Relative contribution of various factors to the formation of the energy spectrum of fast, medium-energy, charged particles and ions transmitted through a thin target with fluctuations of the target thickness

The characteristics of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil are investigated theoretically and experimentally as functions of the angle of incidence of the beam on the target. Analytical expressions for the average characteristics of the transmitted-particle energy spectrum are determined for the case of small-angle scattering. The combined influence of various factors affecting the formation of the energy spectra is taken into account: systematic stopping of particles in the medium, fluctuations of the particle energy losses in inelastic collisions, bending of the particle trajectories due to multiple elastic scattering, and fluctuations of the target thickness. It is shown that the contributions of these factors to the width of the transmitted-particle energy spectrum depend differently on the angle of incidence of the beam on the target surface. On the basis of this differentiation it is inferred from the experimental dependence of the width of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil on the angle of incidence of the beam that fluctuations of the particle energy losses in inelastic collisions are the predominant factor in the formation of the proton energy spectra. Zh. Tekh. Fiz. 67, 81–93 (May 1997)     

Comparative analysis of characteristic electron energy loss spectra and inelastic scattering cross-section spectra of Fe

The inelastic electron scattering cross section spectra of Fe have been calculated based on experimental spectra of characteristic reflection electron energy loss as dependences of the product of the inelastic mean free path by the differential inelastic electron scattering cross section on the electron energy loss. It has been shown that the inelastic electron scattering cross-section spectra have certain advantages over the electron energy loss spectra in the analysis of the interaction of electrons with substance. The peaks of energy loss in the spectra of characteristic electron energy loss and inelastic electron scattering cross sections have been determined from the integral and differential spectra. It has been shown that the energy of the bulk plasmon is practically independent of the energy of primary electrons in the characteristic electron energy loss spectra and monotonically increases with increasing energy of primary electrons in the inelastic electron scattering cross-section spectra. The variation in the maximum energy of the inelastic electron scattering cross-section spectra is caused by the redistribution of intensities over the peaks of losses due to various excitations. The inelastic electron scattering cross-section spectra have been analyzed using the decomposition of the spectra into peaks of the energy loss. This method has been used for the quantitative estimation of the contributions from different energy loss processes to the inelastic electron scattering cross-section spectra of Fe and for the determination of the nature of the energy loss peaks.     

Small angle scattering of electrons

The small angle scattering of low energy electrons has been studied. It has been shown that the cross-sections obtained using the Born's first approximation, corrected for screening effects should be used to study the small angle scattering of low energy electrons.     

Features of the scattering of protons and relativistic electrons intersecting a thin planar target at a small angle to its surface

The processes of scattering of protons and relativistic electrons incident on a planar target at a small angle to its surface have been simulated by the Monte Carlo method. The spatial and energy distributions of the beams of particles both passed through the target and reflected from it have been calculated. The dependence of the characteristics of beams on the initial energy and direction of injection of particles, as well as on the material and thickness of the target, has been considered. The transmission, reflection, and absorption coefficients for electrons in the target have been calculated. The initial energy in the calculations is varied in the range of 7–100 MeV and the angle between the trajectory of particles and the surface of the target is in the range of 1°–45°. The thickness of the target varies from 0.2 to 3 mm. Aluminum, iron, and copper targets have been considered. It has been shown that the intersection of targets at small angles not only increases the transverse dimensions of a beam, but also changes the direction of its motion. The results of the reported calculations of the scattering of relativistic electrons intersecting a foil at small angles to its surface are in qualitative agreement with experimental data.     

Quantitative interpretation of EELS and REELS spectra

A critical analysis of the present day Electron Energy Loss Spectroscopy (EELS) data interpretation methods has been done. The necessity for the consideration of a target as a multilayered structure with different inelastic energy loss cross sections in the surface and the bulk layers has been shown to be a reality both for the transmission EELS and the reflection EELS (REELS). A method to reconstruct inelastic energy loss cross sections in various target layers from the experimental data has been presented. Essential qualitative and quantitative dependence of the path length distribution function for reflected electrons as a function of scattering angle has been revealed. The tested method for extraction of the information from REELS experiments with angular resolution has been presented.Received: 9 October 2003, Published online: 19 February 2004PACS: 34.80.-i Electron scattering - 34.50.Bw Energy loss and stopping power - 25.30.Fj Inelastic electron scattering to continuum     

