Interstitial Configurations Research Articles

Defects in carbon implanted silicon calculated by classical potentials and first-principles methods

A comparative theoretical investigation of carbon interstitials in silicon is presented. Calculations using classical potentials are compared to first-principles density-functional theory calculations of the geometries, formation, and activation energies of the carbon dumbbell interstitial, showing the importance of a quantum-mechanical description of this system. In contrast to previous studies, the present first-principles calculations of the interstitial carbon migration path yield an activation energy that excellently matches the experiment. The bond-centered interstitial configuration shows a net magnetization of two electrons, illustrating the need for spin-polarized calculations.

A New Paramagnetic Nitrogen Center in Natural Titanium-Containing Diamonds

A new type of nitrogen-related center in natural diamond labeled NU1 is identified as a 〈100〉 split interstitial configuration by means of electron paramagnetic resonance (EPR) and photoluminescence (PL) techniques. In PL this center is seen as an electron-vibration system with a zero-phonon line at 485 nm in the crystals containing S1/OK1 and 440.3 nm/N3 centers. NU1 EPR spectra are described by a spin-Hamiltonian with parameters: S = ½, I = 1 and A xx (N) = 22.5 G, A yy (N) = 19.5 G, A zz (N) = 20.55 G, g xx = 2.0043, g yy = 2.0032, g zz = 2.0020. Directions of A zz and g zz coincide and correspond to [001]. The directions of A xx and A yy coincide with those of g xx and g yy and correspond to [110] and [−110], respectively. Analysis of the phonon structure of the NU1 center suggested that titanium can be the second atom together with nitrogen in the structure of a split interstitial.

Ab initio study of intrinsic, H, and He point defects in hcp-Er

Ab initio calculations based on density functional theory have been performed to determine the properties of self-interstitial atoms (SIAs), vacancies, and single H and He atoms in hcp-Er. The results show that the most stable configuration for a SIA is a basal octahedral configuration, while the octahedral (O), basal split, and crowdion (C) interstitial configurations are less stable, followed by the split ⟨0001⟩ dumbbell and tetrahedral configurations. For both H and He defects, the formation energy of an interstitial atom is less than that of a substitutional atom in hcp-Er. Furthermore, the tetrahedral interstitial position is more stable than an octahedral position for both He and H interstitials. The hybridization of the He and H defects with Er atoms has been used to explain the relative stabilities of these defects in hcp-Er.

Interstitials in tetrahedrally close-packed phases: C, N, O, and F inβ-tungsten from first principles

Several tetrahedrally close-packed (tcp) phases, such as $\ensuremath{\beta}\text{-W}$, $\ensuremath{\beta}\text{-Ta}$, and $\ensuremath{\beta}\text{-U}$, are believed to be stabilized by impurities. Here we analyze the various ways in which impurities can be dissolved in tcp structures paying special attention to interstitial configurations in the $\ensuremath{\beta}\text{-W}$ (A15) structure. We find that at most there are only seven interstitial positions possible. Through ab initio calculations we show that common impurities such as C, N, O, and F, dissolve interstitially in $\ensuremath{\beta}\text{-W}$ and that N, O, and F interstitials prefer the same position in the $\ensuremath{\beta}\text{-W}$ (A15) structure.

First-principles study of neutral silicon interstitials in 3C- and 4H-SiC

The structures and stability of single silicon interstitials in their neutral state are investigated via first principles calculations in 3C- and 4H-SiC. By carefully checking the convergence with Brillouin zone (BZ) sampling and supercell size, we explain the disagreement between previous published results and show that the split interstitial along ⟨110⟩ direction and tetrahedrally carbon coordinated structure have competing formation energies in the cubic polytype. A new migration mechanism for the silicon interstitial in the neutral state is presented here, which could be important for the evolution of defect populations in SiC. For 4H-SiC, the most energetically favourable silicon interstitial is found to be the split interstitial configuration ISisp⟨110⟩ but situated in the hexagonal layer. The defect formation energies in 4H-SiC are, in general, larger than those in 3C-SiC, implying that the insertion of silicon interstitial introduces a large lattice distortion to the local coordination environments and affects even the second- or third-nearest neighbours. We also present a comparison between well converged plane-waves calculations and calculations with three localised orbital basis sets; one of them, in spite of providing a reasonable description for bulk properties, is clearly not suitable to describe interstitial defects.

