Condensation Of Point Defects Research Articles

Electric-field-induced point defect redistribution in single-crystal TiO2–x and effects on electrical transport

The spatial redistribution of non-stoichiometric point defects in rutile TiO2 is studied as a function of voltage and time. Single crystals are equilibrated initially to a well-defined stoichiometry with n-type conductivity and a carrier concentration on the order of 1018cm−3. The crystals are subsequently electroded with Pt contacts that exhibit Schottky behavior. When subjected to an applied voltage of 15V, a time-dependent increase and saturation in the leakage current is observed, which is associated with an accumulation of point defects and an attendant decrease in stoichiometry at the cathode electrode. This local change in stoichiometry degrades the Schottky barrier, leading to asymmetric electrodes and thus macroscopic rectifying behavior. Cathodoluminescence spectroscopy shows that Ti interstitials dominate the point defect redistribution process. Under larger applied voltages, of around 30V, qualitatively different behavior is observed in which the resistivity increases as a function of time. This behavior is associated with condensation of point defects into a region of extended defects and Magnéli phases near the cathode, sufficient to increase the bulk stoichiometry and resistivity. These experiments demonstrate that a one-dimensional drift-diffusion process, as opposed to filamentary growth, dominates in these experimental conditions and that the Pt–TiO2–Pt system remains closed, with no significant oxygen transport across the Pt–TiO2 interfaces. We believe this is the first observation of a second higher-voltage regime in which the bulk stoichiometry and thus resistivity is increased as large concentrations of defects condense into metallic Magnéli phases in the near-electrode regions.

Defect mastering - one of the topic challenges for crystal growth

The quality of single crystals, epitaxial layers and devices made there from are very sensitively influenced by structural and atomistic deficiencies generated during the crystal growth. Crystalline imperfections comprise point defects, dislocations, grain boundaries, second-phase particles. Over more than a half-century of the development of crystal growth, most of the important defect-forming mechanisms have become well understood [1-2]. As a result, the present state of technology makes it possible to produce crystals of remarkably high quality. However, that is not to say that all problems are already solved. For instance, in comparison with silicon the point defect dynamics in semiconductor and oxide compounds is not nearly as well understood. The density of equivalent defect types and antisites in each sub-lattice is determined by deviation from stoichiometry. Their charge state depends on the Fermi level position leading via interaction with dopants to certain compensation level and complex formation. One measure proves to be the in situ control of stoichiometry. Due to high-temperature dislocation dynamics heterogeneous dislocation substructures are formed. Both, acting thermo-mechanical stress and given point defect situation force the dislocation to glide and climb. In the course of enthalpy minimization the long-range character of dislocation interaction produces agglomerates and patterns with polygonized cell walls, i.e. small angle grain boundaries [3]. Thanks to the rules of correspondence of Taylor and Kuhlmann-Wilsdorf one is able to estimate the interaction between shear stress, dislocation density and cell diameter (Fig.). In epitaxy the Nye tensor, describing dislocation distribution inhomogeneity, affects the layer stress considerably. The growth under minimum stress, solution hardening and in situ stoichiometry control are effective counteracting methods. One of the most serious consequences during cooling down of as-grown crystals is the point defect condensation in precipitates and micro-voids decorating dislocation patterns or inducing high mechanical misfit stress that generates dislocation loops. It proves to be favourable to anneal the crystal a few degrees below the melting point in order to dissolve the particles and re-diffuse their into the crystal matrix.

Cavitation During Superplastic Forming.

Cavitation is the opening of pores during superplastic forming, typically at grain boundary triple points or on second phase grain boundary particles during slip of grain boundaries. Theories for the initiation of cavitation are reviewed. It seems that cavitation is unlikely to occur by processes intrinsic to metals such as dislocation mechanisms or point defect condensation. It is proposed that cavitation can only occur at non-bonded interfaces such as those introduced extrinsically (i.e., from the outside) during the original casting of the metal. These defects, known as oxide bifilms, are naturally introduced during pouring of the liquid metal, and are frozen into the solid, often pushed by dendritic growth into grain boundaries where they are difficult to detect because of their extreme thinness, often measured in nanometres. Their unbonded central interface acts as a crack and can initiate cavitation. Second phase precipitates probably do not nucleate and grow on grain boundaries but grow on bifilms in the boundaries, explaining the apparent association between boundaries, second phase particles and failure initiation. Improved melting and casting techniques can provide metal with reduced or zero bifilm population for which cavitation would not be possible, promising significant improvements in superplastic behaviour.