Streuung von 25 keV-Elektronen an Gasen

The angular distribution of 25 kev electrons scattered elastically and inelastically by molecular hydrogen has been measured in the angular range 7·10^?4≦?≦4,3·10^?2. By the separation of the inelastically scattered electrons observation of deviations from the Debye Ehrenfest theory of the electron diffraction by molecules at small angles is possible. These deviations are due to the alteration of the electron density distribution of the hydrogen atoms induced by the bonding. The energy loss spectra at different scattering angles (energy resolution ≈1 ev) shows a strong peak atΔE=12,6 ev. At larger angles forΔE>15 ev a continuum appears. That part of the inelastic processes which leads to ionization of the molecule is raising with increasing scattering angle. Normalization of the experimental values to the theoretical elastic differential cross section enables comparison of the angular distribution of the 12,6 ev energy loss with the distribution calculated byRoscoe. The shape of the experimental curve is in fairly good agreement with the calculated one but the experimental values at small angles are 20–30% higher. For zero angle the energy loss spectrum is taken with better resolution (≈0,04 ev). It shows vibrational states of the Lyman and Werner band and higher terms. The probability of the excitation of some vibrational states of the Werner band (square of the overlapp integral) calculated here is inspite of the required approximations in excellent agreement with the measurement, while Hutchisson's result fails for the Lyman band.     

He-O_2转动激发截面的理论计算

用公认精确的密耦 (Close Coupling)方法、采用两种不同的相互作用势计算了He -O2 碰撞的态 态转动激发截面 (E =2 6.8meV) ,通过系统研究和计算发现 :低能散射时 ,He -O2 碰撞的弹性散射主要发生在小角部分 ,而非弹性转动激发主要发生在大角部分。研究表明 :转动激发截面对势能表面的方向性和散射角都非常敏感。     

Electron spectroscopy of iron disilicide

We have reported on the results of a complex investigation of iron disilicide FeSi₂ using characteristic electron energy loss spectroscopy, inelastic electron scattering cross section spectroscopy, and X-ray photoelectron spectroscopy. It has been shown that the main peak in the spectra of inelastic electron scattering for FeSi₂ is a superposition of two unresolved peaks, viz., surface and bulk plasmons. An analysis of the fine structure of the spectra of inelastic electron scattering cross section by their decomposition into Lorentzlike Tougaard peaks has made it possible to quantitatively estimate the contributions of individual energy loss processes to the resulting spectrum and determine their origin and energy.     

Ultrasoft X-ray spectroscopy investigation of the model system Si-SiO2

SiO₂ surface films with different thicknesses (ranging from 20 to 630 Å), grown on a crystal silicon substrate, have been investigated by the method of reflection and scattering of ultrashoft X-rays. It is shown on the basis of a simultaneous analysis of the SiL _{2, 3} reflection spectra and the scattering indicatrix that the critical angle θ_c for total external reflection for SiO₂ at λ = 57 Å lies in the range 4.5 °–°. The angular dependence of the thickness of the surface layer that forms the specular reflection is obtained. It is shown that the surface layer, whose thickness corresponds to the penetration depth of the radiation into the material with glancing angle close to the critical value θ_c, plays a large role in the formation of the anomalous scattering peak (Yoneda peak).     

Determination of the thickness of a gold layer deposited onto silicon via reflected electron spectroscopy

The energy spectra of electrons reflected from a gold layer deposited onto a silicon substrate have been measured when the energy losses are comparable with the energy of a probe electron beam (5 keV) and the elastic energy losses correspond to an electron-beam energy of 14 keV. A subsequent theory for calculating the energy spectra of electrons and light ions reflected from a multilayer target, which is used to interpret the energy spectra measured in the wide range of energy losses, has been developed. It is found that the elastic scattering processes in the gold layer (the thickness of which is tens of monolayers) substantially affect formation of the energy spectra. The Au layer thicknesses calculated by means of the developed theory are compared with those determined from the spectra of elastically reflected electrons. The errors of the Au layer thickness measurements via the proposed method are discussed.     

