Approximation of the erosion zone profile in planar magnetrons with a disk cathode

We have proposed a universal approximation of the normalized erosion zone profile of planar magnetrons with a disk cathode by a composite function that includes the probability density function for the minimal distribution of extremal values for the region from the center of the disk cathode to the maximum of the erosion zone and the survival Weibull distribution function (from the maximum to the outer boundary of the sputtering zone). The accuracy of the approximation has been verified for six magnetrons differing in the cathode size or in the design of the magnetic systems. In all cases, good agreement has been observed between the approximation and experimentally measured values. The results reported here can be used to analyze processes that occur on the cathode during sputtering and to refine the calculations of coating profiles.     

Microwave plasma enhanced low pressure d.c. sputtering of copper films

This paper reports on d.c. sputtering of copper films using a cylindrical magnetron (CyM) with the discharge enhanced and/or ignited by a microwave plasma produced in an external magnetic fieldB _e . The sputtering system was optimized with the aim to achieve high deposition rate of films at low argon pressures. It was achieved by enhancing the ionization degree of the discharge plasma by microwaves absorbed in the plasma and by the control of the distribution ofB _e (z) along the device axis, i.e. by controlling the transport of the plasma to within a close vicinity of the sputtered target of the CyM. The optimized sputtering system can sputter films at low argon pressures from about 0.1 Pa down to 0.005 Pa and at quite large discharge currentsI _d up to 1 A, i.e. at quite large deposition ratesa _D of about several hunderds of nanometers per minute. The sputtering system operates at pressures lower than conventional magnetrons, i.e., under conditions when fast neutrals play a significant role. It opens the possibility to produce films of new properties. As an example, the microwave enhanced sputtering discharge was used to deposit Cu films. Resistivity and preferred crystal orientation of Cu films prepared under different argon pressures and at microwave powers ranging from about 100 W to 800 W is reported.This work was supported in part by the Grant Agency of Czech Republic under Grant No. 202/93/0508.     

The distribution of first-passage times and durations in FOREX and future markets

Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter t_max, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail.     

On the energy distribution and angular distribution of sputtered particles

Abstract

The influence of the anisotropy of the momentum recoil density of collision cascades in solids on the energy and angular distribution of sputtered particles is considered. Various sputtering mechanisms are discussed. For some of those mechanisms this anisotropy leads to deviations from a ε^?2 asymptotic form in the energy distribution and to an asymmetry in the angular distribution as a function of the angle of incidence of the projectile.     

Erosion of Thin Foils by Sputtering in Hollow Cathodes

A thin copper foil placed diagonally in a cylindrical copper hollow cathode undergoes fast erosion caused by cathode sputtering. Changes in the foil shape are related to current distribution along the hollow cathode axis. The experimental results aid in understanding the increase in spectral lines intensities emitted from conical bottom hollow cathode lamps.     

A study of TiMoN nano-multilayer coatings deposited by CFUBMSIP using DC and HIPIMS power

TiMoN nano-multilayer hard coatings have been deposited using the closed field unbalanced magnetron sputter ion plating (CFUBMSIP) technique. In one set of experiments, standard DC power supplies were used on four magnetrons in the CFUBMSIP system (4DC magnetrons). The second set of experiments was also in the same magnetic field configuration of CFUBMSIP, but three magnetrons were as again powered with standard DC whilst one magnetron with Ti target was supplied by a high power impulse magnetron sputtering (HIPIMS) power generator (3DC + 1HIPIMS magnetrons). Two elemental titanium sputtering targets and two of molybdenum were used to produce the TiMoN nano-multilayer coatings. Analysis of the coatings was carried out to investigate the differences in terms of properties, compositions and microstructures of the coatings deposited by these two sets of experiments. It was found that the coatings deposited by both sets of the experiments exhibited similar properties of high hardness, good adhesion and exceptional wear resistance, with a lower sliding friction than more commonly used hard coatings including TiN, CrN, TiAlN, CrTiAlN etc. Although the initial TiN coating as formed at the coating-substrate interface using the process of 3DC + 1HIPIMS magnetrons appeared to show a less oriented microstructure in comparison with that of the coating produced by the process using 4DC magnetrons, the compositions and cross sectional microstructures of the bulk of the coatings did not show significant differences, as observed by the cross sectional Transmission Electron Microscopy microstructures of these two types of TiMoN coatings.     

