On the basis of the Green function method, analytical solutions of the diffusion equation which describes nonstationary migration of nonequilibrium interstitial impurity atoms have been derived. It is supposed that the initial distribution of nonequilibrium impurity interstitials is formed due to ion implantation and, therefore, is described by the Gaussian function. The condition of the constant concentration of impurity interstitials (the Dirichlet boundary condition) or reflecting boundary condition was imposed on the surface of a semiconductor. The Dirichlet boundary condition was also enforced for the concentration of impurity interstitials in the infinity, i.e., in the bulk of a semiconductor. On the basis of the solutions derived the redistribution of ion-implanted boron in silicon substrate during low-temperature thermal treatment has been simulated. The calculated profile of boron atoms after annealing agrees well with experimental data. It means that the analytical solutions derived can be used both for verifying the numerical results and for modeling the long-range migration of nonequilibrium impurity interstitials during low-temperature thermal treatments.
The diffusion equation for nonequilibrium interstitial impurity atoms taking into account their charge states and drift of all mobile interstitial species in the built-in electric field and in the field of elastic stress was obtained. The obtained generalized equation is equivalent to the set of diffusion equations written for the interstitial impurity atoms in each individual charge state. Due to a number of the characteristic features the generalized equation is more convenient for numerical solution than the original system of separate diffusion equations. On this basis, the macroscopic des…
An analytical solution of the equations describing impurity diffusion due to the migration of nonequilibrium impurity interstitial atoms was obtained for the case of the Robin boundary condition on the surface of a semiconductor. The solution obtained can be useful for verification of approximate numerical solutions, for simulation of a number of processes of interstitial diffusion, and for modeling impurity diffusion in doped layers with the decananometer thickness because in these layers a disequilibrium between immobile substitutionally dissolved impurity atoms, migrating self-interstitials…
The analytical solutions of the equations describing impurity diffusion due to migration of nonequilibrium impurity interstitials were obtained for the impurity redistribution during ion implantation at elevated temperatures and for diffusion from a doped epitaxial layer. The reflecting boundary condition at the surface of a semiconductor and the conditions of constant concentrations at the surface and in the bulk of it were used in the first and second cases, respectively. On the basis of these solutions hydrogen diffusion in silicon during high-fluence low-energy deuterium implantation and b…
A model of interstitial impurity migration is proposed which explains the redistribution of ion-implanted boron in low-temperature annealing of nonamorphized silicon layers. It is supposed that nonequilibrium boron interstitials are generated either in the course of ion implantation or at the initial stage of thermal treatment and that they migrate inward and to the surface of a semiconductor in the basic stage of annealing. It is shown that the form of the "tail" in the boron profile with the logarithmic concentration axis changes from a straight line if the average lifetime of impurity inter…
The macroscopic behavior of polycrystalline materials is influenced by the local variation of properties caused by the presence of impurities and defects. The effect of these impurities at the atomic scale can either embrittle or strengthen grain boundaries within. Thus, it is imperative to understand the energetics associated with segregation to design materials with desirable properties. Here, molecular statics simulations were employed to analyze the energetics associated with the segregation of various elements (He, H, C, P, and V) to four <100> (Sigma 5 and 13 GBs) and six <110> (Sigma 3,…
It has been shown by means of impurity diffusion simulation that ion-implanted boron redistribution at the annealing temperatures 800^{\circ}C and lower is governed by the long-range migration of nonequilibrium impurity interstitials regardless of the methods used for the transient enhanced diffusion suppression. The relative amounts of impurity atoms, which are being transferred to the transient interstitial position, have been determined and time-average migration lengths of nonequilibrium boron interstitials have been obtained.
