Electronic Structure Of Point Defects Research Articles

Identifying native point defect configurations in α-alumina

Intimately intertwined atomic and electronic structures of point defects govern diffusion-limited corrosion and underpin the operation of optoelectronic devices. For some materials, complex energy landscapes containing metastable defect configurations challenge first-principles modeling efforts. Here, we thoroughly reevaluate native point defect geometries for the illustrative case of α-Al2O3 by comparing three methods for sampling candidate geometries in density functional theory calculations: displacing atoms near a naively placed defect, initializing interstitials at high-symmetry points of a Voronoi decomposition, and Bayesian optimization. We find symmetry-breaking distortions for oxygen vacancies in some charge states, and we identify several distinct oxygen split-interstitial geometries that help explain literature discrepancies involving this defect. We also report a surprising and, to our knowledge, previously unknown trigonal geometry favored by aluminum interstitials in some charge states. These new configurations may have transformative impacts on our understanding of defect migration pathways in aluminum-oxide scales protecting metal alloys from corrosion. Overall, the Voronoi scheme appears most effective for sampling candidate interstitial sites because it always succeeded in finding the lowest-energy geometry identified in this study, although no approach found every metastable configuration. Finally, we show that the position of defect levels within the band gap can depend strongly on the defect geometry, underscoring the need to conduct careful searches for ground-state geometries in defect calculations.

First-principles calculation of point-defective structures of B2-NiSc intermetallics

ABSTRACTA pseudo-potential plane-wave method based on first principles was used to calculate the physical parameters of B2-NiSc intermetallics and the geometrical, energetic, and electronic structures of point defects. The possible types of point defects in B2-NiSc intermetallics were analyzed and predicted by comparing the formation enthalpy and formation energy for different kinds of point defect structures. The results show that Ni vacancy defects and Ni anti-position defects are the main point defects in the B2-NiSc intermetallics, and that these point defects emerge as double vacancy defects or double anti-position defects. When the double Ni atoms at Sc sites are in the first nearest neighborhood, the point defect structures are found to be the most stable. An analysis of the electronic structure of NiSc point defects shows that the Ni anti-position defect is more stable than the Sc vacancy defect in the Ni-rich alloy, and the Ni vacancy defect is more stable than the Sc anti-position defect in the Sc-rich alloy. These results are consistent with the energy calculation. Through analysis of C11–C12, G/B and Poisson's ratio, it was found that the NiSc point defect has little effect on crystal plasticity, and that the VNi point defect improves crystal plasticity.

Real-space formulation of orbital-free density functional theory using finite-element discretization: The case for Al, Mg, and Al-Mg intermetallics

We propose a local real-space formulation for orbital-free density functional theory (DFT) with density dependent kinetic energy functionals and a unified variational framework for computing the configurational forces associated with geometry optimization of both internal atomic positions as well as the cell geometry. The proposed real-space formulation, which involves a reformulation of the extended interactions in electrostatic and kinetic energy functionals as local variational problems in auxiliary potential fields, also readily extends to all-electron orbital-free DFT calculations that are employed in warm dense matter calculations. We use the local real-space formulation in conjunction with higher-order finite-element discretization to demonstrate the accuracy of orbital-free DFT and the proposed formalism for the Al-Mg materials system, where we obtain good agreement with Kohn-Sham DFT calculations on a wide range of properties and benchmark calculations. Finally, we investigate the cell-size effects in the electronic structure of point defects, in particular, a monovacancy in Al. We unambiguously demonstrate that the cell-size effects observed from vacancy formation energies computed using periodic boundary conditions underestimate the extent of the electronic structure perturbations created by the defect. On the contrary, the bulk Dirichlet boundary conditions, accessible only through the proposed real-space formulation, which correspond to an isolated defect embedded in the bulk, show cell-size effects in the defect formation energy that are commensurate with the perturbations in the electronic structure. Our studies suggest that even for a simple defect like a vacancy in Al, we require cell sizes of $\ensuremath{\sim}{10}^{3}$ atoms for convergence in the electronic structure.

