Density-functional Supercell Calculations Research Articles

Boron and indium incorporation in GaP(0 0 1) surfaces by vapour deposition: Density-functional supercell calculations of the surface stability

Using surface supercells and the density-functional method, surface formation energies are calculated for probable GaP(0 0 1) reconstructions without and with indium or/and boron substitutions. Obtained surface stability diagrams provide surface compositions and surface structures in dependence on the growth conditions: indium atoms are built into the c(4 × 4) patterns under strongly P-rich conditions and into the β2(2 × 4) reconstruction under less P-rich conditions. Under In-rich and non-P-rich conditions, initial structures of metallic InGa phases are formed in the (2 × 4) mixed-dimer reconstruction. In the c(4 × 4) and (2 × 4) mixed-dimer patterns the full range of In:Ga content is accessible by variation of the In:Ga ratio in the gas phase. Boron can be built into the c(4 × 4) patterns of the GaP(0 0 1) surface in form of isolated atoms or nearest-neighbours under strongly P-rich and moderately to strongly B-rich conditions. The boron incorporation is strongly enhanced at the surface in respect to theoretical predictions for the bulk, what explains the larger content found experimentally. Assuming P-rich conditions, which are suitable for the growth of the ternary alloys, the obtained surface stability diagram for the quaternary (BInGa)P shows that nearly the full range of In:Ga content is accessible. However, the boron content in the alloy is restricted as found analogously for (BGa)P and is independent of the indium content. The expected increase of the boron content in presence of indium cannot be confirmed. Contrary to the analogous GaAs systems, boron atoms do not substitute phosphor atoms (antisite position) in GaP, (InGa)P, (BGa)P, and (BInGa)P.

Supercell studies of the Fermi surface changes in the electron-doped superconductorLaFeAsO1−xFx

We study the changes in the Fermi surface with electron doping in the ${\text{LaFeAsO}}_{1\ensuremath{-}x}{\text{F}}_{x}$ superconductors with density-functional supercell calculations using the linearized augmented plane-wave method. The supercell calculations with explicit F substitution are compared with those obtained from the virtual-crystal approximation (VCA) and from a simple rigid-band shift. We find significant differences between the supercell results and those obtained from the rigid-band shift with electron doping, although quite remarkably the supercell results are in good agreement with the VCA where the nuclear charges of the O atoms are slightly increased to mimic the addition of the extra electrons. With electron doping, the two cylindrical hole pockets along $\ensuremath{\Gamma}\text{\ensuremath{-}}Z$ shrink in size, and the third hole pocket around $Z$ disappears for an electron-doping concentration in excess of about 7%--8%, while the two elliptical electron cylinders along $M\text{\ensuremath{-}}A$ expand in size. The spin-orbit coupling does not affect the Fermi surface much except a somewhat reduction in the size of the third hole pocket in the undoped case. We find that with the addition of the electrons the antiferromagnetic state becomes energetically less stable as compared to the nonmagnetic state, indicating that the electron doping may provide an extra degree of stability to the formation of the superconducting ground state.

The magnetic interaction of Fe doped ZnO with intrinsic defects: A first principles study

By density functional supercell calculations we have studied the magnetic properties of intrinsic vacancies in ZnO doped with diluted Fe impurities. We found that the more energetically favored Fe Zn – V O configuration corresponds to the one in which the two defects are far apart. On the contrary, among the investigated configurations of Fe Zn – V Zn , the one having the lower formation energy corresponds to the complex in which one defect is in the next nearest neighbor position with respect to the other. For Zn-poor growth condition the thermal population of the latter complex provide a key to understand the magnetism of the system.

