A comparative study is carried out of the electrophysical parameters of plasma, concentrations of fluorine atoms, and kinetics of reactive ion etching of Si and SiO2 in CF4 + Ar/He, CHF3 + Ar/He, and C4F8 + Ar/He mixtures of variable (0–45

The tasks of analyzing and visualizing the dynamics of viscous incompressible flows of complex geometry based on traditional grid and projection methods are associated with significant requirements for computer performance necessary to achieve the set goals. To reduce the computational load in solving this class of problems, it is possible to apply algorithms for constructing artificial neural networks (ANNs) using exact solutions of the Navier–Stokes equations on a given set of spatial regions as training sets. An ANN is implemented to construct flows in regions that are complexes made up of training sets of standard axisymmetric domains (cylinders, balls, etc.). To reduce the amount of calculations in the case of 3D problems, invariant flow manifolds of lower dimensions are used. This makes it possible to identify the structure of solutions in detail. It is established that typical invariant regions of such flows are figures of rotation, in particular, ones homeomorphic to the torus, which form the structure of a topological bundle, for example, in a ball, cylinder, and general complexes composed of such figures. The structures of flows obtained by approximation based on the simplest 3D unsteady vortex flows are investigated. Classes of exact solutions of the incompressible Navier–Stokes system in bounded regions of ℝ_3 are distinguished based on the superposition of the above-mentioned topological bundles. Comparative numerical experiments suggest that the application of the proposed class of ANNs can significantly speed up the computations, which allows the use of low-performance computers.

The tasks of analyzing and visualizing the dynamics of a viscous incompressible fluid in conditions of complex flow geometry based on traditional grid and projection methods are associated with significant requirements for computer performance to achieve the set goals. To reduce the computational load in solving this class of problems, algorithms for constructing artificial neural networks (ANNs) can be used, using exact solutions of the Navier–Stokes equation system on a given set of spatial regions as training sets. An ANN is implemented to construct flows in areas that are complexes made up of training sets of standard axisymmetric regions (cylinders, balls, etc.). To reduce the amount of calculations in the case of 3-D problems, invariant flow manifolds with smaller dimensions are used. This allows you to identify the detailed structure of solutions. It is established that the typical invariant regions of such flows are rotation figures, in particular, homeomorphic torus, forming the structure of a topological bundle, for example, in a ball, a cylinder and in general complexes composed of such figures. The structures of the flows obtained by approximation by the simplest 3-D vortex unsteady flows are investigated. Classes of exact solutions of the Navier–Stokes system for an incompressible fluid in bounded regions of space based on the superposition of the above topological bundles are distinguished. Comparative computational experiments indicate a significant acceleration of computational work in the case of using the proposed class of ANNs, which allows the use of computing equipment with low performance.

This work discusses the influence of inert carrier gases, Ar and He, on both gas-phase plasma characteristics and ZnO etching rate under typical reactive-ion etching conditions in the hydrogen bromide environment. Plasma diagnostics by Langmuir probes and 0-dimensional plasma modeling allowed one to compare how the content of given carrier gas does influence electrons-and ions-related plasma parameters, kinetics and densities of plasma active species. It was found that the transition toward Ar- or He-rich plasmas a) causes the growth of electron temperature (due to lower electron energy losses in collisions with atomic species); b) reduces plasma electronegativity; and c) results in opposite changes in both ion density and ion flux. The last phenomenon is due to opposite changes in total ionization rates determined by sufficient difference in ionization rate coefficients for Ar and He atoms. Important features of HBr + Ar plasma at 0-80% Ar are also the slower-than-linear fall of Br atom density (due to the intensification of electron impact dissociation for both HBr and Br2 molecules) as well as an increase in H atom density (due to decreasing their loss rate in gas-phase reactions). Etching experiments indicated that the ZnO etching rate is mostly contributed by the ion-assisted chemical reaction while the reaction rate decreases faster compare with the Br atom flux. The corresponding decrease in the effective reaction probability may be related to changes in both ion bombardment intensity and hydrogen passivation effect.