Implementation of density functional embedding theory within the projector-augmented-wave method and applications to semiconductor defect states

We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.

Electronic structure of carbon nanotubes with an impurity point defect

A method for calculating the electronic structure of point defects in nanotubes is developed on the basis of the linear augmented cylindrical wave (LACW) method. The Green function of a defect nanotube is calculated using the Dyson matrix equation. The consideration is carried out in terms of the local density functional theory and the muffin-tin approximation for the electronic potential. Local densities of state are calculated for boron and nitrogen dopants in metal, semimetal, and semiconductor and chiral and nonchiral nanotubes. An increased density of states at the Fermi level is the most significant effect of boron and nitrogen dopants in metal nanotubes. In all semiconductor nanotubes, localized boron states close the optical band-gap. The effect of nitrogen atoms is restricted to a small rise in local densities of state at the Fermi level.

Green's function scattering-theoretic methods for point defects, surfaces, and interfaces in solids

We have recently developed novel ways to describe the electronic structure of point defects, surfaces, and interfaces in semiconductors, making use of the original Koster-Slater ideas for localized perturbations in otherwise periodic solids. In this article we give a brief review of the method and our applications to the vacancy, free surfaces, and interfaces of several tetrahedral semiconductors and SiO2, using both empirical tight-binding and self-consistent Hamiltonians.

Ab initio calculations of the geometry and electronic structure of point defects in ferroelectrics with a perovskite structure

Ab initio calculations of the optimized geometry and the electronic structure of lattice defects in incipient perovskite ferroelectrics SrTiO3 and KTaO3 are performed in the framework of the density functional theory. The results are presented for the Li+ impurity ion at the A site in the KTaO3 and SrTiO3 ferroelectrics; the Mn2+, Cd2+, Ca2+, Mg2+, and Zn2+ ions at the A site and the Mn4+ and Mg2+ ions at the B site in the SrTiO3 compound; and the MNTi2+-VO and MgTi2+-VO complexes in the SrTiO3 ferroelectric. The results are obtained by the cluster method with allowance made for the structural relaxation initiated by the defect and, for nonisovalent substitutional impurities, with due regard for the charge and spin states of the defect. It is established that the CaSr2+, CdSr2+, MnTi4+, and MgTi2+ ions have a stable central position, whereas the LiK+ ion in the KTaO3 compound and the LiSr+, MnSr2+, and ZnSr2+ defects in the SrTiO3 ferroelectric are off-center ions. The shape of the multiminimum adiabatic potential and the parameters of dielectric relaxators (activation barrier, dipole moment) for polar defects are obtained. The electronic impurity levels are determined for the LiSr+ and MgTi2+ neutral defects.

Simplified embedding schemes for the quantum-chemical description of neutral and charged point defects in SiO2 and related dielectrics

Embedding methods specifically designed to treat large molecules with bulky ligands or in polar solvents are used to describe the electronic structure of point defects in the covalently bonded solids SiO2, Si3N4, and Si2N2O. The mechanical relaxation of the lattice around a given defect, in particular an anion vacancy or interstitial, is described using the ONIOM approach where the system is partitioned in two regions, the local defect treated at the gradient corrected DFT level, and the surrounding matrix treated with a semiempirical Hamiltonian. In this way clusters of 100 atoms and more are used to describe a portion of the solid of 10–15 Å of diameter. The long-range lattice polarization induced by a charged defect, a charged oxygen vacancy or a proton bound to O or N atoms, is estimated by means of the isodensity polarized continuum model, IPCM, and compared with the approximate Born’s formula. The two simplified embedding schemes provide a simple way to improve cluster models of neutral and charged defects in covalent materials.

