On the influence of extrinsic point defects on irradiation-induced point-defect distributions in silicon

A semi-quantitave model describing the influence of interfaces and stress fields on {113}-defect generation in silicon during 1-MeV electron irradiation, is further developed to take into account also the role of extrinsic point defects. It is shown that the observed distribution of {113}-defects in high-flux electron-irradiated silicon and its dependence on irradiation temperature and dopant concentration can be understood by taking into account not only the influence of the surfaces and interfaces as sinks for intrinsic point defects but also the thermal stability of the bulk sinks for intrinsic point defects. In heavily doped silicon the bulk sinks are related with pairing reactions of the dopant atoms with the generated intrinsic point defects or related with enhanced recombination of vacancies and self-interstitials at extrinsic point defects. The obtained theoretical results are correlated with published experimental data on boron-and phosphorus-doped silicon and are illustrated with observations obtained by irradiating cross-section transmission electron microscopy samples of wafers with highly doped surface layers.     

Evidence for a new class of defects in highly n-doped Si: donor-pair-vacancy-interstitial complexes

Electron channeling experiments performed on individually scanned, single columns of atoms show that in highly n-type Si grown at low temperatures the primary electrically deactivating defect cannot belong to either the widely accepted class of donor-vacancy clusters or a recently proposed class of donor pairs. First-principles calculations suggest a new class of defects consisting of two dopant donor atoms near a displaced Si atom, which forms a vacancy-interstitial pair. These complexes are consistent with the present experimental results, the measured open volume of the defects, the observed electrical activity as a function of dopant concentration, and the enhanced diffusion of impurities in the presence of deactivated dopants.     

Nano-scale properties of defects in compound semiconductor surfaces

The present work reviews atomic-scale properties of point defects and dopant atoms exposed on and in cleavage surfaces of III–V and II–VI semiconductors. In particular, we concentrate on the identification of the types of defects and dopant atoms, the determination of the localized defect states, the electrical charge, and lattice relaxation, as well as the measurement of the interactions between different defects and/or dopant atoms. The physical mechanisms governing the formation of defect complexes, the compensation of dopant atoms, the pinning of the Fermi level, and the stability of defects are discussed in the light of the available theoretical information and experimental results obtained mostly by scanning tunneling microscopy.     

Defects in III–V semiconductor surfaces

This work reports the measurement of the nano-scale physical properties of surface vacancies and the extraction of the types and concentrations of dopant atoms and point defects inside compound semiconductors, primarily by cross-sectional scanning tunneling microscopy on cleavage surfaces of III–V semiconductors. The results provide the basis to determine the physical mechanisms governing the interactions, the formation, the electronic properties, and the compensation effects of surface as well as bulk point defects and dopant atoms. Received: 10 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Dependence of anomalous phosphorus diffusion in silicon on depth position of defects created by ion implantation

Transient enhanced diffusion of phosphorus in silicon has been investigated for implants below and above the threshold for a complete amorphization. Rapid thermal processes (electron beam) and conventional furnaces have been used for the annealing. In the case of implants below amorphization, a strong enhanced diffusion, proportional to the amount of damage produced, has been observed. The extent of the phenomenon is practically independent of the damage depth position. In contrast to this, the formation of extended defects at the original amorphous-crystalline interface makes the diffusivity strongly dependent on depth in the case of post-amorphized samples. No enhanced diffusion effect is observed if the dopant is confined in the amorphous layer, while a remarkable increase in the diffusivity is detected for the dopant located in the crystalline region beyond the amorphous-crystalline interface.Damage distribution after implantation and its evolution during annealing have been determined by double crystal x-ray diffraction and correlated to anomalous P diffusivity. A qualitative distribution of the interstitial excess in solution in the silicon lattice during annealing is proposed for the two different cases. These point defects, released by the dissolution of the interstitial clusters produced by the implanted ions, have been identified as responsible for the observed enhanced P diffusion.     