An analysis of the equations used for modeling thermal arsenic diffusion in silicon has been carried out. It was shown that for arsenic diffusion governed by the vacancy-impurity pairs and the pairs formed due to interaction of impurity atoms with silicon self-interstitials in a neutral charge state, the doping process can be described by the Fick's second law equation with a single effective diffusion coefficient which takes into account two impurity flows arising due to interaction of arsenic atoms with vacancies and silicon self-interstitials, respectively. Arsenic concentration profiles ca…
Impurity diffusion in Zr is potentially important for many applications of Zr alloys, and in particular for their use of nuclear reactor cladding. However, significant uncertainty presently exists about which elements are vacancy vs. interstitial diffusers, which can inhibit understanding and prediction of their behavior under different temperature, irradiation, and alloying conditions. Therefore, first-principles calculations based on density functional theory (DFT) have been employed to predict the temperature-dependent dilute impurity diffusion coefficients for 14 substitutional alloying el…
We use new equations for the interstitial impurity diffusion fluxes under strain to study impurity atom redistribution in the vicinity of dislocations. Two levels of simulation are applied. The first one is evaluation of coefficients that determine the influence of strain tensor components on interstitial diffusion fluxes in FCC structures. For this purpose we have developed a model into the framework of a molecular static method taking into account an atom environment both near the interstitial site and for the saddle-point configuration. The second level is modeling the interstitial segregat…
The mechanism underlying the long-range interstitial migration of nonequilibrium impurity interstitial species is used to simulate arsenic redistribution in ion implantation. An excellent agreement of the calculated arsenic concentration profiles with experimental data allows one to assume that the migration of nonequilibrium arsenic interstitial atoms makes a significant contribution to the formation of a low concentration region on thermal arsenic diffusion. The arsenic concentration profile calculated for a temperature of 1050 Celsius degrees within the framework of this assumption agrees w…
Modeling of the phosphorus radiation-enhanced diffusion in the course of implantation of high-energy protons into an elevated-temperature silicon substrate and during its treatment in a hydrogen-containing plasma with addition of a diffusant has been carried out. It follows from the results obtained that the radiation-enhanced diffusion occurs by means of formation, migration, and dissociation of "impurity atom -- silicon self-interstitial" pairs being in a local thermodynamic equilibrium with substitutionally dissolved impurity atoms and nonequilibrium point defects generated due to external …
Density-functional studies of the electron states in the dilute magnetic semiconductor GaN:Mn reveal major differences for the case of the Mn impurity at the substitutional site Mn_Ga versus the interstitial site Mn_I. The splitting of the two-fold and the three-fold degenerate Mn(d)states in the gap are reversed between the two cases, which is understood in terms of the symmetry-controlled hybridization with the neighboring atoms. In contrast to Mn_Ga, which acts as a deep acceptor, Mn_I acts as a donor, suggesting the formation of Coulomb-stabilized complexes such as (Mn_Ga Mn_I Mn_Ga), wher…
It has been shown that many of the phenomena related to the formation of "tails" in the low-concentration region of ion-implanted impurity distribution are due to the anomalous diffusion of nonequilibrium impurity interstitials. These phenomena include boron implantation in preamorphized silicon, a "hot" implantation of indium ions, annealing of ion-implanted layers et cetera. In particular, to verify this microscopic mechanism, a simulation of boron redistribution during low-temperature annealing of ion-implanted layers has been carried out under different conditions of transient enhanced dif…
The following scenarios of Re-embedding into SiO2-host by pulsed Re-implantation were derived and discussed after XPS-and-DFT electronic structure qualification: (i) low Re-impurity concentration mode -> the formation of combined substitutional and interstitial impurities with Re2O7-like atomic and electronic structures in the vicinity of oxygen vacancies; (ii) high Re-impurity concentration mode -> the fabrication of interstitial Re-metal clusters with the accompanied formation of ReO2-like atomic structures and (iii) an intermediate transient mode with Re-impurity concentration increase, whe…
Electrides are an emerging class of materials with highly-localized electrons in the interstices of a crystal that behave as anions. The presence of these unusual interstitial quasi-atom (ISQ) electrons leads to interesting physical and chemical properties, and wide potential applications for this new class of materials. Crystal defects often have a crucial influence on the properties of materials. Introducing impurities has been proved to be an effective approach to improve the properties of a material and to expand its applications. However, the interactions between the anionic ISQs and the …
A model of the interstitial diffusion of ion-implanted boron during rapid thermal annealing of silicon layers previously amorphized by implantation of germanium has been proposed. It is supposed that the boron interstitials are generated continuously during annealing due to dissolution or rearrangement of the clusters of impurity atoms which are formed in the ion-implanted layers with impurity concentration above the solubility limit. The local elastic stresses arising due to the difference of boron atomic radius and atomic radius of silicon also contribute to the generation of boron interstit…