In this work, we investigated the influence of inert carrier gas on electro-physical plasma parameters, steady-state densities of active species and kinetics of their interaction with ZrO2 under the condition of "soft" reactive-ion etching in chlorine. This regime assumes the lower-than-usual negative bias voltage in order to reduce both ion bombardment energy and etched surface damage. The combination of plasma diagnostics by Langmuir probes and 0-dimensional plasma modeling allowed one to analyze formation and decay kinetics for neutral and charged species at various gas mixing ratios. It was found that the mixing of Cl-2 with Ar or He at constant total gas pressure a) causes an increase in both electron temperature and plasma density; b) increases the Cl-2 dissociation degree through the acceleration of electron-impact processes; and c) intensifies the ion bombardment by the change of ion flux. From etching experiments, it was found also that the ZrO2 etching rate is mostly composed by its chemical component, but does not correlate with the change in the Cl atom flux. The latter reveals that a) the dominant ZrO2 etching mechanism is the ion- assisted chemical reaction and b) an increase in the effective reaction probability toward Ar or He rich plasmas reflects the acceleration of ion-induced heterogeneous effects, such as the destruction of Zr-O bonds and/or the desorption of low-volatile ZrClx compounds. The lower neutral/charged ratio obtained in Ar-containing plasma allows one to assume the more anisotropic etching. It was shown that above findings are surely valid in the pressure range of 4-12 mTorr as well at bias powers of 100 - 300 W.

The problem of ensuring the guaranteed normal functioning of digital systems in the Russian oil and gas industry in the context of the sanctions war of the United States and the European Union against this industry is discussed. To solve it, it is proposed to use hardware and software with built-in intelligent self-monitoring and self-correction mechanisms. It is proposed to counter bans on the supply of supercomputers for hydrodynamic calculations by using computational methods based on exact solutions and coarse grids.

This work investigated the influence of component ratio, input power and gas pressure on electro-physical plasma parameters, steady-state densities of active species and reactive-ion etching kinetics for SiO2 in CF4 + Ar and Cl2 + Ar plasmas. The combination of plasma diagnostics by Langmuir probes and plasma modeling indicated that the variation of processing conditions causes similar changes in physical and chemical factors influencing the reactive-ion etching (RIE) rate for SiO2. The only one exception is the opposite effect of gas pressure on densities of fluorine and chlorine atoms. The analysis of RIE kinetics was carried out using model-predicted data on fluxes of ions and chemically active species. It was found that the dominant etching mechanism in both gas mixtures is the heterogeneous chemical reaction while the reaction rate correlates with fluxes of fluorine or chlorine atoms. The effective probability for the Si + nF -SiFn reaction decreases with an increase in the ion bombardment intensity. Such situation reveals no ion-driven limiting stages while the negative effect of ion bombardment may result from desorption of F atoms under conditions of high adsorption degree and spontaneous interaction mechanism. The effective prob-ability for the Si + nCl -SiCln reaction exhibits much lower absolute values as well as always traces the change in the ion bombardment intensity. This allows one to assume the ion-assisted reaction regime which is activated by the formation and/or cleaning of adsorption sites for chlo-rine atoms.

This work investigated the influence of component ratio in the HBr + Ar gas mixture on electro-physical plasma parameters, steady-state densities of active species and reactive-ion etching (RIE) kinetics for SiO2 and Si3N4 under conditions of inductive RF (13.56 MHz) discharge. The combination of plasma diagnostics by Langmuir probes and plasma modeling indicated that an increase in Ar content at constant gas pressure and input power a) caused an increase in electron temperature and densities of charged species; b) results in increasing ion bombardment intensity; and c) leads to the nearly proportional decrease in Br atoms density and flux. It was found that variations of SiO2 and Si3N4 etching rates vs. mixture composition are qualitatively similar while the maximum difference in corresponding absolute values takes place in pure HBr plasma. The analysis of RIE mechanisms was carried out using model-predicted data on fluxes of ions and bromine atoms. It was found that the dominant SiO2 etching mechanism is the ion-assisted chemi-cal reaction which is characterized by the nearly-constant rate in the range of 0-80% Ar due to an increase in the effective reaction probability. That is why the noticeable intensification of physical sputtering with increasing Ar fraction in a feed gas causes the only weak growth of obtained SiO2 RIE rate. Oppositely, the Si3N4 etching process is mainly contributed by the physical sputtering while the efficiency of ion-stimulated chemical reaction is limited by the low reaction probability. This provides both slower etching process (especially in Ar-poor plasmas) and stronger sensitivity of etching rate to the change in mixture composition.

A comparative study of the effect of small (up to 20%) substituting additives F 2 , H 2 , and HF on the kinetics and stationary concentrations of neutral particles in 50% CF 4 + 50% Ar plasma under the typical conditions of reactive ion etching (RIE) of silicon and its compounds is carried out. It is shown that the variation of the CF 4 /F 2 and CF 4 /H 2 ratios leads to opposite, interrelated, and nonadditive changes in the concentrations of fluorine atoms and fluorocarbon radicals. This provides wide ranges of regulation of the etching rate and polymerization capacity with the minimal disturbance of the parameters of the electronic and ionic components of the plasma. In contrast, the CF 4 /HF relation has the minimal effect on the rate of surface polymerization, but noticeably changes the concentration of fluorine atoms. Thus, there is a selective effect on the rate of the heterogeneous chemical reaction.

