Equilibrium Concentrations Of Point Defects Research Articles

Computer modeling of diffusion in Ni-richNi3Al and compositiondependence of diffusion in γ′ Ni3Al

Atomistic simulations of diffusion in off-stoichiometric Ni-richNi3Al (Ni77Al23) at temperatures ranging from 1300 to 1550 K and comprehensiveanalysis of the composition dependence of Ni and Al diffusion inγ′ Ni3Al of threecompositions, 73, 75 and 77 at.% Ni, are presented. The interatomic forces are described by Finnis–Sinclairtype N-body potentials. The simulations reveal that Ni diffusion is dominated by Ni vacancy mechanisms;Al diffusion is via both the intrasublattice and antistructure bridge (ASB) mechanism inNi77Al23 at the temperatures investigated. The presence of an extra 2% of antisitedefects enhances diffusion of both Ni and Al at off-stoichiometric Ni-enrichedNi3Al via the vacancy–antisite interaction. The single vacancy diffusivity of Ni and Al inNi3Al of three compositions, 73, 75 and 77 at.% Ni, at the above temperatures are corrected withthermal equilibrium concentration of point defects. The corrected Ni and Al diffusion dataare in good agreement with available experimental data. The Ni diffusivity decreases withthe Ni concentration, while Al diffusivity has a minimum at the stoichiometric compositionin the simulated temperature range.

Nonlocal reduced boron diffusivity in silicon below strained Si[sub 1−x]Ge[sub x] surfaces

The silicon (Si) surface can be the dominant source of self-interstitials for many annealing conditions. Incorporation of germanium (Ge) and strain into the surface may be expected to perturb the equilibrium point defect concentrations at the surface (i.e., the atomic steps at which the point defects are generated and annihilated) and consequently in the bulk Si. In this work, boron (B) diffusion marker layers were epitaxially grown in Si by rapid thermal chemical vapor deposition followed by either undoped Si, 45nm of Si0.75Ge0.25, or 5nm of Si0.55Ge0.45 leaving a surface with three different Ge contents. The B diffusivity (DB) below the Si1−xGex surface layers was found to be as much as two times slower than that in the all-Si samples between 800 and 900°C. The activation energy for the DB in the Si1−xGex capped samples was also observed to increase to ∼4.1eV. This work demonstrates that a Si1−xGex surface can reduce the DB in the underlying Si during N2 annealing. Furthermore, this novel test structure...

Modeling of He-bubble migration in bcc Fe

Kinetic Monte-Carlo simulations were performed to investigate the migration of He-bubbles in bcc Fe, using the binding energies of point defects to a He-bubble and the migration energies of an Fe atom on bubble surface, both of which are obtained by molecular dynamics and molecular static calculations. This approach linking multiple simulation methods can remove the degrees of freedom for lattice vibrations effectively and enables us to perform long time scale simulations successfully. When the equilibrium concentration of point defects in a matrix is assumed, a He-bubble can migrate by the surface diffusion mechanism and show the Brownian motion. The diffusion coefficient of larger He-bubbles than about 0.8 nm in diameter is proportional to d −4, where d is bubble diameter. It is in good agreement with conventional continuum theory predictions.

Nonstoichiometry and point defects in nonlinear optical crystals A 2B 4C 25

Using thermodynamic calculation, the equilibrium concentrations of point defects in ZnGeP 2 and CdGeAs 2 depending on a liquidus temperature are obtained. The conclusion about a high degree of compensation of native donors and acceptors is made. The methods of a model pseudo-potential and large unit cell are used for investigation of deep levels created by vacancies and antisites in the forbidden band of ZnGeP 2. Optical transitions with participation of the defects are defined. It is supposed the possibility of conditions favourable for mid-IR optical absorption, as a result of the interaction of ionized zinc vacancies with GeP clusters.

Interatomic potentials for atomistic simulations of the Ti-Al system

Semi-empirical interatomic potentials have been developed for Al, alpha-Ti, and gamma-TiAl within the embedded atomic method (EAM) by fitting to a large database of experimental as well as ab-initio data. The ab-initio calculations were performed by the linear augmented plane wave (LAPW) method within the density functional theory to obtain the equations of state for a number of crystal structures of the Ti-Al system. Some of the calculated LAPW energies were used for fitting the potentials while others for examining their quality. The potentials correctly predict the equilibrium crystal structures of the phases and accurately reproduce their basic lattice properties. The potentials are applied to calculate the energies of point defects, surfaces, planar faults in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al system, the proposed potentials provide reasonable description of the lattice thermal expansion, demonstrating their usefulness in the molecular dynamics or Monte Carlo studies at high temperatures. The energy along the tetragonal deformation path (Bain transformation) in gamma-TiAl calculated with the EAM potential is in a fairly good agreement with LAPW calculations. Equilibrium point defect concentrations in gamma-TiAl are studied using the EAM potential. It is found that antisite defects strongly dominate over vacancies at all compositions around stoichiometry, indicating that gamm-TiAl is an antisite disorder compound in agreement with experimental data.

