Self-interstitial Clusters Research Articles

A study of fully coordinated precursors in silicon using the Ackland potential

Structural models of compact fully coordinated self-interstitial clusters in silicon are reported. Such clusters can play an important role during the initial stages of formation of a dangling bond chain in the 〈1 1 0〉 direction. The chains form basic units for the formation of six, seven and eight membered rings observed in {3 1 1} defects. Energy minimisation for sizes up to 4 occurs due to elimination of dangling bonds. A change in the growth model by dissolution from compact cluster to dangling bond chain can possibly explain the experimentally reported statistical barrier in the formation of clusters of size greater than 8.

Mobility of self-interstitial atom clusters in vanadium, tantalum and copper

Molecular dynamics (MD) simulations were performed to investigate the mobility of isolated self-interstitial atoms (SIAs) and their clusters in V, Ta and Cu. The migration of an isolated SIA is accompanied by rotation of a dumbbell axis to the close-packed direction of metals. The migration of an SIA cluster strongly depends on its structure. A relatively smaller-size cluster can migrate with simultaneous rotation of the axes of SIA pairs in the cluster to the same close-packed direction, which is the glissile configuration of the cluster. The transformation to the glissile configuration takes place more frequently than the dumbbell rotation of an isolated SIA in V and Ta, while it takes place less frequently in Cu. The smaller cluster can still change its diffusion direction. A greater-size cluster in the bcc metals, on the other hand, has the thermally stable form of densely-packed, parallel crowdions. It migrates without any changes of diffusion direction. The migration behavior of 7-SIAs clusters in Ta was also evaluated as a function of tensile and compressive strains.

Unexpected dynamics for self-interstitial clusters in silicon.

Ab initio molecular-dynamics simulations of self-interstitial clusters in Si show that I2 and the most stable of the I3 (" I(a)(3)") clusters diffuse extremely fast. In these clusters, the I's share a single bond-centered (BC) site. The metastable I(b)(3) cluster involves three adjacent BC sites. Simulations show that the three I's exchange sites with each other, but the center of the defect remains at the same place. Simulations with I1 and I4 show no diffusion on the same time scale.

Migration kinetics of the self-interstitial atom and its clusters in bcc Fe

Abstract Self-interstitial atoms (SIAs) and SIA clusters are produced in displacement cascades during irradiation of a material with high-energy particles. The migration kinetics of such defects are a critical factor in controlling microstructure evolution and the ensuing changes in mechanical properties. In this study, extensive molecular dynamics (MD) simulations were performed on the diffusion of the SIA and its clusters in bcc Fe. Diffusivities were calculated for various SIA cluster sizes. It was found that, although the diffusivity itself decreases as the SIA cluster size increases, their activation energy for migration is very small and does not increase with size, in contrast with previous assumptions. Based on previous results obtained by Wirth et al. and the current calculations, we study the mechanism of single SIA diffusion by a kinetic Monte Carlo technique. The resulting model is consistent with experiments. An important conclusion of this study is that the ‘effective’ migration energy of the single SIA (0.17eV in the present MD study) is smaller than the activation energy for stage IE recovery. The proposed model explains all the details of the low temperature recovery stages. ID and IE, of bcc Fe without the need to invoke the existence of two independent interstitial configurations.

Modeling Cascade Aging in Dilute Fe-Cu Alloys

ABSTRACTThe continued safe operation of nuclear reactors and their potential for lifetime extension depends on ensuring reactor pressure vessel integrity. Reactor pressure vessels and structural materials used in nuclear energy applications are exposed to intense neutron fields that create highly non-equilibrium defect concentrations, consisting of a shell of self-interstitial atom and clusters surrounding a vacancy-rich core, over picosecond time scales. This spatially correlated defect production initiates a long chain of events responsible for microstructure evolution and hence irradiation embrittlement. In this paper, we describe the combined use of molecular dynamics (MD) and kinetic lattice Monte Carlo (KMC) to simulate the long-term rearrangement (aging) of displacement cascades in dilute Fe-Cu alloys. The simulations reveal the formation of a continuous distribution of three dimensional cascade vacancy-Cu cluster complexes and demonstrate the critical importance of spatial, as well as short and long-time correlated processes that mediate the effective production of primary defects. Finally, this approach can generate production cross-sections for vacancy-Cu clusters that can then be used in rate theory type models of long term global micro and microstructural evolution.

