Initial Point Defect Research Articles

Self-diffusion mechanisms in Ti5Si3

The mechanisms of the Ti and Si self-diffusion in the Ti5Si3 compound are investigated by using the projector augmented-wave method within the density functional theory. The migration and activation energies for Ti and Si atoms were calculated for both vacancy and interstitial mechanisms. It is shown that the smallest migration energy of Ti atom corresponds to the interstitial mechanism, whereas it is by 0.08 eV lower for the Si own-sublattice mechanism than for interstitial one. The concentration of initial point defects within canonical formalism is calculated and the most preferred defects are determined. The temperature-dependent self-diffusion coefficients along two crystallographic directions are calculated. It is shown that Ti atom diffuses faster than Si one. The influence of metals of IVB–VIIB groups on the Ti migration energy is estimated. It is shown that almost all considered impurities increase the migration energy and can lead to a decrease in Ti diffusivity in Ti5Si3.

Investigation of the influence of off-stoichiometry on the radiation damage evolution in uranium dioxide

The work presented herein brings in valuable contribution to the study of radiation damage in uranium dioxide. In particular, the effect of off-stoichiometric compositions on the damage evolution during a displacement cascade has been investigated, which appears to be a novel study, to the best of literature review achieved. The study has been performed by means of molecular dynamics simulations and, using a powerful tool developed for the purpose, the damage has been analysed thoroughly as cascade-induced point defects and point defect clusters. The results have revealed first of all that the composition does not affect the damage development in the time frame corresponding to the thermal spike. Second of all, as the displacement cascade relaxes and persistent damage shows up in the structures, the results have indicated that off-stoichiometric compositions induced mitigation or even recovery of the damage created by the cascade, due to different mechanisms that depend on the nature and the amount of initial point defects distributed in the material due to off-stoichiometry. Third and last of all, it has been observed that the clustering behaviour in off-stoichiometric structures is also affected accordingly, and overall, the results have evidenced the formation in hyper-stoichiometric structures of interstitial clusters referred to as “split-interstitial clusters”, as alluded to in other very recent studies.

Characterizing and modeling the evolution of silicon oxide precipitates during thermal cycles

The effects of oxidizing annealing cycles on Si high-quality wafers (as used to monitor IC production tools or SOI applications) were studied using different techniques (nano-scale observations and chemical analysis in Transmission Electron Microscope (TEM), but also large scale measurements, such as Laser Scattering Tomography (LST) and chemical etching (CE), thus coupling local analyses with global measurements of defects density and size) to determine their characteristics. Interstitial oxygen loss during cycles was also measured using Fourier Transform Infra-Red spectroscopy (FTIR).It appeared that each cycle is composed of a defect nucleation stage and a growth stage, and that the distribution of these defects (mainly oxide precipitates) along wafer radius essentially depends on the initial point defect density. The evolution of these precipitates was described by a diffusion-and-growth model derived from Ham's model and taking into account various phenomena: oxygen loss, point-defect distribution and cycle effects (up/down ramp and high-temperature plateau). Extensions and limits of the model are also discussed.

Modeling of Defects Generation in 300 mm Silicon Monocrystals during Czochralski Growth

Defect generation was usually predicted by using the V/G (where V is growth rate and G is axial temperature gradient at the interface of melt/solid) theory, but it was hard to get appropriate critical V/G value and the value could not show the distribution of grown-in defects. Otherwise, direct defect simulation is a very useful method of interpreting initial point defect behavior and micro void generation. In this research, the direct defect simulation was preformed with variable process parameters and optimized by comparing with experiment results. With optimized direct defect analysis, the critical V/G value was modified as 0.00155 cm2 min-1 K-1. The critical pulling rate range was defined as that has low residual point defect concentration in silicon crystal, thus a high-quality wafer can be obtained at the critical pulling rate. The initial point defect distribution and the critical pulling rate range were analyzed by using direct defect model. Additionally, the generation of micro void density was also calculated with variable pulling rates and compared with experiment results. In this research, the initial point defect incorporation and the tendency of micro void generation were well explained by using direct defect model.

Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes

An investigation is reported of the thermal buckling and postbuckling of axially compressed double-walled carbon nanotubes (CNTs) subjected to a uniform temperature rise. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small-scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics (MD) simulations, and an initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. The small-scale parameter, e 0 a, is estimated by matching the buckling temperature of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical illustrations concern the thermal postbuckling response of perfect and imperfect, single- and double-walled CNTs with different values of compressive load ratio. The results show that buckling temperature and postbuckling behavior of nanotubes are very sensitive to the small-scale parameter. The results reveal that temperature-dependent material properties have a significant effect on the thermal postbuckling behavior of both single- and double-walled CNTs.

Nonlocal Shear Deformable Shell Model for Post-Buckling of Axially Compressed Double-Walled Carbon Nanotubes Embedded in an Elastic Matrix

Buckling and post-buckling analysis is presented for axially compressed double-walled carbon nanotubes (CNTs) embedded in an elastic matrix in thermal environments. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small scale effects and van der Waals interaction forces. The surrounding elastic medium is modeled as a tensionless Pasternak foundation. The post-buckling analysis is based on a higher order shear deformation shell theory with the von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects are also included and the material properties are assumed to be temperature-dependent and are obtained from molecular dynamics (MD) simulations. The nonlinear prebuckling deformations of the shell and the initial local point defect, which is simulated as a dimple on the tube wall, are both taken into account. A singular perturbation technique is employed to determine the post-buckling response of the tubes and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the tube and the elastic medium. The small scale parameter e0a is estimated by matching the buckling loads of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. Numerical solutions are presented to show the post-buckling behavior of CNTs surrounded by an elastic medium of conventional and tensionless Pasternak foundations. The results show that buckling and post-buckling behavior of CNTs is very sensitive to the small scale parameter e0a. The results reveal that the unilateral constraint has a significant effect on the post-buckling response of CNTs when the foundation stiffness is sufficiently large.

Parametric variations of the interatomic potential in atomistic analysis of nano-scale metal plasticity

Atomistic simulations of plastic deformation in nano-scale copper crystals are carried out. Attention is devoted to adjusting interatomic potential parameters with the objective of gaining fundamental insight into the crystal defect processes in FCC metals. An initial point defect is utilized in the molecular statics model to trigger plasticity in a controlled manner. Two different potential models have been employed: Morse and Embedded Atom Method. With the Morse potential, the interaction range has been parameterized to view dislocation slip behavior and/or phase transformation without the influence of an unstable surface state of the specimen. We focus on tensile loading along a low-symmetry orientation where single slip prevails upon yielding. When the Morse interaction distance is small, dislocation slip is seen to be the dominant deformation mechanism. A slight increase in the interaction range results in phase transition from the FCC structure to a BCC structure when using the Morse potential. Re-orientation of the BCC lattice also occurs at later stages of the deformation via a twinning operation. When the atomic interaction range is increased further, the effect of surface stress becomes increasingly important. Plastic yielding occurs in the form of partial slip which creates stacking faults. The initial point defect plays a less significant role and phase transition during deformation is suppressed. Detailed mechanisms of these atomistic features, as well as comparisons between the two potentials, are discussed.

Sintering of an ultra pure α-alumina powder: I. Densification, grain growth and sintering path

Sintering in air of an ultra pure α-alumina powder has been investigated. Isothermal experiments have been conducted on green samples shaped by slip casting. The grain growth and densification kinetics have been established. The “relative density/grain size” trajectory, called “sintering path”, has been drawn. Hypotheses concerning the mechanisms controlling grain growth and densification have been formulated. For the first time, it is shown that grain growth and densification kinetics exhibit two distinct regimes, where an initial point defect formation step plays a key role. When point defects have been generated, the diffusion of the associated Al3+ cations controls grain growth and densification.