Phosphorus and boron diffusion in silicon under equilibrium conditions

The intrinsic diffusion of phosphorus and boron in high-purity epitaxial silicon films has been studied. Phosphorus diffusion in a wide temperature range (810 to 1100 °C) revealed diffusion coefficients with an Arrhenius behavior exhibiting an activation energy of 2.74±0.07 eV and a pre-exponential factor of (8±5)×10−4 cm2/s. In the temperature range of 810 to 1050 °C, boron was found to diffuse with an activation energy of 3.12±0.04 eV and a pre-exponential factor of 0.06±0.02 cm2/s. These results differ from those of many previous studies, but this deviation may to a large extent be attributed to slow transients before equilibrium concentrations of point defects are established at temperatures below ∼1000 °C. Despite a similar diffusion mechanism mediated by Si self-interstitials, P exhibits a lower activation energy than B because of stronger bonding to the Si self-interstitial.

Embedded-atom potential forB2−NiAl

An embedded-atom potential has been constructed for the intermetallic compound $B2\ensuremath{-}\mathrm{NiAl}$ by fitting to both experimental properties and ab initio data. The ab initio data have been generated in the form of energy-volume relations for a number of alternative structures of NiAl and ${\mathrm{Ni}}_{3}\mathrm{Al},$ as well as for Ni and Al. The potential accurately reproduces the basic lattice properties of $B2\ensuremath{-}\mathrm{NiAl},$ planar faults, and point-defect characteristics. It also reproduces the energetics and stability of all other structures included in the fit. The potential is applied to calculate equilibrium point-defect concentrations in $B2\ensuremath{-}\mathrm{NiAl}$ as functions of temperature and composition near the stoichiometry. In contrast to previous calculations, the defect formation entropies arising from atomic vibrations are included in our calculation within the quasiharmonic approximation. Such entropies tend to increase the concentrations of thermal point defects in $B2\ensuremath{-}\mathrm{NiAl}$ at high temperatures, but the atomic disorder mechanism remains triple-defect type up to the melting point.

Diffusion Coefficient and Equilibrium Concentration of Point Defects in Silicon Crystals, Estimated via Grown-in Defect Behavior

Diffusion Coefficient and Equilibrium Concentration of Point Defects in Silicon Crystals, Estimated via Grown-in Defect Behavior

Equilibrium point defect concentration in a growing silicon crystal

Equilibrium concentrations of point defects in various stages of Si crystal growth are theoretically analyzed. Local equilibrium concentration at the free surface, in the bulk and during the formation of secondary defects, is considered. We show that local equilibrium concentration is not unique during the crystal growth.

シリコン成長各期における点欠陥の平衡濃度

Equilibrium concentration of point defects under various stages in growing silicon crystal is theoretically examined. Formulas of concentration of point defects corresponding to solid-liquid interface, early cooling stage and including secondary defects are proposed. It is suggested that equilibrium concentration is not unique and that previous consideration is not applied for actual crystal growth.

Fractional contributions of microscopic diffusion mechanisms for common dopants and self-diffusion in silicon

An identical set of thermal oxidation and nitridation experiments has been performed for four common dopants and self-diffusion in Si. Selectively perturbing the equilibrium point-defect concentrations by these surface reactions is a powerful tool for identifying the relative importance of the various atomic-scale diffusion mechanisms. We obtain bounds on the fractional contributions of the self-interstitial, vacancy, and concerted exchange mechanisms for arsenic, boron, phosphorus, antimony, and self-diffusion in Si at temperatures of 1100 and 1000 °C. These bounds are found by simultaneously solving a system of equations making only very conservative assumptions. The validity of common approximations found in previous work and their effects on the results are also analyzed in detail. We find that B and P diffuse by a self-interstitial mechanism, whereas Sb diffusion is almost exclusively vacancy mediated. As and self-diffusion, on the other hand, exhibit evidence for a dual vacancy-interstitial mechanism with the possibility of some concerted exchange component.