Stability and band gaps of InGaAs, BGaAs, and BInGaAs alloys: Density‐functional supercell calculations

AbstractThe influence of arrangement and content of substituents (B, In) in BGaAs, InGaAs, and BInGaAs alloys on the stabilities and band gaps is investigated using density‐functional supercell calculations. The stability of ternary alloys decreases from InGaAs over BGaAs to GaAsN. Typical substituent structures show the following stability order: isolated substituents – [110] chains – clusters – twisted [111] chains – (200/211) arrangements (most stable). This is valid for both the In‐ and B‐poor as well as the In‐ and B‐rich alloys. From the fact that grown InGaAs provides a different gap than the most stable arrangement one can conclude that other structures (isolated indium atoms or Inm As clusters) are formed during the growth. Simultaneous substitutions (BInGaAs) of larger (In) and smaller (B) atoms prefer arrangements in larger distances (220) for isovalent boron substitution and in In–B bonds for antisite boron substitution. The high degree boron antisite substitution induces partially occupied acceptor bands which lead to a strong reduction of the band gap in comparison to the isovalent substitution. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonstoichiometry as a source of magnetism in otherwise nonmagnetic oxides: Magnetically interacting cation vacancies and their percolation

We discuss the physical conditions required for the creation of collective ferromagnetism in nonmagnetic oxides by intrinsic point defects such as vacancies. We use ${\mathrm{HfO}}_{2}$ as a case study because of recent pertinent calculations and observations. It was previously noted theoretically that charge-neutral Hf vacancies in ${\mathrm{HfO}}_{2}$ have partially occupied electronic levels within the band gap, and thus the vacancies carry a nonvanishing local magnetic moment. Such density functional supercell calculations have further shown that two such vacancies interact ferromagnetically if they are separated by up to third-neighbor distance. This suggested to the authors that Hf vacancies could explain the observed collective ferromagnetism in thin ${\mathrm{HfO}}_{2}$ films. Here we use our previously developed more complete methodology [Phys. Rev. Lett. 96, 107203 (2006)] to inquire if such vacancies can lead to collective ferromagnetism. Applying this methodology to ${\mathrm{HfO}}_{2}$, we find the following: (i) Hf vacancies appear in a few possible charge states but not all of these have a local magnetic moment. (ii) We calculate the energy required to form such vacancies in ${\mathrm{HfO}}_{2}$ as a function of the chemical potential and Fermi energy, and from this we compute, as a function of growth temperature and oxygen pressure, the equilibrium concentration of those vacancies that have a nonvanishing local magnetic moment. We find that under the most favorable equilibrium growth conditions the concentration of Hf vacancies with magnetic moment at room temperature does not exceed $6.4\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ (fractional composition of ${x}_{\mathrm{eq}}=2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}%$). (iii) Independently, we calculate the minimum Hf vacancy concentration needed to achieve wall-to-wall percolation in the ${\mathrm{HfO}}_{2}$ lattice, given the range of the magnetic ${V}_{\mathrm{Hf}}\text{\ensuremath{-}}{V}_{\mathrm{Hf}}$ interaction (five neighbors) obtained from our supercell calculations. It turns out that the minimum percolation concentration ${x}_{\mathrm{perc}}=13.5%$ needed for collective ferromagnetism is eight orders of magnitude higher than the equilibrium vacancy concentration ${x}_{\mathrm{eq}}$ in ${\mathrm{HfO}}_{2}$ under the most favorable growth conditions. We conclude that equilibrium growth cannot lead to ferromagnetism and that ferromagnetism can be established only if one beats the equilibrium Hf vacancy concentration during growth by as much as eight orders of magnitude. This paper presents also an Appendix that gives the Monte Carlo--calculated percolation thresholds of various lattices as a function of the percolation radius of the interaction.

Boron and indium substitution in GaAs(0 0 1) surfaces: Density-functional supercell calculations of the surface stability

Using the density-functional method and surface supercells the surface formation energies are calculated for the most stable GaAs(0 0 1) surface reconstructions without and with up to four indium or/and boron substitutions. Optimal conditions for the growth of the alloys are derived from calculated surface stability diagrams. The incorporation of indium into GaAs without phase separation is possible under strong As-rich conditions and medium to In-rich conditions. Less As-rich conditions can lead to the formation of an InAs phase. Ga-rich conditions give an InGa phase. Isovalent boron incorporation into GaAs without phase separation is possible under strong arsenic and reduced boron exposure. A BAs phase can be formed under more B-rich conditions. More Ga-rich conditions lead to the boron substitution in arsenic positions. The formed boron dimers can be a starting point for the formation of a boron phase. A true antisite boron substitution is less probable. Using the suitable growth conditions obtained for the ternary alloys it is energetically more favourable to incorporate both indium and boron (formation of BInGaAs) than to incorporate only one of the two elements (In or B). The antisite boron incorporation is not favoured in combination with isovalent boron or indium.

