Kinetics of the diffusion of an impurity atom on a square lattice

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is presented. The case of small surface coverages of both vacancies ϑ _v and impurity atoms ϑ _i , with ϑ _i ≪ ϑ _v ≪ 1, is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor η. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, at ω ≪ 1, the diffusion coefficient of impurity atoms depends linearly on ω, whereas at ω ≫ 1, a saturation is observed; i.e., the dependence on the frequency of jumps of the impurity atom disappears. Nevertheless, the value of η remains less than unity, and no total entrainment of impurity atoms with vacancies occurs.     

Kinetics of the diffusion of an impurity atom on a fcc(111) surface

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is performed. The case of small surface coverages of both vacancies and impurity atoms is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, when the frequency of jump ω of the imurity atom is small, the diffusion coefficient of the impurity depends linearly on ω, whereas in the opposite case, a saturation occur and its dependence on the frequency of jumps of the impurity atom disappears.     

Divacancy complexes induced by Cu diffusion in Zn-doped GaAs

Positron annihilation spectroscopy was applied to investigate the nature and thermal behavior of defects induced by Cu diffusion in Zn-doped p-type GaAs crystals. Cu atoms were intentionally introduced in the GaAs lattice through thermally activated diffusion from a thin Cu capping layer at 1100 °C under defined arsenic vapor pressure. During isochronal annealing of the obtained Cu-diffused GaAs in the temperature range of 450?850 K, vacancy clusters were found to form, grow and finally disappear. We found that annealing at 650 K triggers the formation of divacancies, whereas further increasing in the annealing temperature up to 750 K leads to the formation of divacancy-copper complexes. The observations suggest that the formation of these vacancy-like defects in GaAs is related to the out-diffusion of Cu. Two kinds of acceptors are detected with a concentration of about 10¹⁶ ? 10¹⁷ cm^?3, negative ions and arsenic vacancy copper complexes. Transmission electron microscopy showed the presence of voids and Cu precipitates which are not observed by positron measurements. The positron binding energy to shallow traps is estimated using the positron trapping model. Coincidence Doppler broadening spectroscopy showed the presence of Cu in the immediate vicinity of the detected vacancies. Theoretical calculations suggested that the detected defect is V _Ga V _As-2Cu_Ga.     

Electrically stimulated movement of edge dislocations in silicon in the temperature range 300–450 K

The movement of edge dislocations and the related acoustic emission of Si (111) carrying a direct current of density 0.5?5×10⁵ A/m² in the [110] direction are studied in the temperature range T=300–450 K. It is shown that the basic mechanism of dislocation movement is the electric wind determining the magnitude of the effective charge (per atom of the dislocation line) Z _eff=0.06 (n-Si) and ?0.01 (p-Si). Matching theory with experimental data has made it possible to determine the main contribution of edge dislocations to the acoustic-emission response of the silicon samples under investigation. The characteristic transition frequencies of dislocations in n-and p-Si from one metastable state into another are found to be f _max=0.1–0.5 Hz. The numerical values of the diffusion coefficient for atoms in the dislocation impurity atmosphere are estimated as 3.2×10^?18 m²/s (n-Si) and 1.5×10^?18 m²/s (p-Si).     

Mass transport in cuprous oxide

The chemical diffusion coefficient of Cu₂O has been obtained for an oxygen partial pressure near 5 10^?4 atm as a function of the temperature in the range 700–900°C D? = 1 62 10^?4 exp(?5140 ± 600 cal mol ^?1)/RT cm²s^?1 This was easily achieved according to the electrochemical method used for the preparation of gaseous mixtures whose Po₂; is lower than 10^?5 atm The slight difference observed with the previously published results by Maluenda, and obtained for Po₂ values which increase with T between 10^?4 and 0.21 atm, may be due to an oxygen partial pressure effect already observed in the case of CoO. An ambipolar treatment of the chemical diffusion, in the case of p-type semiconductor M_aO_b, oxides, has allowed us to express the chemical diffusion coefficient as a function of the concentration of the prevailing defects and of their diffusion coefficient In the case where the prevailing defects are cationic vacancies α times ionized we have shown that the expression D? = (1 + α)D_vα can be generalized to the A₂O compounds This set of results has allowed us, according to the copper self diffusion data obtained recently by Peterson etal, to estimate the apparent enthalpy of formation of the catiomc vacancies ΔH_f 23 ± 0 8 kcal mol^?1.     