Application of the grand canonical ensemble to the study of equilibrium point defect concentrations in binary intermetallic phases with the B2-structure

A statistical thermodynamic model of ordering in nonstoichiometric B2-phases is developed, based on the oldest and simplest theory of ordering, the mean-field approximation with constant pair-wise interaction energies between nearest-neighbor atoms. This approximation is limited to the description of the distribution of atoms and vacancies on the different sublattices, a possible short-range ordering tendency of point defects is neglected. The expressions for the point defect concentrations as a function of composition and temperature are derived from the grand canonical ensemble. In B2-phases the vacancy concentration depends on composition and temperature and it is therefore necessary to consider an open system, where the transfer of atoms to or from the outside is allowed. In B2-phases not only one defect equilibrium is involved, but there are four defect equilibria to be considered. It is shown that, if a series of defect equilibria is involved, it is necessary to apply the principle of microscopic reversibility to formulate the required number of independent equilibrium conditions. Expressions for the activities and partial molar enthalpies of the alloy components as a function of composition and temperature are derived, and a comparison with experimental data for β′-FeAl is given, which shows the practicability of this approach.

The contribution of vacancies to carbon out-diffusion in silicon

Diffusion of carbon is mostly assumed to be governed by carbon interstitials via the kick-out mechanism. Carbon in-diffusion experiments are associated with thermal equilibrium concentrations of point defects, whereas in the case of carbon out-diffusion a remarkable undersaturation of Si self-interstitials may develop provided the carbon concentration is several orders of magnitude over its solubility value. New carbon out-diffusion experiments demonstrate that this model qualitatively describes the observed carbon diffusion profiles. However, we demonstrate that an accurate description of the experimental profiles is only possible if the Frank–Turnbull mechanism, involving vacancies, is additionally taken into account. Detailed investigations of carbon and boron profiles in the same sample can be used to determine the splitting of the known vacancy component of the silicon self-diffusion coefficient into the vacancy diffusion coefficient and the vacancy thermal equilibrium concentration at 900 °C.

シリコン結晶中の点欠陥形成に対する不純物原子の応力効果

Equilibrium concentration change of point defects in Si crystal due to the stress by doping impurities is estimated. The relationship between equilibrium concentration of point defects and secondary defect generation are discussed. It is considered that the changing point defect concentration only about 0.1% affects the secondary defect generation.

Defects and Diffusion in Silicon: An Overview

ABSTRACTAt the current pace of semiconductor technology development, transistor dimensions in advanced IC products will approach the range of a few tens of nanometers within the next decade. This presents a major challenge for our understanding of defects and diffusion in these tiny devices during processing. In response, an almost explosive growth in research on process physics has taken place at universities, national institutes and industry research labs worldwide. The central issue is the phenomenon of nonequilibrium diffusion driven by processing steps such as oxide growth, high concentration gradients of impurities, and annealing of damage caused by ion implantation. Nonequilibrium diffusion arises from perturbations to the natural thermal equilibrium concentrations of point defects - interstitial atoms and vacancies - in the silicon crystal. This paper gives a snapshot of our current understanding of the atomic-scale interactions between point defects and impurity atoms, extended defects and interfaces, as revealed by recent experimental and theoretical studies. The paper emphasizes the important role played by defect cluster ripening during transient enhanced diffusion and dopant activation.

Equilibrium vacancies and thermophysical properties of metals

Despite a significant progress in studies of point defects, some important problems have not received unambiguous solutions. One of the most practically important questions relates to equilibrium concentrations of point defects. It is indeed surprising that this fundamental problem is still under debate. There exist two opposite viewpoints on equilibrium point defects in metals: (1) Defect contributions to the physical properties of metals at high temperatures are small and cannot be separated from the effects of anharmonicity. The only suitable methods are the positron-annihilation spectroscopy providing enthalpies of the vacancy formation and the differential dilatometry yielding equilibrium vacancy concentrations. The equilibrium vacancy concentrations at the melting points are in the range 10 −4 to 10 −3. Reasonable values of the formation enthalpies deduced from the nonlinear increase in the high-temperature specific heat of metals are accidental and the derived defect concentrations are improbably large, so that this approach is generally erroneous. (2) In many cases, defect contributions to the specific heat of metals are much larger than nonlinear effects of the anharmonicity and can be separated without crucial errors. This approach is quite adequate for determination of the defect parameters, especially, the equilibrium vacancy concentrations. The equilibrium concentrations at the melting points are of the order of 10 −3 in low-melting-point metals and of 10 −2 in high-melting-point metals. The strong nonlinear effects in the specific heat and thermal expansivity of metals at high temperatures can be explained by the formation of point defects. Examination of these effects rules out the anharmonicity as a possible origin of this phenomenon. Important arguments supporting this viewpoint have appeared in the last decade. It may turn out that just calorimetric determinations provide most reliable values of equilibrium vacancy concentrations in metals. The aim of the review is to discuss the experimental results and theoretical considerations favoring both claims. At present, the first point of view is shared by the majority of the scientific community. Regrettably, the data supporting the second viewpoint were never displayed and discussed together, and the criticism of this viewpoint never included a detailed analysis. In this review, the main attention is paid to equilibrium vacancies in metals and their relation to thermophysical properties of metals. Along with a discussion of experimental data and theoretical estimates now available, some approaches are proposed that seem to be most suitable to solve the question.

