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  • 1.
    Castleton, Christopher
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Uppsala universitet, Sweden.
    Höglund, Andreas
    Uppsala universitet, Sweden.
    Mirbt, Susanne
    Uppsala universitet, Sweden.
    Managing the supercell approximation for charged defects in semiconductors: Finite-size scaling, charge correction factors, the band-gap problem, and the ab initio dielectric constant2006In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 73, no 035215Article in journal (Refereed)
    Abstract [en]

    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 < or = 200 atom supercells with no corrections, continuing to consider levels into the theoretical conductin 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.

  • 2.
    Castleton, Christopher
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Linköpings universitet, Tekniska högskolan, Sweden.
    Kullgren, J.
    Department of Materials Chemistry, Uppsala University, Box 538, SE-75121, Sweden.
    Hermansson, K.
    Department of Materials Chemistry, Uppsala University, Box 538, SE-75121, Sweden.
    Tuning LDA+U for electron localization and structure at oxygen vacancies in ceria2007In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 127, no 24Article in journal (Refereed)
    Abstract [en]

    We examine the real space structure and the electronic structure (particularly Ce4f electron localization) of oxygen vacancies in Ce O2 (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˜3 eV and that the degree of localization reaches a maximum at ~6 eV for LDA+U or at ~5.5 eV 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=3-4 eV, while the experimental band structure is obtained with U=7-8 eV. (For GGA+U the lattice parameters worsen for U>0 eV, but the band structure is similar to LDA+U.) The best overall choice is U˜6 eV with LDA+U and ˜5.5 eV for GGA+U, since the localization is most important, but a consistent choice for both Ce O2 and Ce2 O3, with and without vacancies, is hard to find. 

  • 3.
    Castleton, Christopher
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Nottingham Trent University, UK.
    Lee, A.
    Nottingham Trent University, UK.
    Kullgren, J.
    Uppsala University, Sweden.
    Benchmarking Density Functional Theory Functionals for Polarons in Oxides: Properties of CeO22019In: The Journal of Physical Chemistry C, ISSN 1932-7447, E-ISSN 1932-7455, Vol. 123, no 9, p. 5164-5175Article in journal (Refereed)
    Abstract [en]

    We examine methods for studying polarons in metal oxides with density functional theory (DFT), using the example of cerium dioxide and the functionals, local density approximation + U (LDA+U), generalized gradient approximation + U (GGA+U) in the Perdew-Burke-Ernzerhof parametrization (PBE+U), as well as the hybrid functionals B3LYP, Heyd?Scuseria?Ernzerhof (HSE)03, HSE06, and PBE0. We contrast the four polaron energies commonly reported in different parts of the literature: formation energy, localization/relaxation energy, density-of-states level, and polaron-hopping activation barrier. Qualitatively, all these functionals predict "small" (Holstein) polarons on the scale of a single lattice site, although LDA+U and GGA+U are more effective than the hybrids at localizing the Ce 4f electrons. The improvements over pure LDA/GGA appear because of changes in the filled Ce 4f states when using LDA/GGA+U but due to changes in the empty Ce 4f states when using the hybrids. DFT is shown to have sufficient correlation to predict both adiabatic and (approximate) diabatic hopping barriers. Overall, LDA+U = 6 eV provides the best description in comparison to the experiment, followed by GGA+U = 5 eV. The hybrids are worse, tending to overestimate the gap and significantly underestimate the polaron-hopping barriers.

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  • 4.
    Castleton, Christopher
    et al.
    Linköpings universitet, Tekniska högskolan, Sweden.
    Nokbin, S.
    Materials Chemistry, The Ångström Laboratory, Box 538, SE-751 21 Uppsala, Sweden, Laboratory for Computational and Applied Chemistry, Department of Chemistry, Kasetsart University, Bangkok, 10900, Thailand.
    Hermansson, K.
    Materials Chemistry, The Ångström Laboratory, Box 538, SE-751 21 Uppsala, Sweden.
    Correlations between magnetic properties and bond formation in Rh-MgO(0 0 1)2007In: Surface Science, ISSN 0039-6028, E-ISSN 1879-2758, Vol. 601, no 5, p. 1218-1230Article in journal (Refereed)
    Abstract [en]

    We present the results of first principles calculations for the magnetism of Rh adlayers on MgO(0 0 1), 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 one 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 Rh-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(0 0 1) system is most likely to be found experimentally at reduced coverages and at low temperatures.

  • 5.
    Castleton, Christopher
    et al.
    Uppsala universitet, Sweden.
    Nokbin, Somkiat
    Uppsala universitet, Sweden.
    Hermansson, Kersti
    Uppsala universitet, Sweden.
    Charge transfer and adhesion in Rh/MgO(001)2008In: Proceedings of the 17th international vacuum congress/13th international conference on surface science/international conference on nanoscience and technology / [ed] Johansson LSO; Andersen JN; Gothelid M; Helmersson U; Montelius L; Rubel M; Setina J; Wernersson LE, 2008, p. 082027-Conference paper (Refereed)
    Abstract [en]

    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.