Multiple ion scattering

The energy spectra and the angular distributions of noble gas ions, reflected from a metal surface, yield information about a number of important properties of this surface. A large number of investigations have been carried out in the past decades, not only to get insight into the interaction mechanism but also to develop methods for applying of the knowledge gained. To obtain information about the outermost surface layer, it appears necessary to use noble gas ions as primary particles, and to detect the scattered particles in the charged state only; the fraction of noble gas ions reaching the detector, after reflection from target atoms in the second layer, is very small because of the high probability of neutralization. However, this is only valid if the initial energy of the incoming ions is relatively low, namely ? 10 KeV. Under certain experimental circumstances it appears justifiable, down to a lower limit of about 20 eV, to conceive the interaction of these ions with the target atoms as single collisions. The relation between the initial energy and the post-collision energy is then very simple if the collision is an elastic one; it depends upon the scattering angle and upon the ratio of the two given masses only and not upon the interaction potential. The shift of the peaks in an energy spectrum is caused by inelastic collisions and is relatively small in the considered energy region. The causes of this shift will be discussed. As opposed to single collisions, the post-collision energies after a multiple collision depend largely upon the interaction potential. Attention will be paid to the search for these potentials. Utilization of the multiple collision phenomenon in the study of surface geometry is hampered by the vibrational motion of the surface atoms. As a result, the energy spectra are blurred and a shift of the so-called quasi-single and quasi-double peaks can occur. Under certain conditions a third peak emerges which can give additional information about the surface vibrations. The intensity of the scattered ions depends upon the cross section for scattering. Recently it has been shown that the relation between this cross section and the initial energy has an oscillating character for certain combinations of incident ions and target atoms. This phenomenon has very important consequences, e.g. in the use of single ion scattering as an analytical tool. To investigate surface structures it appears that single and multiple ion scattering, combined with LEED and AES, can provide valuable information.     

Energy and charge distribution of helium atoms reflected from a Cu surface under grazing incidence

The energy and charge distributions of helium ions and atoms reflected from a Cu surface at grazing incidence have been measured at the energies 250 and 300 keV. The dependence of the relative number of helium atoms in the scattered beam on the scattering angle at incidence angles less than 2° and scattered particle energies below 150 keV has been discovered. It is shown that, for a theoretical estimation of the charge fractions of particles reflected from the target surface, charge-exchange cross sections used in calculations must be corrected when solids are considered instead of gases.     

Double scattering of ions from polycrystalline materials

In this paper double scattering of ions from polycrystalline materials has been theoretically investigated. It is shown that double collision events contribute to the yield at low energy as well as to the high energy flanks of the peaks depending on whether or not the azimuthal angle ø₁ is greater than or less than a critical angle ø_1c at a given first scattering angle θ₁. There are various combinations of first scattering angle θ₁ and second scattering angle θ₂ which give the required retained energy in two successive collisions. Scattering cross sections derived from the Bohr potential and a double interpolation sub-routine are used to calculate the scattering yield at various angles. Two systems, Ne⁺ scattered from copper and Ar⁺ scattered from gold, each at 30 keV primary energy, have been compared with experimental results.     

Direct numerical reconstruction of inelastic cross sections from REELS and ISS spectra

The reconstruction of inelastic scattering cross sections faces two problems: the measured signal (energy spectrum) is a multiple scattering signal; the inelastic energy loss is nonuniform over the target depth. In this paper, we present a method for numerical reconstruction of cross sections from characteristic energy loss spectra, which efficiently solves both problems within a multilayer model. It is shown that the inverse problem of cross section extraction in the three-layer model is ill-conditioned, and the method is practically inapplicable to the three-layer model. The direct numerical reconstruction method yields a strongly “noised” result and can be applied only to obtain a priori information on the inelastic cross section form for further fitting. Using a combination of two methods, inelastic scattering cross sections were reconstructed for aluminum from characteristic energy loss spectra at probe beam energies of 5 and 40 keV. It is shown that ionization in solids should be described as a local process and as a collective one using the dispersion formula similarly to the case of excitation plasmons.     

