For pentacene sandwich cell or organic FET, what is the expression to find out the deep trap concentration like Nt or Et-Ev or fraction of total charges(Theta)?
I am really sorry, but there is no easy way. If you have two devices (one with defects/traps and second as a reference "without traps"), you can compare treshold voltages. The threshold voltage shift (in approximation of all charges transferred on semiconductor-gate insulator interface) is proportional to trapped charge concentration as Q=C.V, where C is a gate capacitance per unit of area.
All common ways such as subtheshold slope (i.e. swing) were not proven correct.
What exactly do you want to find? What does deep mean for you?
If you can measure transfer curves of field-effect transistors at various temperatures, you can analyze your transfer curves analytically. I have never done this myself, but several methods have been compared by Kalb et al.
“Calculating the trap density of states in organic field-effect transistors from experiment: A comparison of different methods.” Phys. Rev. B 81 35327 (2010)
These methods will give you a good estimate of the density of trap states in the energy range 0.1-0.3 eV (+- 0.1 eV)below the transport level. You can even push the lower range to about 0.6 eV when using high quality single crystals. I do not know if the so determined trap states are deep enough for you.
If you only have measurements at room temperature you can estimate the density of trap states via the subthreshold swing (discussed in the same paper). It works quite nicely, but unfortunately it does not give you a depth of the calculated density of trap states.
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