Self-interstitial Defects Research Articles

Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals

We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the ``local'' $d$ band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

Driven mobility of self-interstitial defects under electron irradiation

In situ electron microscope observations of defects show that the incident high-energy electrons influence the evolution of microstructure of an irradiated material, reducing the number of defects seen in the field of view of the microscope. We investigate the origin of this phenomenon, using tungsten as a case study. We find that displacements of atoms due to electron impacts give rise to the stochastic jumps of a defect over several interatomic distances, but the frequency of these events under normal conditions is too low to influence the high thermal mobility of defects in a pure material. At the same time our analysis shows that migration of defects driven by electron impacts provides the dominant mechanism of diffusion in a material where the defects are pinned by solute atoms or impurities.

Multi-scale modelling of defect behavior in bcc transition metals and iron alloys for future fusion power plants

A multi-scale materials modelling approach is developed in order to investigate the structure, energy, mobility as well as the dynamical behavior of the neutron-induced defects in bcc transition metals and alloys for future fusion power plants. Our focus is on exploring quantum mechanical effects (directional bonding, magnetism and bond screenings) present in these specific materials. Using density functional theory (DFT) we have generated a comprehensive database of formation energies for self-interstitial atom defects for all bcc TM. We found that the energies of various defect structures in non-magnetic bcc transition metals show a striking systematic trend different to those found in ferromagnetic iron. Our new ab initio database is going to be used to develop genetic and reliable interatomic potentials based on the tight binding approximation. These potentials have been applied for studying the core structure and glide of the (1/2)〈1 1 1〉 screw dislocation bcc transition metals and magnetic properties of point defects in Fe based on Stoner model. A large-scale molecular dynamic cascade simulations based on quantum core effects is also investigated. Finally, one-dimensional analytic solutions for strain fields of interstitial cluster are presented to compare with our predictions of DFT calculations.

Self-interstitial atom defects in bcc transition metals: Group-specific trends

We present an investigation of systematic trends for the self-interstitial atom (SIA) defect behavior in body-centered cubic (bcc) transition metals using density-functional calculations. In all the nonmagnetic bcc metals the most stable SIA defect configuration has the $⟨111⟩$ symmetry. Metals in group 5B of the periodic table (V, Nb, Ta) have significantly different energies of formation of the $⟨111⟩$ and $⟨110⟩$ SIA configurations, while for the group 6B metals (Cr, Mo, W) the two configurations are linked by a soft bending mode. The relative energies of SIA defects in the nonmagnetic bcc metals are fundamentally different from those in ferromagnetic bcc $\ensuremath{\alpha}$-Fe. The systematic trend exhibited by the SIA defect structures in groups 5B and 6B transition metals correlates with the observed thermally activated mobility of SIA defects.

Molecular-Dynamics Study of Self-Interstitial Diffusion in bcc-Iron

Self-interstitial diffusion in α-iron is investigated using an embedded-atom-method potential and molecular-dynamics simulations. Curved Arrhenius plot is obtained for the temperature dependence of diffusion coefficients, which is well explained by the superposition of two transition processes among the two allotropic states of self-interstitial defects, the reformation of 〈110〉 dumbbell into another 〈110〉 configuration and one-dimensional solitonic propagation of a crowdion on 〈111〉 axis.

Solitonic Migration and Collisions of Self-Interstitial Defects in BCC Iron

Self-interstitial atoms in bcc iron display unusual migration behaviors; strong anisotropy toward a h111i direction with occasional rotation to an equivalent direction as well as retracing the same way as it has come, and also ultra-high mobility when they are clustered. These singularities cannot be explained by simple interstitial or interstitialcy diffusion mechanisms. However, some of them will be well accounted if the SIA could behave as a soliton, which makes three-dimensional movements in appearance, but essentially a serial combination of onedimensional migration. Indeed, a crowdion, one of isomeric configurations of the self-interstitial atom, has an atomic arrangement very similar to the one-dimensional dislocation core structure, whose migration kinetics has been well modelled by a one-dimensional soliton equation. Here we report a decisive observation that both a single and colliding two crowdions really behave as solitons in iron crystals using molecular dynamics simulations. In addition, we ascertain that the present results are attributed to the intrinsic nature of the crowdion where an overall potential felt by atoms therein is very shallow and periodical along the migration direction. [doi:10.2320/matertrans.47.2658]

