequence of electrostatics and the charge accumulation at the organic-insulator interface? After all, sections 3.1 and 3.2 or the article explain why such a picture should not hold in the organic materials used. (This point is not really appreciated enough by people who work in the field).
Other useful and more recent reviews are here and here.
Both reviews stress that charge transport in these materials is still poorly understood.