Model-based quantification of EELS spectra: Including the fine structure

An extension to model-based electron energy loss spectroscopy (EELS) quantification is reported to improve the possibility of modelling fine structure changes in electron energy loss spectra. An equalisation function is used in the energy loss near edge structure (ELNES) region to model the differences between a single atom differential cross section and the cross section for an atom in a crystal. The equalisation function can be shown to approximate the relative density of unoccupied states for the given excitation edge. On a set of 200 experimental h-BN spectra, this technique leads to statistically acceptable models resulting into unbiased estimates of relative concentrations and making the estimated precisions come very close to the Cramér-Rao lower bound (CRLB). The method greatly expands the useability of model-based EELS quantification to spectra with pronounced fine structure. Another benefit of this model is that one also gets an estimate of the unoccupied density of states for a given excitation edge, without having to do background removal and deconvolution, making the outcome intrinsically more reliable and less noisy.     

An accurate approximation for the highly efficient sampling of polar scattering angle of electron elastic single-scattering events

In single-event Monte Carlo electron transport simulations, elastic scattering events dominate the changes in electron trajectories due to collisions. Classically, the polar scattering angle due to an elastic collision can be sampled efficiently from the screened Rutherford cross section. However, the screened Rutherford cross section fails for both high Z materials and when the incident electron energy becomes too low. Alternatively, improved simulation accuracy for electrons in all energy ranges and through all materials may be obtained by sampling directly from differential data derived from partial-wave-expansion method (PWEM) calculations based on theoretical atomic potential models. While sampling directly from wave calculations will yield simulation results to the best known physical accuracy, it comes at the cost of simulation time. This is due to a sampling process that is typically more involved when compared with using the screened Rutherford cross section. In this work we present a relationship capable of reproducing the moments of the differential cross section derived from PWEM calculations, resulting in good preservation of forward and backscattering peaks. The relationship is directly invertible and is as easily sampled as the Rutherford cross section. Most important, the data presented in this paper in combination with this relationship produce Monte Carlo simulation results which are comparable with those using the exact differential cross section from PWEM calculations for elements Z = 1 to 96 and for incident electron energies from 300,000 down to 50 eV.     

Influence of the angular distribution of backscattered electrons on signals at different take-off angles in low-voltage scanning electron microscopy (LVSEM)

It is well known that the differential Mott cross section for large-angle elastic scattering shows maxima and minima at angles depending on material and electron energy. For electron energies of 10–30 keV, the averaging by frequent elastic scattering processes results in approximate Lambert angular distributions of backscattered electrons (BSE). However, the present Monte Carlo calculations for electron energies E = 1–5 keV and different angles of incidence show strong deviations from a Lambert distribution which increases with decreasing energy. The signals of the BSE detector with five annular segments for different take-off directions show good agreement with the calculations for normal electron incidence.     

Polarization dependence in ELNES: influence of probe convergence, collector aperture and electron beam incidence angle

The differential scattering cross section in electron energy loss near edge spectroscopy (ELNES) generally depends on the orientation of the Q wave vector transferred from the incident electron to an atomic core electron. In the case where the excited atom belongs to a threefold, fourfold or sixfold main rotation axis, the dipole cross section depends on the angle of Q with respect to this axis. In this paper, we restrict to this situation called dichroism. Furthermore, if we take into account the relativistic effects due to the high incident electron velocity, this dipole cross section also depends on the angle of Q with respect to the electron beam axis. It is due to these dependences that the shape of measured electron energy loss spectra varies with the electron beam incidence, the collector aperture, the incident beam convergence and the incident electron energy. The existence of a particular beam incidence angle for which the scattering cross section becomes independent of collection and beam convergence semi-angles is clearly underscored. Conversely, it is shown that EELS spectra do not depend on the beam incidence angle for a set of particular values of collection and convergence semi-angles. Particularly, in the case of a parallel incident beam, there is a collection semi-angle (often called magic angle) for which the cross section becomes independent of the beam orientation. This magic angle depends on the incident beam kinetic energy. If the incident electron velocity V is small compared with the light velocity c, this magic angle is about 3.975theta(E) (theta(E) is the scattering angle). It decreases to 0 when V approaches c. These results are illustrated in the case of the K boron edge in the boron nitride.     

