Calculated Defect Formation Energies Research Articles

Defects in SiC for quantum computing

The successful implementation of the nitrogen-vacancy (NV) center in diamond as a qubit has spawned a great deal of interest in this defect. In principle, similar defects suitable for quantum computing should exist in other material systems; however, very little work has been done on identifying NV-like centers in other materials. We discuss the key properties of the NV center in diamond in the context of uncovering similar defects in other materials, with the specific example of SiC. Using first-principles calculations, we compare the properties of the NV center in diamond to the analogous defect in 4H-SiC. We also compare the properties of the bare vacancies. We calculate defect formation energies and charge-state transition levels to determine which defects are likely to form. Then, by analyzing the defect-induced electronic states, we determine whether stable defects in 4H-SiC may have properties similar to those of the NV center in diamond.

First Principles Calculations of Defects in Unstable Crystals: Austenitic Iron

ABSTRACTFirst principles calculations have given a new insight into the energies of point defects in many different materials, information which cannot be readily obtained from experiment. Most such calculations are done at zero Kelvin, with the assumption that finite temperature effects on defect energies and barriers are small. In some materials, however, the stable crystal structure of interest is mechanically unstable at 0K. In such cases, alternate approaches are needed. Here we present results of first principles calculations of austenitic iron using the VASP code. We determine an appropriate reference state for collinear magnetism to be the antiferromagnetic (001) double-layer (AFM-d) which is both stable and lower in energy than other possible models for the low temperature limit of paramagnetic fcc iron. Another plausible reference state is the antiferromagnetic (001) single layer (AFM-1). We then consider the energetics of dissolving typical alloying impurities (Ni, Cr) in the materials, and their interaction with point defects typical of the irradiated environment. We show that the calculated defect formation energies have fairly high dependence on the reference state chosen: in some cases this is due to instability of the reference state, a problem which does not seem to apply to AFM-d and AFM-1. Furthermore, there is a correlation between local free volume magnetism and energetics. Despite this, a general picture emerge that point defects in austenitic iron have geometries similar to those in simpler, non-magnetic, thermodynamically stable FCC metals. The defect energies are similar to those in BCC iron. The effect of substitutional Ni and Cr on defect properties is weak, rarely more than tenths of eV, so it is unlikely that small amounts of Ni and Cr will have a significant effect on the radiation damage in austenitic iron at high temperatures.

Energetics and concentration of defects in Gd2Ti2O7 and Gd2Zr2O7 pyrochlore at high pressure

Using first-principles calculations and complementary experiments, the defect formation energies and defect concentrations were calculated as a function of pressure. The results show that at high pressure, the defect formation energies decrease with pressure for both systems. In Gd2Ti2O7, the dominant defect type is cation anti-site defect, the local structure around a defect is highly distorted, and the energetically favorable defect–defect interactions at shorter distance suggest the possibility of defect clustering. In Gd2Zr2O7, anion Frenkel-pair defects are favored at all pressures and the dominant defect type involving a cation is a coupled defect of a cation anti-site and an anion Frenkel-pair defect. There are only minor distortions around the defects, and the defect–defect interactions are weak, which suggests almost-ideal non-interacting defect formation. Comparison of experimentally observed defect concentrations and those based on the calculated defect formation energies suggests that the defects formed at high pressure are better estimated with a concentrated limit approximation, while those formed at ambient pressure can be evaluated at a dilute limit approximation.

Effect of Nb on electronic structure of NiTi intermetallic compound: A first-principles study

The electronic structure of pure and Nb doped B2 NiTi have been calculated with the first-principle ultrasoft pseudopotential approach of the plane wave based on the density functional theory aiming at examining the effect of Nb on the electronic structure and bonding characteristic of NiTi. The point defect formation energy calculation results show that the introduction of Nb largely enhances the energy required to form the vacancies and anti-sites of both Ni and Ti sublattice. Furthermore, the calculation results on the partial density of states (PDOS) suggest that the addition of Nb increase the s-s, p-p and d-d electronic interactions between Nb and neighboring Ni and Ti atoms. The electron density of NiTi was also increased with the introduction of Nb. All these Nb-inuced results on electronic structure and bonding characteristic may hamper the hop of Ni and Ti atoms, which may facilitate to improve of oxidation resistance of NiTi intermetallic compound in the experimental findings.

