The errors arising in ab initio density functional theory studies of semiconductor point defects using the super-cell approximation were analyzed. It was demonstrated that (a) the leading finite size errors were inverse linear and inverse cubic in the super-cell size and that (b) finite-size scaling over a series of super-cells gave reliable isolated charged defect formation energies to around ±0.05eV. The scaled results were used to test 3 correction methods. The Makov-Payne method was insufficient but, combined with the scaling parameters, yielded an ab initio dielectric constant of 11.6 for InP. The Γ-point corrections for defect level dispersion were completely incorrect, even for shallow levels, but realigning the total potential in real-space between defect and bulk cells also corrects the electrostatic defect-defect interaction errors. Isolated defect energies to ±0.1eV were then obtained by using a 64 atom super-cell, although this did not improve for larger cells. Finally, finite-size scaling of known dopant levels showed how to treat the band-gap problem: in upto 200-atom super-cells with no corrections. Continuing to consider levels into the theoretical conduction band (extended gap) came closest to experiment. For larger cells, or when super-cell approximation errors were removed, a scissors scheme which stretched the theoretical band-gap onto the experimental one was correct.

Managing the Super-Cell Approximation for Charged Defects in Semiconductors - Finite-Size Scaling, Charge Correction Factors, the Band-Gap Problem and the ab initio Dielectric Constant. C.W.M.Castleton, A.Höglund, S.Mirbt: Physical Review B, 2006, 73[3], 035215 (11pp)

Figure 3

Diffusivity of Zn in InGaAs/InP

(Zn = 1 x 1018/cm3)