Energetics and electronic structure of point defects associated with oxygen excess at a tilt boundary of ZnO

The formation energies and electronic structure of zinc vacancies and oxygen interstitials at a tilt boundary of ZnO were investigated by a combination of static lattice and first-principles molecular orbital methods. For both of the defect species, the formation energies were lower than those of the bulk defects at certain sites in the grain boundary. The defects with low formation energies formed electronic states close to the top of the valence band. The interfacial electronic states observed experimentally in ZnO varistors cannot be explained solely by the point defects associated with the oxygen excess: the effects of impurities should be significant for the states.

Investigation of the electronic structure of point defects in ionic crystals by the cluster scattered wave method with the self-consistent calculation of the lattice distortion and long-range polarization

Abstract This paper describes the calculations of the electronic structures of the F-center in NaCl, pure anion vacancy. F+ and F-centers in MgO by the embedded cluster method. This work is an alternative approach relative to the ICECAP method within which the embedded cluster model based on Johnson's Scattered Wave method is combined with the Mott-Littleton method. The main features of the model are: self-interaction correction of single-particle energies in the case of perfect crystals and point defects whose states are in the band gap of a perfect crystal: Mott-Littleton method modification allowing for the description of the defect wave function in the analytical form: construction of the cluster one-electron potential when describing the rest of the crystal in shell model terms.

Electronic structure of point defects in rutile TiO2.

We present results of a computation of the electronic structure of point defects in reduced rutile using a semiempirical self-consistent method. Calculations on models of both titanium interstitials and oxygen vacancies are reported. We find donor levels in the range 0.7--0.8 eV for isolated defects in each case. The defects have an effective screening radius of less than 5 \AA{}. We also report results on clusters of defects. These suggest that a model in which the screening charges of multiple defects are added would be quite accurate for systems with multiple defects. Comparison of our results with infrared experiments suggests the presence of defect clustering in nearly stoichiometric rutile, as proposed earlier on the basis of other experiments.

Electronic structure of point defects in antiferromagnetic insulating cuprates

AbstractThe energies and wave functions of impurity (defect) states which appear in the energy gap of La2CuO4 due to doping are calculated by the unrestricted Hartree‐Fock method. It is shown that the state vectors have such a structure that localized carriers (holes) can occupy not only oxygen ions but also copper ones.

Electronic structure of point defects in SiO 2, NaCl and diamond: cluster model with features of molecular cluster and cyclic models

The cluster model is proposed for calculating the structure and spectroscopic properties (by means of Hartree-Fock-Roothaan and configuration interaction methods) of neutral and charged point defects in any non-metallic crystals (both in the bulk and on the surface). The defectless quasicluster has the point symmetry of a crystal, is stoichiometric, uncharged and is characterized by closed electron shells. Semiempirical INDO calculations of the electronic structure and potential surface of a number of defects in SiO 2, NaCl and diamond were carried out with the use of the proposed, periodic supercell 3periodic defect) and molecular cluster models. The presented results of quasicluster and periodic supercell calculations of the perfect crystal electronic structure are almost identical. Application of the proposed model to non-crystalline solids is discussed.

The electronic structure of point defects in semiconductor alloys: simplified approximations

The authors present a simplified tight-binding-based coherent-potential approximation (CPA) formalism for the host electronic structure of semiconductor alloys (e.g. Ga1-xAlxAs). Several schemes to locate the gap level due to point defects are discussed. In particular, they introduce a novel scheme: the deep-level approximation. They also point out that the vacancy results in the CPA are identical with the simpler virtual-crystal approximation. They discuss their results by presenting numerical results in Ga1-xAlxAs and GaAs1-xSbx.

Electronic Structure of Point Defects in Semiconductor Alloys

AbstractA simplified tight‐binding approach based on the coherent potential approximation (CPA) formalism is presented for the host electronic structure of semiconductor alloys (e.g. Ga1−xAlxAs). Several schemes to locate the gap level due to point defects are discussed. In particular, a novel scheme is introduced: the deep level approximation (DLA). It is pointed out that the vacancy results in the CPA are identical to the simpler virtual crystal approximation (VCA). In addition, the electronic band structure of SixGe1−x alloys is presented using a non‐orthogonal tight‐binding approach, namely the extended Hückel theory (EHT). Preliminary calculations of the dependence of the band gap on concentration are also presented.