A New Kinetic Model for The Nucleation and Growth of Self-Interstitial Clusters in Silicon

ABSTRACTA model for nucleation and growth of {311} defects is proposed on the basis of thermodynamic and kinetic considerations. Simulated results are discussed and compared to experimental results found in the literature. According to our model it is found that formation energies of self-interstitial clusters depends on the local interstitial supersaturation. Physical parameters extracted from experimental results by inverse modeling are in good agreement with recent values published in the literature.

Computer simulation of defects interacting with a dislocation in Fe and Ni

In order to investigate the fundamental aspects of damage evolution under irradiation computer simulations of the interaction between a dislocation and point defects such as a self-interstitial atom (SIA), a vacancy and interstitial clusters have been performed for various configurations. It is found both in Fe and Ni that a crowdion with axis parallel to the Burgers vector of an edge dislocation interacts more strongly than those with other axis orientations. The same tendency was seen for the dumbbell. The capture range (capture area) within which SIAs are trapped by an edge dislocation is larger for Ni than for Fe, and that for vacancies is much smaller than that for SIAs, suggesting that the bias factor in Ni is larger than that in Fe.

Mechanism of one-dimensional glide of self-interstitial atom clusters in α-iron

Mechanism of one-dimensional glide of self-interstitial atom clusters in α-iron

Mechanism of one-dimensional glide of self-interstitial atom clusters in α-iron

Abstract Recent molecular dynamics (MD) computer simulations of pure copper and iron have shown that clusters consisting of up to a few tens of self-interstitial atoms (SIAs) are highly mobile along close-packed crystallographic directions. This effect has important consequences for microstructure evolution in irradiated metals and so it is desirable to investigate the mechanisms of cluster motion. In the present paper, results of MD modelling of the thermally-activated motion of clusters of three, nine and 17 SIAs in α-iron in the temperature range from 90 to 1400 K are analysed. The correlation between the motion of the centre of mass of a cluster and the individual jumps of its constituent SIAs is revealed. It is found that the SIAs in a cluster jump almost independently and their jump frequency depends on the number of SIAs in the cluster. This leads to a simple relationship between the jump frequency of a cluster and the number of SIAs in it. The reason for the deviation of the cluster jump frequency from a simple Arrhenius relationship is discussed. It is shown that such clusters only exhibit an effectively random walk, that is a correlation factor of one, when the jump length defining diffusion is taken to be 3b to 4b, where b is the magnitude of the vector ½(111).

Simulation of Boron Diffusion in High-Dose BF2 Implanted Silicon

We have simulated the transient enhanced diffusion (TED) of boron (B) after amorphizing BF2 ion implantation in silicon. A unified simulation is done based on the models for B diffusion, for TED by self-interstitial clusters, for B clustering and B precipitation, and for end-of-range (EOR) defects. The simulation overestimates the diffusion using the normal values for the efficiency of EOR defects as a source of self-interstitials. The simulation well reproduces the experimental profiles when the efficiency is reduced so that the defects maintain self-interstitial concentration at thermal equilibrium values. This reduction is attributable to the presence of fluorine at EOR defect sites, which may prevent the release of self-interstitials. In addition, the second peak near the amorphous/crystalline (a/c) interface observed in experimental profiles is reproduced, and the peak is attributed to B precipitates.

Transient Enhanced Diffusion and Deactivation of High-Dose Implanted Arsenic in Silicon

We have simulated the transient enhanced diffusion (TED) of high-concentration arsenic (As) in silicon during post-implantation annealing. A unified simulation was done, based on models for As diffusion, for TED by self-interstitial clusters, and for end-of-range (EOR) defects. We have taken into account As complex formation and As precipitation, which cause the As deactivation. We have satisfactorily fitted As depth profiles at high doses (1–5×1015 cm-2) in a wide range of annealing conditions (750–1000°C). The As complex formation plays an important role in determining the diffusion profiles through the self-interstitial emission upon the formation at lower temperatures and through As deactivation at higher temperatures. The simulation results suggest that boron (B) segregation toward the As tail regions is associated with self-interstitial distributions determined by EOR defects and As profiles.