A general topological approach is proposed for the construction of converging artificial neural networks (ANN) by applying decision-making algorithms tuned on a sequence of iterations of continuous mappings (ANN layers). The mappings are selected using optimization principles underlying ANN training, and decision-making based on the results of training a multilayer ANN corresponds to finding a sequence converging to a fixed point. It is found that problems of this class are computationally unstable, which is caused by the phenomenon of dynamic chaos associated with the ill-posedness of the problems. Stabilization methods converging to stable fixed points of the mappings are proposed, which is the starting point for a wide variety of mathematical studies concerning the optimization of training sets in ANN construction.

The parameters of the gas phase and the kinetics of reactive ion etching of SiO 2 and Si 3 N 4 under conditions of an induction RF (13.56 MHz) discharge with a varying HBr/Cl 2 ratio is studied. The study includes plasma diagnostics using Langmuir probes, plasma modeling to find stationary concentrations of active particles, measuring velocities, and analyzing etching mechanisms in the effective interaction probability approximation. It is found that the substitution of HBr by Cl 2 at a constant argon content (a) is accompanied by a noticeable change in the electrical parameters of the plasma; (b) leads to a weak increase in the intensity of ion bombardment of the treated surface; and (c) causes a significant increase in the total concentration and flux density of reactive particles. It is shown that the etching rates of SiO 2 and Si 3 N 4 increase monotonically as the proportion of Cl 2 increases in a mixture, while the main etching mechanism is an ion-stimulated chemical reaction. The model description of the kinetics of such a reaction in the first approximation assumes (a) the additive contribution of bromine and chlorine atoms and (b) the direct proportional dependence of their effective interaction probabilities on the intensity of ion bombardment. The existence of an additional channel of heterogeneous interaction with the participation of HCl molecules is proposed.

The influence of the initial composition of a CF4 + CHF3 + Ar mixture and bias power on the electrical parameters of the plasma, the composition of the gas phase, and the kinetics of heterogeneous processes on the treated surface under conditions of an induction RF (13.56 MHz) discharge is studied. It is found that the variation of the CF4/CHF3 ratio does not lead to significant perturbations of the parameters of the electronic and ionic components of the plasma, but significantly changes the concentrations of fluorine atoms and polymer-forming radicals. In contrast, an increase in the bias power at a fixed initial composition of the mixture has practically no effect on the concentrations of active particles, but is characterized by a proportional change in the energy of the bombarding ions. The model analysis of the kinetics of heterogeneous processes shows that the CF4/CHF3 ratio provides wider ranges of regulation of the etching rate of the base material, as well as the deposition rate of the fluorocarbon polymer film and its thickness.

The characteristics of the gas phase and the kinetics of reactive-ion etching of silicon in a 50% C6F12O + 50% Ar plasma are studied. The study scheme includes plasma diagnostics using Langmuir probes and optical emission spectroscopy, as well as the measurement of etching rates with varying input power (200–600 W) and gas pressure (4–12 mTorr). It is shown that (a) the nature of the change in the parameters of the electron and ion components of the plasma generally corresponds to the regularities known for other fluorocarbon gases; and (b) the kinetics of the formation of fluorine atoms is significantly affected by bulk processes of the form CFx + O → COFx–1 + F. It is established that the change in the silicon etching rate is determined by the kinetics of the heterogeneous reaction Si + xF → SiFx flowing in the mode of limitation by the flow of fluorine atoms. It is assumed that the effective probability of this reaction under constant temperature conditions is determined by the processes of competitive adsorption of oxygen atoms and/or surface oxidation.

The article shows that the primacy of profit, enshrined by law in the Civil Code of the Russian Federation, is the cause of the country's import dependence, due to the degradation of both the industrial production sector, primarily high-tech, and the personnel training system that ensures the development and production of such products. A possible alternative is a model for the implementation of the State Armament Program.

The investigation of electro-physical plasma parameters, steady-state gas phase composition and reactive-ion etching kinetics of silicon in Cl-2 + BCl3 + Argas mixture under conditions of RF 13.56 MHz inductive discharge was carried out. The investigation procedure included plasma diagnostics by Langmuir probes as well as the 0-dimensional (global) modeling of plasma chemical kinetics. Fixed processing parameters were represented by the argon fraction in a feed gas (10%), total gas pressure (6 mTorr) and bias power (300 W). It was found that the substitution of Cl-2 for BCl3 at constant input power a) does influence electrons- and ions- related plasma parameters; b) lowers plasma electronegativity; and c) causes opposite changes in densities of chlorine atoms and BClx radicals. An increase in input power at any fixed feed gas composition results in increasing both dissociation degrees for original molecules and densities of dissociation products. It was shown that the dependence of SiO2 etching rate on the Cl-2/BCl3 mixing ratio exhibits the non-monotonic shape (with a maximum of similar to 120 nm/min for Cl-2 + 40% BCl3 + 20% Ar gas mixture), and an increase in both BCl3 fraction and input power caused the same effect for the SiO2 + Cl reaction probability. This contradicts with the change in ion energy flux. It was suggested that BClx radicals also play a role of chemically active species being involved in SiOy + BClx -> SiOy-1 + BClxO heterogeneous reactions. Such reactions provide an increase in the amount of adsorption sites for chlorine atoms.