Magnetic properties of point defects in iron within the tight-binding-bond Stoner model

The tight-binding Stoner model of band magnetism is generalized to account for local charge neutrality by working within the tight-binding-bond (TBB) representation of the binding energy. We show that the analytic forces within this TBB Stoner model take a very simple form because neither the renormalization in the on-site energies due to local charge neutrality nor the change in local magnetic moments due to atomic displacement enters explicitly. This $d$ band TBB Stoner model is found to reproduce qualitatively the variations in local moments on and around point defects that are predicted by first principles density functional theory. In agreement with experiments, the formation energies show that the most stable self-interstitial defect is the ⟨110⟩ dumbbell.

Density-functional calculations of defect formation energies using supercell methods: Defects in diamond

Density-functional theory combined with periodic boundary conditions is used to systematically study the dependence of defect formation energy on supercell size for diamond containing vacancy and self-interstitial defects. We investigate the effect of the electrostatic energy due to the neutralization of charged supercells and the effect of the alignment of the valence band maximum (VBM) on the formation energy. For negatively charged vacancies and positively charged interstitials, the formation energies show a clear dependence on supercell size, and the electrostatic corrections agree with the trend given by the Makov-Payne scheme (Ref. 28). For positively charged vacancies and negatively charged interstitials, the size dependence and the electrostatic corrections are quite weak. An analysis of the spatial charge density distributions reveals that these large variations in electrostatic terms with defect type originate from differences in the screening of the defect-localized charge, as explained by using a simple electron-gas model. Several VBM alignment schemes are also tested. The best agreement between the calculated and asymptotically exact ionization levels is obtained when the levels are based on the formation energies referenced to the VBM of the defect-containing supercell.

Diffusion of radiation damage in Fe–P systems

The dimer method has been applied to determine the transition energy barriers for defect motion in α-Fe containing a phosphorus impurity. The principal defects analysed were those that were found to exist after a classical molecular dynamics (MD) simulation of the collisional phase of a cascade. We have found two different diffusion mechanisms when the P is in an interstitial site. The P interstitial can diffuse through the lattice by hopping between 〈110〉 dumbbell and tetrahedral sites, taking a few nanoseconds per transition at 300K. This is much slower than the transition times found in previous studies of Fe self-interstitial defects, in which transitions can be observed over normal MD time scales of a few tens of picoseconds at 300K.

ESR detection of Ga self-interstitial defects in GaP nano-solids

The intrinsic point defects of GaP nano-solids have been investigated by means of electron spin resonance (ESR). An ESR spectrum attributed to the Ga self-interstitial in GaP nano-solids was observed with value g=2.0028 or 2.0030. The collapse of hyperfine splitting and narrowing of peak-to-peak linewidth (Δ H pp) of the ESR spectrum result from the possible rapid electron spin exchange effect. The concentration of dangling bonds for GaP nano-solids decreases when decreasing compaction pressure and with higher heat-treatment temperature. Both detection and control of the intrinsic point defects of nano-sized GaP materials are beneficial for further exploration of its fundamental properties and applications.

Interpretation of ion-channeling spectra in ion-implanted Si with models of structurally relaxed point defects and clusters

