Defect Equilibria Research Articles

V N-Mg defect complexes as compensating centers in GaN:Mg

Defect equilibrium diagrams have been constructed for intrinsic and extrinsic defects in GaN:Mg crystals using the quasi-chemical formalism, and the formation of (VN-MgGa)× and (VN-MgGa••) defect complexes has been analyzed. The results indicate that, under equilibrium conditions, VN vacancies in the charge state 3+ and Mg′Ga impurities form (VN-MgGa)•• defect complexes, which compensate acceptors.

Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations

The stability range of intrinsic point defects in uranium dioxide is determined as a function of temperature, oxygen partial pressure, and non-stoichiometry. The computational approach integrates high accuracy ab initio electronic-structure calculations and thermodynamic analysis supported by experimental data. In particular, the density functional theory calculations are performed at the level of the spin polarized, generalized gradient approximation and includes the Hubbard U term; as a result they predict the correct anti-ferromagnetic insulating ground state of uranium oxide. The thermodynamic calculations enable the effects of system temperature and partial pressure of oxygen on defect formation energy to be determined. The predicted equilibrium properties and defect formation energies for neutral defect complexes match trends in the experimental literature quite well. In contrast, the predicted values for charged complexes are lower than the measured values. The calculations predict that the formation of oxygen interstitials becomes increasingly difficult as higher temperatures and reducing conditions are approached.

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 $[1\overline{1}0]$ 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.

Defect equilibria and chemical expansion in non-stoichiometric undoped and gadolinium-doped cerium oxide

Chemical expansion and oxygen non-stoichiometry of undoped and Gd-doped cerium oxide exposed to different partial pressures of oxygen was studied at 800 ° C by dilatometry and thermo-gravimetry, respectively. The results were modeled in terms of isolated defects and defect complexes to successfully predict non-stoichiometry and chemical expansion behavior. A chemical expansion coefficient for isolated defects was determined using the model. A separate chemical expansion coefficient for defect complexes was found to match an empirically predicted value for lattice parameter versus dopant concentration from the literature showing that at room temperature, a considerable fraction of defects are in complexes. The chemical expansion coefficients used were the same for both the undoped and Gd-doped cerium oxide displaying consistency in the model. The results of the model are not only useful in interpreting strain behavior upon reduction in ceria based oxides, but are also useful in explaining conductivity behavior.

Oxygen nonstoichiometry and defect structure analysis of B-site mixed perovskite-type oxide (La, Sr)(Cr, M)O 3−δ ( M=Ti, Mn and Fe)

The defect chemical relationships in various B-site mixed LaCrO 3-based ceramics were investigated by means of high-temperature gravimetry. The nonstoichiometric deviation, δ, in (La 0.7Sr 0.3)(Cr 1− y Ti y )O 3− δ ( y=0.1, 0.2 and 0.3) (LSCT) , (La 0.75Sr 0.25)(Cr 0.5Mn 0.5)O 3− δ (LSCM) and (La 0.75Sr 0.25)(Cr 0.5Fe 0.5)O 3− δ (LSCF) were measured as a function of oxygen partial pressure, P O 2 , at temperatures between 973 and 1373 K. The effects of partial replacement of the donor on Cr-sites were examined in LSCT. In LSCM and LSCF, effects of the partial substitution of isovalent transition metals on Cr-sites are discussed. Oxygen nonstoichiometries of various B-site mixed LaCrO 3-based ceramics were compared with those of A-site substituted perovskite-type oxides, (La 1− x Sr x ) MO 3− δ (where x=0–0.3, M=Cr, Mn and Fe). The partial substitution of the different elements on Cr-sites drastically changed the P O 2 and temperature dependence of oxygen vacancy formation in LaCrO 3-based ceramics. The defect equilibrium relationships of the localized electron well explained the oxygen vacancy formation in B-site mixed LaCrO 3-based ceramics. Oxygen vacancy formation in (La 0.7Sr 0.3)(Cr 1− y Ti y )O 3− δ ( y=0.1 and 0.2) and (La 0.7Sr 0.3)(Cr 0.7Ti 0.3)O 3− δ was explained by redox reaction of Cr and Ti ions, respectively. The defect equilibrium relationships of LSCM and LSCF were interpreted by redox reaction of Mn ions and Fe ions, respectively. No significant change in valence state of Cr 3+ ions in LSCM and LSCF was confirmed under the experimental conditions.