Low-energy electron/atom elastic scattering cross sections from 0.1–30 keV

Empirical forms for electron/atom scattering cross sections predict backscattering factors that compare well with those calculated using tabulated Mott data from 0.1 to 30 keV. The form of the empirical total cross section is similar to the screened Rutherford cross section. The fit to the tabulated differential Mott cross sections is decomposed into two parts, one part being of the same mathematical form as the screened Rutherford cross section (σ_R), and the second part being an isotropic distribution (σ_I). The ratio of the total cross sections (σ_R/σ_I) between the screened Rutherford part of the differential scattering cross section and the isotropic part of the distribution is fitted to give the same ratio of forward to backscattered currents as the tabulated Mott differential cross sections. The three equations, one for the total elastic cross section and two describing the differential cross section—one for the Rutherford screening parameter and one for the ratio σ_R/σ_I—give backscattering results covering all the major trends with energy and atomic number compared with the backscattering coefficients calculated using tabulated Mott cross sections. However, agreement with experiment is poor for some well-researched examples such as Au. Monte Carlo calculations using the empirical cross sections show that surface effects may be critical in interpreting experimental results.     

A large-area continuous accelerator with the extraction of a high-density electron beam

The design features of the electron accelerator with a large-area 200-keV beam and results of its investigation are described. The accelerator is based on a set of discrete longitudinal filament cathodes and operates in the continuous mode. The cross section of the beam extracted into the atmosphere is 40 × 50 cm², and the maximal current density of the extracted electron beam is up to 100 μA/cm². The nonuniformity of the current density distribution over the electron beam cross section is 10% or less.     

Determination of paper filler Z-distribution by low-vacuum SEM and EDX

Paper, mainly constituted of cellulose fibres, often contains mineral fillers. These fillers increase some of the properties of the paper (whiteness, printability, etc.) and are cheaper than the cellulose fibres. Nevertheless, the fillers reduce the mechanical properties of the sheet. Paper presents an anisotropy corresponding to three main directions. This anisotropy characterises the sheet mechanical properties, structure and filler distribution. Analyses of the cross section of the paper sheet with a low‐vacuum scanning electron microscope with an energy dispersive spectrometer analysis module can show this distribution. The procedure developed consists in analysing discrete profiles to build the mean profile known as filler Z‐distribution for each of the fillers. To develop this method, problems such as determination of the surface points, the number of points to analyse to define a cross section profile and the time required for the test, have been solved. Paper is sensitive to electron irradiation. In order to avoid deterioration of the material and to obtain satisfactory results, the time span for analyses is restricted to 40 s with a 12 kV electron beam accelerating voltage. Monte Carlo simulations are used to determine the diffusion cloud size and thus to determine the number of points that constitute a profile. The samples are gold sputtered and, with the aid of backscattered imaging, the coated surface allows determination of the sample surface points.     

Evaluation of the effective cross‐sections for recombination and trapping in the case of pure spinel

In this paper, we have investigated the evolution of the secondary electron emission in the case of pure spinel during electron irradiation, achieved in a scanning electron microscope at room temperature, which is derived from the measurement of the induced and the secondary electron currents. It was observed from the experimental results, that there are two regimes during the charging process: a plateau followed by a linear variation, which are better identified by plotting the logarithm of the secondary electron emission yield lnσ as function of the total surface density of trapped charges in the material Q_T. For positive charging, E₀ = 1.1 and 5 keV, the slope of the linear part, whose value is of about 10^?10 cm² charge^?1, is independent of the primary electron energy. It is interpreted as a microscopic cross section for electron–hole recombination. For negative charging of pure spinel, E₀ = 15 and 30 keV, the slope is associated with an electron trapping cross section close to 10^?14 cm² charge^?1, which can be assigned to the microscopic cross section for electron trapping. This trapping cross section is four orders of magnitude lower than the recombination one.     

A forevacuum pulse arc-discharge-based plasma electron source

An arc-discharge-based electron source is described, which is designed for forming a pulsed wideaperture electron beam in the forevacuum pressure range (4–15 Pa). At an accelerating voltage of 12 kV, a current of 80 A was extracted from the emitting surface with an area of 80 cm² in the submillisecond range of pulse durations. The current density distribution over the beam cross section is close to a Gaussian function, and the surface-averaged beam energy density in a pulse reached 10 J/cm².     