In this work, we investigated gas-phase plasma characteristics and reactive-ion etching kinetics of silicon in the C6F12O + O-2 gas mixture with using CF4 + O-2 as the reference system. An interest to C6F12O is due to its low global warming potential (GWP) and totally unknown dry etching performance in respect to silicon-based materials. The research scheme included plasma diagnostics by Langmuir probes and optical emission spectroscopy as well as the 0-dimensional (global) modeling for CF4 + O-2 plasma. The main focus was on electrons- and ions-related plasma parameters, densities of F and O atoms (as main etchants for target materials and fluorocarbon polymer film, respectively) as well as on Si etching rates vs. gas pressure (4-12 mTorr) and input power (200-600 It was shown that both gas systems exhibit similar behaviors of plasma density, ion flux and ion bombardment energy while the principal feature of the C6F12O + O-2 plasma is the systematically lower density of both F and O atoms. Etching experiments indicated a) the negligible contribution of sputter etching; and b) identical changes in the chemical etching kinetics vs. processing parameters. The C6F12O + O-2 plasma is featured by lower absolute etching rates (that correlates with differences in F atom fluxes) as well as by higher effective probabilities for Si + F reaction. Perhaps, the last phenomenon is due to heterogeneous processes involving oxygen atoms.

Classes of exact solutions corresponding to vortex and potential flows are presented within the framework of a hydrodynamic model describing flows of a viscous incompressible fluid. The study of exact solutions is a prerequisite for creating a core simulator, which is associated with modeling fluid dynamics in a porous medium and the response of the field to dynamic influences in order to increase oil recovery.

In this paper, we investigate the kinetics and mechanisms of reactive-ion etching of Si and SiO 2 in the plasma of an HBr + O 2 mixture with a variable initial composition under conditions of the high-frequency (13.56 MHz) inductive discharge. In the experimental and theoretical (model) analysis of the plasma parameters, the key plasma-chemical processes that form the stationary composition of the gas phase are identified and the densities of active particle fluxes onto the surface under processing are determined. It is found that the increase in the O 2 concentration in the plasma-forming mixture is accompanied by a decrease in the kinetic coefficients (probability of effective interaction and etching yield) that characterize the heterogeneous stages of the etching process. It is assumed that the main mechanism of this effect is the oxidation of SiBr x etching products to low volatile compounds of the SiBr x O y type.

The kinetics of reactive ion etching of Si and SiO2 in the plasma of a high-frequency (13.56 MHz) inductive discharge in a CF4 + O2 mixture in the range of input power of 200–600 W (0.02–0.06 W/cm3) is studied. The key plasma-chemical processes that form stationary electrophysical parameters and composition of the gas phase are identified (a), and the flux densities of neutral and charged particles on the treated surface are determined (b) with the combined use of plasma diagnostics by Langmuir probes and 0-dimensional (global) plasma modeling. It is found that the dominant etching mechanism for both materials is an ion-stimulated chemical reaction proceeding in the kinetic mode and limited by the fluorine flux. It is shown that the decrease in the effective probability of interaction in Si/SiO2 + F systems with an increase in the input power and gas pressure may be due to heterogeneous processes with the participation of oxygen atoms.

The kinetics and mechanisms of reactive ion etching of titanium oxides (TiO 2 ), indium (In 2 O 3 ), tin (SnO 2 ), and zinc (ZnO) in HBr + Ar plasma. It is found that an increase in the fraction of Ar is accompanied by a decrease in the etching rates of all the materials under study, while the absolute values of the rates for any composition of the mixture are correlated to the value of the breaking energy of the oxide bond and/or the volatility of the interaction products. With the combined use of methods of diagnostics and plasma modeling, the stationary concentrations of active particles and the density of their fluxes on the treated surface are determined. The use of these data for the analysis of the kinetics of heterogeneous processes showed that (a) the dominant etching mechanism in the range 0–75% Ar is an ion-stimulated chemical reaction; and (b) the effective probability of the interaction of bromine atoms increases (for TiO 2 ) or decreases (for In 2 O 3 , SnO 2 , and ZnO) with the increasing dilution of HBr with argon. Assumptions are made about the reasons for this dependence.