Defect Structure of Heteroepitaxial SnO2 Thin Films Grown on TiO2 Substrates

Heteroepitaxal SnO2 thin films were grown on rutile (100) TiO2 single crystal substrates by pulsed laser deposition. The defect structure and surface morphology were investigated by transmission electron microscopy, reflection high-energy electron diffraction, and atomic force microscopy. The misfit-induced large biaxial compressive stress in the 200-nm-thick SnO2 thin film was almost fully relaxed to yield the high-density interfacial misfit dislocations and related planar defects. The misfit dislocation network on the hetero-interface consisted of two types of partial edge dislocations with Burgers vectors of 1/2<101> and 1/2<110>, which involved {101} and {010} planar defects formed in the film, respectively. The evolution of the surface morphology and cross-sectional structure for thinner films suggested that the introduction of such defects occurs at the early growth stage, due to large lattice misfit, and is strongly affected by point defect condensation.

New virtual substrate concept for vertical MOS transistors

We propose a new concept of thin SiGe virtual substrates in which the interactions of point defects with dislocations play a key role. Being purposely introduced in the thin SiGe buffer layers during their metastable growth, point defects promote the relaxation of strain. Firstly, they cause dislocations to climb which helps to annihilate threading dislocation arms with opposite Burgers vectors. Secondly, condensation of point defects results in prismatic dislocation loops inside the layers which avoids nucleation from the surface sites. As a consequence, point defects reduce the density of existing threading dislocations and prevent the generation of new ones. This solution should allow the formation of virtual substrates with thin relaxed SiGe buffer layers and low threading dislocation density. In this paper, we explain how point defects can be injected using modified MBE process techniques. These techniques utilize either the injection of low energy Si + ions or supersaturation of point defects resulting from very low temperature growth.

Precipitation and migration of point defects in MOCVD CdxHg1 − xTe

Cross-sectional TEM studies of CdxHg1−xTe layers grown by the interdiffused multilayer process have shown that the microstructures can be related to the diffusion mechanisms during the annealing. Layers on CdTe buffers on GaAs contain extrinsic faulted loops produced by point defect condensation whereas layers on lattice-matched CdxZn1 − xTe substrates contain dislocation networks which have migrated away from the original interface.

Hydrogen interactions with self-interstitials in silicon.

We present a first-principles investigation of complexes between one or two hydrogen atoms and a Si self-interstitial (${\mathrm{Si}}_{\mathit{i}}$). The atomic structure of these complexes is a distortion of the 〈110〉 split-interstitial configuration. The (H,${\mathrm{Si}}_{\mathit{i}}$) complex has donor and acceptor levels in the band gap, both about 0.4 eV above the valence band. The (2H,${\mathrm{Si}}_{\mathit{i}}$) complex is electrically inactive, with all Si atoms bonded to four neighbors. The binding energy of H to the self-interstitial is about 2.4 eV (referenced to free atomic H). Consequences of these results for observation of self-interstitials and for processes such as point-defect condensation and dislocation nucleation are discussed.

Critical Evaluation of Atomistic Simulations of 3D Dislocation Configurations

AbstractThough atomistic simulation of 3D dislocation configurations is an important objective for the analysis of problems ranging from point defect condensation to the operation of Frank-Read sources such calculations pose new challenges. In particular, use of finite sized simulation cells produce additional stresses due to the presence of fixed boundaries in the far field which can contaminate the interpretation of these simulations. This paper discusses an approximate scheme for accounting for such boundary stresses, and is illustrated via consideration of the lattice resistance encountered by straight dislocations and simulations of 3D bow out of pinned dislocation segments. These results allow for a reevaluation of the concepts of the Peierls stress and the line tension from the atomistic perspective.

Critical Evaluation of Atomistic Simulations of 3D Dislocation Configurations

AbstractThough atomistic simulation of 3D dislocation configurations is an important objective for the analysis of problems ranging from point defect condensation to the operation of Frank-Read sources such calculations pose new challenges. In particular, use of finite sized simulation cells produce additional stresses due to the presence of fixed boundaries in the far field which can contaminate the interpretation of these simulations. This paper discusses an approximate scheme for accounting for such boundary stresses, and is illustrated via consideration of the lattice resistance encountered by straight dislocations and simulations of 3D bow out of pinned dislocation segments. These results allow for a reevaluation of the concepts of the Peierls stress and the line tension from the atomistic perspective.