Electronic structures of point defects in III-V compound semiconductors

The self-consistent electronic structures of ideal vacancies in nine III-V compound semiconductors and in Si and Ge have been calculated using the spin-unrestricted density-functional theory and the linear muffin-tin-orbital Green function method. Moreover, anti-site defects in these compound semiconductors have been investigated. The ionisation levels in the band gap have been determined from the total energies for all types of vacancies in different charge states. The trends in the ionisation level positions are studied when the width of the band gap and the 'size' of the vacancy are varying from one host to another. The results are compared with previous calculations and experiments, and the effects due to lattice relaxation are discussed.

An embedded-molecular-cluster method for calculating the electronic structure of point defects in non-metallic crystals. I. General theory

A new approach, called the embedded-molecular-cluster method, is proposed to calculate the electronic structure of point defects in a non-metallic crystal in the framework of the molecular cluster model. The method is applicable to defects with any perturbation radius of the crystal and is based on the concept of the latter as the sum of weakly overlapping structural elements, (atoms, ions, bonds, molecules, etc.). It accounts for Coulomb and exchange interaction between the cluster and the rest of the crystal, as well as (self-consistently) for polarisation of the latter. The present work contains a calculation of the full energy of a crystal with a point defect and arbitrary types of structural elements.

An embedded-molecular-cluster method for calculating the electronic structure of point defects in non-metallic crystals. II. Structural elements in the form of molecules

For pt.I see ibid., vol.21, p.5041 (1988). The embedded-molecular-cluster method, as proposed in the authors previous paper for the calculation of the electronic structure of point defects in non-metallic crystals, has been applied in the present work for the case of crystals containing structural elements in the shape of rigid molecules, molecular ions, etc. Using the Green function of perfect-crystal lattice dynamics, equations have been obtained describing polarisation of the remainder of the crystal. The operator Veff, which accounts for exchange and Coulomb interaction between the cluster and the rest of the crystal, including its polarisation, and is an addition to the Hartree-Fock operator, has been evaluated. Both problems (calculation of polarisation of the rest of the crystal and the solution of the effective Schrodinger equation for the cluster) have to be solved in a self-consistent way. Parameterisation effected for the method has made it possible to express explicitly both the operator Veff and the response function necessary for evaluating polarisation. A detailed investigation of the lattice dynamics of an ideal crystal allowed the author to connect the parameters of the method with the dynamic matrix of an ideal crystal, i.e. eventually with its phonon spectra and eigenvectors, which can be found experimentally.

Electronic structure of point defects in α-quartz

The electronic properties of a large class of point defects in alpha -quartz are calculated using a fist-principles tight-binding method. The point defects examined include all atoms from the first three periods of the periodic system (hydrogen to argon) and they are treated as interstitials and as silicon and oxygen substitutes as well as ideal silicon and oxygen vacancies. For most of the point defects deep levels are found in the band gap. In some cases agreement with experiment is seen to be good.

Electronic structure of point defects on oxide surfaces.

We report results of a theoretical study of the electronic structure of point defects on semiconducting oxide surfaces, with an application to ${\mathrm{SnO}}_{2}$(110). The scattering theoretical method is used and detailed formal developments are given for the rutile crystal structure. For the ${\mathrm{SnO}}_{2}$(110) surface a series of monovacancy and divacancy models are studied, corresponding to the removal of one or two atoms from the outer surface layers. None of these defect models gives rise to a bound defect state in the optical gap. Similar to the case of the defect-free surface, the main defect-induced features are O p--derived resonances in the valence-band region and Sn s--derived resonances in the conduction-band region. The results are interpreted in terms of the ionicity of the material and compared with those for other oxide surfaces.