Mid Sweden University

The errors arising in ab initio density functional theory studies of semiconductor point defects using the supercell approximation are analyzed. It is demonstrated that (a) the leading finite size errors are inverse linear and inverse cubic in the supercell size and (b) 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. Gamma 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 <= 200 atom supercells with no corrections, continuing to consider levels into the theoretical conduction band (extended gap) 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.

We report resonant x-ray scattering data of the orbital and magnetic ordering at low temperatures at the Mn L-2,L-3 edges in La0.5Sr1.5MnO4. The orderings display complex energy features close to the Mn absorption edges. Systematic modeling with atomic multiplet crystal field calculations was used to extract meaningful information regarding the interplay of spin, orbital, and Jahn-Teller order. These calculations provide a good general agreement with the observed energy dependence of the scattered intensity for a dominant orbital ordering of the d(x)(2)-z(2)/d(y)(2)-z(2) type. In addition, the origins of various spectral features are identified. The temperature dependence of the orbital and magnetic ordering was measured and suggests a strong interplay between the magnetic and orbital order parameters.

The relaxed and unrelaxed formation energies of neutral antisites and interstitial defects in InP are calculated using ab initio density functional theory and simple cubic supercells of up to 512 atoms. The finite-size errors in the formation energies of all the neutral defects arising from the supercell approximation are examined and corrected for using finite-size scaling methods, which are shown to be a very promising approach to the problem. Elastic errors scale linearly, while the errors arising from charge multipole interactions between the defect and its images in the periodic boundary conditions have a linear plus a higher order term, for which a cubic provides the best fit. These latter errors are shown to be significant even for neutral defects. Instances are also presented where even the 512 atom supercell is not sufficiently converged. Instead, physically relevant results can be obtained only by finite-size scaling the results of calculations in several supercells, up to and including the 512 atom cell and in extreme cases possibly even including the 1000 atom supercell.

The formation energies and relaxed structures of the neutral vacancies in InP are calculated by planewave density functional theory, using supercells of 8, 64, 216 and 512 atoms together with finite size scaling. The effects of electrostatic defect-defect interactions and the truncation of elastic relaxations by the finite supercell are examined. The unrelaxed formation energies are 4.95+/-0.10 and 3.00+/-0.10eV for V-In(+0) and V-P(+0) respectively, and the relaxed formation energies are 4.20+/-0.05 and 2.35+/-0.15 eV. When relaxed, V-In(+0) remains very nearly symmetric with a 40% volume reduction, V-P(+0) on the other hand develops a double dimerized structure, with an similar to12% Jahn-Teller distortion and a 45% volume reduction. It is shown that finite size scaling sometimes reveals that energies are not converged even in the 512 atom supercell, and can thus be important tool in theoretical studies of defects in semiconductors, if sufficient care is taken with strongly Jahn Teller active defects.