Cross-sectional transmission electron microscopy parallel to the active stripe of degraded buried heterostructure distributed feedback laser devices

We demonstrate for the first time that cross-sectional transmission electron microscopy can be applied parallel to the active stripe of a distributed feedback buried heterostructure laser diode to identify the cause for degradation during reliability qualification. A dominant defect mechanism is found to be the generation of dislocation loops at or near the grating/waveguide-layer interface which subsequently propagate up through the multilayer structure. The vertical segments of the loops tend to be trapped onto the {111} planes to form a V-shaped configuration as revealed in the (011) cross section. A dislocation reaction mechanism is proposed to explain the observed dislocation configuration. Furthermore, complicated dislocation loops are grown out of the segments of dislocation threading through the active region forming &amp;lt;100≳ dark line defects revealed by the electroluminescence. The defect growth mechanism is believed to be a condensation of point defects induced by the nonradiative recombination assisted point defect migration process similar to that previously observed in degraded channeled substrate buried heterostructure lasers. The nucleation of dislocations at or near the grating/waveguide layer interface is consistent with a high interfacial strain observed in the degraded devices.

Relationship between dislocation generation, vapour phase supersaturation and growth rate in InP layers obtained by vapour phase epitaxy

Abstract The interrelationship between growth conditions, dislocation generation mechanisms and layer growth rate has been studied in InP/InP layers prepared by hydride vapour phase epitaxy. In the present experiments, only the PH3 flow rate was varied, whereas the HCl flow rate was kept constant. Contrary to what is generally believed, even very low growth rates yield a very high dislocation density. The dislocations are generated by the condensation of point defects that are incorporated in supersaturation into the layer during the whole growth sequence. Under higher flow rate conditions, dislocation generation by glide processes seems to prevail. Layers with minimum defect density are obtained for intermediate PH3 flow rates. The influence of either the spiral growth or the two-dimensional nucleation mechanism on the macroscopic layer growth is discussed. A procedure to reduce the morphological defects, termed hillocks, is also suggested.

On the core structures of edge dislocations in NaCl and MgO. Consequences for the core configurations of dislocation dipoles

Abstract Stacking faults (α/2)[100](010) are unstable in alkali halides and oxides with the rock-salt structure. They produce local decohesion of the crystal. The atomistic computations reported in this paper show that these kinds of defects can be preferential sites for point-defect condensation. They are found in the relaxed configuration of atomistically calculated, narrow vacancy dislocation dipoles and vacancy loops that are associated with a volume expansion. The strain energy and volume expansion of a narrow vacancy dipole can explain the microscopic and macroscopic features found in stage I of the deformation curve of NaCl as conjectured by Strecker and Strunk. These computations show that the core of an (a/2) [110](110) edge dislocation can be seen as being built up of either two (110) or two (100) and (010) extra half-planes. The former configuration controls the glide properties whilst the latter controls the point-defect absorption at the core. This latter core configuration can be split when submitted to external stress or interaction forces arising from other dislocations. Using such an elastic analogue, it is possible to explain satisfactorily the interaction, formation and evolution of the atomistic configurations of microdefects found during vacancy condensation.

Atomic modelling of homogeneous nucleation of dislocations from condensation of point defects in silicon

Abstract An energetically favourable atomic modelling scheme for homogeneous nucleation of dislocations in silicon by condensation of point defects is described. For extrinsic dislocation dipoles, a chain of interstitial atoms is used to form intermediate defect configurations having non-six-membered atomic rings with matrix atoms. For intrinsic dislocation dipoles, a chain of matrix atoms is cut out and the remaining atoms surrounding the cut are used to form intermediate defect configurations having non-six-membered atomic rings. Climb and glide motions of the intermediate defect configurations then produce the 90° edge, the 60° and the Frank partial dislocation dipoles. The intermediate defect configurations and the dislocation dipoles generated have {110} rod-like morphologies. A model with all four-coordinated interstitial atoms for {113} stacking fault is also obtained.

Mechanisms of radiation induced creep and growth

Irradiation creep occurs primarily because the applied stress causes the evolving microstructure to respond in an anisotropic fashion to the interstitial and vacancy fluxes. On the other hand, irradiation growth requires the response to be naturally anisotropic in the absence of applied stress. Four fundamental mechanisms of irradiation creep have been conjectured: stress induced preferred absorption (SIPA) of the point defects on the dislocations, stress induced preferred nucleation (SIPN) of point defects in planar aggregates (edge dislocation loops), stress induced climb and glide (SICG) of the dislocation network and stress induced gas driven interstitial deposition (SIGD). These mechanisms will be briefly outlined and commented upon. The contributions made by these mechanisms to the total strain are not, in general, mutually separable and also depend on the prevailing (and changing) microstructure during irradiation. The fundamental mechanism of irradiation growth will be discussed: it is believed to arise by the preferred condensation of point defects and climb of dislocation loops and network on certain crystallographic planes. The preferred absorption and nucleation is thus a consequence of natural crystallographic anisotropy and not due to any external stresses. Again the effectiveness of this mechanism depends on the prevailing microstructure in the material. In this connection attention will be particularly drawn to the significance of solute trapping, segregation at grain boundaries, dislocation bias for interstitials and transport parameters for an understanding of irradiation growth in materials like zirconium and its alloys; the relevance of recent simulation studies of growth in such materials using electrons to the growth under neutron irradiation will be discussed in detail and a consistent model of growth in these materials will be presented.