Aging behavior and ionic conductivity of ceria-based ceramics: a comparative study

An understanding of high-temperature aging effects on the electrical properties of electrolytes is very important in selecting optimum compositions for practical applications. The aging behavior and mechanisms of doped zirconia ceramics have been extensively studied. However, little information is available regarding the aging behavior of ceria-based electrolytes. The present study has demonstrated that a high-temperature aging at 1000 °C has a significant effect on the ionic conductivity of the Y- or Gd-doped ceria (Ce_1−xY_xO_2−δ and Ce_1−xGd_xO_2−δ), especially in the case of the Gd doping. The aging behavior is characterized by a critical dopant concentration, above which the aging has a detrimental effect on the conductivity of the doped ceria ceramics. The aging behavior in the doped ceria cannot be explained using the aging mechanisms applied to the doped zirconia. Instead, the formation of the microdomains in the doped ceria has been acknowledged to be the main contribution to the aging behavior of the Y- or Gd-doped ceria ceramics. The formation ability of microdomains has been estimated to be in the order of La³⁺>Gd³⁺>Y³⁺, based on the degree of size mismatch between the dopant ion and Ce⁴⁺ ion. The critical dopant concentrations at which the microdomains start to form for La³⁺, Gd³⁺ and Y³⁺ in the doped ceria ceramics are x=0.15, 0.2 and 0.25, respectively. This critical dopant concentration is also an important indication: below which the conductivity is governed by only the association enthalpy, and above which the conductivity is dominated mainly by the microdomains rather than the association enthalpy.     

Vacancy-impurity complexes in highly Sb-doped Si grown by molecular beam epitaxy

Positron annihilation measurements, supported by first-principles electron-structure calculations, identify vacancies and vacancy clusters decorated by 1-2 dopant impurities in highly Sb-doped Si. The concentration of vacancy defects increases with Sb doping and contributes significantly to the electrical compensation. Annealings at low temperatures of 400-500 K convert the defects to larger complexes where the open volume is neighbored by 2-3 Sb atoms. This behavior is attributed to the migration of vacancy-Sb pairs and demonstrates at atomic level the metastability of the material grown by epitaxy at low temperature.     

Point defects patterning in irradiated α-zirconium: numerical study in the framework of the rate theory

We study point defects patterning in irradiated α-zirconium numerically. In our consideration, we exploit reaction-rate theory by taking into account sink density dynamics and a change in internal stress fields due to the presence of defects. Dynamics of defect populations are studied at different irradiation conditions. It is found that point defects patterning is accompanied by a formation of vacancy clusters; their morphology change is governed by irradiation temperature and damage rate. By using statistical analysis of spatially distributed vacancy clusters, it was shown that the characteristic size of these clusters is of several nanometers. Vacancy clusters' occupation densities and distributions over their sizes are studied in detail.     

Transformation of point defects in silicon dioxide during annealing

In our previous studies, we have demonstrated that annealing of silicon dioxide in the absence of oxygen leads to the formation of silicon clusters near the surface. The mechanism of the formation of silicon clusters by this technique has not been sufficiently investigated. However, it has been found that the rate of the formation of nanoclusters and their sizes depend on the concentration of point defects in the silicon dioxide and on the concentration of impurities, for example, hydroxyl groups. As a continuation of these studies, in the present work we have investigated changes in the concentration of point defects in silicon dioxide films during high-temperature annealing. A new method has been proposed for the evaluation of changes in the concentration of point defects in silicon dioxide films before and after annealing. A model of the transformation of point defects in silicon dioxide into silicon nanoclusters due to the high-temperature annealing has been developed.     

Dopant type dependency of domain development in rare-earth-doped ceria: An explanation by computer simulation of defect clusters

Defect clusters in several rare-earth-doped ceria (doped with Y, Sm, Gd, Dy and Yb) containing up to four oxygen vacancies and eight dopant cations have been simulated and compared. In all doped ceria systems, the binding energy of the clusters increases with increasing cluster size and the oxygen vacancies tend to form curved chains in the clusters. Moreover, the capability of the growth of defect cluster is affected by dopant type, which can explain the dopant type dependency of domain development with increasing doping concentration in heavily doped ceria.     