Microstructure and high temperature transport properties of high quality epitaxial SrFeO 3 − δ films

We report the high temperature electronic transport properties of SrFeO 3 − δ epitaxial thin films obtained by pulsed laser deposition on NdGaO 3(110) substrates. The films show total conductivity higher than the bulk material and apparent activation energy of about 0.12 eV in O 2, lower than reported values for SrFeO 3 − δ films. The conductivity dependence with oxygen partial pressure shows a power dependence with an exponent close to + 1/4, in agreement with expected point defect equilibrium. For a given oxygen partial pressure, the temperature coefficient of resistance (TCR) shows a low positive value of about 1.5–2.5 10 − 3 K − 1 , which is still suitable for resistive oxygen sensing applications. The transport properties of the films are discussed in view of their particular microstructure.

Oxygen nonstoichiometry of the perovskite-type oxides BaCe 0.9M 0.1O 3 − δ (M [dbnd6]Y, Yb, Sm, Tb, and Nd)

The oxygen nonstoichiometry, δ, of B-site doped BaCeO 3 − δ under dry condition was determined as a function of oxygen partial pressures, P O 2 , between 1 bar and 10 − 4 bar and temperatures between 773 K and 1373 K. The variation of δ in BaCe 0.9Y 0.1O 3 − δ , BaCe 0.9Yb 0.1O 3 − δ , BaCe 0.9Sm 0.1O 3 − δ and BaCe 0.9Tb 0.1O 3 − δ was very small through the experimental conditions. This indicates that charge imbalance due to the trivalent dopants is compensated essentially by the oxygen vacancy formation. A large variation was found for δ of BaCe 0.9Nd 0.1O 3 − δ by P O 2 and temperature. This result indicates that the valence of the metal elements change under the experimental conditions. The X-ray absorption spectroscopy (XAS) measurement was carried out to examine the valence of the B-site elements of BaCe 0.9Nd 0.1O 3 − δ . The samples of different δ were prepared. From the XANES spectra of Ce and Nd, no spectra change for Ce L3-edge was observed, while spectra change was observed for Nd L3-edge and L2-edge. This indicates that the valence of Ce stay unchanged, while the valence of Nd may be changed by the different δ conditions. The measured δ of BaCe 0.9Nd 0.1O 3 − δ was analyzed by considering the valence change of neodymium. By considering the defect equilibrium among Nd′ Ce, Nd × Ce, V O ••, and O O ×, the change of δ against P O 2 was well explained by assuming the defect equilibrium 1 2 O 2 + V O • • + 2Nd Ce ' = O O × + 2Nd Ce × .

Theoretical investigation of the defect formation mechanism relevant to nonstoichiometry in hydroxyapatite

Electronic and atomic structures of vacancies and protons in hydroxyapatite (HAp) are analyzed by using first-principles band structure calculations. From total energies of supercells for monoclinic HAp, defect formation energies and equilibrium concentrations are evaluated, assuming chemical equilibrium between HAp and aqueous solution saturated with respect to HAp. It is found that interstitial and Ca-substitutional protons form ${\mathrm{H}}_{2}\mathrm{O}$ groups or acid phosphates of ${\mathrm{HPO}}_{4}^{2\ensuremath{-}}$ and are stabilized by making hydrogen bonding with adjacent ${\mathrm{PO}}_{4}^{3\ensuremath{-}}$ groups. Moreover, defect association considerably decreases the defect formation energies, and, in particular, interstitial protons bonded to ${\mathrm{OH}}^{\ensuremath{-}}$ groups become most stable when associated with Ca-substitutional protons. Due to abundant formation of the associated defect comprising interstitial and Ca-substitutional protons, Ca contents in HAp decrease with lowering pH, which explains pH dependence of $\mathrm{Ca}∕\mathrm{P}$ molar ratios of HAp observed experimentally.