Microdefects and striations in dislocation-free LEC-GaP crystals

Dislocation-free GaP crystals grown by the liquid encapsulated Czochralski technique were characterized chiefly by the use of X-ray transmission topography and EBIC-mode scanning electron microscopy. Preliminary results obtained with transmission electron microscopy are also presented. X-ray topographs reveal a crystal inhomogeneity which is mainly attributed to the presence of non-stoichiometric striations. High densities (10 11-10 12 cm -3 of microdefects were detected, distributed both homogeneously and in a striated pattern. Various types of microdefects (perfect and faulted dislocation loops and (semi) coherent precipitates) were revealed. Although most microdefects are less than 1 μm across, significantly larger defects can form. Evidence for macroscopic dislocation generation due to point defect condensation is presented.

The introduction of dislocations during the growth of floating-zone silicon crystals as a result of point defect condensation

During growth of dislocation-free floating-zone crystals two types of “swirl defects” (A- and B-clusters) are formed as a result of point defect condensation. The diffusion coefficient of these point defects (vacancies, silicon interstitials) in the temperature interval 1050–1100 °C, is found to be 2 × 10 -5 cm 2/sec. Section topographic analysis showed that the A-clusters (dislocation loops) rapidly increase in size with decreasing crystal cooling rate. This is attributed to a combined climb-glide process. Evidence is presented that the predominant cause for the loss of dislocation-free growth, particularly of large-diameter crystals, is due to emission of dislocation arrays from the A-clusters.

The loss of coherency of precipitates and the generation of dislocations

Abstract The theory of Brown, Woolhouse and Valdre (1968) is extended to include the possibility of the nucleation of interface dislocations by prismatic punching and the condensation of point defects. It is shown that neither process can occur spontaneously (i.e. without the introduction of dislocations by another process such as deformation or irradiation) unless the misfit exceeds a critical value, estimated to be 0·05. Furthermore, unless the radius of the precipitate exceeds certain critical values, the processes will not occur because the energy of the system is not thereby lowered. A comparison of the theory with experiment enables limits to be placed on the stress necessary to cause the generation of dislocations in a perfect lattice, and at an incoherent interface. In the former case the generation stress is higher than hitherto supposed; but in the latter case it appears that an incoherent interface behaves as an ideal source of dislocations, in the sense that when the energy of the system can b...

Dislocation loops in irradiated iron

Abstract Dislocation loops have been observed in iron foils irradiated with protons or Fe+ ions of energy 150 kev. Those produced by irradiation with Fe+ ions are shown to lie on {100} planes and to be pure edge in character. They are normally square, with the sides in the corresponding directions, and are formed by the condensation of interstitial atoms. It is believed that the loops are formed because of the excess concentration of interstitial atoms resulting from the direct insertion of atoms on bombardment. It is shown that either a homogeneous or a heterogeneous nucleation mechanism can account for the loop density observed. Finally, an estimate is made of the strain energy of various modes of condensation of point defects in iron. The most favoured are ½[111] (110), ½[111] (111), and [100] (100).

Production of Dislocation Loops by a Combined Climb and Glide Mechanism

Studies of dislocations in elongated aluminum crystals by diffraction electron microscopy revealed narrow dislocation loops lying parallel to 〈112〉. These loops formed only behind screw dislocations, their long parts then having edge character. Four mechanisms have been proposed to account for the formation and stabilization of the narrow loops through the condensation of point defects.

Stacking Faults in Zinc

Configurations of individual dislocations in zinc have been studied by electron transmission microscopy and by x-ray diffraction microscopy. Loops of sessile dislocation have been observed surrounding stacking faults lying on (0001) planes. These loops were evidently formed by condensation of point defects. Changes in loop size with climb of the surrounding dislocation have been observed occurring in the electron microscope. Separation of glissile dislocations into partial dislocations separated by stacking faults on (0001) planes have also been observed. Various interactions among the several types of dislocations occur.