Impurity Diffusion Research Articles

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed. Mass sources of various power are uniformly distributed in a certain internal interval of the body. Statistics of random sources are given. The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources. The solution is averaged over both certain internal subinterval and the entire body region. Simulation units are designed for modeling of the behavior of the averaged concentration function with acting system of point mass sources of various power. On this basis, the averaged concentration field is investigated depending on the internal interval length, power and number of sources in the system as well as the concentration values at the layer boundaries.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out. Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer. The statistics of random sources is given. The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources. Averaging of the solution is performed on the internal subinterval and in the entire body region. The formulas for the variance, correlation function of the concentration field and coefficient of correlation are expressed in terms of the second moment of random mass sources. Software modules are developed for simulating the behavior of the averaged concentration, variance and correlation function. Their numerical analysis also is performed. General properties of the considered function are determined depending on the problem parameters.

Probing and controlling oxygen impurity diffusion in h-BN semi-bulk crystals

Combining its unique features of ultrawide bandgap (UWBG) and two-dimensional nature, h-BN has been explored for emerging applications such as deep ultraviolet optoelectronic devices and single photon emitters. One of the unusual applications of h-BN is for solid-state neutron detectors by utilizing the property of high thermal neutron capture cross section of B-10 as well as its UWBG properties. Although a record high detection efficiency of 59% has been attained by h-BN detectors, the understanding/minimization of defects and impurities is still needed to further advance the h-BN material and detector technologies. We report metal organic chemical vapor deposition growth and oxygen (O) impurity diffusion in thick h-BN. The diffusion coefficient (D) of O impurities has been measured via the evolution of an oxygen related emission with the etching depth, providing a value of D of ∼ 2 × 10−13 cm2/s at 1450 °C and supporting the interpretation that oxygen in h-BN is a substitutional donor. A multiple-buffer-layer approach was employed to mitigate to a certain degree the issue of oxygen diffusion from sapphire substrate during growth. It was demonstrated that the performance of h-BN neutron detectors fabricated from the wafer incorporating multiple buffer layers was significantly improved, as manifested by the enhanced thermal neutron detection efficiency. The advancement of the crystal growth technology of h-BN semi-bulk crystals creates applications in optoelectronic and power electronic devices utilizing the UWBG semiconductor properties of h-BN, while high efficiency h-BN neutron detectors have the potential to supplant the traditional He-3 gas detectors in various application areas by offering the obvious advantages of UWBG semiconductor technologies.

Grain boundary self- and Mn impurity diffusion in equiatomic CoCrFeNi multi-principal element alloy

Grain boundary self-diffusion of Co, Cr and Fe and impurity diffusion of Mn are measured in a coarse-grained equiatomic CoCrFeNi multi-principal alloy. The tracer diffusivities are determined in a wide temperature range of 643 K to 1273 K, which encompasses both the C- and B-type kinetic regimes of grain boundary diffusion in polycrystalline materials after Harrison’s classification. At higher temperatures (T>800 K), only one short-circuit (grain boundary) contribution is observed, while the existence of two distinct contributions is elucidated by thorough analysis of the penetration profiles corresponding to the C-type kinetic regime (643–703 K). The latter observations are explained in terms of a grain boundary phase decomposition after prolonged annealing below 700 K. The product of the segregation factor and the grain boundary width is found to be about 0.5 nm for all constituting elements. The grain boundary diffusion data indicate that Mn does not reveal a strong (if any) segregation in the equiatomic CoCrFeNi alloy.

Interdiffusion behaviors and mechanical properties in Zr-Nb-Hf system

The diffusion behavior and mechanical properties of the Zr-Nb-Hf system were analyzed using diffusion couple technology and nanoindentation techniques. The diffusion couples were annealed at 1523 K for 24 h, and the compositional profile of the diffusion region was determined using electron probe microanalysis. The main diffusion coefficients, cross-diffusion coefficients, and impurity diffusion coefficients were calculated using the Whittle and Green method, as well as the generalized Hall method. Furthermore, the hardness and Young's modulus of the alloy with different compositions were calculated by Oliver method, based on load-displacement curves obtained from nanoindentation tests. Additionally, the wear resistance and resistance to plastic deformation of the Zr-Nb-Hf alloys were inferred. These results contribute to the existing database of diffusion kinetics and mechanical properties in the Zr-Nb-Hf system, providing valuable references for the development of Zr-Nb-Hf-based alloys with exceptional properties.