Defect Chemistry and Electrical Properties of Titanium Dioxide. 1. Defect Diagrams

The present work reports defect diagrams showing the effect of oxygen activity on the concentration of both electronic and ionic defects in TiO2 and its solid solutions with donor- and acceptor-type ions. These diagrams were determined by using defect equilibrium constants related to defect reactions describing the formation of defects. A good agreement between the derived diagrams and defect-related experimental data, including electrical conductivity and thermoelectric power, was revealed. These diagrams may be used for the selection of the optimal processing conditions, including oxygen activity, temperature, and the concentration of aliovalent ions, in order to obtain TiO2 with controlled semiconducting properties that are desired for specific applications.

A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory

This paper presents a hybrid stress approach for the analysis of laminated composite plates. The plate mechanical model is based on the so called First-order Shear Deformation Theory, rationally deduced from the parent three-dimensional theory. Within this framework, a new quadrilateral four-node finite element is developed from a hybrid stress formulation involving, as primary variables, compatible displacements and elementwise equilibrated stress resultants. The element is designed to be simple, stable and locking-free. The displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and a suitable approximation for stress resultants is selected, ruled by the minimum number of parameters. The transverse stresses through the laminate thickness are reconstructed a posteriori by simply using three-dimensional equilibrium. To improve the results, the stress resultants entering the reconstruction process are first recovered using a superconvergent patch-based procedure called Recovery by Compatibility in Patches, that is properly extended here for laminated plates. This preliminary recovery is very efficient from the computational point of view and generally useful either to accurately evaluate the stress resultants or to estimate the discretization error. Indeed, in the present context, it plays also a key role in effectively predicting the shear stress profiles, since it guarantees the global convergence of the whole reconstruction strategy, that does not need any correction to accommodate equilibrium defects. Actually, this strategy can be adopted together with any plate finite element. Numerical testing demonstrates the excellent performance of both the finite element and the reconstruction strategy.

Defect Chemistry of Undoped and Acceptor‐Doped BaPbO3

The equilibrium defect chemistry of polycrystalline, undoped, and acceptor‐doped BaPbO3 was studied by measurement of the equilibrium electrical conductivity as a function of temperature, 800°–900°C, and oxygen activity, 10−18–1 atm. Both equilibrium electrical conductivity data of undoped and acceptor‐doped samples were quantitatively fit to a defect model involving only doubly ionized oxygen vacancies, lead vacancies, holes, and acceptor impurities. The results in low and midrange of oxygen activity are dominated by acceptor impurities, whether deliberately added or not. Only in the highly oxidized condition is the conductivity independent of impurity content, confirming that this region represents the intrinsic behavior of BaPbO3.

Influence of boron on the point defect equilibrium in highly n-doped gallium arsenide single crystals

High n-type conductivity of melt-grown gallium arsenide single crystals is usually achieved by doping with tellurium or silicon. The lower carrier concentration and Hall mobility in silicon-doped crystals is attributed to the formation of acceptor defects, in particular Si As - , the isolated gallium vacancy V Ga 3 - and the ( Si Ga – V Ga ) 2 - complex. We show that the contamination of the crystals with boron, which is unavoidable in growing techniques using a boron oxide encapsulant, is decisive for the degree of compensation. In highly n-doped gallium arsenide crystals boron is not only incorporated as the isoelectronic defect B Ga 0 . Additionally, high concentrations of B As 2 - and the negatively charged B As -donor complex are formed. These acceptors can dominate the equilibrium of point defects depending on the concentration ratio of the n-dopant and boron.

