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

Magnetic properties of 3d-impurities substituted in GaAs

We have calculated the magnetic properties of substituted 3d-impurities (Cr-Ni) in a GaAs host by means of first principles electronic structure calculations. We provide a novel model explaining the ferromagnetic long rang order of III-V dilute magnetic semiconductors. The origin of the ferromagnetism is shown to be due to delocalized spin-uncompensated As dangling bond electrons. Besides the quantitative prediction of the magnetic moments, our model provides an understanding of the halfmetallicity, and the raise of the critical temperature with the impurity concentration

Diffusion mechanism of Zn in InP and GaP from first principles

The diffusion mechanism of Zn in GaP and InP has been investigated using first-principles computational methods. It is found that the kickout mechanism is the favored diffusion process under all doping conditions for InP, and under all except n-type conditions for GaP. In n-type GaP the dissociative mechanism is probable. In both p-type GaP and InP, the diffusing species is found to be Zni+2. The activation energy for the kickout process is 2.49 eV in GaP and 1.60 eV in InP, and therefore unintentional diffusion of Zn should be a larger concern in InP than in GaP. The dependence of the activation energy both on the doping conditions of the material and on the stoichiometry is explained, and found to be in qualitative agreement with the experimentally observed dependencies. The calculated activation energies agree reasonably with experimental data, assuming that the region from which Zn diffuses is p type. Explanations are also found as to why Zn tends to accumulate at pn junctions in InP and to why a relatively low fraction of Zn is found on substitutional sites in InP

Breakdown of cation vacancies into anion vacancy-antisite complexes on III-V semiconductor surfaces

An asymmetric defect complex originating from the cation vacancy on (110) III-V semiconductor surfaces which has significantly lower formation energy than the ideal cation vacancy is presented. The complex is formed by an anion from the top layer moving into the vacancy, leaving an anion antisite–anion vacancy defect complex. By calculating the migration barrier, it is found that any ideal cation vacancies will spontaneously transform to this defect complex at room temperature. For stoichiometric semiconductors the defect formation energy of the complex is close to that of the often-observed anion vacancy, giving thermodynamic equilibrium defect concentrations on the same order. The calculated scanning tunneling microscopy (STM) plot of the defect complex is also shown to be asymmetric in the [11¯0] direction, in contrast to the symmetric one of the anion vacancy. This might therefore explain the two distinct asymmetric and symmetric vacancy structures observed experimentally by STM

The Structure of the [Zn_In - V_P] Defect Complex in Zn Doped InP

We study the structure, the formation and binding energies and the transfer levels of the zinc-phosphorus vacancy complex [Zn_In - V_P] in Zn doped p-type InP, as a function of the charge, using plane wave ab initio DFT-LDA calculations in a 64 atom supercell. We find a binding energy of 0.39 eV for the complex, which is neutral in p-type material, the 0/-1 transfer level lying 0.50 eV above the valence band edge, all in agreement with recent positron annihilation experiments. This indicates that, whilst the formation of phosphorus vacancies (V_P) may be involved in carrier compensation in heavily Zn doped material, the formation of Zn-vacancy complexes is not. Regarding the structure: for charge states Q=+6 to -4 the Zn atom is in an sp^2 bonded DX position and electrons added/removed go to/come from the remaining dangling bonds on the triangle of In atoms. This reduces the effective vacancy volume monatonically as electrons are added to the complex, also in agreement with experiment. The reduction occurs through a combination of increased In-In bonding and increased Zn-In electrostatic attraction. In addition, for certain charge states we find complex Jahn-Teller behaviour in which up to three different structures, (with the In triangle dimerised, antidimerised or symmetric) are stable and are close to degenerate. We are able to predict and successfully explain the structural behaviour of this complex using a simple tight binding model.Comment: 10 pages text (postscript) plus 8 figures (jpeg). Submitted to Phys. Rev.

Density functional theory calculations of defect energies using supercells

Reliable calculations of defect properties may be obtained with density functional theory using the supercell approximation. We systematically review the known sources of error and suggest how to perform calculations of defect properties in order to minimize errors. We argue that any analytical error-correction scheme relying on electrostatic considerations is not appropriate to derive reliable defect formation energies, especially not for relaxed geometries. Instead we propose finite size scaling of the calculated defect formation energies, and compare the use of this with both fully converged and "Gamma" (Γ) point only k-point integration. We give a recipe for practical DFT calculations which will help to obtain reliable defect formation energies and demonstrate it using examples from III-V semiconductors

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

Point defects on the (110) surfaces of InP, InAs and InSb: a comparison with bulk

The basic properties of point defects, such as local geometries, positions of charge-transfer levels, and formation energies, have been calculated using density-functional theory, both in the bulk and on the 110 surface of InP, InAs, and InSb. Based on these results we discuss the electronic properties of bulk and surface defects, defect segregation, and compensation. In comparing the relative stability of the surface and bulk defects, it is found that the native defects generally have higher formation energies in the bulk. From this it can be concluded that at equilibrium there is a considerably larger fraction of defects at the surface and under nonequilibrium conditions defects are expected to segregate to the surface, given sufficient time. In most cases the charge state of a defect changes upon segregation, altering the charge-carrier concentrations. The photo-thresholds are also calculated for the three semiconductors and are found to be in good agreement with experimental data