Postbuckling prediction of axially loaded double-walled carbon nanotubes with temperature dependent properties and initial defects

Buckling and postbuckling analysis is presented for a double-walled carbon nanotube subjected to axial compression in thermal environments. The analysis is based on a continuum mechanics model in which each tube of a double-walled carbon nanotube is described as an individual orthotropic shell with the presence of van der Waals interaction forces, and the interlayer friction is negligible between the inner and outer tubes. The governing equations are based on higher order shear deformation shell theory with a von K\'arm\'an-Donnell type of kinematic nonlinearity, and they include thermal effects. Temperature-dependent material properties, which come from molecular dynamics simulations, and initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, axially loaded armchair, and zigzag carbon nanotubes under different sets of thermal environments. The results reveal that temperature change has a significant effect on the postbuckling behavior of the single-walled carbon nanotube, but it has a small effect on the postbuckling behavior of the double-walled carbon nanotube. The single-walled carbon nanotube has an unstable postbuckling path, and the structure is imperfection sensitive. In contrast, the double-walled carbon nanotube has a very weak ``snap-through'' postbuckling path, and the structure is virtually imperfection insensitive.

Postbuckling of double-walled carbon nanotubes with temperature dependent properties and initial defects under combined axial and radial mechanical loads

Buckling and postbuckling analysis is presented for a double-walled carbon nanotube subjected to combined axial and radial loads in thermal environments. The analysis is based on a continuum mechanics model in which each tube of a double-walled carbon nanotube is described as an individual orthotropic shell with presence of van der Waals interaction forces and the interlayer friction is negligible between the inner and outer tubes. The governing equations are based on higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics simulations, and initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. A singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, double-walled carbon nanotubes subjected to combined axial and radial mechanical loads under different sets of thermal environments. The results reveal that temperature change only has a small effect on the postbuckling behavior of the double-walled carbon nanotube. The axially-loaded double-walled carbon nanotube subjected to radial pressure has an unstable postbuckling path, and the structure is imperfection–sensitive. In contrast, the pressure-loaded double-walled carbon nanotube subjected to axial compression has a very weak “snap-through” postbuckling path, and the structure is virtually imperfection–insensitive.

Atomistic simulation of dislocation interactions in a model crystal subjected to shear

The interaction of edge dislocations in a two-dimensional (2D) model crystal subjected to “simple shear” is studied using molecular statics simulations. An initial point defect is introduced in the model to trigger the dislocation activities in a controlled manner. We consider dislocations gliding towards one another on parallel slip planes separated by various distances. The overall load-displacement response of the crystal is obtained from the simulations, which can be correlated with the nano-scale atomistic mechanisms. Although the crystal is inherently anisotropic, the incipient dislocation plasticity is such that slip is parallel to the primary shear direction as clearly demonstrated in this work. It is also illustrated that dislocation annihilation, as well as dislocation encounter which leaves behind a point defect, can be unambiguously modeled. Throughout the deformation history, more dislocations capable of gliding in the crystal tend to generate a weaker mechanical response and more pronounced plasticity. The present study also offers mechanistic insight into experimentally observed small-scale crystal plasticity.

A Selective Review of the Quantification of Defect Dynamics in Growing Czochralski Silicon Crystals

A vast majority of modern microelectronic devices are built on the monocrystalline silicon substrates produced from the crystals grown by the Czochralski (CZ) process and the float-zone (FZ) process. Silicon crystals inherently contain various precipitates known as microdefects that often affect the yield and the performance of many devices. Hence, the quantitative understanding and the control of the microdefect formation and the microdefect distributions in silicon crystals play a central role in determining the quality of silicon substrates. This paper reviews significant developments in the field of the quantification of the defect dynamics in growing CZ and FZ crystals. The breakthrough discovery of the initial point defect incorporation in the vicinity of the melt/crystal interface made in the early 1980s allowed a simplified quantification of the CZ and the FZ defect dynamics. A deeper insight into the formation and the growth of microdefects was provided over the past decade by various treatments of the agglomeration of the intrinsic point defects of silicon. In particular, a rigorous quantification of the agglomeration of the point defects using the classical nucleation theory, a recently developed lumped model that captures the microdefect distribution by representing the actual population of microdefects by an equivalent population of identical microdefects, and another rigorous treatment involving the Fokker−Planck equations are discussed in detail.