Super-flat and uni-oriented cobalt film electrodeposited by modulating the crystal nucleation and growth behavior

A precise control of the microstructure of electrodeposited cobalt film is crucial for attaining the desired and reproducible electrical performance in edge nanoelectronic devices. Here we realize the super-flat and uni-oriented cobalt film through a one-step electrodeposition process using benzenesulfinic acid (BNS) as additive. We find that the unsaturated sulfite group in BNS plays a key role in the super-flat cobalt electroplating. Molecular activity analysis and electrochemical test results suggested that the electron donating ability of the sulfite group was higher than that of the sulfonate group, resulting in stronger adsorption of BNS on the cobalt surface and enhanced cathodic polarization. Nucleation model fitting and surface morphology evolution studies revealed that the cobalt nucleation with BNS shifted to progressive nucleation from instantaneous nucleation in the additive-free electrolyte, leading to a more uniform and compact film morphology. Furthermore, equilibrium adsorption calculations indicated that the selective and strong adsorption of BNS on cobalt planes was responsible for the preferential orientation of the (002) crystal plane growth. After annealing, cobalt films prepared with BNS exhibited substantial grain growth and impurity diffusion, which further improved the electrical performance.

The effect of different AlGaN insertion layer thicknesses on the photoelectric properties of InGaN/AlGaN near UV light emitting diodes

In this paper, a near-ultraviolet LED structure was fabricated on a sapphire substrate by using metal–organic chemical vapor deposition with an undoped AlGaN insertion layer introduced between multiple quantum wells and electron blocking layers, and the effect of layer thickness on light-electric performance was investigated. Results of epitaxial structure characterization show that the introduction of an undoped AlGaN insertion layer almost does not affect the crystal quality and surface morphology of the LED epitaxial structure. Electroluminescence testing results indicate that as the insertion layer thickness increases, the device performance initially increases and then decreases. Furthermore, simulation analysis suggests that increasing the insertion layer thickness reduces the injection efficiency of carriers, lowers the radiative recombination rate and light emission performance of the active region's carriers. Additionally, the AlGaN insertion layer can effectively suppress the diffusion of Mg impurities, reduce the non-radiative recombination rate in the multiple quantum well active region, and thus improve the LED's light emission performance. Overall, under the competing effects of these two mechanisms, the optimal light emission performance for the near-ultraviolet LED is achieved when the insertion layer thickness is 1 nm.

Evidence of interstitial-mediated boron self-diffusion in boron carbide

Boron carbide is an important high-temperature material with interesting structural and functional properties. However, self-diffusion is very poorly known on this material, and also the few impurity diffusion studies, devoted in particular to helium and lithium, overlook the possible diffusion coupling with intrinsic defects. In this paper we present a study of boron self-diffusion in boron carbide based on first principles calculations and kinetic cluster expansion. Our results show that boron self-diffusion may occur with a migration activation energy on the order of 1.5–1.6 eV and with a global activation energy between 4 and 5.5 eV, depending on the doping conditions, which is significantly lower than the self-diffusion activation energies in other semiconducting carbides, like silicon carbide.We believe that our results are of interest for many applications of boron carbide and for tuning the best conditions for controlling the synthesis routes at specific stoichiometries for boron carbide.

