First-principles calculations based upon density functional theory permitted the quantification of the thermal equilibrium concentration of a point defect by calculating the formation energy of the defect. In order to know the formation energy, 3 parameters were required: the energy difference between defective and perfect systems, the chemical potential of the constitutive atoms and the Fermi level. The energy difference was obtained from calculations based on the super-cell method. The energy of a super-cell with a charged defect could be corrected in an appropriate manner such as alignment of electrostatic potential. The chemical potential and Fermi level could be deduced from the conditions of phase equilibrium and charge neutrality.

Theoretical Investigation of Thermal Equilibrium Concentration of Point Defect Through First-Principles Calculation. A.Kuwabara: Science and Technology of Advanced Materials, 2007, 8[6], 519-23