05/01546 The present status and future prospects of theITER project

The work presented herein brings in valuable contribution to the study of radiation damage in uranium dioxide. In particular, the effect of off-stoichiometric compositions on the damage evolution during a displacement cascade has been investigated, which appears to be a novel study, to the best of literature review achieved. The study has been performed by means of molecular dynamics simulations and, using a powerful tool developed for the purpose, the damage has been analysed thoroughly as cascade-induced point defects and point defect clusters. The results have revealed first of all that the composition does not affect the damage development in the time frame corresponding to the thermal spike. Second of all, as the displacement cascade relaxes and persistent damage shows up in the structures, the results have indicated that off-stoichiometric compositions induced mitigation or even recovery of the damage created by the cascade, due to different mechanisms that depend on the nature and the amount of initial point defects distributed in the material due to off-stoichiometry. Third and last of all, it has been observed that the clustering behaviour in off-stoichiometric structures is also affected accordingly, and overall, the results have evidenced the formation in hyper-stoichiometric structures of interstitial clusters referred to as “split-interstitial clusters”, as alluded to in other very recent studies.

On the Atomistic Simulation of Plastic Deformation and Fracture in Crystals

Tensile stretching of a two-dimensional model crystal was computationally studied using molecular statics simulations. Attention was directed to the atomistics of defect activities throughout the deformation history. It is shown that the incorporation of an initial point defect is able to trigger dislocation slip in a repetitive and controlled manner. The initial defect is also seen to have potential bearing on the formation of voiding damage that leads to ductile fracture of the crystal. Implications to the nanoscale mechanical behavior and its modeling are discussed.

An Atomistic View of Interface-Mediated Dislocation Plasticity in Thin Metal Films

ABSTRACTAtomistic simulations using molecular statics are carried out to study dislocation plasticity in thin metal films attached to stiff substrates. The analysis utilizes a sample two-dimensional crystal, with an embedded initial point defect used for triggering dislocation activities in a controlled manner. The existence of an interface between the film and the substrate is shown to delay plastic yielding and lead to film strengthening. The capability of atoms to slide along the interface plays a crucial role in determining the macroscopic stress-strain response and the microscopic dislocation activities. Within the modeling framework we examine the quantitative interfacial sliding behavior and the resulting dislocation-interface interactions and their consequences.

Vacancy and interstitial depth profiles in ion-implanted silicon

An experimental method of studying shifts between concentration-versus-depth profiles of vacancy- and interstitial-type defects in ion-implanted silicon is demonstrated. The concept is based on deep level transient spectroscopy measurements utilizing the filling pulse variation technique. The vacancy profile, represented by the vacancy–oxygen center, and the interstitial profile, represented by the interstitial carbon–substitutional carbon pair, are obtained at the same sample temperature by varying the duration of the filling pulse. The effect of the capture in the Debye tail has been extensively studied and taken into account. Thus, the two profiles can be recorded with a high relative depth resolution. Using low doses, point defects have been introduced in lightly doped float zone n-type silicon by implantation with 6.8 MeV boron ions and 680 keV and 1.3 MeV protons at room temperature. The effect of the angle of ion incidence has also been investigated. For all implantation conditions the peak of the interstitial profile is displaced towards larger depths compared to that of the vacancy profile. The amplitude of this displacement increases as the width of the initial point defect distribution increases. This behavior is explained by a simple model where the preferential forward momentum of recoiling silicon atoms and the highly efficient direct recombination of primary point defects are taken into account.

Native Point Defect Interactions in ZGP Crystals under Influence of e-Beam Irradiation.

