I read about charge transport models in organic thin film transistors, there are three models as far as I know: VRH, MTR, Polaron. Is there any other models? How are they used to model the OTFT itself?
The most efficient model for OTFT would be drift-diffusion model. It will give you nearly expected results without complications. The models you mentioned are dependent on trap and odefects incorporation which are not needed in transistors.
there are several experimental works and two good reviews by Gilles Horowitz in Adv. Mater. (1998) and Adv. Polym. Sci. (2010) which discuss precisely this topic. If you want to read more on the precise physics on a molecular scale, you might also find the attached paper interesting
From an experimental physics point of view, the general opinion is that a gate-voltage dependent OFET mobility points to VRH or MTR, as both predict this dependence and are also quite likely to occur in OFETs due to the transport at the gate-dielectric interface (which is certainly not trap-free). But in order to figure out which transport model best describes an individual semiconductor, you would have to properly test for it, e.g. via temperature-dependent measurements of mobility etc.
I agree with Fiheon that you are probably on the right track with just using drift-diffusion if you want a generic OFET model rather than something that describes one particular material system.
Article Materials Meets Concepts in Molecule‐Based Electronics
In agreement with the two previous posts, I would mention as basic concepts drift-diffusion and hopping transport through localised states. To that, I would add percolation. There is an excellent recent review by Sergei Baranovskii here:
Nenashev, A. V.; Oelerich, J. O.; Baranovskii, S. D., Theoretical tools for the description of charge transport in disordered organic semiconductors. Journal of physics. Condensed matter (2015) 27 (9), 093201.