Cluster formation and growth in Si ion implanted c-Si

Formation condition and annealing kinetics of self-interstitial (I) clusters in ion implanted Si have been investigated. Deep level transient spectroscopy (DLTS) and photoluminescence (PL) measurements were performed on both p-type Czochralski Si samples implanted with Si ions at energies ranging from 40 keV to 1.2 MeV. They reveal that I-clusters form for implantation fluences above 1012 cm−2 and annealing temperatures higher than 550°C. Analysis of the annealing kinetics at temperatures in the range 550–700°C reveals that I-clusters dissociate with an energy depending on the implantation dose. The characteristic dissociation energy is ∼2.3 eV for 1×1012 cm−2 implants, and this value increased towards the typical {311} extended defects dissociation energy value (∼3.8 eV) by increasing the implantation fluence. Finally, the transition from I-clusters to {311} defects was followed using PL and DLTS in combination with transmission electron microscopy analysis. A PL line at 1375 nm has been associated to {311} extended defects and a threshold dose and annealing temperature for the extended defects formation identified.

Self-Interstitial clusters in silicon

AbstractIn this paper we propose structural models of self-interstitial clusters in silicon using the empirical potential method. Novel, fully co-ordinated compact clusters based on the hexagonal interstitial up to size four have been proposed. The energetics of their formation indicates that energy minimisation occurs due to elimination of dangling bonds. While the conventional dangling bond model yields an exponential decrease in the formation energy with size, we observe stable defects for sizes in multiples of four. The energy barrier required for a transition from compact model to the dangling bond chain model can possibly explain the experimentally observed energy barrier for sizes greater than eight.

The Effect of Carbon/Self-Interstitial Clusters on Carbon Diffusion in Silicon Modeled by Kinetic Monte Carlo Simulations

AbstractA new model for carbon diffusion in silicon that explains carbon diffusion during annealing at 850°C and 900°C in superlattice carbon structures grown by MBE is implemented using the Monte Carlo atomistic simulator DADOS. Carbon concentrations in the delta layers are 2×1020 cm−3, exceeding by far the solid solubility. The simple kick-out mechanism which incorporates the well established values of the product of diffusivity and equilibrium concentrations of intrinsic point defects and in-diffusion experiments of carbon in silicon does not explain the observed C diffusion profiles. A more detailed analysis of the experiments shows that, in order to fit them, a more unstable Ci is required. Therefore, we include the formation of clusters in the simulations. The formation of carbon/Si self-interstitial clusters promotes the premature break-up of Ci and the increase of the Si self-interstitial concentration in the carbon rich regions and, consequently, provides a better fit to the experiments. The low solubility of carbon in silicon at the annealing temperatures explains why these clusters are formed, even under conditions where the self-interstitial concentration is below the equilibrium value.

Interactions between mobile dislocation loops in Cu and α-Fe

The relevance of one-dimensionally gliding clusters in the understanding of the damage accumulation produced by the displacement cascades has been underlined by the production bias model. The properties and mobility of isolated clusters of vacancies and self-interstitials have been recently studied by molecular dynamics and valuable information about their diffusional characteristics is obtained. The next step in the understanding of radiation damage should include the possible reactions of these clusters with other clusters, dislocations and other sinks. In this paper we present the first results of a molecular dynamics study of interactions between glissile interstitial clusters and small dislocation loops in α-Fe and Cu. Different types of interactions have been studied between clusters of different sizes (from 12 to 91 defects) in the temperature range from 300 to 1000 K. As a result of the inter-cluster interactions both glissile and sessile clusters can be obtained and this depends on the metal, reaction type and size of the clusters. In general the probability to form sessile clusters increases for larger clusters and it is higher in Cu. The results obtained are discussed from the point of view of the difference in radiation damage effects in fcc Cu and bcc Fe.