Formation of Frenkel pairs and diffusion of self-interstitial in Si under normal and hydrostatic pressure: Quantumchemical simulation

A theoretical modeling of the formation of Frenkel pairs and the diffusion of a self-interstitial atom in silicon crystals at normal and high (hydrostatic) pressures has been performed using quantum-chemical (NDDO-PM5), methods. It is shown that, in a silicon crystal, the most stable configuration of a self-interstitial atom in the neutral charge state ( I 0 ) is the split configuration 〈1 1 0〉. The tetrahedral configuration is not stable, an interstitial atom being shifted from T position in a new position T 1 on a distance Δ d =0.2 Å. The hexagonal configuration is not stable in NDDO approximation. The split 〈1 1 0〉 interstitial configuration remains the more stable configuration under hydrostatic pressure ( P <80 kbar). The activation barriers for diffusion of self-interstitial atoms in silicon crystals are determined to be as follows: E a (〈1 1 0〉→ T 1 )=0.59 eV, E a ( T 1 →neighboring T 1 )=0.1 eV and E a ( T 1 →〈1 1 0〉)=0.23 eV. The hydrostatic pressure ( P <80 kbar) increases the activation barrier for diffusion of self-interstitial atoms in silicon crystals. The energies of the formation of a separate Frenkel pair, a self-interstitial atom, and a vacancy are determined. It is demonstrated that the hydrostatic pressure decreases the energy of the formation of Frenkel pairs.

Formation and diffusion of self-interstitial atoms in silicon crystals under hydrostatic pressure: Quantum-chemical simulation

A theoretical modeling of the formation of Frenkel pairs and the diffusion of a self-interstitial atom in silicon crystals at normal and high (hydrostatic) pressures has been performed using molecular dynamics, semiempirical quantum-chemical (NDDO-PM5, PM6), and ab initio (SIESTA) methods. It is shown that, in a silicon crystal, the most stable configuration of a self-interstitial atom in the neutral charge state (I 0) is the split configuration 〈110〉. The shifted tetrahedral configuration (T 1) is stable in the singlet and triplet excited states, as well as in the charge state Z = +2. The split 〈110〉 interstitial configuration remains stable under hydrostatic pressure (P ≤ 80 kbar). The activation barriers for diffusion of self-interstitial atoms in silicon crystals are determined to be as follows: ΔE a (Si)(〈110〉 → T 1) = 0.59 eV, ΔE a (Si)(T 1 → T′1) = 0.1 eV, and ΔE a (Si)(T 1 → 〈110〉) = 0.23 eV. The hydrostatic pressure (P ≤ 80 kbar) increases the activation barrier for diffusion of self-interstitial atoms in silicon crystals. The energies of the formation of a separate Frenkel pair, a self-interstitial atom, and a vacancy are determined. It is demonstrated that the hydrostatic pressure decreases the energy of the formation of Frenkel pairs.

First-principles approach to the properties of point defects and small helium-vacancy clusters in palladium

First-principles calculations based on density functional theory (DFT) have been performed to study the properties of interstitial helium atoms, the vacancy, substitutional, and small helium-vacancy clusters HemVn (m, n=0–4) in palladium. The result indicates that the vacancy has the strongest ability of capturing helium atoms and the octahedral interstitial configuration is more stable than the tetrahedral one, while the energy difference between them is very small. In the palladium crystal, helium atom will migrate from one octahedral interstitial site to another one through the O–T–O path. The formation energies and binding energies of an interstitial helium atom and an isolated vacancy to the helium-vacancy clusters are also determined in palladium. It is found that the formation energies increase with the increasing of helium atoms and the binding energies mainly depend on the helium to vacancy ratio of the clusters rather than the cluster size.

Study on C–W interactions by molecular dynamics simulations

By means of molecular dynamics simulations using bond-order potential (BOP), we have investigated the interactions between carbon (C) atoms and bcc tungsten (W). At finite temperature (T=300K) with incident energy of C atoms ranging from 0.5 to 100eV at normal incidence, the projected range distribution as a function of incident energy and the average depth have been depicted. The properties of vacancy, vacancy migration, interstitial and substitutional C atoms in W have been determined. The most stable configuration for an interstitial C atom in W is in octahedral position and the lattice distortion around the C atom in octahedral interstitial configuration occurs along 〈100〉 and 〈110〉 directions. The mutual interaction between a vacancy and near interstitial C atom is also studied.