Migration of vacancies and impurities on the (111) surface of a face-centered cubic lattice

The paper presents an analytic study of impurity atom movements over the (111) surface of a face-centered cubic lattice initiated by the diffusion of vacancies. If multiple collisions of a single impurity with vacancies are taken into account, impurity movement acquires the character of Brownian movement. At long times, the time dependence of the mean-square displacement of the impurity insignificantly differs from linear, and its spatial distribution is close to normal, which allows us to introduce a diffusion coefficient. An analytic equation obtained for this diffusion coefficient differs from the product of the diffusion coefficient of vacancies by their relative concentration by a numerical factor only.     

Surface diffusion of lead on tungsten

Field electron microscopy is used to study the surface diffusion of lead on tungsten. A simple method to measure rough values of the diffusion coefficient and its dependence on sub-monolayer coverage is described and tested. In the region around (001) the displacement energy found is about 1.30 eV/atom up to 10¹⁵ atoms/cm² where it decreases to 0.78 eV/atom. In the residual region except (110) this energy at 1.5×10¹⁴ atoms/cm² is 1.22 eV/atom, it decreases at 4 × 10¹⁴ atoms/cm² to 0.61 eV/atom and increases at 10¹⁵ atoms/cm² to 0.78 eV/atom. Corresponding values of the diffusion coefficient D and of the preexponential D₀ are given. The dependence of D on submonolayer coverage is discussed.     

Simulation of diffusion instability of a mercury atomic distribution in the cadmium-mercury-tellurium alloy

The formation of inhomogeneities in Cd_xHg_1-x Te alloys upon post-growth cooling or upon low-temperature annealing is simulated numerically. The mechanism of the formation of inhomogeneities is based on the diffusion instability in a system involving mercury atoms located at lattice sites, interstitial mercury atoms, and cation vacancies. It is revealed that, upon prolonged annealing of the Cd_xHg_1-x Te alloys with a cadmium content x = 0.2 at a temperature of ∼200°C, the concentrations of mercury atoms at lattice sites, interstitial mercury atoms, and vacancies are characterized by an inhomogeneous nearly periodical distribution arising from a small fluctuation when the initial equilibrium concentration of interstitial mercury atoms exceeds a threshold value (∼3 × 10¹⁷ cm⁻³). The spatial and time scales of the concentration distribution are determined primarily by the equilibrium concentration of vacancies and do not depend on the type of fluctuation involved. The spatial period of the concentration distribution increases linearly from 0.01 to 3.00 μm as the equilibrium concentration of vacancies changes from 10¹⁹ to 10¹⁴ cm⁻³. At lower concentrations of vacancies, the periodic structure is formed for a considerably longer time.     

Substitutional impurity in the graphene quantum dots

The process of formation of the localized defect states due to substitutional impurity in sp²-bonded graphene quantum dot is considered using a simple tight-binding-type calculation. We took into account the interaction of the quantum dot atoms surrounding the substitutional impurity from the second row of elements. To saturate the external dangling sp² orbitals of the carbon additionally 18 hydrogen atoms were introduced. The chemical formula of the quantum dot is H₁₈C₅₁X, where X is the symbol of substitutional atom. The position of the localized levels is determined relative to the host-atoms (C) ε_p energies. We focused on the effect of substitutional doping by the B, N and O on the eigenstate energies and on the total energy change of the graphene dots including for O the effect of lattice distorsion. We conclude that B, N, and O can form stable substitutional defects in graphene quantum dot.     

Superconductivity in heavily vacant diamond

Using first principle electronic structure calculations we investigated the role of substitutional doping of B, N, P, Al and vacancies (V) in diamond (X_αC_1-α). In the heavy doping regime, at about ∼1-6% doping an impurity band appears in the mid gap. Increasing further the concentration of the impurity substitution fills in the gap of the diamond host. Our first principle calculation indicates that in the case of vacancies, a clear single-band picture can be employed to write down an effective one band microscopic Hamiltonian, which can be used to further study various many-body and disorder effects in impurity band (super)conductors.     

