I am interested to know the exact relationship between dislocation density, free carrier concentration and impurity present in the semiconductor materials. Does the free carrier concentration have any kind of dependency on Frankel and Schottky defects?.
The procedure how to calculate the free carrier concentration is known and well described in textbooks on semiconductor physics. Bonch-Bruevich Kalashnikov is popular for those who can read Russian. Maybe an English translation exists. Anyway, there are books. The first part is quite simple n = N_eff exp((\mu -E_c)/kT), where N_eff is the effective density of states, \mu is the Fermi level. Finding the FErmi level requires solving the electroneutrality equation. Writing down this equation requires knowledge of the trap depths, for example the depth of the trap a vacancy from a Frenkel pair introduces. So, this is well known, not difficult to perform, but you have to have a model for your semiconductor.
A dislocation typically can deplete the carriers within the carrier diffusion length. If you know the defect density and the carrier diffusion length, you can estimate the loss. Despite having a relatively large defect density, because of having a small diffusion length, the defect induced loss turns out to be relatively small in (In)GaN.
Dr. Goliney has described a theoretical method to calculate the free carrier concentration, you may also use experimental techniques, such as PL, CL, or EL imaging (see the link below) to get the carrier spatial distribution, and compared to a measured macroscopic value, say from Hall measurement.
https://www.nature.com/articles/srep10542
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