Dependence of atomic diffusion in GaAs upon experimental design

The rate of impurity diffusion in GaAs depends upon the concentration of point defects such as vacancies and interstitials. The concentration of those point defects is strongly affected by the region of the phase diagram corresponding to the chosen experimental design. Different regions of phase diagrams are used to illustrate why nominally similar experiments can lead to dramatically different results. When the equilibrium point defect concentrations can be approached in a time which is short compared to the anneal time, the measured diffusivities tend to be reproducible. However, when the point defect concentrations approach their equilibrium values over times which are long compared to the anneal time, the measured diffusivities tend to be irreproducible and time dependent. Examples of "anomalous" diffusion are discussed and shown to be associated with fundamental differences in experimental design that tend to bring the point defect concentration toward equilibrium in different regions of the phase diagram.

On the dynamics of the oxidation-induced stacking-fault ring in as-grown Czochralski silicon crystals

The behavior of the oxidation-induced stacking-fault ring (OSF ring) in Czochralski (CZ)-grown silicon crystals is predicted based on the dynamics of point defects during growth. Preexponential constants for the equilibrium point defect concentrations and diffusivities are determined by fitting the predictions of the model to a single set of experimental data for OSF-ring dynamics. Other experimental data is well fit by this model. Moreover, point defect properties used are consistent with other estimates. Asymptotic analysis of the point defect model leads to a closed-form expression for the dependence of the OSF-ring location on processing conditions and thermophysical properties of point defects at the melting temperature. These results indicate that differentiation between defect types in CZ-grown material can be done entirely on the basis of point defect dynamics.

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models4He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of4He with the product (Jastrow) form that corresponds to a classical 1/rb pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10−5 for 1/r9 and 6.36×10−6 for 1/r6, while the interstitial fractional concentrations are 1.32×10−3 and 1.08×10−5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r9 potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)4He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in4He is probably much lower than our results.

Thermal equilibrium concentrations of point defects in gallium arsenide

Expressions of the thermal equilibrium concentrations of point defects in GaAs, including the neutral and charged species, are derived. These expressions are explicit functions of well-defined thermodynamic quantities, which in turn yield explicit expressions for the reaction constant K in the usual As 4 pressure power law representation of the point defect thermal equilibrium concentrations. Such power laws have been of little quantitative value in the past, because values for K were not known. In the present derivation, emphases are placed upon the difference between the Gibbs free energies of an As atom in the interior of a GaAs crystal and in an As vapor phase molecule, and the role of the crystal Fermi level. Numerical values of the thermal equilibrium concentrations of the neutral and three negatively charged Ga vacancies (V 0 Ga, V − Ga, V 2− Ga and V 3− Ga), the neutral As vacancies V 0 As and the two neutral antisite de Ga 0 As and As 0 Ga have been obtained. The calculated thermal equilibrium concentration of the anion antisite defect As 0 Ga reaches a peak value of about 1 sx 10 17 cm −3 and is practically temperature independent, in agreement with experimental findings. The thermal equilibrium concentrations of the triply negatively charged Ga vacancy V 3− Ga, C eq v 3− Ga ( n), have been found to exhibit a temperature independence or a negati temperature dependence behavior under strong n-doping conditions. That is, the C eq v 3− Ga ( n) value is either unchanged or increases as the temperature is lowered. This C eq v 3− Ga ( n) property provided explanations to a number of outstanding experimental results, either requiring the interpretation that V 3− Ga has attained its thermal equilibrium concentration at the onset of each experiment, or requiring mechanisms involving point defect nonequilibrium phenomena. The calculated C eq v 3− Ga ( n) values are in agreement with available experimental results.