Comparison between experimental and theoretical determination of the local structure of theGaAs1−yNydilute nitride alloy

We present a combined experimental and theoretical study of the local structure of the $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}y}{\mathrm{N}}_{y}$ dilute nitride alloy. Experimental results obtained by x-ray absorption spectroscopy have been compared with first-principles density-functional supercell calculations and with the predictions of three different valence force field models. Both experiments and calculations find that inclusion of N induces static disorder in the $\mathrm{Ga}\text{\ensuremath{-}}\mathrm{As}$ bond length distribution. An increase of the $\mathrm{Ga}\text{\ensuremath{-}}\mathrm{As}$ bond length upon N incorporation in gallium arsenide has been observed; this is due to the competing effects of the decrease of the free lattice parameter and the tensile strain due to pseudomorphic growth. The different theoretical calculations reproduce more or less accurately this bond length expansion; we discuss the performance of the different valence force field models in predicting the measured bond lengths.

Clustering of Mn in (Ga,Mn)As

Clustering of (Ga,Mn)As is studied with the supercell density-functional calculations using the projector augmented-wave method. We find large binding energies for a single substitutional Mn atom to existing dimers and trimers giving rise to trimer and tetramer formation. For larger clusters this binding energy drops. In all cases studied, ferromagnetic alignment is found to be energetically more favourable than the antiferromagnetic one.

Electronic levels of interstitial carbon and carbon–oxygen centers in SiGe alloys

Density-functional supercell calculations are employed to follow the location of the donor levels arising from interstitial carbon and interstitial carbon–oxygen complexes in SiGe alloys. We show that these complexes interact weakly with neighboring Ge atoms, and that energetics rules out the existence of defect-Ge complexes involving direct Ge C or Ge O bonds. The C iO i defect is predicted to produce a hole trap that varies as E(0/+) − E v = 0.41 − 0.76 x eV, implying its disappearance for Ge fractions x greater than 0.5.

Stability and band gaps of As‐rich and N‐rich GaAsN alloys: Density‐functional supercell calculations

AbstractTotal energies and band gap energies of cubic cells with various arrangements of Ga32As32−nNn (n = 0–8 and n = 28–32 corresponding to 0.0–25.0% N and 12.5–0.0% As) are calculated using the density‐functional supercell method. In the As‐rich limit up to an exchange of 6.2% N isolated N atoms (maximum N distance) are the most stable arrangement and provide the typical reduction of the band gap energy from about 1.5 eV (GaAs) to about 1 eV caused by reduction of the N distance. For higher N content special N distributions are the most stable arrangements. GaNm clusters (m = 2–4) and isolated N atoms are less stable. The band gap remains nearly constant at about 1 eV between 6.2 and 18.8% N. The good agreement between the experimental band gap energies and ones calculated for the most stable arrangements points out that the experimental distribution of the atoms is the thermodynamic equilibrium distribution. In the N‐rich limit, linear As chains in [110] direction or fragments of them are the most stable arrangement. At 9.4% As the band gap disappears. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Oscillations in photoemission from Cr/Fe/W(100) and Cr/W(100)

The electronic structure of thin Cr films on Fe/W(1 0 0) and W(1 0 0) has been studied by angle-resolved photoemission (PE). The data have been compared with results of density functional supercell calculations. A thickness-dependent PE intensity variation at the Fermi level is observed, which is assigned to Cr quantum-well-like states.

Oscillations in photoemission from Cr/Fe/W(1 0 0) and Cr/W(1 0 0)

The electronic structure of thin Cr films on Fe/W(1 0 0) and W(1 0 0) has been studied by angle-resolved photoemission (PE). The data have been compared with results of density functional supercell calculations. A thickness-dependent PE intensity variation at the Fermi level is observed, which is assigned to Cr quantum-well-like states.