Electronic spectra of aliphatic carbonyl compounds by electron impact spectroscopy: III. Unsaturated compounds

Electron impact energy loss spectra at an impact energy of 100 eV and a scattering angle of 2 degrees are presented for propenal (CH₂ = CHCHO) and methyl vinyl ketone (CH₂ = CHCOCH₃). The spectra are tentatively assigned using quantum defects and term values derived from ionization potentials measured by photoelectron spectroscopy. The duality of Rydberg and valence transition assignments in propenal is discussed. It is shown that a transition earlier assigned by Walsh to be π → π* is most probably a Rydberg transition.     

高能闪光照相X射线能谱的理论研究

 用Monte-Carlo方法模拟球对称客体系统的闪光照相中X光光子的输运过程。分别在单客体情况和全系统情况下,给出了记录平面上各种光子谱及其在记录平面上的空间分布。结果表明：记录区边缘的谱形与源光子谱形很相似;深穿透区各点之间的谱形差别不大,谱平均光子能量近似相同,并且位于使高Z材料的光子线吸收系数最小的能量范围内。 结果还表明,高能闪光照相的光子能谱会因客体中光子的光程不同而有较大的差别。     

Correlation of process parameters and properties of TiO<Subscript>2</Subscript> films grown by ion beam sputter deposition from a ceramic target

The correlation between process parameters and properties of TiO₂ films grown by ion beam sputter deposition from a ceramic target was investigated. TiO₂ films were grown under systematic variation of ion beam parameters (ion species, ion energy) and geometrical parameters (ion incidence angle, polar emission angle) and characterized with respect to film thickness, growth rate, structural properties, surface topography, composition, optical properties, and mass density. Systematic variations of film properties with the scattering geometry, namely the scattering angle, have been revealed. There are also considerable differences in film properties when changing the process gas from Ar to Xe. Similar systematics were reported for TiO₂ films grown by reactive ion beam sputter deposition from a metal target [C. Bundesmann et al., Appl. Surf. Sci. 421, 331 (2017)]. However, there are some deviations from the previously reported data, for instance, in growth rate, mass density and optical properties.     

Simulation of methods for a rapid determination of the energy spectrum of bremsstrahlung from electron accelerators

Semiempirical computational methods for determining the energy spectrum of bremsstrahlung from pulsed electron accelerators are proposed. Input information for employing these methods includes the energy spectrum of electrons in a pulse, the effective angle of their incidence on the target, and the parameters of the converter target. It is shown that the methods in question can be used in a rapid determination of bremsstrahlung spectra for an arbitrary angle of the escape of bremsstrahlung, including its escape in the forward direction. Among other things, this provides a solution to the problem of dosimetry in radiation tests of electron systems.     

Wechselwirkung von Elektronen mit Gitterschwingungen in Ammoniumchlorid und Ammoniumbromid

Energy loss spectra of polycrystalline NH₄Cl and NH₄Br films have been studied between 10 and 400 meV using 30-keV electrons. The resolution of the spectrometer was between 4 and 10 meV, the scattering angle smaller than 1.2×10^?4 radian. Strong energy losses and gains were found near 20 meV corresponding to excitation of translational lattice vibrations wellknown from reststrahl measurements. Weaker energy losses above 100 meV are due to excitation of ammonium ion fundamentals and their interaction with torsional vibrations and, presumably, with translational lattice vibrations. In this energy loss range agreement is stated concerning the general behaviour between energy loss and infra-red absorption spectra. In the finer details, however, striking deviations occur, which must be ascribed to the different interaction mechanisms of lattice vibrations with electrons and photons, respectively.     

Development of dipole-dipole intermolecular forces in the vibration spectra of organic compounds

Possible line broadening of the vibrational spectra of organic liquids as a result of intermolecular vibrational reactions has been theoretically assessed. It has been shown that the frequency scattering connected with fluctuations in the energy of local electrostatic forces can explain the width observed in some cases. It has been found possible to link line broadening with the temperature behavior of the frequencies.The author would like to express his sincere thanks to N. A. Prilezhaev for his interest in this work and for valuable discussions of it.