dft-defects

DFT Point Defect Calculations

Description

This skill covers the first-principles modeling of point defects in crystalline materials: vacancy, interstitial, antisite, substitutional, and complex defect construction; charge-state calculations; defect formation energy formalism with chemical potential constraints; finite-size corrections (Freysoldt-Neugebauer-Van de Walle, Kumagai-Oba, Makov-Payne); Fermi-level-dependent thermodynamics; transition levels; band-edge alignment; and defect concentration estimates. It uses VASP as the primary DFT backend with pymatgen (including the doped and shakenbreak packages) for automated defect generation, correction calculation, and thermodynamic analysis. Invoke this skill when computing defect formation energies, charge transition levels, defect concentrations, or carrier compensation in semiconductors and insulators.

Domain Context

Point defects are local disruptions of the perfect crystal lattice that control a wide range of functional properties: carrier concentration in semiconductors, ionic conductivity in solid electrolytes, color centers in optical materials, magnetic impurities, and catalyst poison tolerance. Even at thermodynamic equilibrium, defect concentrations of 10¹⁰–10¹⁸ cm⁻³ are common and technologically significant.

The fundamental challenge of DFT defect modeling is that defects break translational symmetry. A defect must be embedded in a finite supercell large enough that the defect's strain and electrostatic fields decay before the cell boundary. For charged defects, the periodic boundary conditions introduce spurious long-range interactions between charge images that must be corrected analytically. For semiconductors with DFT band-gap underestimation, formation energies of charged defects are biased by the incorrect VBM and CBM positions.

Defect formation energy is the central quantity:

E_f[X^q] = E_tot[X^q] - E_tot[bulk] - Σ_i n_i μ_i + q(E_VBM + E_F) + E_corr[q]

where:

• E_tot[X^q] is the DFT total energy of the defect supercell in charge state q
• E_tot[bulk] is the DFT total energy of the perfect bulk supercell (identical size)
• n_i is the number of atoms of species i added (+) or removed (−) to form the defect
• μ_i is the chemical potential of species i (eV; relative to its DFT elemental reference)
• q is the formal charge state (integer; q > 0 = electron removed)
• E_VBM is the DFT valence-band maximum energy of the bulk (in the same potential reference frame)
• E_F is the Fermi level measured from the VBM (0 ≤ E_F ≤ E_gap)
• E_corr[q] is the finite-size correction for charged defects (zero for q = 0)