The efficiency of doping crystalline semiconductors is often associated with the solubility of the dopant. However, the scope of doping is usually a high density of extrinsic carriers, which is not necessarily guaranteed by a high solubility of the dopant but by the high concentrations of a certain type of defects. We present a universal approach to relate the concentrations of defects resulting in extrinsic carriers in crystalline semiconductors as a function of the doping process experimental parameters. Based on quantum multiple scattering, our method features two main theoretical novelties: the transition operators are calculated by iteratively “switching on” the interaction potentials and the temperature effects are introduced as semiclassical vibrations. The bulk and doped configurations are characterized by their ground state electronic structures obtained from first-principles calculations. The dependency on substrate temperature of the carrier concentration calculated with our method is shown to reproduce well the experimental results not only for well-known processes (the n-type doping of ZnO with Al and the p-type doping of GaAs with Be) but also for challenging processes such as the p-type doping of ZnO with P. This proves that our approach is reliable and that it can become a powerful tool in the search for optimal growth condition.