I have made OFET with different nanometer range of channel length and I would like to measure the mobility. Can anybody suggest to me how to measure it?
Generally, the mobility is calculated by measurement of the saturation current (equations can be found on Google and in research publications). As you write, in short channels, the effects of other physical quantities become important. If you are worried about the injection "resistance", you can eliminate that by measuring the saturation current with different channel lengths. If you are worried about other short channel effects, the mobility in OFETs is generally too low to be hugely impacted by velocity saturation - especially for 900nm channels. Scattering effects are important, and it is crucial to test with the right insulator interface, but they can be problematic even for long channel devices.
You could try to estimate the carrier concentration from the threshold voltage of your field effect measurements and then calculate the field effect mobility. We have done this for InAs nanowires (c.f. doi:10.1063/1.3631026).
This method has certain drawbacks but it can deliver a first estimate.
Article Effect of Si-doping on InAs nanowire transport and morphology
The effective mobility also can be extracted via C-V split measurement, remember that the effective mobility is larger tht field effect mobility (µFE =(L gm) / (WCox Vd ) ), it can be found in lots of sources, but the capacitance is very important here.
And, please, keep in mind, that we try to apply a formalism developed for MOS devices (solid state devices), whereas in OFETs the transport mechanism is different.
There are many works considering the topic. E.g. I've found a PhD thesis, which may be helpful for you.: www.ruf.rice.edu/~natelson/theses/behranghamadani_thesis.pdf
or another work http://inside.mines.edu/~zhiwu/research/papers/G02_charge_transfer.pdf
An appropriate query in Google will indicate a number of papers.
Our group has been working on organic field effect transistors for years and of course, mobility. Please feel free to check out our homepage and our papers, were mobility measurements are described.
I think mobility in organic devices, could be extracted versus time of fiy(TOF) and addmittance spectroscopy(AS) methods. For OFET you should add additional bias.