Simulation of retarded diffusion of antimony and enhanced diffusion of phosphorus in silicon

The paper is concerned with the influence of point defects on dopant diffusion in silicon. This influence is analysed by means of comparing the experimental results of Mizuo and Higuchi with our simulation. The experiments deal with the oxidation retarded diffusion (ORD) of Sb and the oxidation enhanced diffusion (OED) ofP in FZ silicon at 1100°C. The simulation is carried out by using a physical model without simplifying assumptions. It is shown that simplifying assumptions are not admissible. A reasonable set of parameters is deduced from this analysis. As each parameter represents a physical effect, information about the importance of bulk and surface recombination of point defects and about the equilibrium concentration values and diffusion coefficients of diffusing species are obtained. It turns out that the influence of the surface is decisive for the distribution of point defects.Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Point Defect Production Under High Internal Stress Without Dislocations in Ni and Cu

Kiritani et al. have observed a large number of small vacancy clusters without dislocations at the tip of torn portions of fcc metals such as Au, Ag, Cu and Ni. Small vacancy clusters, rather than dislocation cell structures, have also been observed after high-speed compressive deformation, suggesting the possibility of plastic deformation without dislocations. In this paper, in order to investigate the mechanism of deformation without dislocations, change in formation energy of point defects under high internal stress was estimated by computer simulation. Elastic deformation up to - 20% strain was found to provide a remarkable lowering of formation energy of point defects. For example, when Ni is subjected to elastic strain, the formation energy of an interstitial atom decreases to 40% that without strain and the formation energy of a vacancy decreases to 51% that without strain. The number of point defects formed under thermal equilibrium during deformation was evaluated. The number was judged to be insufficient for explaining the formation of vacancy clusters as observed in experiments.     

Evolution of ion-irradiated point defect concentration by cluster dynamics simulation

The relationship between ions irradiation and the induced microstructures(point defects, dislocations, clusters, etc.)could be better analyzed and explained by simulation. The mean field rate theory and cluster dynamics are used to simulate the effect of implanted Fe on the point defects concentration quantitatively. It is found that the depth distribution of point defect concentration is relatively gentle than that of damage calculated by SRIM software. Specifically, the damage rate and point defect concentration increase by 1.5 times and 0.6 times from depth of 120 nm to 825 nm, respectively. With the consideration of implanted Fe ions, which effectively act as interstitial atoms at the depth of high ion implantation rate, the vacancy concentration C_v decreases significantly after reaching the peak value, while the interstitial atom concentration C_i increases significantly after decline of the previous stage. At the peak depth of ion implantation, C_v dropped by 86%, and C_i increased by 6.2 times. Therefore, the implanted ions should be considered into the point defects concentration under high dose of heavy ion irradiation, which may help predict the concentration distribution of defect clusters, further analyzing the evolution behavior of solute precipitation.     

X-ray diffraction study of the effect of neutron irradiation on the defect formation in silicon crystals grown by the Czochralski method and annealed at high temperatures

The effect of x-ray scattering by neutron-irradiated and reference (unirradiated) silicon crystals grown by the Czochralski method and annealed at temperatures of 850–1050°C on the defect formation is comparatively investigated using triple-crystal x-ray diffractometry. The sizes and concentrations of clusters composed of point defects and dislocation loops formed during decomposition of an oxygen-containing solid solution and subsequent clusterization of the point defects are calculated.     

The stability of homogeneous microstructure development under cascade-damage conditions

The development of microstructure, under cascade-damage conditions, in regions far away from any major sink is considered. Within the mean-field theory, a homogeneous distribution of point defects and their clusters is a pre-imposed artificial constraint on the kinetic system. The resulting excessive recombination of the vacancies and interstitials at a high density of accumulated point-defect clusters dictates a low rate of void growth. Considerations beyond the mean-field theory, by taking into account the concentration fluctuations of both the point defects and their clusters, relax the restriction of the homogeneous distribution. In this paper, we consider a system without pre-existing sinks, except the void nuclei, in which vacancies, interstitials and their clusters are continuously produced. Taking into account the mobility of small clusters and the stochastic fluctuations of the point-defect fluxes, a kinetic theory is formulated from first principles. It is rigorously shown that through the stochastic fluctuations, and the positive-feedback action of the mobility of the small clusters on the interstitial concentration, the homogeneous interstitial distribution is unstable at temperatures above stage V, leading to the formation of a spatially heterogeneous microstructure in pure metals at low irradiation doses. The characteristics of the microstructure evolution and void swelling, predicted from the theory, are found to be in good agreement with the experimental results. Received: 17 March 2000 / Accepted: 17 October 2000 / Published online: 25 July 2001     