Diffusion of atoms incorporated in the surface layer of the fcc(111) face

The kinetics of the migration of the impurity atom due to the diffusion of vacancies on the fcc(111) face was investigated. The study focused on the dependence of the diffusion coefficient of the impurity on the degree of surface coverage with vacancies. It was shown by molecular dynamics that this dependence is linear in the limit of the vanishingly small concentration of vacancies 1; the results of modeling coincided with the predictions of our analytical theory. The diffusion coefficient increased nonlinearly with and its growth correlated with that of the size of the percolation clusters. After the percolation threshold was overcome, the diffusion coefficient of the impurity quickly tended toward its value for the surface without hindrances.     

Study of the electric quadrupole interaction at Ta impurities in rare earth metal hosts

The time differential perturbed angular correlation technique has been used to measure the electric fieldgradient (EFG) at the site of¹⁸¹Ta impurities in the heavy Rare Earth metals Gd, Tb, Dy, Ho and Er at room temperature. It is found that the ratio α ≡ ¦V _zz ^eff /V _zz ^lat ¦ between the measured EFGV _zz ^eff and the lattice EFGV _zz ^lat , which is known from lattice sum calculations, is in the order of α?300, suggesting that an important contribution to the EFG is due to electrons localized at the impurity. The ratio α is not constant throughout the Rare Earth series. It decreases from Gd to Tb and increases between Tb and Er. This behaviour is compared to the results of a previous investigation with the impurity Cd in the same hosts.     

Determination of the nonequilibrium concentration of vacancies in silicon crystals by measuring the concentration of nickel atoms at lattice sites

A method is proposed for determining the nonequilibrium concentration of vacancies and vacancy complexes in silicon crystals by measuring the concentration of electrically active nickel atoms at the sites of the silicon lattice, [Ni _s ], after the diffusion of nickel at temperatures from 550 to 650°C. It is shown experimentally that, after the diffusion of nickel from the surface into silicon samples with different initial nonequilibrium concentrations of vacancy complexes, [V]_init, formed during crystal growth, the concentration [Ni _s ] in the bulk of a sample to a good degree of accuracy corresponds to the vacancy concentration [V]_init determined by a standard method based on the analysis of the concentration profiles of [Au _s ] after the diffusion of gold from the surface. This method for determining the concentration of vacancies is much simpler than the standard method and allows one to use lower temperatures and a lower thermal budget.     

A molecular dynamics investigation of the micro-mechanism for vacancy formation between Ag3Sn and βSn under electromigration

In this paper, the vacancy formation at the interface between different grains (Ag₃Sn and βSn) induced by electromigration was investigated from the perspective of atom diffusion. To explain the micro-mechanism of void formation near the interface, the diffusion coefficient was specifically studied here via molecular dynamics (MD) simulation. By comparing the atom diffusion rates of atoms in βSn and Ag₃Sn, a significant difference could be observed when the temperature is up to 400 K. The Sn atoms in βSn have a higher diffusion coefficient (8E ? 9 cm²/s) than atoms in Ag₃Sn (4E ? 9 cm²/s), which indicated that the void would be prone to appear in βSn near the interface. Moreover, the effect of grain size and pressure on atom diffusivity was studied. Results show that the atom diffusivity depends heavily on the grain size of Ag₃Sn. When the thickness of Ag₃Sn is increased from 4 to 12 nm, this difference is significant when the temperature is only 375 K. On the other hand, the atom diffusion character of Ag₃Sn and βSn changes substantially under constant pressure. The difference of the atom diffusion rate would be inhibited by pressure perpendicular to the interface, which indicated voids have less possibility to appear herein.     