Measurement of total gas scattering cross‐section

Experimental measurements are presented of the total scattering cross‐section of four gases: He, Air, CH₄, and Argon as a function of electron beam energy. The method used was that of Gauvin. A comparison of theoretical estimates of the total scattering cross‐section with the experimental data indicates that the model used gives generally reliable results. The data confirm that the gases tend to be molecular rather than atomic in nature in this pressure range (1–300 Pascal). The factors affecting the accuracy of these results are examined.     

A system for real-time measurements of current-density distribution in low-energy electron beams with large cross sections

A system for real-time measurements of the current-density distribution in electron beams ejected from large-area electron accelerators has been developed. The system, which is based on Faraday cups, a microprocessor, and a PC, is designed for measuring the parameters of the electron beams ejected from large-area accelerators—devices for ionizing electroionization lasers and technological accelerators—and ensures real-time monitoring of the current-density distribution over the electron-beam cross section with a relative measurement accuracy of at least ±2%.     

Angle-resolving time-of-flight electron spectrometer for near-threshold precision measurements of differential cross sections of electron-impact excitation of atoms and molecules

This article presents a new type of low-energy crossed-beam electron spectrometer for measuring angular differential cross sections of electron-impact excitation of atomic and molecular targets. Designed for investigations at energies close to excitation thresholds, the spectrometer combines a pulsed electron beam with the time-of-flight technique to distinguish between scattering channels. A large-area, position-sensitive detector is used to offset the low average scattering rate resulting from the pulsing duty cycle, without sacrificing angular resolution. A total energy resolution better than 150 meV (full width at half maximum) at scattered energies of 0.5-3 eV is achieved by monochromating the electron beam prior to pulsing it. The results of a precision measurement of the differential cross section for electron-impact excitation of helium, at an energy of 22 eV, are used to assess the sensitivity and resolution of the spectrometer.     

Monte Carlo simulation of scanning electron microscope signals for lithographic metrology

Two computer codes for simulating the backscattered, transmitted, and secondary-electron signals from targets in a scanning electron microscope are described. The first code, MONSEL-II, has a model target consisting of three parallel lines on a three-layer substrate, while the second, MONSEL-III, has a model target consisting of a two-by-two array of finite lines on a three-layer substrate. Elastic electron scattering is determined by published fits to the Mott cross section. Both plasmon-generated electrons and ionized valence electrons are included in the secondary production. An adjustable quantity, called the residual energy loss rate, is added to the formula of Joy and Luo to obtain the measured secondary yield. The codes show the effects of signal enhancement due to edge transmission, known as blooming, as well as signal reduction due to neighboring lines, known as the “black-hole” effect.     

槽式光伏聚光器能流密度均匀化设计

从理论上推导了常规槽式光伏聚光器能流聚光比的计算模型,分析了该聚光器能流密度极不均匀的原因,探讨了改善聚光器能流密度均匀性的可能性。在此基础上,提出了一种新型聚光器结构形式,即太阳能电池呈V形槽式的抛物槽式聚光器,从理论上推导了新型聚光器结构的能流聚光比计算模型,分析了聚光器参数对能流密度分布的影响。最后通过粒子群优化算法对该新型模型参数进行了优化。计算和优化结果表明,该新型结构的能流聚光比的标准差小于常规聚光器的30%,极大地改善了槽式光伏聚光器能流密度分布。     

A Matrix Carbon Detector for Measuring the Energy Flux of a High-Power Beam of Hydrogen Ions

A matrix detector consisting of small calorimeters based on УПВ-1 pyrolytic carbon is described. The detector allows measurements of the spatial distribution of the energy flux of a high-power hydrogen ion beam to be taken over its cross section. Each calorimeter occupies an area of 4 cm², and the area of its working body is 0.25 cm². An unambiguous relation between the heat flux value, the irradiation time, and the calorimeter temperature is established by calculations. The calorimeter measurement error was estimated at ～4%, and the spread of the sensitivity coefficients between the calorimeters was 5–6% (1σ). The detector was used to measure the distribution of the energy flux of hydrogen ions over the cross section of the “scanned” beam 10 cm in diameter from a high-current accelerator of the НГ-12И facility.     