  • 6. Höglund, A
    et al.
    Castleton, Christopher W.M
    KTH, Materialfysik, Sweden.
    Mirbt, S
    Relative concentration and structure of native defects in GaP2005In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 19, p. 195213-Article in journal (Refereed)
    Abstract [en]

    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 V-P and P-Ga. The concentration of V-Ga 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 P-Ga(+2) in p-type and V-Ga(-3) in n-type GaP under P-rich conditions, and for Ga-P(-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.

  • 7.
    Höglund, Andreas
    et al.
    Uppsala universitet, Sweden.
    Castleton, Christopher
    Uppsala universitet, Sweden.
    Göthelid, Mats
    Johansson, Börje
    Uppsala universitet, Sweden.
    Mirbt, Susanne
    Uppsala universitet, Sweden.
    Point defects on the (110) surfaces of InP, InAs, and InSb: A comparison with bulk2006In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 74, no 7, p. 075332-Article in journal (Refereed)
    Abstract [en]

    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 photothresholds are also calculated for the three semiconductors and are found to be in good agreement with experimental data.

  • 8.
    Höglund, Andreas
    et al.
    Uppsala universitet, Sweden.
    Castleton, Christopher
    Uppsala universitet, Sweden.
    Mirbt, Susanne
    Uppsala universitet, Sweden.
    Diffusion mechanism of Zn in InP and GaP from first principles2008In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 77, no 11, p. 113201-Article in journal (Refereed)
    Abstract [en]

    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 Zn. 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.

  • 9.
    Höglund, Andreas
    et al.
    Uppsala universitet, Sweden.
    Eriksson, Olle
    Uppsala universitet, Sweden.
    Castleton, Christopher
    Uppsala universitet, Sweden.
    Mirbt, Susanne
    Uppsala universitet, Sweden.
    Increasing the equilibrium solubility of dopants in semiconductor multilayers and alloys2008In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 100, no 10, p. 105501-Article in journal (Refereed)
    Abstract [en]

    We have theoretically studied the possibility to control the equilibrium solubility of dopants in semiconductor alloys, by strategic tuning of the alloy concentration. From the modeled cases of C-0 in SixGe1-x, Zn- and Cd- in GaxIn1-xP it is seen that under certain conditions the dopant solubility can be orders of magnitude higher in an alloy or multilayer than in either of the elements of the alloy. This is found to be due to the solubility's strong dependence on the lattice constant for size mismatched dopants. The equilibrium doping concentration in alloys or multilayers could therefore be increased significantly. More specifically, Zn- in a GaxIn1-xP multilayer is found to have a maximum solubility for x=0.9, which is 5 orders of magnitude larger than that of pure InP.

  • 10.
    Kullgren, Jolla
    et al.
    Uppsala universitet, Sweden.
    Castleton, Christopher W.M
    Nottingham Trent Univ, Sch Sci & Technol, Nottingham NG11 8NS, England.
    Müller, Carsten
    Uppsala universitet, Sweden.
    Ramo, David Muñoz
    London Ctr Nanotechnol, London WC1E 6BT, England.
    Hermansson, Kersti
    Uppsala universitet, Sweden.
    B3LYP calculations of cerium oxides2010In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 132, no 5, p. 054110-Article in journal (Refereed)
    Abstract [en]

    In this paper we evaluate the performance of density functional theory with the B3LYP functional for calculations on ceria (CeO2) and cerium sesquioxide (Ce2O3). We demonstrate that B3LYP is able to describe CeO2 and Ce2O3 reasonably well. When compared to other functionals, B3LYP performs slightly better than the hybrid functional PBE0 for the electronic properties but slightly worse for the structural properties, although neither performs as well as LDA+U(U = 6 eV) or PBE+U(U = 5 eV). We also make an extensive comparison of atomic basis sets suitable for periodic calculations of these cerium oxides. Here we conclude that there is currently only one type of cerium basis set available in the literature that is able to give a reasonable description of the electronic structure of both CeO2 and Ce2O3. These basis sets are based on a 28 electron effective core potential (ECP) and 30 electrons are attributed to the valence space of cerium. Basis sets based on 46 electron ECPs fail for these materials

  • 11. Kullgren, Jolla
    et al.
    Hermansson, Kersti
    KTH, Teoretisk kemi och biologi.
    Castleton, Christopher
    Nottingham Trent Univ, Sch Sci & Technol, Nottingham NG11 8NS, England.
    Many competing ceria (110) oxygen vacancy structures: From small to large supercells2012In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 137, no 4, p. 044705-Article in journal (Refereed)
    Abstract [en]