Ab initio study of Kr in hcp Ti: Diffusion, formation and stability of small Kr–vacancy clusters

Ab initio electronic structure calculations have been performed to study the formation and migration of Kr impurities, and the stability of small Kr–vacancy clusters for clusters with up to four vacancies and four Kr atoms, in hcp Ti. Both the substitutional and the interstitial configurations of Kr are found to be stable. The octahedral configuration is however found to be more stable than the tetrahedral. Interstitial Kr atoms are shown to have attractive interactions and a low migration barrier, suggesting that, at low temperature, Kr bubble formation is possible, even in the absence of vacancies. We also find vacancy clusters to be stable. The binding energies of an interstitial Kr atom and a vacancy to a Kr–vacancy cluster are obtained from the calculated formation energies of the clusters. The stability of small-vacancy clusters is found to be dependent on Kr–vacancy ratio. The trends of the calculated binding energies are discussed in terms of providing further insights on the behaviour of Kr in implanted Ti.

Hydrogen in beryllium: Solubility, transport, and trapping

The paper presents the results of ab initio simulation of hydrogen properties in beryllium. Both interstitial hydrogen positions in the lattice and various hydrogen positions in a vacancy have been studied. The most energetically favorable interstitial hydrogen configuration among the four considered high-symmetry configurations is the basal tetrahedral one, in agreement with the earlier predictions. The most probable diffusion pathway for hydrogen atoms in the bulk involves the exchange of octahedral and basal tetrahedral positions with the effective migration energy of $\ensuremath{\sim}0.4\text{ }\text{eV}$. For hydrogen atom in a vacancy, an off-center (nearly basal tetrahedral) configuration is definitely preferred. Addition of more hydrogen atoms to a vacancy remains energetically favorable up to at least five hydrogen atoms, though the binding energies fall down with the increase in the number of hydrogen atoms in the vacancy.

The energetics of helium and hydrogen atoms in β-SiC: an ab initio approach

Silicon carbide is a prime candidate for plasma-facing materials in future fusion reactors. The formation energies of various interstitial configurations of helium and hydrogen atoms in β-SiC were estimated based on density functional theory. Special consideration was given to the helium and hydrogen interstitials as the bubble seeds in β-SiC. From an energetic point of view, only one helium atom could position itself into the tetrahedral sites. However, up to three hydrogen atoms could easily position themselves into the tetrahedral sites by forming a stable H2 molecule or a 3H-trimer that was newly identified in this study. Based on the different behaviors of helium and hydrogen, an explanation is proposed for the experimental observations of bubble formation in irradiated β-SiC.

Possible origins of defect-induced magnetic ordering in carbon-irradiated graphite

We investigated possible sources of defect-induced magnetic ordering in carbon-irradiated graphite from first-principles calculations. Among candidate structures with interstitial defect configurations that could be generated during carbon irradiation processes, two metastable configurations with finite magnetic moments were identified. They are coupled ferromagnetically to their neighboring defects, thereby enabling them to contribute to the observed macroscopic magnetic ordering. The Ruderman-Kittel-Kasuya-Yosida interaction is considered as a possible mechanism for the ferromagnetic ordering.

Stability of Neutral Silicon Interstitials in 3C- and 4H-SiC: A First-Principles Study

The structural stability and properties of single silicon interstitials in their neutral state are investigated via ab initio methods in 3C- and 4H-SiC. By carefully checking the convergence with Brillouin Zone (BZ) sampling and supercell size we show that the split interstitial along &lt;110&gt; direction and tetrahedrally coordinated structure have similar formation energies in the cubic polytype. We discuss possible artifacts coming from the well known Density Functional Theory (DFT) underestimation of the band gap, which is particularly relevant for 3C-SiC. For 4H-SiC, the most energetically favorable silicon interstitial is found to be the split interstitial configuration ISisp&lt;110&gt; but situated in the hexagonal layer. The defect formation energies in 4H-SiC are in general larger than those in 3C-SiC, implying that the insertion of silicon interstitial introduces a large lattice distortion to the local coordination environments and affect even the second- or third-nearest neighbors. We also present an extensive comparison between well converged plane waves calculations and SIESTA [1,2] calculations based on localised orbitals basis sets.

Transportation of Na and Li in Hydrothermally Grown ZnO

AbstractSecondary ion mass spectrometry has been applied to study the transportation of Na and Li in hydrothermally grown ZnO. A dose of 1015 cm-2 of Na+ was implanted into ZnO to act as a diffusion source. A clear trap limited diffusion is observed at temperatures above 550 °C. From these profiles, an activation energy for the transport of Na of ∼1.7 eV has been extracted. The prefactor for the diffusion constant and the solid solubility of Na cannot be deduced independently from the present data but their product estimated to be ∼3 × 1016 cm-1s-1. A dissociation energy of ∼2.4 eV is extracted for the trapped Na. The measured Na and Li profiles show that Li and Na compete for the same traps and interact in a way that Li is depleted from Na-rich regions. This is attributed to a lower formation energy of Na-on-zinc-site than that for Li-on-zinc-site defects and the zinc vacancy is considered as a major trap for migrating Na and Li atoms. Consequently, the diffusivity of Li is difficult to extract accurately from the present data, but in its interstitial configuration Li is indeed highly mobile having a diffusivity in excess of 10-11 cm2s-1 at 500 °C.