We investigate the application of atomistic models of self-interstitial defects to the simulation of Rutherford backscattering-channeling (RBS-C) spectra in ion irradiated Si. By the comparison of simulated and experimental measurements, we verify the ability of different models, either of elementary interstitials or of small clusters, to reproduce experimental spectra measured under different alignment conditions in Si lightly damaged by ${\mathrm{Si}}^{+}$ ion implantation. A model system for RBS-C simulation is built by inserting a distribution of defects in a supercell with size of $\ensuremath{\sim}{10}^{6}$ atoms. The system is then structurally relaxed by the application of the classical environment-dependent interatomic potential (EDIP). After adjusting the defect distribution in order to fit the $〈100〉$ RBS-C spectrum, simulations are performed under the other alignment conditions investigated. The scattering factors of defects are then extracted from both experimental and simulated RBS-C spectra and compared. It is shown that the anisotropy of experimental damage is not compatible with a significant presence of random (incoherent) disorder, but can be reproduced by some of the defect models under consideration: the split-$〈110〉$ interstitial, the diinterstitial formed by the addition of an interstitial to the split-$〈110〉$ interstitial, and two different configurations of the four-interstitial aggregate; one formed by two close diinterstitials and the other by the aggregation of four split-$〈100〉$ interstitials. Due to the different $〈100〉$ scattering factors of the four defect configurations which are found to reproduce experimental spectra, there is an inherent uncertainty of a factor of 2 in the estimate of the amount of interstitials by $〈100〉$ RBS-C analysis. The agreement between simulations and experiments is remarkable, considering that the method makes use of physical, although empirical, models of defects, where the only adjustable parameter is the absolute concentration of interstitials.

Evidence on the mechanism of boron deactivation in Ge-preamorphized ultrashallow junctions

We investigate the thermal stability of boron-doped junctions formed by Ge preamorphization and solid phase epitaxial regrowth. Isochronal annealing and characterization by sheet resistance, secondary-ion mass spectrometry, and spreading-resistance measurement are used to extract detailed information on the thermal stability of the boron activation. Using a previously established model of self-interstitial defect evolution from clusters to dislocation loops, we perform simulations of the release of interstitials from the end-of-range region. The simulations indicate that the measured deactivation is driven by interstitials emerging from the end-of-range defect region.

Complexity of small silicon self-interstitial defects.

The combination of long-time, tight-binding molecular dynamics and real-time multiresolution analysis techniques reveals the complexity of small silicon interstitial defects. The stability of identified structures is confirmed by ab initio relaxations. The majority of structures were previously unknown, demonstrating the effectiveness of the approach. A new, spatially extended tri-interstitial ground state structure is identified as a probable nucleation site for larger extended defects and may be key for the compact-to-extended transition.

Diffusion of ion beam injected self-interstitial defects in silicon layers grown by molecular beam epitaxy

In this work the silicon self-interstitial (I) diffusion in trap-containing molecular beam epitaxy Si layers is investigated. The I’s are produced by Si ion implantation, and the I supersaturation is reported as a function of the depth and the annealing time. These data are discussed on the basis of two alternative models proposed in literature (“effective diffusivity” model and “filling trap” model). This analysis demonstrates that the second model is more appropriate to describe the proposed phenomenology, since it explains both the increase of the I penetration depth as a function of the implant dose and the very rapid change of the supersaturation versus time. Moreover, the proposed model takes account for the I recombination at the surface.

Interstitial-related reactions in silicon doped with isovalent impurities

Evolution of self-interstitials and interstitial carbon-related defects under electron irradiation and subsequent annealing has been studied by means of infrared absorption spectroscopy in silicon doped with tin or germanium. It has been found that doping of Si with both Sn and Ge results in an increase of the efficiency rate of formation of self-interstitial oxygen-related defects I2OI. Doping with germanium does not affect reactions with the participation of carbon interstitials CI, whereas tin atoms turn to be effective sinks for CI in silicon. Two types of (CISn)-related centers were found to appear under the CI annealing. Disappearance of the (CISn) complexes under annealing is accompanied by occurrence of CIOI and CICS centers.