Bifurcation of equilibrium solutions and defects nucleation

The purpose of this article is to revise some concepts on defects nucleation based on bifurcation of equilibrium solutions. Equilibrium solutions are obtained on a homogeneous body and on a body with an infinitesimal defect such as cavity under the same prescribed dead load. First void formation and growth in non linear mechanics are examined. A branch of radial transformation bifurcates from the undeformed configuration in presence of a small cavity. Two cases of behaviour are examined. One case is the growth of the cavity by only the deformation of the shell. In another modelling the cavity evolves like a damaged zone, the transition between the sound part and the damaged one is governed by a local criterium. Each configuration leads to the definition of a nucleation criterion based on a presence of a bifurcation state, common state of the homogeneous body and a body with an infinitesimal defect.

High Temperature Properties of CdTe Crystals, Doped by Sb

Electrical properties of CdTe single crystals doped by Sb were studied in situ at high temperature point defect equilibrium under well defined Cd and Te vapour pressure. Up to samples revealed p-type conductivity both under Cd and Te saturation. The position of the deep acceptor level was determined using hole density temperature dependency at 350-650 K. The point defects responsible for hole density are supposed to be acceptors. The n-type conductivity above is determined by intrinsic point defects: electrons under Te saturation due to native disorder and Cd interstitials under Cd saturation.

Origins of thep-type nature and cation deficiency inCu2Oand related materials

While most of crystalline wide gap oxides are both stoichiometric and insulating, a handful of them including ZnO and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ are naturally anion-deficient and electron conductors. Even fewer of the oxides are naturally cation-deficient and hole conductors, the arch-type of which is ${\mathrm{Cu}}_{2}\mathrm{O}$. Based on first principles calculation of equilibrium nonstoichiometry and defect stability, we explain why the ${\mathrm{Cu}}^{(I)}({d}^{10})$ oxide-based materials are both $p$-type and naturally cation-deficient, and why cation vacancies lead to delocalized, conductive states, whereas in other oxides (e.g., ZnO and MgO), they lead to localized, nonconductive states.

High temperature electrical properties of CdTe〈Pb〉 crystals under Te saturation

AbstractThe point defect equilibrium of CdTe〈Pb〉 single crystals under well‐defined Te vapor pressure was investigated up to 1070 K. At 630–900 K these crystals showed p‐type conductivity and at higher temperatures – native n‐type one. During measurements the hole density reached up to ∼2 × 1017 cm–3 at 800 K. The main acceptor dominant species, which determined the electrical properties of crystals, was supposed to be the (Pb$ ^+_{\rm Cd} $V$ ^{2-}_{\rm Cd} $)– associate with its level in the gap located at EV + 0.42–0.45 eV. Above 900 K native electrons began to influence the conductivity type. Three models of point defect structure were used to describe the galvanomagnetic data – (i) frozen defect structure, (ii) defect structure with shallow or deep acceptor levels fixed during thermal cycles and native defects being in three‐phase solid–liquid–gas (SLG) equilibrium, and (iii) defect structure without any fixed energy level and defect densities being determined by the SLG equilibrium. The FWM technique confirmed p‐type photoconductivity at 300 K, but also revealed bipolar carrier generation at high photoexcitation levels with very fast electron trapping. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electrical Conductivity of Mixed Conductors (YO<sub>1.5</sub>)<sub>x</sub>-(CeO<sub>2</sub>)<sub>y</sub>-(ZrO<sub>2</sub>)<sub>1-x-y</sub>

The Y2O3-ZrO2 binary system ceramic is considered to be most developed in application to the ZrO2-based materials. A cubic fluorite structure is generally achieved, as the metal ion of the additive (Y) takes place of the Zr4+ and oxygen ion vacancies are produced in the lattice to maintain the charge balance. This leads to almost totally ionic conductivity. The introduction of changeable valued CeO2 can further improve the total electronic conductivity through the defect equilibrium reaction between tetravalent Ce4+ and trivalent Ce3+ at high temperature and reducing atmosphere. In this study, solid phase synthesis method was employed for the preparation of (YO1.5)x-(CeO2)0.08-(ZrO2)0.9-x and (YO1.5)0.05-(CeO2)y- (ZrO2)0.95-y ceramics, while four probe DC conductivity measurement method was also applied under the temperature between 300 to 800°C. The results prove that the concentration of Y3+ is the main contribution of the electrical conductivity at low temperature.