    We present periodic "DFT+U" studies of single oxygen vacancies on the CeO2(110) surface using a number of different supercells, finding a range of different local minimum structures for the vacancy and its two accompanying Ce(III) ions. We find three different geometrical structures in combination with a variety of different Ce(III) localization patterns, several of which have not been studied before. The desired trapping of electrons was achieved in a two-stage optimization procedure. We find that the surface oxygen nearest to the vacancy either moves within the plane towards the vacancy, or rises out of the surface into either a symmetric or an unsymmetric bridge structure. Results are shown in seven slab geometry supercells, p(2 x 1), p(2 x 2), p(2 x 3), p(3 x 2), p(2 x 4), p(4 x 2), and p(3 x 3), and indicate that the choice of supercell can affect the results qualitatively and quantitatively. An unsymmetric bridge structure with one nearest and one next-nearest neighbour Ce(III) ion (a combination of localizations not previously found) is the ground state in all (but one) of the supercells studied here, and the relative stability of other structures depends strongly on supercell size. Within any one supercell the formation energies of the different vacancy structures differ by up to 0.5 eV, but the same structure can vary by up to similar to 1 eV between supercells. Furthermore, finite size scaling suggests that the remaining errors (compared to still larger supercells) can also be similar to 1 eV for some vacancy structures.

  • 12. Lu, Zhansheng
    et al.
    Yang, Zongxian
    He, Bingling
    Castleton, Christopher
    Nottingham Trent Univ, Sch Sci & Technol, Nottingham NG11 8NS, England; Uppsala Univ, Angstrom Lab, SE-75121 Uppsala, Sweden.
    Hermansson, Kersti
    KTH, Teoretisk kemi och biologi.
    Cu-doped ceria: Oxygen vacancy formation made easy2011In: Chemical Physics Letters, ISSN 0009-2614, E-ISSN 1873-4448, Vol. 510, no 1-3, p. 60-66Article in journal (Refereed)
    Abstract [en]

    DFT + U calculations of Cu-doped bulk ceria are presented. The first oxygen vacancy in Cu-doped ceria forms almost spontaneously and the second vacancy is also easily created. Whether zero, one or two oxygen vacancies, the Cu dopant is in the form Cu(+ II), and prefers to be 4-coordinated in a close to planar structure. Charge compensation, structural relaxation and available Cu-O states all play roles in lowering the O vacancy formation energies, but to different degrees when the first and second oxygen vacancies are formed. The Cu-doped ceria(1 1 1) surface system behaves in a similar fashion.

  • 13. Wilkins, S. B.
    et al.
    Stojic, N.
    Beale, T. A. W.
    Binggeli, N.
    Castleton, Christopher
    KTH, Mikroelektronik och Informationsteknik, IMIT, Sweden.
    Bencok, P.
    Prabhakaran, D.
    Boothroyd, A. T.
    Hatton, P. D.
    Altarelli, M.
    Resonant soft x-ray scattering investigation of orbital and magnetic ordering in La0.5Sr1.5MnO42005In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 71, no 24, p. 245102-Article in journal (Refereed)
    Abstract [en]

    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.

  • 14.
    Wolf, Matthew J.
    et al.
    Uppsala Univ, Dept Chem, Angstrom Lab, Uppsala, Sweden.;Univ Bath, Dept Phys, Claverton Down, England..
    Castleton, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Nottingham Trent Univ, Sch Sci & Technol, Nottingham, England.
    Hermansson, Kersti
    Uppsala Univ, Dept Chem, Angstrom Lab, Uppsala, Sweden..
    Kullgren, Jolla
    Uppsala Univ, Dept Chem, Angstrom Lab, Uppsala, Sweden..
    STM Images of Anionic Defects at CeO2(111)-A Theoretical Perspective2019In: Frontiers in Chemistry, E-ISSN 2296-2646, Vol. 7, article id 212Article in journal (Refereed)
    Abstract [en]

    We present a theoretically oriented analysis of the appearance and properties of plausible candidates for the anionic defects observed in scanning tunneling microscopy (STM) experiments on CeO2(111). The simulations are based on density functional theory (DFT) and cover oxygen vacancies, fluorine impurities and hydroxyl groups in the surface and sub-surface layers. In the surface layer, all three appear as missing spots in the oxygen sublattice in filled state simulated STM images, but they are distinguishable in empty state images, where surface oxygen vacancies and hydroxyls appear as, respectively, diffuse and sharp bright features at oxygen sites, while fluorine defects appear as triangles of darkened Ce ions. In the sub-surface layer, all three defects present more complex patterns, with different combinations of brightened oxygen ion triangles and/or darkened Ce ion triangles, so we provide image maps to support experimental identification. We also discuss other properties that could be used to distinguish the defects, namely their diffusion rates and distributions.

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