On the influence of reactive gases on sputtering and secondary ion emission

As a continuation of earlier sputtering yield measurements in an ion microprobe, the influence of oxygen and nitrogen on sputtering yield, ionisation efficiency and depth resolutions has been studied. For inert gas bombardment the yield of Ti and V falls sharply at a certain oxygen exposure. While this decrease in yield can be correlated with an increase in surface binding energy in the case of titanium, cone formation causes the yield to drop for oxygen exposed vanadium. In contrast, during nitrogen bombardment the only effect of oxygen exposure is a drastic increase of the ionisation efficiency; the sputtering yield or the depth resolution Δz/z is hardly influenced by oxygen coverage. As was observed earlier in the case of Cu?Ni layers, Δz is essentially constant for erosion depthsz?800 Å, thus yielding better resolution at large depths than is to beexpected from a sequential layer removal model. The extent of the transition zone Δz, is determined by surface topography and thus depends on the target composition as well as its structure.     

Nonlocal phenomena in the positive column of a medium-pressure glow discharge

Commercial CFDRC software () is used to self-consistently simulate the plasma of the positive column (PC) of a medium-pressure dc discharge in argon. The software allows simulations in an arbitrary 3D geometry by using Poisson’s equation for the electric potential and fluid equations for the heavy components and by solving a nonlocal kinetic equation for electrons. It is shown that, in calculating the electron distribution function, the local approximation is almost always inapplicable not only at relatively low pressures (pR<1 cm Torr), but also at relatively high pressures (pR<10 cm Torr), i.e., under the real conditions of a diffuse PC usually met in practice. The use of the local approximation in solving the kinetic equation for electrons leads to significant errors in determining the main parameters of the PC. A paradoxical effect has been revealed: the peaks of the profiles of the excitation rates shift from the discharge axis toward the periphery as the pressure increases from low to medium values (1 cm Torr<pR<10 cm Torr). It is shown that the effect is related to the nonlocal character of the electron distribution function.     

Strength statistics and the distribution of earthquake interevent times

The Weibull distribution is often used to model the earthquake interevent times distribution (ITD). We propose a link between the earthquake ITD on single faults with the Earth’s crustal shear strength distribution by means of a phenomenological stick–slip model. For single faults or fault systems with homogeneous strength statistics and power-law stress accumulation we obtain the Weibull ITD. We prove that the moduli of the interevent times and crustal shear strength are linearly related, while the time scale is an algebraic function of the scale of crustal shear strength. We also show that logarithmic stress accumulation leads to the log-Weibull ITD. We investigate deviations of the ITD tails from the Weibull model due to sampling bias, magnitude cutoff thresholds, and non-homogeneous strength parameters. Assuming the Gutenberg–Richter law and independence of the Weibull modulus on the magnitude threshold, we deduce that the interevent time scale drops exponentially with the magnitude threshold. We demonstrate that a microearthquake sequence from the island of Crete and a seismic sequence from Southern California conform reasonably well to the Weibull model.     

Calculation of the inverse bremsstrahlung absorption in unmagnetized plasmas

Inverse bremsstrahlung is one important way to deliver laser energy to the plasma in inertial confinement fusion. In this article, we study the collisional absorption rate as obtained from the Fokker–Planck treatment of an unmagnetized plasma in harmonic laser field. The electron–ion collision rate is considered in the Krook approximation, and the electron distribution function is considered a Maxwellian function. We evaluate the inverse bremsstrahlung absorption near the irradiated plasma surface in the critical layer. We observe that absorption increases with shorter laser wavelength and lower electron temperatures. When the maximum electron velocity in the limit of q → 1 reaches infinity, the q-non-extensive distribution function reduces to the standard Maxwell-Boltzmann distribution.     