An empirical energy loss equation of electrons

A modified Love-Cox-Scott (1978) equation of electron energy loss has been suggested. The stopping powers predicted by the modified Love-Cox-Scott equation are compared with those by the Tung et al. (1979) model, the Joy and Luo (1989) equation, and the experimental data given in database of Joy at: http://web.ukt. edu/-scrutk. In the energy range of E0< or = 5 keV, the Monte Carlo simulations of the electron scattering in Al, Ag, and Au have been performed, applying the Mott cross section for elastic scattering and the modified Love-Cox-Scott equation (1978) and the equations by Love et al. (1978) and Joy and Luo (1989), respectively, for the inelastic scattering. The calculated results on the backscattering coefficients, the energy distributions of the backscattered electrons, and the energy dissipation of the electron based on the three equations are compared.     

Mass thickness determination by electron energy loss for quantitative X-ray microanalysis in biology

As is well known, electron energy loss spectroscopy can be used to determine the relative sample thickness in the electron microscope. This paper considers how such measurements can be applied to biological samples in order to obtain the mass thickness for quantitative X-ray microanalysis. The important quantity in estimating the mass thickness from an unknown sample is the total inelastic cross section per unit mass. Models for the cross section suggest that this quantity is constant to within ±20% for most biological compounds. This is comparable with the approximation made in the continuum method for measuring mass thickness. The linearity of the energy loss technique is established by some measurements on evaporated films and quantitation is demonstrated by measurements on thin calcium standards. A significant advantage of the method is that the energy loss spectrum can be recorded at very low dose, so that mass thickness determination can be made before even the most sensitive samples suffer damage resulting in mass loss. The energy loss measurements avoid the necessity to correct the continuum measurement for stray radiation produced in the vicinity of the sample holder. Unlike the continuum method the energy loss technique requires uniform mass thickness across the probe area, but this is not usually a problem when small probes (<100 nm diameter) are used.     

Monte Carlo Simulation of CD‐SEM Images for Linewidth and Critical Dimension Metrology

In semiconductor industry, strict critical dimension control by using a critical dimension scanning electron microscope (CD‐SEM) is an extremely urgent task in near‐term years. A Monte Carlo simulation model for study of CD‐SEM image has been established, which is based on using Mott's cross section for electron elastic scattering and the full Penn dielectric function formalism for electron inelastic scattering and the associated secondary electron (SE) production. In this work, a systematic calculation of CD‐SEM line‐scan profiles and 2D images of trapezoidal Si lines has been performed by taking into account different experimental factors including electron beam condition (primary energy, probe size), line geometry (width, height, foot/corner rounding, sidewall angle, and roughness), material properties, and SE signal detection. The influences of these factors to the critical dimension metrology are investigated, leading to build a future comprehensive model‐based library. SCANNING 35: 127‐139, 2013. © 2012 Wiley Periodicals, Inc.     

Spectroscopy of the cross section of inelastic scattering of electrons in SiO2/Si(100) layered systems

Spectra of the cross section of inelastic scattering of electrons (product of the mean free path of inelastic scattering and its differential cross section) are obtained for SiO₂/Si(100) layered structures from experimental spectra of energy losses of reflected electrons with different energies of primary electrons. Computer simulations of the spectra of the cross section of inelastic scattering of reflected electrons for these layered structures are performed with the use of the dielectric function of the film and substrate materials. It is found that the SiO₂ layer thickness determined through comparisons of experimental and model spectra agrees with results of ellipsometric measurements.     

Monte Carlo simulation of electron backscattering from compounds with low mean atomic number

This paper reports a Monte Carlo simulation where a single atom scattering model is adopted. The element taking part in each electron-atom interaction is selected on the basis of its contribution eitherto the total elastic cross section or to the electron's mean free path. Both Rutherford and Mott scattering are considered, with the continuous slowing down process of Bethe used to calculate the energy loss to the system. The backscattered electron coefficients show good agreement with experimental results from a large group of low atomic number materials when using a model which selects the scattering atom by its contribution to the whole compound calculated from its atomic fraction of the total elastic cross-section.