Mikhail Ziegler, the First Professor of Metallurgy at Warsaw Polytechnic, and His Contribution for Developing our Knowledge about Steels

The article presents results of research on the origin and development of scientific schools in the field of metallurgy in Eastern Europe at the turn of the 19th–20th centuries, associated with the scientific and pedagogical activities of the famous scientist Professor Mikhail Karlovich Ziegler in the higher technical educational institutions of Warsaw (Warsaw Polytechnic Institute of Emperor Nicholas II), Kharkiv (Kharkov Technological Institute of Emperor Alexander III), St. Petersburg (Petrograd Polytechnic Institute) and Moscow (Moscow Mining Academy). The main facts of the biography of this scientist and educator are given. The stages of formation of M.K. Ziegler as a personality and a scientist against the backdrop of occurring historical processes are shown. The Soviet period of his activity was considered separately. The scientific achievements of Professor Ziegler in the field of steel metallurgy, in particular, in determining the strength of steels depending on the conditions of their crystallization, studying the diffusion of impurities in steels, which became the foundation for the development of continuous casting technology, i.e.one of the most important world inventions of the 20th century, are systematized and analyzed. His organizational and educating contribution for the training of scientific and engineering personnel for the metallurgical industry is also estimated. The article includes interesting forgotten and little-known facts from the history of metallurgical science and the training of the higher engineering and technical personnel in educational institutions located on the territory of modern Ukraine and Poland.

Development and analysis of thick GaN drift layers on 200 mm CTE-matched substrate for vertical device processing

This work reports the epitaxial growth of 8.5 µm-thick GaN layers on 200 mm engineered substrates with a polycrystalline AlN core (QST by QROMIS) for CMOS compatible processing of vertical GaN power devices. The epitaxial stack contains a 5 upmum thick drift layers with a Si doping density of 2 × 1016 cm−3 and total threading dislocation density of 4 × 108 cm−2. The thick drift layer requires fine-tuning of the epitaxial growth conditions to keep wafer bow under control and to avoid the formation of surface defects. Diode test structures processed with this epitaxial stack achieved hard breakdown voltages > 750 V, which is shown to be limited by impurity or metal diffusion from the contact metal stack into threading dislocations. Conductive Atomic Force Microscopy (cAFM) reveals some leakage contribution from mixed type dislocations, which have their core structure identified as the double 5/6 atom configuration by scanning transmission electron microscopy images. Modelling of the leakage conduction mechanism with one-dimensional hopping conduction shows good agreement with the experimental data, and the resulting fitting parameters are compared to similar findings on silicon substrates. The outcome of this work is important to understand the possibilities and limitations of vertical GaN devices fabricated on large diameter wafers.

Magnetic Properties of Silicon with Paramagnetic Impurity Atoms

One of the possible ways to obtain silicon with magnetic properties is the introduction of paramagnetic impurities into silicon: Cr, Mn, Fe, Ni, and Co. In our opinion, silicon materials containing magnetic nanosized clusters are most suitable for spintronic devices. The possibility of obtaining silicon with magnetic properties by diffusion doping was studied in this work. To obtain silicon doped with Cr, Mn, Fe and Ni impurity atoms, p-type single-crystal silicon with a specific resistance of ρ = 5 Ohm·cm and ρ = 0.5 Ohm·cm was used, and for doping with Co atoms, n-type silicon with resistivity ρ=10 Ohm·cm was used. The diffusion temperature and time were chosen such that, after diffusion annealing, the samples with impurity Cr, Fe, and Mn atoms remained highly compensated p-type, and when doped with impurity Co atoms, they remained high-resistance n-type. The results of the study showed that with decreasing temperature, the value of the negative magnetoresistance Δρ/ρ in the Si<Mn> samples increases and reaches its maximum value (about 800%) at T = 240 K, a further decrease in temperature leads to a decrease in the magnetoresistance, and at a temperature T = 170 K, the sign of the magnetoresistance is inverted. In Si <Cr> samples, with decreasing temperature, the positive magnetoresistance turns into a negative one, the value of which increases with decreasing temperature, and is achieved at T=100 K Δρ/ρ = 45–50%. In Si<Fe> samples, with decreasing temperature, the value of negative magnetoresistance increases monotonically and at T=100 K its value is Δρ/ρ = (100÷120) %. The study in Si<Сo> samples showed that with decreasing temperature the value of positive magnetoresistance increases and at Т=100 K it reaches Δρ/ρ = (17÷20) %. The study of magnetoresistance in samples - Si<Ni> showed that with decreasing temperature the value of positive magnetoresistance increases and at T=100 K it reaches Δρ/ρ = (10÷15) %. When studying the magnetic properties of p-Si <B, Mn> samples at low temperatures (below T=30 K), a ferromagnetic state was found, i.e. succeeded in obtaining a magnetic semiconductor material by the method of diffusion of a paramagnetic impurity. In the overcompensated Si <B, Mn> (n‑type) samples, no magnetic hysteresis was found. This shows a significant effect on the magnetic properties of the manganese impurity in silicon of its charge and, accordingly, spin state. Based on the results obtained, it can be argued that diffusion doping of silicon with manganese can be used to obtain silicon with magnetic properties.