Linear approximation in classical scattering by a moliégre potential

Abstract

In the context of a Monte Carlo simulation of channeling, it is shown how the scattering angle of an ion by a Molière potential can be calculated by linear interpolation. In the case of impulse approximation, this reduces the computing time to ?1/17 of that needed by the usual procedure.

The maximum error introduced by the linear approximation is calculated as a function of the interval width used for interpolation. Using Firsov's inversion formula, the corresponding approximation to the atomic potential is also evaluted. It is shown that such approximation is very good, if compared with the present knowledge of atomic potential.     

Energy flux of a Gaussian beam in microwave band beyond the paraxial approximation

Through the analytic method beyond the paraxial approximation, the energy flux for the general fields of a Gaussian laser beam in microwave band (∼10⁸–10¹⁰ Hz) with different diffraction angles and longitudinal positions are derived. The results indicate a Gaussian beam (GB) has a certain number of transverse energy flux, and it would be enhanced with larger diffraction angle. In the range of beyond paraxial approximation, the transverse flux plays an important role in energy distribution, so that it cannot be ignored when the GB is highly focused. Meanwhile both transverse and longitudinal energy decay along the propagation direction, and the proportion of transverse energy far from beam axis is much more than the counterpart in paraxial area. The transverse energy as mainly characteristic of GB will be much useful for the interactions between electromagnetic field and other field.     

Ion sputtering of minerals and glasses: a first step to the simulation of solar wind erosion

Selected rockforming minerals (plagioclase, augite, olivine, ilmenite, silicate and metal phases of the meteorite “Brenham”) as well as silicate and phosphate glasses were irradiated with heavy ions (⁴He⁺, ¹⁴N+, ²⁰Ne⁺, ⁴⁰Ar+, ⁵⁶Fe+, Xe⁺ _nat) in the energy range of 50-130 keV in order to study ion-induced sputtering. Sputtering yields were measured independently by means of multiple beam interferometry and particle track autoradiography.

The theory of sputtering by Sigmund, modified by Smith, was used to convert experimental heavy ion sputtering yields to H⁺- and He⁺-sputtering yields of the same target. Taking into account solar wind irradiation conditions at the lunar surface, an estimate of lunar erosion rates due to solar wind sputtering is given for the targets studied.     

Investigation of oxidation process and properties of indium and tin-based thin-film heterostructures

Solid-phase processes in thin films (～200 nm) based on tin and indium oxides (ITO structures) prepared by magnetron sputtering from a composite target (93 at % In and 7 at % Sn) and by layer-by-layer deposition of In/Sn/Si and Sn/In/Si structures from two magnetrons in a single vacuum cycle have been investigated in the work under their oxidation in an oxygen flow. Two ways of optically transparent semiconductor film formation have been compared using near-edge fundamental absorption spectroscopy, x-ray diffraction analysis, and electron microscopy and dynamics of the change in their optical and structure properties has been studied. In the case of oxidation of the layer-by-layer deposited structures, the heterogeneous phase composition of the film is confirmed both by the XRD data and by the optical results. Only wide-band-gap phases with an energy of direct transitions of 3.5–3.6 eV have been found in the films prepared by magnetron sputtering from a composite target after their oxidation. These wide-band-gap phases are associated with In₂O₃ oxide and a tin-doped indium oxide compound.     