Dislocation loop structure, energy and mobility of self-interstitial atom clusters in bcc iron

Molecular-statics and molecular-dynamics (MD) simulations based on the embedded-atom method (EAM) were used to model the energy and mobility of self-interstitial atom (SIA) clusters in bcc α-iron. Isolated SIAs and SIA clusters, directly produced in displacement cascades have significant impact on the microstructural evolution under neutron and high-energy charged particle beam irradiations. The SIA clusters are composed of 〈1 1 1〉 split dumbbells and crowdions bound by energies in excess of 1 eV. The clusters can be described as perfect prismatic dislocation loops with Burgers vector b=( a/2) 〈1 1 1〉. As the loops grow, SIAs fill successive jogged edge rows, with minimum free energy cusps found at the ‘magic’ numbers corresponding to un-jogged filled hexagonal shells. The total energy of the clusters is in excellent agreement with continuum elasticity dislocation theory predictions. However, the core region is extended compared to an isolated edge dislocation. The extended regions are preferentially located at the hexagonal corners of the loop, forming intrinsic kinks. As a result of the intrinsic kinks, the SIA clusters are highly mobile and undergo one-dimensional motion on their glide prism. The high cluster mobility is related to the easy motion of the edge segments which propagate the kinks along the loop periphery resulting in increments of prismatic glide. The corresponding activation energy for SIA cluster diffusion is less than 0.1 eV. Linking atomistic point defect cluster calculations dislocation theory provides a powerful tool in understanding radiation damage.

Electron irradiation effects in Si observed at 4.2–25 K by means of in situ transmission electron microscopy

We have observed electron-irradiation effects in Si at low temperature, utilizing in situ transmission electron microscopy. Amorphization is induced in crystalline silicon (c-Si) by high-energy electron (MeV) irradiation at low temperatures. The mechanism of amorphization in Si is discussed in terms of self-interstitial clustering. In addition, we have also observed the electron (0.3MeV) irradiation effects at 4.2K in c-Si by means of high-resolution transmission electron microscopy. We have found that numerous defects of a few nanometer in diameter are introduced. The characteristics of the defects differs from those of the known interstitial clusters such as the {113} defects. The accumulation of the defects never leads to amorphization.

Simulation of High-Concentration Phosphorus Diffusion in Silicon Taking into Account Phosphorus Clustering and Pile-Up

We have simulated the transient enhanced diffusion (TED) of high-concentration phosphorus (P) in silicon during post-implantation annealing. Based on the models for P diffusion, for TED by self-interstitial clusters, and for end-of-range (EOR) dislocations as both a sink for and source of self-interstitials, a unified simulation is done, taking into account P clustering and P pile-up. P clustering is taken into account only beneath EOR dislocations, and P pile-up is estimated by a diffusion-segregation term in the diffusion equations. We have satisfactorily fitted P depth profiles at high doses (∼1015 cm-2) in a wide range of annealing conditions (700–1000°C).

Stability of proximity gettering of platinum in silicon implanted with alpha particles at low doses

Platinum has been diffused into epitaxial n-type silicon at 700 °C from 10 to 50 min in steps of 10 min following implantation with 3.3 MeV alpha particles at a dose of 1×1013 cm−2. Thereafter, the samples were characterized using deep level transient spectroscopy (DLTS). All samples show only one deep level at 0.23 eV below the conduction band that is attributed to substitutional platinum. DLTS profiling reveals a decoration of the region of maximal damage by the platinum for diffusion times of 30 min or shorter with a platinum concentration peak in the region of the maximal vacancy concentration. However, for longer diffusion times, the peak of the platinum concentration decreases. An explanation is proposed where silicon self-interstitial clusters behind the projected range dissociate, and where the liberated self-interstitials will drive the platinum away from the region of maximal damage. In order to achieve an equilibrium distribution, the platinum then diffuses further into the bulk.

Simulation of High-Concentration Boron Diffusion in Silicon during Post-Implantation Annealing

We have simulated the transient enhanced diffusion (TED) and electrical activation of high-concentration boron (B) in silicon during post-implantation annealing. Based on the models for B diffusion, for TED by self-interstitial clusters, and for B clustering, a unified simulation is done, taking into account implantation-induced dislocations as a sink for self-interstitials and the solid solubility limit of B. To establish the initial profiles for higher doses, we used the maximum area density of self-interstitials and B concentration effective for the TED and B clustering. We have satisfactorily fitted B depth profiles at different doses (5×1014–5×1015 cm-2) in a wide range of experimental conditions (800–1000°C and 10 s–8 h).