Estimation of diffusion coefficients in NiCoFeCrAl multi-principal element alloy following an inventive design strategy of diffusion couples

An inventive design strategy of producing the diffusion couples for intersecting the diffusion paths in multicomponent space is described in Ni-Co-Fe-Cr-Al multi-principal element alloy. This, for the first time, facilitates the estimation of the tracer, intrinsic, and interdiffusion coefficients of all the elements purely experimentally in this quinary system. This was not possible until now following any other experimental methods. The tracer diffusion coefficients estimated in this quinary system are compared with the impurity and tracer diffusion coefficients in pure Ni, and at (or near) equiatomic compositions of binary Ni-Co, ternary Ni-Co-Cr, and quaternary Ni-Co-Fe-Cr systems. The relative mobilities of the elements are found to follow the trend DNi*≤DCo*<DFe*≤DCr*<DAl* in all the systems. However, the tracer diffusion coefficients of the elements first decrease and then increase with the increasing order of the systems. The contribution of the vacancy wind effect on certain cross-intrinsic diffusion coefficients is found to be very significant and cannot be ignored. The influence of the vacancy wind effect on interdiffusion coefficients is less significant than the intrinsic diffusion coefficients since interdiffusion coefficients are the average of multiple intrinsic diffusion coefficients. This may lead to the wrong statement that the vacancy wind effects are negligible. We have further shown that describing the relative diffusion rates of the elements with main interdiffusion coefficients instead of the tracer diffusion coefficients can be misleading or confusing. Different elements as the dependent variables of interdiffusion coefficients indicate a very different or even opposite trend of relative diffusivities in this system.

ATOMISTIC SIMULATION OF SELF- DIFFUSION AND DIFFUSION Co ALONG SYMMETRIC TILT GRAIN BOUNDARIES [2¯1 ¯1 0] IN α-Ti

The structure, point defects, self-diffusion, and diffusion of Co for four energetically preferred grain boundaries (GB) with the tilt axis [21 1 0] in α-Ti are being investigated by computer modeling methods. The structure and energies of the boundaries and the energies of the formation of point defects in GB, were calculated by molecular static modeling. The dependencies of point defect formation energies on the distance from the grain boundary plane are demonstrated. The coefficients of grain boundary self-diffusion are calculated by the method of molecular dynamics. The results of self-diffusion modeling are compared with the available experimental data. The simulation of grain boundary diffusion of the impurity Co in titanium is also performed. It is shown that the structure of GB affects the parameters of grain-boundary diffusion both in the case of self-diffusion and in the case of impurity diffusion, and the coefficients of grain-boundary diffusion may differ by several orders of magnitude depending on the structure.

The influence of Soret and Dufour cross-effects on laser surface treatment of metal accompanied by solid-phase chemical reaction

The paper presents a mathematical model of the process of heat treatment of surface of solid material by short thermal impulse, corresponding to laser developed in the line. The absorption and reflection of the laser beam according to the Lambert-Bouguer law, the Soret and Dufour cross effects, which appear due to high temperature and concentration gradients, and possible chemical transformations due to impurity diffusion into the material, are taken into account. The dimensionless variables are used for the problem solution. The temperature and concentration fields in solid materials are calculated analytically and numerically. For analytical solution, Laplace transform method is used. Numerically, the problem is solved using finite differences method. For the first time in such a problem, both possible chemical transformations and cross effects are simultaneously taken into account. It is found that, in the region of the high temperature and composition gradients, the Soret and Dufour effects lead to a decrease in temperature near the surface and a decrease in concentration at a certain distance from the surface both during heating and after the termination of the pulse. In the case of an exothermic reaction that converts a reactant into a product, cross effects lead to an increase in the concentration of the reaction product in the heated zone outside the region with the high concentration gradient.