Density functional theory calculations of defect energies using supercells

Reliable calculations of defect properties may be obtained with density functional theory (DFT) 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 alone is not appropriate to derive reliable defect formation energies, certainly not for relaxed geometries. Instead we propose finite size scaling of the calculated defect formation energies, and compare the application of this with both fully converged and ‘Gamma’ (Γ) point only k-point integration. We provide a recipe for practical DFT calculations which will help to obtain reliable defect formation energies and demonstrate it using examples from III–V semiconductors.

Supercell size scaling of density functional theory formation energies of charged defects

We address the calculation within density functional theory (DFT) of defect formation energies in alumina, a ceramic oxide often considered an archetype for a wide variety of other similar oxides. We examine the conditions under which calculated defect formation energies, especially those of charged defects, are independent of the principal approximations of the plane-wave DFT formalism, most significant of which is the finite-sized supercell in which the calculation must be performed. We introduce a variation on existing methods of extrapolation to infinite system size to reduce dependence of the result on finite-size errors in the electrostatic and elastic energies of a periodic supercell containing a defect. We also show how the results can be made relatively insensitive to the choice of exchange-correlation functional and pseudopotential by a suitable treatment of the chemical potentials of the atomic species. Our results for formation energies of charged defects are less sensitive than traditional approaches to supercell size and choices of exchange-correlation functional and pseudopotential, and differ notably from previous results.

First-principles calculation of defect formation energies and electronic properties in stannate pyrochlores

The electronic structures and defect formation energies for a series of stannate pyrochlores Ln2Sn2O7 (Ln=La, Pr, Nd, Sm, Gd, Tb, Ho, Er, Lu, and Y) have been investigated using the first-principles total energy calculations. The calculated results show that Ln-site cation ionic radius, x-O48f, lattice constant and the covalency of the ⟨Sn–O48f⟩ bond have a significant affect on the defect formation energies. The cation-antisite defect has the lowest formation energy, as compared with that of other defects, indicating that cation disorder causes local oxygen disordering. The present studies suggest that Lu2Sn2O7 is the most resistant to ion beam-induced amorphization. The electronic structure calculations reveal that Ln2Sn2O7 compounds have direct band gaps of 2.64–2.95 eV at the Γ point in the Brillouin zone.

First-principles study of substitutional magnesium and zinc in hydroxyapatite and octacalcium phosphate

First-principles calculations are performed for Mg(2+) and Zn(2+) substitution in hydroxyapatite (HAp) and octacalcium phosphate (OCP), because the foreign ions are known to play an important role for bone formation. In order to study their possible location in the system of HAp in contact with the aqueous solution, OCP is considered as a structural model of the transition region between HAp and the solution. It is found that, when the foreign ions substitute for Ca sites, the surrounding oxygen ions undergo considerable inward relaxation, due to their smaller ionic sizes than Ca(2+), which results in the smaller coordination numbers with oxygen as compared with those of Ca in bulk HAp and OCP. From the calculated defect formation energies, it is likely that the substitutional foreign ions are quite difficult to dissolve into HAp whereas can be more easily incorporated in OCP. In particular, Zn(2+) can more favorably substitute for the specific Ca site of OCP, as compared to Mg(2+), which is attributed with covalent bond formation between Zn and the surrounding oxygen ions. It is thus considered that zinc may play its role to promote bone formation by being incorporated into the transition region between HAp and the surrounding solution.