Modification of the electronic properties of rubrene crystals by water and oxygen-related species

The presence of impurities in organic semiconductors is an important limitation for the performance of related devices. Here, we investigate with density-functional theory calculations the effect of water and oxygen-related species on the properties of the prototype system of rubrene, the current record-holder organic semiconductor in terms of carrier mobilities. We identify the most stable impurity structures, with species in either substitutional or interstitial configurations, and we analyze their complex role in changing the shape and profile of rubrene energy bands. In certain cases the impurities either give rise or help annihilate carrier traps, and we discuss the relevance of our findings for the optimization of rubrene-based electronic systems.

A density functional theory assessment of the clustering behaviour of He and H in tungsten

We have used density functional theory based ab initio calculations to investigate the tendency of He and H to form clusters. For both species the most stable interstitial configuration is in a tetrahedral site, however their clustering tendencies are totally different. The He–He interaction is purely elastic in nature and as such highly binding at close separation distances. The H–H interaction on the other hand is almost negligible since the elastic binding effect is compensated for by the change in effective position of the H states in the density of states. He atoms always bond more strongly to He xH y complexes in a vacancy than H atoms.

Deuterium occupation of tetrahedral sites in palladium

The long-standing controversy over the occupation by hydrogen of tetrahedral interstices in palladium has been addressed experimentally and theoretically. Using the highest resolution neutron powder diffractometer available, diffraction profiles were recorded from single-phase samples obtained by loading Pd with deuterium in situ at 310 i at D2 pressures up to 90 bar. Rietveld profile analysis showed that a model including tetrahedral occupancy was necessary to properly fit the experimental diffraction profiles. The maximum absolute tetrahedral occupancy was found at a deuterium-to-metal atomic ratio of 0.6, where about one-third of all D atoms were in tetrahedral sites. At the lowest and highest D concentration, the tetrahedral fraction approached zero. The energy of formation was calculated, based on density-functional theory, for numerous configurations of octahedral and tetrahedral interstitials in a supercell, which modeled stoichiometries Pd8Hn such that n=1,2, . . .8. For Pd8H3, the minimum formation energy was found with 1-2 tetrahedral atoms. For all other stoichiometries, the minimum formation energy was 0-1 tetrahedral atoms. Thus, the calculations are in excellent qualitative agreement with experiment and support the reality of tetrahedral occupancy.

Influence of hydrostatic pressure on the native point defects in wurtzite ZnO: Ab initio calculation

The formation energies and transition energy levels of native point defects in wurtzite ZnO under applied hydrostatic pressure are calculated using the first-principle band-structure methods. We find that the pressure coefficient of the ( 2 + / 0 ) level for oxygen vacancy is larger than that of the ( 2 + / 1 + ) level for zinc interstitial, which demonstrates that the donor level of oxygen vacancy is deeper than that of zinc interstitial, therefore the latter is the more probable electron resource in native n-type ZnO. And the significantly different pressure dependence of the transition levels between them can be used to determine the origin of the green luminescence center in ZnO. Zinc octahedral interstitial and oxygen tetrahedral interstitial configurations became the dominant defects under 5 GPa at their favorable growth conditions, respectively. The formation of defects under applied pressure is the result of fine interplay between internal strains, charges on the defects and applied external pressures.

First-principles study of the hydrogen doping influence on the geometric and electronic structures of N-doped TiO 2

We employed DFT calculations to study the geometric and electronic structures of N- and NH-doped anatase TiO 2 systems. With N dopant concentrations of 2.1% and 1.0%, the substitutional NH-doping resulted in bandgap narrowings of 0.12 and 0.13 eV, respectively, very close to that resulted from substitutional N-doping (0.12 and 0.11 eV). For interstitial N- and NH-doping with a nitrogen concentration of 2.1%, only NH-doping resulted in a bandgap narrowing of 0.07 eV. For both substitutional and interstitial NH-doping configurations, the crystalline structure adjacent to the NH dopants was heavily distorted, which might enhance the photocatalytic efficiency.