RBS-channeling analysis of ion-irradiation effects in heavily-doped Si:As

Structural modification of heavily-doped, laser annealed Si:As induced by 2MeV Si+ irradiation, is investigated by the Rutherford backscattering-channeling (RBS-C) technique. Aligned 〈001〉 spectra, 〈001〉 to {110} angular scans and electrical activation measurements are compared with results previously obtained in silicon-on-insulator layers containing the same concentration of As, but activated by furnace instead of laser. Defects injected by ion bombardment interact with As, leading in laser annealed sample to strong electrical deactivation and to an increase in As RBS-C yield much larger than the one of Si. Comparison of samples with different initial location of As, shows that the distribution of dopant among the different kinds of lattice arrangements (schematized as substitutional, slightly displaced and random/incoherent) is nearly the same after irradiation. This result can be explained with the achievement under MeV irradiation, of a stationary state in the near-surface region, characterized by a dynamic equilibrium of intrinsic and extrinsic defects, in which the memory of As location before irradiation is substantially lost.

Signature of lattice defects in far infrared reflectivity of Ba(Mg 1/3Ta 2/3)O 3

Far infrared reflectivity spectra of Ba(Mg 1/3,Ta 2/3)O 3 prepared at several sintering temperatures were measured, and the eigenfrequencies and damping constants of the TO modes were determined. The reflectivity spectra were fitted with the four-parameter semi-quantum model. The variation in the E u(O II) at 222 cm −1 and A 2u(O II) at 238 cm −1 modes in well ordered ceramics was attributed to the variation in the concentration of the B site defects. It was also found that the change in the oxygen partial pressure of the sintering atmosphere causes a change in the seventh (316 cm −1) and eighth (352 cm −1) modes. We attribute these changes to the oxygen site defect although we cannot evaluate the concentration of this defect at this moment. From the behavior of the damping constants it is suggested that the Ba(Mg 1/3Ta 2/3)O 3 (BMT) attains equilibrium defect density at the heat treatment temperature of more than 1630 °C (120 h).

Light- and bias-induced metastabilities in Cu(In,Ga)Se2 based solar cells caused by the (VSe-VCu) vacancy complex

We investigate theoretically light- and bias-induced metastabilities in Cu(In,Ga)Se2 (CIGS) based solar cells, suggesting the Se–Cu divacancy complex (VSe-VCu) as the source of this hitherto puzzling phenomena. Due to its amphoteric nature, the (VSe-VCu) complex is able to convert by persistent carrier capture or emission from a shallow donor into a shallow acceptor configuration, and vice versa, thereby changing in a metastable fashion the local net acceptor density inside the CIGS absorber of the solar cell, e.g., a CdS/CIGS heterojunction. In order to establish a comprehensive picture of metastability caused by the (VSe-VCu) complex, we determine defect formation energies from first-principles calculations, employ numerical simulations of equilibrium defect thermodynamics, and develop a model for the transition dynamics after creation of a metastable nonequilibrium state. We find that the (VSe-VCu) complex can account for the light-induced metastabilities, i.e., the “red” and “blue” illumination effects, as well as for the reverse-bias effect. Thus, our (VSe-VCu) model implies that the different metastabilities observed in CIGS share a common origin. A defect state in the band gap caused by (VSe-VCu) in the acceptor configuration creates a potentially detrimental recombination center and may contribute to the saturation of the open circuit voltage in larger-gap Cu(In,Ga)Se2 alloys with higher Ga content. Therefore, the presence of metastable defects should be regarded as a concern for solar cell performance.