Atomistic Simulation of Defect Energy in Pyrochlores and its Effect on Disorder

To enhance the high-temperature stability of zirconate pyrochlore structures, one has to focus on their transformation to the disordered state, fluorite. An atomistic simulation calculation is presented in this paper to predict the propensity of rare earth zirconate pyrochlores to transform to fluorite at high temperature. By detailed calculation of defect formation energy of cation antisites and Frenkel pair, as well as their interactions, the mechanisms of disorder transformation are ascertained. The results show that the tendency of cation disorder is less than the anion’s and disorder transformation will accelerate in advanced stage. The calculation of defect energy in pyrozirconates with different cation on the A site have proved helpful in unraveling their different order-disorder transformation tendency.

The electronic properties of an oxygen vacancy at ZrO2-terminated (001) surfaces of a cubic PbZrO3: computer simulations from the first principles

Combining B3PW hybrid exchange-correlation functional within the density functional theory (DFT) and a supercell model, we calculated from the first principles the electronic structure of both ideal PbZrO(3) (001) surface (with ZrO(2)- and PbO-terminations) and a neutral oxygen vacancy also called the F center. The atomic relaxation and electronic density redistributions are discussed. Thermodynamic analysis of pure surfaces indicates that ZrO(2) termination is energetically more favorable than PbO-termination. The O vacancy on the ZrO(2)-surface attracts approximately 0.3 e (0.7 e in the bulk PbZrO(3)), while the remaining electron density from the missing O(2-) ion is localized mostly on atoms nearest to a vacancy. The calculated defect formation energy is smaller than in the bulk which should lead to the vacancy segregation to the surface. Unlike Ti-based perovskites, the vacancy-induced (deep) energy level lies in PbZrO(3) in the middle of the band gap.

Theoretical study of native point defects on anatase TiO2 (101) surface

First-principles plane-wave pseudopotential calculations were performed to study the energetics and the geometical structures of intrinsic vacancies and interstitials on the anatase TiO2 (101) crystal surface. Firstly，we analyzed the effects of point defects on the geometrical structures. For the O vacancy，all the nearest-neighbor Ti atoms move away from the vacancy toward the other O neighborhood. As Ti1 or Ti2 is missing here，O1 atom spontaneously and strongly binds with nearest-neighbor O on the lattice site to form an O2 molecule. The results also show that interstitial Tii2 affects little host lattice and the interstitial Oi would spontaneously bind to lattice oxygen. By investigating the calculated defect formation energies，we found that under the O-rich condition，the VTi1 and Oi formation are favorable，however，under the Ti-rich condition，although the point defects of Tii2 and VO1 easily appear，the formation energy of the Tii2 is lower than that of the VO1. Finally，to determine the relative stability of the point defects，the formation enthalpies of several point defects were considered.

First-principles calculation of defect energetics in cubic-BaTiO 3 and a comparison with SrTiO 3

The structural relaxation and formation energies of intrinsic vacancies in cubic-BaTiO 3 were studied by using a first-principles plane-wave-based pseudopotential calculation. The calculated defect formation energies and the atomic relaxations were compared with previously reported data for SrTiO 3 [Tanaka T, Matsunaga K, Ikuhara Y, Yamamoto T. Phys Rev B 2003;68:205213]. It was found that the formation energies of the partial Schottky species, V Ti 2 - + V O 2 + and V Ba 2 - + V O 2 + , are the lowest in the oxidized condition. In contrast, as the oxygen chemical potential decreased, namely the reduced condition, the O vacancy becomes dominant in cubic-BaTiO 3. Concerning the atomic relaxation, it was found that BaTiO 3 and SrTiO 3 show a difference in magnitude. It was also found that the overall vacancy formation energy in BaTiO 3 is higher than that in SrTiO 3.

First-principles study on the formation energies of intrinsic defects in LiNbO 3

First-principles plane-wave ultrasoft pseudopotential method within local density approach (LDA) has been used to study three possible vacancy-defect models for non-stoichiometric lithium niobate (LiNbO 3): (1) the oxygen-vacancy model V O 2 + + 2 V Li - , (2) the niobium-vacancy model 5 Nb Li 4 + + 4 V Nb 5 - , and (3) the lithium-vacancy model 4 V Li - + Nb Li 4 + . The corresponding formation energies are obtained via energy minimization of a supercell. In Nb-rich environment, the calculated defect formation energies, both under oxidation and reduction conditions, show little effect on the intrinsic defect structures. We find that the lithium vacancy model 4 V Li - + Nb Li 4 + has the most stable configuration in the non-stoichiometric lithium niobate crystals. Our calculations also show that the formation of any type of neutral defects and Frenkel pairs in a Nb-rich environment is difficult.