Thermodynamics and reactivity for the interconversion of active sites on a magnesium surface in the Grignard reaction

Density functional theory (B3PW91/6-31G (d)) is used to study the energy and electronic parameters of Mg₄₂-Mg₅₈ clusters simulating the structure of point defects in a magnesium surface, which are supposed to act as active sites in the Grignard reaction. The energy effects of detachment of a Mg atom from defects of various structures and the energies required for their mutual transformations and migration over the (0001) crystallographic plane are calculated. It is demonstrated that, for clusters containing single-atom and noncompact defects, the energy of detachment of a magnesium atom is less than 20–60 kJ mol^-1, which is comparable with the activation energy of the formation of the Grignard reagent, whereas for most other structures, it can substantially exceed this value. It is shown that defective clusters have more pronounced metallic properties than perfect structures with similar nuclearity. The reactivity of different models of defects in terms of the possibility of the activation of molecules of organic halides is analyzed.     

The influence of defects in compound single crystals on the critical angle of planar channeling

The theoretical treatment of the relation between the critical angle of planar channeling and the characteristics of crystal lattice defects is carried out. The predictions are made about some typical forms of the critical angle dependence on the mean-square static displacement produced by defects, and then these predictions are detailed for the cases of homogeneous disordering, spherical clusters of point defects and dislocation loops. Analytical results are supported by the exact computer calculations for the defects in the intermetallic A-15 compounds.     

The non-Arrhenius migration of interstitial defects in bcc transition metals

Thermally activated migration of defects drives microstructural evolution of materials under irradiation. In the case of vacancies, the activation energy for migration is many times the absolute temperature, and the dependence of the diffusion coefficient on temperature is well approximated by the Arrhenius law. On the other hand the activation energy for the migration of self-interstitial defects, and particularly self-interstitial atom clusters, is very low. In this case a trajectory of a defect performing Brownian motion at or above room temperature does not follow the Arrhenius-like pattern of migration involving infrequent hops separated by the relatively long intervals of time during which a defect resides at a certain point in the crystal lattice. This article reviews recent atomistic simulations of migration of individual interstitial defects, as well as clusters of interstitial defects, and rationalizes the results of simulations on the basis of solutions of the multistring Frenkel–Kontorova model. The treatment developed in the paper shows that the origin of the non-Arrhenius migration of interstitial defects and interstitial defect clusters is associated with the interaction between a defect and the classical field of thermal phonons. To cite this article: S.L. Dudarev, C. R. Physique 9 (2008).     

The influence of chromium on the defect structure and their mobility in nonstoichiometric cobaltous oxide

Defect structure and the mobility of point defects in pure metal deficient cobalt oxide (Co_1−yO) and in Co_1−yO-Cr₂O₃ solid solutions have been studied as a function of temperature (1223-1573 K) and oxygen pressure (10-10⁵ Pa) using microthermogravimetric techniques. It has been shown that the predominant defects in pure and Cr-doped cobaltous oxide are singly ionized cation vacancies, and 3% at of dopant is high enough to fix the concentration of predominant defects in such solid solutions on a constant level being much higher than in pure Co_1−yO. Re-equilibration rate measurements have demonstrated that the chemical diffusion coefficient and thereby the mobility of point defects in pure Co_1−yO is concentration independent, strongly suggesting that in spite of rather high their concentration no interactions and clustering of defects is to be expected. On the other hand, in Cr-doped cobaltous oxide, re-equilibration rate measurements have shown, that in this case the defect structure is more complicated, although singly ionized cation vacancies seem to be still predominant defects.