ABSTRACTOptical absorption in the defect-related region of highly efficient non-linear ZnGeP2 crystals under e-beam irradiation and post-irradiation anneals has been investigated.Partially irreversible changes of the absorption were found in the spectral range 0.9–2.5 μm (0.5–1.3 eV) after irradiation and subsequent low-temperature anneals. Data obtained do not support the vacancy model for ZnGeP2 absorption in the 0.5–1.3 eV range.The least squares fit for the parameters of the theoretical dependence of optical absorption cross-section to the experimentally measured ZnGeP2 optical absorption coefficient spectra show that the defect-related absorption in 0.5–1.3 eV region is caused by deep donor levels with energy position E=Ev+(0.85–0.90) eV.Significant changes in the energy spectrum of the dominant optically active centers have been observed under influence of e-beam irradiation and post-irradiation anneals.Based on the optical absorption measurements obtained for as-grown, annealed and e-irradiated ZnGeP2 crystals, a model of point defect interactions has been proposed. This takes into account both the reversible interactions, such as the formation of donor-acceptor pairs, and the irreversible interactions of a quasi-chemical type.The behavior of the energy spectrum of the optically active defects is discussed in terms of the modes of interaction between the initial point defects and those generated by irradiation. The analysis performed showed that the best agreement with experimental data is reached when it is assumed that optical defect-related absorption in the 0.5–1.3 eV range related mainly to the disordering defect in the cation sublattice of ZnGeP2, namely, to atoms of Ge substituting for Zn.Defect concentration profiles created by e-irradiation in ZGP crystals of different thickness were calculated. The optimum conditions for providing a uniform defect distribution with depth in irradiated ZnGeP2 samples were determined.The optimal e-beam irradiation fluences, giving maximum ZnGeP2 enlightenment, allowed us to reduce the defect-related absorption down to a value of 0.01 cm-1 at 2 μm.

Influence of low thermal budget pre-anneals on the high temperature redistribution of low energy boron implants in silicon

ABSTRACTIt is now well established that the transient enhanced diffusion (TED) of ion implanted boron in silicon limits the formation of the ultra-shallow junctions required for the extreme deep sub- micron devices. It is also known that this TED is linked to the fate (elimination and agglomeration) of ion implantation related excess self-interstitials. Thus it can be expected that the final high temperature redistribution is at least partly governed by the effective initial point defect distribution at the onset of the high temperature plateau.In this contribution we present the experimental evidence that low thermal pre-anneals, by affecting the initial self-interstitials distribution, affects boron redistribution during a subsequent high temperature anneal. Samples implanted with high dose boron at 3 keV were first annealed at 700°C for various durations. These samples, as well as reference samples without the pre-anneal, were then RTA annealed at various high temperatures around 1000°C. The resulting B profiles were measured by SIMS. It is found that the pre-annealed samples exhibits a clear reduction of the TED as compared with the reference ones.

Point defect movement and annealing in collision cascades

The effect of collision cascades on preexisting point defects in crystalline materials was studied by simulating 5 keV collision cascades in gold, copper, aluminum, platinum, and silicon. The results indicate that collision cascades do not significantly affect interstitials or vacancies outside the liquid core of the cascade, although in the fcc metals the heating of the crystal due to the cascade causes some thermal migration of the interstitials. Within the liquid cascade core, both interstitials and vacancies move towards the center of the molten region when it resolidifies and recombine or cluster there. At elevated temperatures, random jumps of interstitials during the thermal-spike phase can cause significant additional trapping of interstitials in the liquid. In contrast to the annealing effects of preexisting damage in the fcc metals, in silicon the amount of new damage created by a cascade is roughly independent of the number of initial point defects. The difference is attributed to the nature of the bonding in the materials.

Arsenic precipitation from thin surface layers of low-temperature grown GaAs

Arsenic precipitation from a thin, 100-nm surface layer of GaAs grown at low temperature (LT) by molecular beam epitaxy is investigated. The precipitate depth distribution is examined for different rapid thermal annealing cycles. It is found that the precipitate distribution can tail a long distance into the underlying stoichiometric GaAs layer, depending on the peak annealing temperature. The distribution for an 800 °C anneal is virtually unaffected by a prior low temperature ‘‘soak’’ at 600 °C, thus showing that the precipitation is insensitive to the initial point defect concentrations in this temperature range. The relevance of these results to the precipitation process and to the use of thin LT layers in device applications is discussed.