Simulation study of the defect models of Cr-doped PbWO 4 crystal and Cr, La-co-doped PbWO 4 crystal

The possible defect models of Cr:PbWO 4 (PWO) and Cr:La:PWO crystal are proposed and studied by the defect formation energy calculation using the general utility lattice program code (GULP). The calculated results support the proposed models that in lightly doped Cr:PWO crystal, Cr substitutes Pb 2+ in the (Cr Pb 3+) + state forming electrical neutral dipole defect [2(Cr Pb 3+) +–( V Pb) 2−]. However in heavily doped Cr:PWO crystal or Cr:La:PWO crystal, when the Cr doping level exceeds a certain critical value, Cr occupies W 6+ site in the (Cr W 4+) 2− state forming electrical neutral defects [2(Cr Pb 3+) +–(Cr W 4+) 2−], [(La Pb 3+) +–(Cr Pb 3+) +–(Cr W 4+) 2−] or [2(La Pb 3+) +–(Cr w 4+) 2−]. The appearance of (Cr W 4+) 2− marks a sudden change of the lattice site of the impurity Cr ion and would introduce a sudden change of the physical properties of the crystal and result in a Cr doping level threshold effect existing in the heavily Cr doped PWO crystal and Cr:La:PWO crystal.

A pseudopotential density functional theory study of native defects and boron impurities inFeAl

The structures and energies of point defects and point defect complexes inB 2 iron aluminium FeAl are calculated using a local density functional theory based methodwith large supercells. Particular emphasis is given to pseudopotential quality, choice ofchemical potentials used to calculate defect formation energies, and how these are affectedby magnetism. Both purely native defects and those containing boron atomsare considered. It is found that the relative stabilities of isolated point defectsversus defect complexes depends on whether the material contains excess iron oraluminium. The situation in material containing boron is further complicated by theexistence of iron borides in more than one form. We propose that the interactionbetween point defects, dislocations, and antiphase boundaries, where the localatomic environment has some similarities with antisite defects, also depends on thealloy composition. It is likely that these interactions are part of the underlyingmechanism responsible for the unusual mechanical properties of iron aluminides.

Ionic Conductivity of Li2B4O7

The formation and mobility of Li point defects in Li(2)B(4)O(7) are investigated theoretically with periodic quantum chemical calculations. Calculated defect formation energies obtained with a density functional theory/Hartree-Fock hybrid method and with the Perdew-Wang density functional method are compared. The basis set effect is investigated by comparison of results obtained with atom-centered basis functions and plane waves. With both methods only a moderate relaxation is observed for the atoms surrounding the Li defect position. The defect-induced change of electronic properties is investigated by calculating the density of states for the stoichiometric and defective supercells. The activation energy for the movement of a Li(+) ion along the (001) direction is calculated. It is observed that Li(+) ion migrates through a one-dimensional channel formed by the five-vertex lithium-oxygen (LiO(5)) polyhedra. The calculated activation energies are in excellent accord with experiment.

Theoretical Analysis of Structural, Energetic, Electronic, and Defect Properties of Li2O

