Finite size scaling as a cure for supercell approximation errors in calculations of neutral native defects in InP

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, whilst 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.Comment: 13 pages, 11 figures. Errata in tables I and III correcte

Managing the supercell approximation for charged defects in semiconductors: finite size scaling, charge correction factors, the bandgap problem and the ab initio dielectric constant

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 re-aligning 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 less than about 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.Comment: 11 pages, 3 figures (6 figure files). Accepted for Phys Rev

Correlations between magnetic properties and bond formation in Rh–MgO(001)

We present the results of first principles calculations for the magnetism of Rh adlayers on MgO (001), at three different adsorption sites and three different coverages, corresponding to 1, 1/2 and 1/8 monolayers. Finite magnetization is found in all cases except that of 1 Rh monolayer above the oxygen site, which is also the most stable. We examine how the magnetization changes as a function of the Rh-surface distance and relate this to changes in the real space charge density and in the density of states (DOS) as the Rh adlayer interacts with the surface. We find that increasing either the Rh-Rh interaction strength or the R h-surface interaction strength leads to reduced magnetization, while increasing the former drives a crossover from localized (atomic) to itinerant magnetism. Neither the magnetic transition itself, nor the localized-to-itinerant magnetism crossover, is found to be directly related to the formation of Rh- surface bonds. From a practical point of view, we predict that magnetism in the Rh-MgO(001) system is most likely to be found experimentally at reduced coverages and at low temperatures

Varying facial expressions in studies of interpersonal judgements and pedestrian lighting

This paper reports two analyses carried out to investigate the influence of facial expression choice in work exploring interpersonal judgements and lighting for pedestrians. An experiment was conducted to compare performance on a facial recognition task using target and reference images of either the same or different expressions: these data demonstrated that matching with different expressions led to a significant reduction in recognition. Regarding the results from previous studies of facial emotion recognition, a post-hoc analysis was carried out to draw conclusions from analysis of individual expressions rather than the collation of all six expressions: it was concluded that these data were consistent for all individual expressions

Description of polarons in ceria using Density Functional Theory

The performance of various density functional theory (DFT) functionals in reproducing the localization of Ce4f electrons to form polarons in cerium dioxide (ceria) is studied. It is found that LDA+U with U=6eV provides the best description, followed by GGA+U with U=5 eV. Hybrids perform worse, with PBE0 better than HSE06 and HSE03. It is also demonstrated that the improvement in the description of the polarons obtained from LDA+U and GGA+U is due primarily to the effect the U has on the filled Ce4f states, but the improvement obtained using the hybrids is primarily due to their effect on the empty states. This difference can be expected to strongly impact some detailed predictions for the properties of ceria obtained using the two classes of functional

Controlling dopant solubility in semiconductor alloys

We consider the formation energies and stabilities of dopants in semiconductor alloys. We show that they are not bounded by the formation energies in the related pure materials. On the contrary, by tuning the alloy composition, dopant solubility can be increased significantly above that in the pure materials. Furthermore, it is not always necessary to carry out full defect calculations in alloy supercells, since good estimates of the formation energies at the most stable substitution sites can be obtained by calculating the formation energies in the various component pure materials, but strained to the lattice parameter of the alloy

Does expression choice affect the analysis of light spectrum and facial emotion recognition?

Facial emotion recognition has been used as a representative pedestrian activity in studies examining the effect of changes in road lighting. Past studies have drawn conclusions using results averaged across performance with the six universally recognised expressions. This paper asks whether expression choice matters. A reanalysis of past data for each unique expression does not suggest a change in the conclusion that facial emotion recognition is not significantly affected by the spectral power distribution of the lighting

Fano effect and Kondo effect in quantum dots formed in strongly coupled quantum wells

We present lateral transport measurements on strongly, vertically coupled quantum dots formed in separate quantum wells in a GaAs/AlGaAs heterostructure. Coulomb oscillations are observed forming a honeycomb lattice consistent with two strongly coupled dots. When the tunnel barriers in the upper well are reduced we observe the Fano effect due to the interfering paths through a resonant state in the lower well and a continuum state in the upper well. In both regimes an in plane magnetic field reduces the coupling between the wells when the magnetic length is comparable to the center to center separation of the wells. We also observe the Kondo effect which allows the spin states of the double dot system to be probed.Comment: 4 pages, 5 figure

Relative concentration and structure of native defects in GaP

The native defects in the compound semiconductor GaP have been studied using a pseudopotential density functional theory method in order to determine their relative concentrations and the most stable charge states. The electronic and atomic structures are presented and the defect concentrations are estimated using calculated formation energies. Relaxation effects are taken into account fully and produce negative-U charge transfer levels for VP and PGa. The concentration of VGa is in good agreement with the results of positron annihilation experiments. The charge transfer levels presented compare qualitatively well with experiments where available. The effect of stoichiometry on the defect concentrations is also described and is shown to be considerable. The lowest formation energies are found for PGa +2 in p-type and VGa −3 in n-type GaP under P-rich conditions, and for GaP −2 in n-type GaP under Ga-rich conditions. Finally, the finite size errors arising from the use of supercells with periodic boundary conditions are examined