Cryogenic Electrical Properties of an Aluminum-Beryllium Nanocomposite

Many power distribution networks are desiring lightweight electrical conductors. Cryogenic hyperconducting aluminum (99.999%+ pure) is a competitive option to HTS cables at 20 K, but these cables require mechanical reinforcement for many applications, and this strengthening must be compatible with aluminum's annealing schedule to prevent impurity diffusion. AlBeMet AM162H is a lightweight Al-Be nanocomposite which can be processed similar to aluminum alloys, and similar to hyperconducting aluminum, does not experience the extreme quench characteristics seen in superconducting composites. In this research, we shall investigate the electrical conductivity of cryogenic AlBeMet AM162H, and compare its mass specific engineering current carrying capacity with hyperconducting aluminum composites and high purity copper. Additionally, the AC losses of AlBeMet AM162H will be compared to other cryoresistive metals and state-of-the-art low AC loss BSCCO-2212 and MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> multifilamentary wire.

In Ukrainian

Investigating the formation of inversion layers (IL) at the Si-SiO2 interface in the manufacturing technology of silicon photodetectors, some dynamics of dislocations after isothermal annealing were revealed, which were absent in samples without inversion. After selective etching of samples with inversion layers, localization of dislocations on the periphery of responsive elements (RE) with accumulation of guard rings (GR) or other elements of n+-type topology outside the RE was observed. This testified to the movement of dislocations on the surface of the Si-SiO2 structures with IL in the direction of the periphery of the crystal during isothermal annealing, which contributed to a significant decrease in the density of structural defects in RE. The described phenomenon can be used to obtain highly doped defect-free silicon structures. Since the presence of dislocations or other violations of the crystal lattice negatively affect the parameters of the products. In the case of using the described phenomenon as a technological method of “cleaning” the surface of silicon structures, there is a need for controlled formation of IL. One of the methods of forming inversion layers can be thermal oxidation in hydrochloric acid vapors according to the principle of dry-wet-dry oxidation (for p-type silicon). Another method that does not require additional materials is the annealing of Si-SiO2 structures at a temperature of 900–950 Celsium degrees in a nitrogen atmosphere for ≥ 240 minutes. Inversion channels, in this case, will be formed due to the redistribution and diffusion of metal impurities in the oxide (which were introduced during previous thermal operations) to the Si-SiO2 interface. In the described case, these structural defects after annealing were localized in the GR, which is also an active element of the phododiodes, as it limits the dark current of the RE, accordingly, the dark current of the GR should also be low. To be able to implement this method, it is necessary to create passive n+-regions on the periphery of the crystals, limited by oxide, which will be the locations of defects after annealing. It can be both separate areas of arbitrary shape and a concentric ring outside the GR. Elements that will be the locations of defects on the periphery can be cut off at the stage of separating the substrates into crystals. After annealing, it is necessary to remove the IL and form an anti-reflective coating by any known method, since the presence of inversion channels contributes to the growth of dark currents. When examining the morphology of defect localization areas after annealing under high-magnification microscopes and with the help of an atomic force microscope, the formation of hexagonal and round defects, which are partial marginal Frank dislocation loops, was observed. The mechanism of dislocation movement described in this article has not been thoroughly studied by us and requires additional research, but it may be related to Cottrell atmospheres and their interaction with IL

Effects of Impurity Barrier Layer on the Red Zone at the Bottom of Cast Monocrystalline Si Ingot for Solar Cells

A technique to prepare low‐cost high‐purity quartz sheets as impurity barrier layers between the crucible and the seed crystal is proposed herein to improve the casting process of monocrystalline Si (mono‐Si) ingots. The results show that the diffusion of metal impurities from the crucible toward a cast mono‐Si ingot can be hindered, increasing the minority carrier lifetime of Si crystals and reducing the height of the red zone at the bottom of the ingot. Solar cell devices assembled from cast mono‐Si ingots exhibit the enhancement in their overall photoelectric conversion efficiency (η) by 0.76% in comparison to those based on conventional mono‐Si ingots. Therefore, high‐purity quartz sheets as impurity barrier layers for the casting of mono‐Si ingots have great application potential in the photovoltaic industry.

