Is it easier to obtain n-type TiO2 in reducing environment than in oxidizing environment?

Question

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?

Answer 1

The synthesis environment can be modeled by the chemical potential of chemical component elements, not by the chemical potential (or Fermi level) of eletrons. When O is rich, the material would probably be Ti poor, so Ti vacancy is easy to form.

The formation energy depends on chemical potential of electrons: when close to valence band, donor defects will have reduced formation energy, when close to conduction band, acceptor defects will have reduced formation energy.

You can check the formula for the formation energy of point defects.