Managing the supercell approximation for charged defects in semiconductors: Finite-size scaling, charge correction factors, the band-gap problem, and theab initiodielectric constant

Abstract

The errors arising in ab initio density functional theory studies of semiconductor point defects using the supercell approximation are analyzed. It is demonstrated that ͑a͒ the leading finite size errors are inverse linear and inverse cubic in the supercell size and ͑b͒ finite size scaling over a series of supercells gives reliable isolated charged defect formation energies to around ±0.05 eV. The scaled results are used to test three correction methods. The Makov-Payne method is insufficient, but combined with the scaling parameters yields an ab initio dielectric constant of 11.6± 4.1 for InP. ⌫ point corrections for defect level dispersion are completely incorrect, even for shallow levels, but realigning the total potential in real-space between defect and bulk cells actually corrects the electrostatic defect-defect interaction errors as well. Isolated defect energies to ±0.1 eV are then obtained using a 64 atom supercell, though this does not improve for larger cells. Finally, finite size scaling of known dopant levels shows how to treat the band gap problem: in ഛ200 atom supercells with no corrections, continuing to consider levels into the theoretical conduction band ͑extended gap͒ comes closest to experiment. However, for larger cells or when supercell approximation errors are removed, a scissors scheme stretching the theoretical band gap onto the experimental one is in fact correct.

Negative-Ucarbon vacancy in 4H-SiC: Assessment of charge correction schemes and identification of the negative carbon vacancy at the quasicubic site

“…The appropriate charge correction technique is still under intensive research. [51][52][53][54][55][56][57] Freysoldt and coworkers introduced such a correction scheme, which only depends on the self-consistent electrostatic potential of the defective supercell. 55 This method assumes that the electrostatic potential can be well divided into short and long range parts, where the short range part is induced by the defect and should go to zero far from the defect in the supercell.…”

“…57. Generally speaking, the different schemes can be monitored by scaling tests, 52,53 where the calculated formation energies are plotted as function of the size of the supercell. In a recent study, the choice of the dielectric constant in the Makov-Payne formula as well as the average potential alignment was discussed.…”

Density-functional-theory calculations for silicon vacancy migration

“…As a result we recommended a procedure wherein a maximum likelihood fit is performed on the formation energies computed in a series of supercells, thus yielding the formation energy in an infinite sized supercell corresponding to an isolated defect. [3][4][5][6][7] In the present study, we used this fitting procedure to obtain formation energies at the saddle-point configurations ͑SPCs͒ of a migrating Si vacancy ͑V Si ͒ in the +2, +1, 0, −1, and −2 charge states. Using these values and corresponding ones for the V Si local-energy minimum configurations ͑LEMCs͒, 5 we obtained migration enthalpies of V Si and compared them with results from low temperature experiments and previous DFT studies.…”

Doping in the Valley of Hydrogen Solubility: A Route to Designing Hydrogen-Resistant Zirconium Alloys

“…In Sec. 3 of Supplemental Material [17], we compare the performance of the MP1 correction to the computationally expensive finite-size scaling correction [29] for selected defects. With respect to the finite-size scaling correction, the maximum error for the MP1-corrected formation energies is found to be −0.51 eV in the case of V 0000 Zr .…”