In this paper "Role of Aluminum Doping in Anatase-to-Rutile Transformation from Thermodynamic View Point", the authors simulated different synthesis environment (either reducing or oxidizing) by adjusting the fermi level of Al doped TiO2, as shown in Figure 3 of the paper.
My confusion is: Why the synthesis environment can be approximated by different fermi levels? Is it easier to obtain n-type TiO2 in reducing environment than oxidizing environment? Moreover, for substitutional Al-doped TiO2, the doping induced level is located right above valance band maximum of TiO2, so is it unphysical to calculate its formation energy with a fermi level close to conduction band minimum?