聚变α粒子对第一壁辐照损伤的蒙特-卡罗研究(Ⅱ)——溅射

本文应用蒙特-卡罗方法研究聚变α粒子对不锈钢第一壁的溅射损伤。首先,计算单种元素Fe,Cr,Ni的溅射产额随入射能量的变化,并与实验结果比较,以确定计算中所用到的一些重要参数,如原子位移能等。在此基础上计算聚变α粒子对不锈钢(Fe_0.73Cr_0.18Ni_0.09)的部分(和总)溅射产额,溅射粒子的能谱、角分布和源深度分布,以及上述各量与α粒子入射角的关系。结果表明,在考虑入射α粒子随能量及入射角的分布后,其平均总溅射产额为0.375。由于1     

Correlation functions in the theory of atomic collision cascades: Ion location and the distribution in depth and size of damage clusters

Abstract

Simple depth distribution functions of ion bombardment damage predict the spatial extension of the cumulative damage caused by a beam of ions. Correlation functions need to be considered when more detailed information is desirable, such as the average size or depth of individual damage clusters, the average location of an ion within its damage cluster, and the fluctuations of these quantities. In this paper we establish an integral equation for the pair correlation function, coupling the individual ion range with the deposited energy. This pair correlation function determines the damage caused by all those ions that come to rest at a specific penetration depth. Solutions of the integral equation are found by standard methods. Explicit results are presented for elastic scattering governed by power cross sections. The depth distribution of damage clusters turns out to be significantly narrower than the gross damage distribution at all mass ratios except for M ₁ ? M ₂, and the size distribution appears insensitive to depth when measured perpendicular to the ion beam, but varying with depth when measured parallel. Predictions on ion location suffer from a surprizingly sensitive dependence on the scattering cross section. A note on the fluctuation of the sputtering yield by individual ions concludes the paper.     

Model Experiments on Study of the First Wall Erosion Under the Action of Vacuum Arcs

With d. c. vacuum arc discharges the dependence of cathode erosion rate on the transverse magnetic field induction is non-linear. At first erosion rate rises with the magnetic induction and then drops. The maximum erosion rate value corresponds to the magnetic induction interval (50 – 115) · 10^?4 T. The range of the vacuum arc discharge maximum stability also corresponds to the same interval. When the magnetic induction rises from 2 · 10^?3 up to 1.1 · 10^?2 T (I = 50 A), the erosion products angular distribution monotoneously narrows and with further magnetic ficld enhancement it abruptly widens. Current rise results in increasing extension of erosion products angular distribution. Asymmetry of erosion products angular distribution does not depend on the direction of the magnetic induction vector and gradually vanishes when the magnetic induction rises up to 1 · 10^?2 T and higher.     

Monte Carlo Calculations of XRF Intensities in Annular Arrangements of Radioactive Source,Sample, Cylindrical Collimator and Detector

ABSTRACT

A Monte Carlo (MC) computer program for the calculation of the distribution of characteristic X-ray intensities as a function of the counting geometry is described. The program evaluates the contribution to the intensities of a fluorescent line from each point of the source, sample and detector. The main considerations of the calculation are based on the critical nature of the internal geometry of the main analyzer components within an energy dispersive X-ray fluorescence (EDXRF) spectrometer. The K XRF intensities for the inner and outer radius of the annular-sample and collimator radius were measured. An optimum geometry can be obtained by varying the collimator radius and the detector-sample distance. The results of the calculations show that the intensity distribution of the radioisotope excited fluorescent radiation through annular sample area is strongly dependent on the collimator radius, with a maximum intensity effect with a smaller sample area and with decreasing collimator radius. An investigation of the XRF intensities in the annular sample surface as a function of collimator radius is discussed.     

A necessary condition for the appearance of damage-induced surface-topography during particle bombardment

A first approach to the establishment of an “order-of-magnitude” criterion for the initiation of damage-induced surface topography on clean and well-polished metal single crystals is proposed. It is based on a model proposing a mechanism of preferential erosion of parts from the sample surface due to a local increase of sputtering yield above “extensive defects”. These “extensive defects”, resulting of the migration of the point-defects, created during the collision-cascade started by the incoming ions, can indeed influence the sputtering yield if they are located close under the surface, i.e. when the surface has regressed, due to sputtering, to the level where these “extensive defects” have been formed.

The condition implies that the formation of “extensive defects” must have taken place before the surface reaches them. The condition is written in terms of the irradiation parameters and quantities characteristic for the migration of point-defects due to the presence of a potential gradient related to the “extensive defects” under formation.