Diffusion coefficient measurement and atomic mobility assessment for bcc Ti–V–Fe ternary alloys

Diffusion behaviors in bcc Ti–V–Fe ternary alloys have been investigated at 1273 K and 1473 K by the diffusion couple technique. The composition-distance profiles have been retrieved from Electron Probe MicroAnalysis (EPMA) and analytically represented by the ERror Function EXpansion (ERFEX), and then the ternary inter-diffusion and impurity diffusion coefficients have been extracted by Whittle–Green and generalized Hall methods, respectively. The extracted inter-diffusion coefficients of D˜VVTi and D˜FeFeTi range from 0.89 × 10−13 m2/s to 1.86 × 10−13 m2/s and from 1.33 × 10−12 m2/s to 1.76 × 10−12 m2/s, respectively, at 1273K, and from 6.41 × 10−13 m2/s to 15.98 × 10−13 m2/s and from 82.46 × 10−13 m2/s to 147.08 × 10−13 m2/s at 1473K. D˜VVTi exhibits the similar compositional variation at both temperatures, which decrease with decreasing Fe and minimize at the Ti–V binary. D˜FeFeTi has the maximum value at Ti–corner and eventually decreases with the increasing V and Fe at 1273K, but has the maximum value at Fe-rich Ti–Fe binary and decreases with the increasing V. The atomic mobility parameters of Ti–V, Ti–Fe and V–Fe binary systems have been revised to associate with the lasted ternary interaction parameters in thermodynamics. The ternary atomic mobility parameters for diffusion have been assessed for the first time by reproducing the extracted diffusion coefficients. The composition-distance profiles and the diffusion paths have been successfully reproduced by using the optimized atomic mobility parameters showing a consistency with the experimental data and indicating the accuracy of this work.

On Parameters of Evaporation Refining

The previously presented theory of evaporation refining which takes into account the difference in the vapor pressure of the components and the diffusion of impurities (but not other possible factors) is analyzed. The complexity of the theory is noted: to calculate the refining efficiency depending on the yield at a given temperature, a large number of parameters (nine) of the substance and material are required: molar mass M, density ρ, melting point Tm, equilibrium separation factor β0, vapor pressure of the main component p, the impurity diffusion activation energy in the refined substance Q, the impurity diffusion coefficient Dm at temperature Tm and the material size factor X. The conceptual character of the theory under consideration is noted due to the lack of knowledge of most of these parameters and the neglect of all process factors.

A microscopic mechanism of efflorescence on hemihydrate gypsum: Insight into the formation and diffusion of sodium impurities in hemihydrate gypsum crystals

Using phosphogypsum (mainly composed of dihydrate gypsum) as raw material to prepare α-hemihydrate gypsum (α-HH) is an effective way for high-value utilization of phosphogypsum solid waste. Sodium ions can effectively promote the transformation of dihydrate gypsum to α-HH and enhance the driving force of crystal transformation. However, during this process, sodium impurities may be doped into the α-HH crystals, resulting in an efflorescence phenomenon when α-HH products are used, which affects the use of the products. In this paper, the formation of sodium impurities in the process of preparing α-HH in NaCl solution was studied by the laboratory test, XRD, XPS, SEM and XRF. Possible forms and diffusion paths of sodium impurities in hemihydrate gypsum crystals are studied by density functional based tight binding methods. The results show that sodium impurities tend to exist in hemihydrate gypsum crystals by doping at interstitial sites. Moreover, there are a large number of interstitial sites in hemihydrate gypsum, which are critical for the diffusion of sodium impurities.