An alternative approach to investigate the origin of p-type conductivity in arsenic doped ZnO

P-type conductivity in MOCVD grown ZnO was obtained by directional thermal diffusion of arsenic from semi-insulating GaAs substrate. The films were single crystalline in nature and oriented along (002) direction. Ab initio calculations in the framework of density functional theory have been carried out with different chemical states of arsenic in ZnO. Present calculations suggested As_Zn–2V_Zn defect is a shallow acceptor and results in ferromagnetism in ZnO. The magnetic measurements of the samples indeed showed ferromagnetic ordering at room temperature. X-ray photoelectron spectra confirmed the presence of As_Zn and V_Zn. The core level chemical shift in binding energy of As_Zn indicated the formation of As_Zn–2V_Zn. Diffused arsenic substitutes zinc atom and creates additional zinc vacancies. The zinc vacancies, surrounding the oxygen atoms, result in unpaired O 2p electrons which in turn induce ferromagnetism in the samples.     

Self-diffusion at grain boundaries with a disordered atomic structure

A change in the free energy of a grain boundary is analyzed in the case when lattice vacancies come to the boundary and are then delocalized in its disordered atomic structure. It is shown that the free energy of the boundary is minimized at some excess atomic volume Δv _b =Δv _b ^* , whose value depends on the energy of vacancy formation in the crystal lattice and the boundary energy. The formation of a metastable localized grain-boundary vacancy as a result of thermal fluctuations of the density in a group of n ₀=\gM_v/Δv _b atoms (\gM_v is the vacancy volume), followed by the jump of an adjacent atom into this vacancy, is taken as an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion and the diffusion coefficient are derived for equilibrium (Δv _b =Δv _b ^* ) and nonequilibrium (Δv _b >Δv _b ^* ) boundaries.     

Localized electronic excitations in crystalline phenacite Be2SiO4

The results of coordinated spectroscopic studies of the nature and properties of electronic excitations localized at regular and defect sites of the Be₂SiO₄ lattice are presented. The methods employed are electron-beam-excited pulsed absorption spectroscopy, pulsed cathodoluminescence, and low-temperature VUV spectroscopy with selective excitation by synchrotron radiation. The bands in luminescence spectra of Be₂SiO₄ at 2.70 and 3.15 eV are assigned to [AlO₄]^5? and [SiO₄]^4? centers formed both in direct relaxation of electronic excitations at defect levels and through the formation of exciton-defect complexes. Disruptions of beryllium-oxygen bonds (short-lived defects in the form of beryllium vacancies V _Be ^? ) are considered as initiating the formation of optically active centers with characteristic absorption bands in the range 1.5–4.0 eV. The intrinsic luminescence of the Be₂SiO₄ crystal at 3.6 and 4.1 eV is attributed to radiative decay of self-trapped excitons of two types. A mechanism of exciton self-trapping at the [SiO₄] and [BeO₄] tetrahedral groups is proposed, which involves excitation transfer from a threefold-coordinated oxygen atom to neighboring silicon or beryllium atoms.     

Effect of the fermi level position in silicon on ion-induced displacement of impurities

Abstract

With the channeling technique the lattice location of both As and B is studied in single As-or B-doped and in doubly As-and B-doped silicon single crystals. The influence of the position of the Fermi-level on the displacement of impurity atoms off substitutional lattice sites is investigated by changing the crystals from n- to p?type or vice versa by choosing implant conditions and annealing termperatures for the doubly doped crystals in an appropriate way. Big changes were found in displacement cross sections for As and B after conversion of the crystals from n- to p-type. The results can be explained by assuming that the interaction between primary defects and impurity atoms causing the displacement of the impurity atom is controlled by Coulomb attraction between charged point defects and the impurity atoms.     

On the nature of a lattice vibrational mode at a frequency of 135 cm−1 in Hg1 − x Cd x Te alloys

The vibrational spectrum of a cadmium impurity atom in the HgTe crystal has been calculated using the microscopic theory of lattice dynamics in the approximation of a low impurity concentration. Within this theory, the behavior of the local and quasi-local modes induced upon substitution of the lighter Cd atom for the Hg atom in the region of the zero or very low one-phonon density of states in the HgTe crystal has been considered. It has been found that, apart from the local mode at a frequency of 155 cm^?1, the calculated vibrational spectra exhibit a weak (but clearly pronounced) feature at a frequency of 134 cm^?1, which coincides with the experimentally observed vibrational mode (the “minicluster” mode) at a frequency of 135 cm^?1 in the Hg_{1 ? x} Cd _x Te (x = 0.2–0.3) alloys at 80 K.