The theoretical description of defects and impurities in semiconductors was largely based on density functional theory employing super-cell models. The literature discussion of uncertainties that limit the predictive value of this approach has focused mostly on two issues: (1) finite-size effects, in particular for charged defects; (2) the band-gap problem in local or semi-local density functional theory approximations. It was described here how finite-size effects (1) in the formation energy of charged defects could be accurately corrected in a simple way, i.e. by potential alignment in conjunction with a scaling of the Madelung-like screened first order correction term. The factor involved with this scaling depends only on the dielectric constant and the shape of the super-cell, and quite accurately accounts for the full third order correction according to Makov and Payne. Further discussed in some detail was the background and justification for this correction method, and the effect of the ionic screening on the magnitude of the image charge energy was also addressed. With regard to (2) the band-gap problem, the merits of non-local external potentials that were added to the density functional theory Hamiltonian were discussed and allowance was made for an empirical band-gap correction without significantly increasing the computational demand over that of standard density functional theory calculations. In combination with LDA + U, these potentials were further useful for the prediction of polaronic defects with localized holes in anion-p orbitals.

Accurate Prediction of Defect Properties in Density Functional Supercell Calculations. S.Lany, A.Zunger: Modelling and Simulation in Materials Science and Engineering, 2009, 17[8], 084002