Multiscale modelling of radiation damage in metals: from defect generation to material properties

Atomic- and continuum-scale computer simulation techniques have now become sufficiently powerful that many phenomena associated with radiation damage effects in metals can be modelled with a high degree of realism. Recent studies of several such phenomena are reviewed here. Primary knock-on atoms (PKAs) that recoil under collision from energetic atomic particles such as neutrons or ions are the principal source of damage. At high enough recoil energy, they create cascades of atomic displacements that result in single and clustered self-interstitial and vacancy defects. The time and length scales of the cascade process are ideally suited to atomic-scale computer simulation by molecular dynamics (MD). This method provides data on the number of defects produced and their distribution in clusters. This information was not available from earlier models and so the nature of the primary damage state is now much clearer. MD is also being used to reveal the nature of the motion and interaction of defects. Prediction and understanding of mechanical properties of irradiated metals requires simulation of dislocation–obstacle interactions. Models based on the continuum approximation are now being extended by large-scale MD simulations of the motion of dislocations gliding through irradiation-induced features such as voids and precipitates, and these reveal the strength and weakness of the earlier studies. Dynamic effects at temperatures greater than 0 K are also being investigated. The place of modelling in the multiscale problems of radiation damage is emphasised.

Ion implantation effects in silicon with high carbon content characterised by photoluminescence

The evolution with annealing of defects in self-ion implanted silicon with high carbon content has been investigated by photoluminescence (PL). The PL spectra show that the high-content carbon can effectively prevent the formation of {113} self-interstitial aggregates defect in silicon of implant dose 1013 and 1014cm−2 and largely suppress the formation of {113} defect at higher implant doses. By trapping and storing the excess interstitials a variety of stable carbon-related clusters are formed, which could persist to quite high annealing temperature. The strong asymmetry of the PL band near 910meV, with a long tail on the high-energy side, may originate from the size distribution of Ostwald ripening carbon-related clusters.

Physics-Based Diffusion Simulations for Preamorphized Ultrashallow Junctions

AbstractIn recent years there have been major advances in our understanding of the energetics, Ostwald ripening and transformations between various types of extended self-interstitial defect in Si and Ge ion-implanted silicon. As a result we can now predict the detailed time- and temperature-dependent supersaturation of interstitials during thermal evolution of these defects. This opens the way to predictive simulation of transient enhanced diffusion and dose loss in preamorphized ultrashallow junctions, where dopant movement is driven by free interstitials emitted by self-interstitial “end-of-range” defects. We present recent progress on this topic, emphasizing novel effects in highly doped ultrashallow junctions. Two key influences – the chemical pump effect due to the high concentration of dopants in ultrashallow junctions, and the ‘long hop’ behaviour of the dopant – are discussed in detail. The paper concludes by presenting simulation results that explain the recent observation of ‘uphill diffusion’ of B ultrashallow junction profiles.

Molecular-dynamics simulations of crystal growth from melted Si: Self-interstitial formation and migration

Molecular-dynamics simulations of crystal growth from melted Si have been performed using the Tersoff potential to analyze the defect formation and migration processes. We observed that a five-membered ring generated at the solid/liquid interface initiated self-interstitial defect formation. The formation and migration energies of the obtained defect were calculated to be 3.85 and 0.94 eV, respectively. The sum of the calculated formation and migration energies, 4.79 eV, is in good agreement with the experimental activation energy of self-diffusion in crystal Si.

Modelling atomic scale radiation damage processes and effects in metals

Primary knock-on atoms (PKAs) that recoil under collision from energetic atomic particles such as neutrons or ions are the principal source of radiation damage effects in metals. At high enough recoil energy (greater than ~ 1 keV), a PKA creates a cascade of atomic displacements, which are the origin of the self-interstitial and vacancy defects that give rise to property changes. The time and length scales of the cascade process are of picosecond and nanometre order, respectively, and are ideally suited to atomic scale computer simulations such as molecular dynamics. This method has been used extensively to investigate displacement cascades in metals. The paper reviews recent progress in this field. It includes results dealing with the effect of PKA energy on defect formation in various metals. It is shown that in addition to data on the number of defects produced, computer simulation can provide quantitative information on the distribution of defects created in clusters. This was not available from earlier models and so the nature of the primary damage state is now much clearer. Molecular dynamics is also being used to reveal the nature of the motion and interaction of defects and their clusters, and to simulate dislocation-obstacle interactions. This detailed atomic level information about the stability, motion, and interaction of defects will lead to the successful development of multiscale models to describe the evolution of radiation damage microstructure and its impact on material performance. The place of atomic scale modelling in the multiscale problem of radiation damage is discussed.