This chapter describes typical approaches and levels of approximation and the common sources of uncertainties encountered. On one hand, it provides a generalized framework for carrying out defect calculations. On the other hand, it is intended as a guide to experimentalists how to read theory papers, assess conclusions, and interact with theorists.

Chapter Contents:

• 7.1 Defect levels
• 7.2 Defect thermochemistry
• 7.2.1 Defect formation enthalpy
• 7.2.2 Phase stabilities and chemical potential space
• 7.2.3 Defect formation enthalpy diagrams
• 7.2.4 Configuration coordinate diagrams and optical excitation
• 7.2.5 Defect equilibria and carrier concentrations
• 7.3 Sources of uncertainty in defect formation energy calculations
• 7.4 Total energies using first principles electronic structure calculations
• 7.4.1 Overview and many-particle Schrödinger equation
• 7.4.2 Hartree–Fock
• 7.4.3 Density functional theory
• 7.4.4 Emerging approaches—quantum Monte Carlo
• 7.5 Achieving higher accuracy with density functional theory and other approaches
• 7.5.1 Observations
• 7.5.2 Generalized Koopman's theorem
• 7.5.3 LDA+U and PBE+U
• 7.5.4 Green's function approaches: the GW method
• 7.5.5 Hybrid functionals
• 7.5.6 Fitted chemical potentials
• 7.6 Finite size effects
• 7.6.1 Charged defects
• 7.6.2 Band filling for shallow defects
• 7.7 Recent examples
• 7.7.1 Mg and other possible acceptors in GaN
• 7.7.2 Oxygen vacancies and other defects in metal oxides
• 7.7.2.1 VO in MgO
• 7.7.2.2 VO in ZnO
• 7.7.2.3 NO in ZnO
• 7.7.3 Transition metal impurities
• 7.7.4 Defect clustering and aggregation
• 7.8 Summary and outlook
• References

Inspec keywords: crystal defects; ab initio calculations

Other keywords: electronic structure theory; approximation level; first principles calculations; defects; many-particle Schrodinger equation

Subjects: Defects in crystals; Electronic structure: density of states and band structure (condensed matter); Ab initio calculations (condensed matter electronic structure)