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

Screening and the quantitative π-model description of the optical spectra and polarizations of phenyl based oligomers

The long standing problem of the inability of many semiempirical models to correctly predict the polarization of the higher dipole allowed optical transitions of phenyl based π-conjugated polymers and molecules is examined and related to the issue of internal and external screening of π-π electron Coulomb interactions within the molecules. Following a review of previous theoretical and experimental work, π electron only the Complete Neglect of Differential Overlap (CNDO) model is presented which, for the first time, is able to predict accurately the energies and symmetries of all the observed optical transitions of benzene, biphenyl and trans -stilbene, up to ~8-10 eV. In so doing, it is demonstrated that the problem with previous calculations was the noninclusion of screening from outside the p electron system itself. By fitting separately the spectra in hydrocarbon based condensed phases, in the gas phase and in solid rare gas matrices, and comparing the resulting model parameters, we show that, while the effects of screening from the environment are certainly noticeable, the most important spectral features - in particular the ordering of dipole allowed transitions - come from effective screening by the s electrons. We find that both of these effects can be adequately accounted for within a π electron only model by using a dielectric constant and appropriate parameter renormalization

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

Charge transfer and adhesion in Rh/MgO(001)

Ab initio density functional calculations are reported for Rh adlayers on MgO(001) at coverages of 1, 1/2 and 1/8 monolayers. It is shown that charge is transferred from oxide surface to the Rh adatoms. The transfer ranges from 0.06 e to 0.27 e, depending upon adsorption site and coverage. In comparison, transfers of 0.08 e from adatom to surface and 0.32 e surface to adatom are found for monolayer coverages of Mg and O, respectively. With the Rh adatoms, significant charge polarization of both Rh and the surface are also seen, but it is never-the-less found that the adhesion energy is linearly related to the charge transfer, with the most stable adsorption site at any particular coverage being the one at which the charge transfer is a maximum

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

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

Tuning LDA+U for electron localization and structure at oxygen vacancies in ceria

We examine the real space structure and the electronic structure (particularly Ce4f electron localization) of oxygen vacancies in CeO2 (ceria) as a function of U in density functional theory studies with the rotationally invariant forms of the LDA+U and GGA+U functionals. The four nearest neighbor Ce ions always relax outwards, with those not carrying localized Ce4f charge moving furthest. Several quantification schemes show that the charge starts to become localized at U≈3eV and that the degree of localization reaches a maximum at ∼6eV for LDA+U or at ∼5.5eV for GGA+U. For higher U it decreases rapidly as charge is transferred onto second neighbor O ions and beyond. The localization is never into atomic corelike states; at maximum localization about 80–90% of the Ce4f charge is located on the two nearest neighboring Ce ions. However, if we look at the total atomic charge we find that the two ions only make a net gain of (0.2–0.4)e each, so localization is actually very incomplete, with localization of Ce4f electrons coming at the expense of moving other electrons off the Ce ions. We have also revisited some properties of defect-free ceria and find that with LDA+U the crystal structure is actually best described with U=3–4eV, while the experimental band structure is obtained with U=7–8eV. (For GGA+U the lattice parameters worsen for U>0eV, but the band structure is similar to LDA+U.) The best overall choice is U≈6eV with LDA+U and ≈5.5eV for GGA+U, since the localization is most important, but a consistent choice for both CeO2 and Ce2O3, with and without vacancies, is hard to find

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.