Hydrogen exhibits qualitatively different charge states depending on the host material, as nicely explained by the state-of-the-art impurity-state calculation. Motivated by a recent experiment [Nature 546, 124 (2017)], we show that the complex oxide SrCoO$_{2.5}$ represents an interesting example, in which the interstitial H appears as a deep-level center according to the commonly-used transition level calculation, but no bound electron can be found around the impurity. Via a combination of charge difference analysis, density of states projection and constraint magnetization calculation, it tu…
The theoretical analysis of the process of diffusion of interstitial oxygen atoms and hydrogen molecules in silicon and germanium crystals has been performed. The calculated values of the activation energy and pre-exponential factor for an interstitial oxygen atom Ea(Si) = 2.59 eV, Ea(Ge) = 2.05 eV, D(Si)= 0.28 cm2s-1, D(Ge)= 0.39 cm2s-1 and interstitial hydrogen molecule Ea(Si) = 0.79-0.83 eV, Ea(Ge) = 0.58-0.62 eV, D(Si)= 7.4 10(-4) cm2s-1, D(Ge)= 6.5 10(-4) cm2s-1 are in an excellent agreement with experimental ones and for the first time describe perfectly an experimental temperature depen…
Self-diffusion and impurity diffusion both play crucial roles in the fabrication of semiconductor nanostructures with high surface-to-volume ratios. However, experimental studies of bulk-surface reactions of point defects in semiconductors are strongly hampered by extremely low concentrations and difficulties in the visualization of single point defects in the crystal lattice. Herein we report the first real-time experimental observation of the self-interstitial reactions on a large atomically smooth silicon surface. We show that non-equilibrium self-interstitials generated in silicon bulk dur…
A study based on density functional theory calculations was performed for the three charge states of interstitial hydrogen in Yttria. The present calculations were carried out by employing the GGA-PBE and the HSE06 exchange-correlation functional. It is observed that the ground state H$^0$ and H$^-$ configurations are similar in behaviour; these prefer to relax in the O vacant site, with limited structural relaxation. For the neutral and the negative charged systems more two different geometrical configurations occur with higher energies, which evidence the existence of metastable sites of H i…
A two stream model of boron diffusion in silicon has been developed. The model is intended for simulation of transient enhanced diffusion including redistribution of ion-implanted boron during low temperature annealing. The following mechanisms of boron diffusion were proposed, namely: the mechanism of a long-range migration of nonequilibrium boron interstitials and the mechanism due to the formation, migration, and dissolution of the "impurity atom - silicon self-interstitial" pairs. Based on the model, simulation of the redistribution of boron implanted into silicon substrates for annealing …
How impurity atoms move through a crystal is a fundamental and recurrent question in materials. The previous understanding of oxygen diffusion in titanium relied on interstitial lattice sites that were recently found to be unstable, making the diffusion pathways for oxygen unknown. Using first-principles quantum-mechanical methods, we find three oxygen interstitial sites in titanium, and quantify the multiple interpenetrating networks for oxygen diffusion. Surprisingly, no single transition dominates, but all contribute to diffusion.
This work reports theoretical and experimental study of the X-ray absorption near-edge structure (XANES) at the Mn K-edge in (Ga,Mn)As diluted magnetic semiconductors. The spectra have been calculated from the first-principles using FLAPW including the core-hole effect, a special attention has been paid to consequences of coexistence of Mn impurities in substitutional and tetrahedral interstitial positions. We have performed quantitative component analysis of experimental spectra collected on the (Ga,Mn)As samples before/after annealing and etching, with the aim to determine the proportion of …
Results of a first-principles study of the Li impurity in GaN are presented. We find Li is a channel interstitial, with an onset for diffusion at T$\sim$ 600 K. Above this temperature, Li can transform to a Ga-substitutional acceptor by exothermic recombination with Ga vacancies. This process implies capture of at least one electron; therefore Li acts as an electron sink. Li$_{\rm Ga}$ is stable again interstitialcy, and has a shallow first ionization levels of 0.16 eV, and second ionization at 0.63 eV. Lattice locations and their temperature dependence are in close agreement with recent exper…
Within the framework of the lattice-statics and static fluctuation-wave methods, the available energies of strain-induced interaction of interstitial-interstitial, interstitial-substitutional and substitutional-substitutional impurity atomic pairs are collected and analysed for f.c.c.-(Ni,Fe)-C solutions allowing for discrete atomic structure of the host-crystal lattice. The lattice spacings, elasticity moduli and/or quasi-elastic force parameters of the host-crystal lattice, and concentration coefficients of the dilatation of solid-solution lattice due to the respective solutes are selected a…
It has been shown that during thermal treatments of silicon layers preamorphized by germanium implantation and then implanted with boron ions the transport of impurity atoms occurs right up to a temperature of 850^{\circ}C due to migration of the nonequilibrium boron interstitials.