Polarizability and dielectric constant in density-functional supercell calculations with discretek-point samplings

We address the dielectric constant (or the polarizability for an isolated system) as obtained in density-functional supercell calculations with a discrete k-point sampling. We compare a scheme based on conventional perturbational theory to one based on a discrete Berry phase, which can also be used for treating finite electric fields. We show, both analytically and numerically, that the difference between the dielectric constants in the two schemes converges as 1/L-2, L being the supercell size. Applications to the water molecule and bulk silicon illustrate this behavior. In both cases, the conventional perturbational scheme is found to converge faster with L than the discrete Berry-phase scheme.

First-principles study of As interstitials in GaAs: Convergence, relaxation, and formation energy

Convergence of density-functional supercell calculations for defect formation energies, charge transition levels, localized defect state properties, and defect atomic structure and relaxation is investigated using the arsenic split interstitial in GaAs as an example. Supercells containing up to 217 atoms and a variety of {\bf k}-space sampling schemes are considered. It is shown that a good description of the localized defect state dispersion and charge state transition levels requires at least a 217-atom supercell, although the defect structure and atomic relaxations can be well converged in a 65-atom cell. Formation energies are calculated for the As split interstitial, Ga vacancy, and As antisite defects in GaAs, taking into account the dependence upon chemical potential and Fermi energy. It is found that equilibrium concentrations of As interstitials will be much lower than equilibrium concentrations of As antisites in As-rich, $n$-type or semi-insulating GaAs.

Density functional study of the Σ3(111) [10] symmetrical tilt grain boundary in SrTiO3

Density functional supercell calculations were carried out by amixed-basis pseudopotential method for the Σ3 (111)[11̄0] symmetrical tilt grain boundary in strontium titanate,SrTiO3, as a prototype planar defect in an electro-ceramicmaterial. A low grain boundary energy of 0.52 J m-2 wasobtained. Minor structural relaxations compared to the coincidencesite lattice model are obtained close to the grain boundary plane bytheory and previous experiment. Within the limits of the rathersmall supercell model employed in the calculations, the calculatedgeometric structure agrees well with the experimental one. Ananalysis of calculated local electron densities of states shows thatthe perturbation due to the grain boundary is localized in the nearvicinity of the boundary plane. From the present results for thesmall supercell model, there is no evidence for the build-up of aspace-charge layer at this highly ordered and undoped twin boundaryin SrTiO3.

Possible coexistence of rotational and ferroelectric lattice distortions in rhombohedralPbZrxTi1−xO3

The competitions between ferroelectric and rotational instabilities in rhombohedral ${\mathrm{PbZr}}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{O}}_{3}$ near $x=0.5$ are investigated using first-principles density-functional supercell calculations. As expected, we find a strong ferroelectric instability. However, we also find a substantial R-point rotational instability, close to but not as deep as the ferroelectric one. This is similar to the situation in pure ${\mathrm{PbZrO}}_{3}.$ These two instabilities are both strongly pressure dependent, but in opposite directions so that lattice compression of less than 1% is sufficient to change their ordering. Because of this, and local stress fields due to B-site cation disorder may lead to coexistence of both types of instability are likely present in the alloy near the morphotropic phase boundary.

Amphoteric behavior of H0 in GaAs.

We present the results of pseudopotential density-functional supercell calculations of the properties of neutral hydrogen in bulk GaAs. The equilibrium sites are determined, and the electronic properties for the equilibrium positions are studied. We find that the equilibrium site for unrelaxed GaAs:H is in the low-valence-charge-density region, whereas if the relaxation of the whole lattice is allowed, a shallow equilibrium minimum occurs at an antibonding site near an As ion. The diffusion path is in the high-valence-charge-density region around the As ions with a barrier as low as 0.1 eV. From our results, we suggest that H behaves as a deep acceptor in n-type GaAs and as a deep donor in p-type GaAs, and occupies different positions. Hence passivation of dopants occurs by neutralization.