The structural, energetic, and electronic properties of stoichiometric and defective Li(2)O were studied theoretically. The reliability of the Perdew-Wang method in the framework of density functional theory (DFT), and of two DFT/Hartree-Fock hybrid methods (PW1PW and B3LYP), was examined by comparison of calculated and available experimental data. Atom-centered orbitals and plane waves were used as basis functions for the crystalline orbitals. For both cases, the basis set dependence of calculated properties was investigated. With most of the methods, good agreement with the experimental Li(2)O lattice parameter and cohesive energy was obtained. In accordance with experiment, the analysis of electronic properties shows that Li(2)O is a wide gap insulator. Among the considered methods, the hybrid methods PW1PW and B3LYP give the best agreement with experiment for the band gap. The formation of an isolated cation vacancy defect and an F center in Li(2)O were studied. The effect of local relaxation on the calculated defect formation energies and the defect-induced changes of electronic properties were investigated and compared to available experimental results. The migration of a Li(+) ion in Li(2)O bulk was investigated. The activation energy for the migration of a Li(+) ion from its regular tetrahedral site to an adjacent cation vacancy was calculated, including the effect of local relaxation. The calculated activation barriers, 0.27-0.33 eV, are in excellent agreement with experiment.

Using Elasticity to Correct for Boundary Effects in Calculations of Stress-Diffusion Coupling Parameters

AbstractThe effect of stress on diffusion during semiconductor processing becomes important as device dimensions shrink from microns to nanometers. Simulating these effects requires accurate parameterization of the formation and migration volume tensors of the defects that mediate diffusion on the atomistic scale. We investigate the effect of boundary conditions on the accuracy of atomistic calculations of defect formation energies and formation volume tensors. Linear elasticity provides a correction to the effect of the boundaries on the resulting relaxation volume tensor. By a formal proof we show that the correction term is zero for free boundaries and for periodic boundary conditions with zero mean boundary stress. This is demonstrated in the far field for periodic and free boundary conditions for an isotropic (vacancy) and an anisotropic (<110> intersitial) defect in Stillinger-Weber silicon. For periodic boundary conditions, formation volume tensor components converge to within 5% in a 216 atom simulation cell. For free boundary conditions, slow convergence of elastic constants results in slow convergence of formation volumes. Most significantly, this provides a new method to calculate the formation volume from constant volume calculations. This removes the need for relaxing boundaries, allowing for simpler and more efficient algorithms. We apply this method to both the vacancy and the <110> interstitial in Stillinger-Weber silicon.

Hydeogen-related defect sites in ZnO studied via local vibrational modes

By employing the full potential augmented plane wave and local orbital method (APW+lO), we studied some possible hydrogen-related defect sites in ZnO. In view of the calculated defect formation energy, the most possible defect site should inhabit BC∥ local structure position. But the calculated local vibrational modes (LVMs) of the defect sites, when compared with the infrared absorption result, leads to the conclusion that the hydrogen-related defect sites in ZnO can inhabit both BC∥ and ABo∥ local structure positions.

First-principles calculation of defect formation energy in chalcopyrite-type CuInSe 2, CuGaSe 2 and CuAlSe 2

In order to quantitatively evaluate the formation energies of Cu, In/Ga/Al and Se vacancies in chalcopyrite-type CuInSe 2 (CIS), CuGaSe 2 (CGS) and CuAlSe 2 (CAS), first-principles pseudopotential calculations using plane-wave basis functions were performed. All calculations were performed using a supercell with 64 atoms, which was eight times greater than the number of atoms in a primitive cell with eight atoms. The formation energies of point defects were calculated as a function of the atomic chemical potentials of constituent elements. Atomic arrangements around the vacancy were optimized allowing relaxation of the first- and second-nearest-neighbor atoms of the vacancy. The obtained results were as follows: (1) the formation energy of Cu vacancy was smaller than those of the other vacancies in CIS, CGS and CAS. Under the Cu-poor condition, the formation energy of Cu vacancy in CIS was lowest among those in them; (2) the formation energy of Se vacancy in CIS was relatively lower than those in CGS and CAS; (3) the formation energy of (2V Cu+In Cu) pair in CIS was greatly dependent on the chemical potential of the constituent elements, i.e. Cu, In and Se. On the other hand, the formation energies of (2V Cu+Ga Cu) in CGS and (2V Cu+Al Cu) in CAS were not largely dependent on the chemical potential of the constituent elements. Under the Cu-poor condition, the formation energy of (2V Cu+In Cu) pair in CIS was much lower than those of (2V Cu+Ga Cu) in CGS and (2V Cu+Al Cu) in CAS.