By studying Fe-doped ZnO pellets and thin films with various x-ray spectroscopic techniques, and complementing this with density functional theory calculations, we find that Fe-doping in bulk ZnO induces isovalent (and isostructural) cation substitution (Fe2+ -> Zn2+). In contrast to this, Fe-doping near the surface produces both isovalent and heterovalent substitution (Fe3+ -> Zn2+). The calculations performed herein suggest that the most likely defect structure is the single or double substitution of Zn with Fe, although, if additional oxygen is available, then Fe substitution with interstit…
We report the prediction of temperature-dependent diffusion coefficients of interstitial hydrogen, deuterium, and tritium atoms in $α$-Ti using transition state theory. The microscopic parameters in the pre-factor and activation energy of the impurity diffusion coefficients are obtained from first-principles total energy and phonon calculations including the full coupling between the vibrational modes of the diffusing atom with the host lattice. The dual occupancy case of impurity atom in the hcp matrix are considered, and four diffusion paths are combined to obtain the final diffusion coeffic…
Properties of point defects resulting from the incorporation of inert-gas atoms in bcc tungsten are investigated systematically using first-principles density functional theory (DFT) calculations. The most stable configuration for the interstitial neon, argon, krypton and xenon atoms is the tetrahedral site, similarly to what was found earlier for helium in W. The calculated formation energies for single inert-gas atoms at interstitial sites as well as at substitutional sites are much larger for Ne, Ar, Kr and Xe than for He. While the variation of the energy of insertion of inert-gas defects …
The kinetics of sorption and subsequent desorption of argon gas by a C60 powder has been investigated in the temperature interval 58-290 K. The temperature dependence of the coefficients of Ar diffusion in fullerite has been obtained using the measured characteristic times of sorption. The diffusion coefficients of Ar decrease monotonically with lowering temperature in the whole range of the investigated temperatures, which corresponds to the thermally activated diffusion of Ar atoms in fullerite. The glass transition in fullerite induces an order-of-magnitude decrease in the activation energy…
The interaction of grain boundaries (GBs) with inherent defects and/or impurity elements in multi-crystalline silicon play a decisive role in their electrical behavior. Strain, depending on the types of GBs and defects, plays an important role in these systems. Herein, the correlation between the structural and electronic properties of Σ 3{111} Si-GB in the presence of interstitial oxygen impurities is studied from the first-principles framework, considering the global and local model of strain. It is observed that the distribution of strain along with the number of impurity atoms modifies the…
To simulate the transient enhanced diffusion near the surface or interface, a set of equations describing the impurity diffusion and quasichemical reactions of dopant atoms and point defects in ion-implanted layers is proposed and analyzed. The diffusion equations obtained take into account different charge states of mobile or immobile species and drift the mobile species in the built-in electric field and field of elastic stresses. The absorption of self-interstitials on the surface and drift of the defects due to elastic stresses result in the nonuniform distributions of point defects. It wa…
We study the kinetics of the redistribution of impurity atoms in the elastic fields of dislocations by computer simulation methods. A work consists of several stages. The first is the simulation of a dislocation core structure with a Burgers vector along [100] direction by using the modified molecular static method. The second is obtaining the coefficients that determine the influence of the components of the strain tensor on the diagonal elements of the matrix of diffusion coefficients and in the equations for fluxes of carbon atoms in bcc iron. The third stage is associated with modeling the…
The temperature-dependent diffusion coefficients of interstitial helium atom in $α$-Ti are predicted using the transition state theory. The microscopic parameters in the pre-factor and activation energy of the impurity diffusion coefficients are obtained from first-principles total energy and phonon calculations including the full coupling between the vibrational modes of the diffusing atom and the host lattice. The climbing image nudged elastic band (CINEB) method is used to search for the minimum energy pathways and associated saddle point structures. It is demonstrated that the diffusion co…
The model of hydrogen migration and of the reactions of hydrogen atoms with electrically active impurity, developed earlier, has been applied to simulate hydrogen diffusion and passivation process during plasma deuteration of silicon substrates doped with boron. The calculated deuterium concentration profiles agree well in the length of the passivated region with the experimental data obtained on treatment in hydrogen plasma at a temperature of 200 Celsius degrees for 5, 10, and 15 minutes. On the other hand, to achieve a good fit to the abruptness of the calculated profiles between the passiv…
