Physical background of electron backscattering

The parameters governing electron backscattering from thin films and from bulk solids are reviewed: Atomic scattering cross-section, atomic number, single/multiple scattering, film thickness, scattering angular distribution, angle of incidence, diffraction effects. Their influence on some important contrast mechanisms due to backscattered electrons in scanning electron microscopy (thickness contrast, Z/material contrast, tilting/topography contrast, crystal orientation contrast) is discussed. The most frequently used backscattering electron detection systems are briefly described.     

Calculation and comparison of the surface ionization ϕ(0)

An analytical expression for the surface ionization ?(O) is derived from fundamentals, viz., the ionization cross section and the angular and energy distribution of backscattered electrons. In order to avoid numerical integrations, a simple formula for the energy distribution of backscattered electrons is presented. The values given by the resulting expression for ?(O) are compared with those given by already known formulae and with experimental findings. In general, the agreement is quite satisfactory, although the calculated values generally are smaller than those experimentally found, especially at high overvoltages. This can at least partly be explained by secondary fluorescence excited by the continuous radiation, of which the correction has not been taken into account in the experimental determination of the ?(O) values.     

Contrast and resolution of scanning transmission electron microscope imaging modes

Image blurring due to delocalization of inelastic events was studied for scanning transmission electron microscopy (STEM) of unstained thin sections. The delocalization probability was obtained from the angular distribution of inelastic scattering, which was calculated from experimental electron loss spectra of organic samples. This probability was implemented in a Monte Carlo program to simulate the effects of multiple scattering and delocalization for STEM images collected by either the annular detector or the spectrometer, and images generated by a combination of these two signals. Depending on the illumination, the detector geometry and the energy-loss range selected for imaging the annular detector image is blurred by a non-negligible fraction of inelastically scattered electrons. Simultaneous acquisition of an inelastic image using a spectrometer allows the blurring to be reduced by calculation of either the ratio or the difference of the two darkfield signals. While inherent nonlinearities reduce the interpretability of ratio-contrast images, difference-contrast improves the visibility of details submerged in a diffuse background without introducing artifacts.     

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.     

Energy distribution of electron backscattering from crystals and relation to electron backscattering patterns and electron channeling patterns

This paper reports on the influence of the channeling effect on the energy distribution of electrons backscattered from crystals with different atomic numbers Z. These results can be used for the optimization of the contrast of electron backscattering and electron channeling patterns. Energy and angular resolved electron scattering distributions are obtained using a 4-axial experimental setup with a moveable high-resolution spherical spectrometer. Special care is taken to suppress undesired reflections of electrons inside the spectrometer. This experimental setup allows the direct observation of the excitation of different Bloch waves (anomalous absorption and transmission) within the crystal for different electron incidence angles and the observation of angular distributions of elastically scattered electrons. Results are presented for Si and Au monocrystals, showing that the influence of the channeling effect is more distinct for low atomic numbers.     

Elastic scattering in EELS-fundamental corrections to quantification

Amazingly, elastic scattering has been so far totally ignored in quantitative analytical electron energy-loss spectroscopy. Yet the majority of the electrons typically recorded suffer elastic scattering including a large fraction which, though elastically scattered to beyonf the collecting angle, are inelastically scattered back. A simple procedure, based on a semi-empirical multiple elastic scattering distribution, is described which cam be adopted to take account of multiple elastic-inelastic scattering. With this treatment a fundamental understanding is obtained of many features of EELS which have previously appeared anomalous.     

Direct measurement of electron beam scattering in the environmental scanning electron microscope using phosphor imaging plates

Phosphor imaging plate technology has made it possible to directly image the distribution of primary beam electrons and scattered electrons in the environmental scanning electron microscope. The phosphor plate is exposed under electron scattering conditions in the microscope chamber. When processed, the electron intensity distribution is displayed as a digital image. The image is a visual representation of the electron probe and skirt and may provide the basis for a more accurate model.     

Experimental data and model simulations of beam spread in the environmental scanning electron microscope

This work describes the comparison of experimental measurements of electron beam spread in the environmental scanning electron microscope with model predictions. Beam spreading is the result of primary electrons being scattered out of the focused beam by interaction with gas molecules in the low-vacuum specimen chamber. The scattered electrons form a skirt of electrons around the central probe. The intensity of the skirt depends on gas pressure in the chamber, beam-gas path length, beam energy, and gas composition. A model has been independently developed that, under a given set of conditions, predicts the radial intensity distribution of the scattered electrons. Experimental measurements of the intensity of the beam skirt were made under controlled conditions for comparison with model predictions of beam skirting. The model predicts the trends observed in the experimentally determined scattering intensities; however, there does appear to be a systematic deviation from the experimental measurements.     

Simulations of photon-assisted tunneling using the Fokker-Planck equation to model the scattering of electrons within the emitting metal tip.

A method to simulate photon-assisted tunneling is developed, and applied to model laser-assisted field emission from metals. Our simulations show that most of the exchange of quanta between the electrons and the radiation occurs within the emitting metal tip. In typical experiments (lambda = 670 nm with tungsten metal) the depth of penetration for the radiation is four times the mean free path for electrons at the Fermi level, so it is necessary to allow for scattering. We use a Floquet expansion with the time-dependent Schr?dinger equation to allow for the exchange of quanta between the electrons and the radiation field. Multiparticle effects are modeled with the density functional theory within the local density approximation for the Kohn-Sham exchange and correlation, and the Fokker-Planck formulation is used to determine the effects of scattering on the energy distribution of the electrons.     

Modelling imaging based on core-loss spectroscopy in scanning transmission electron microscopy

Recent experimental realizations of atomic column resolution core-loss spectroscopy in the scanning transmission electron microscope have increased the importance of routinely modelling core-loss images. We discuss different approaches to wave function simulation and how they may be used in conjunction with the mixed dynamic form factor model to simulate images resulting from such inelastic scattering events. It is shown that, as resolution improves and in situations where the degree of thermal scattering is high, detailed quantitative comparisons will require the thermal scattering of electrons to be adequately modelled. Indeed, for sufficiently strong thermal scattering even qualitative interpretation may be affected: we give an example where this leads to a contrast reversal. We describe two methods suited to this purpose, the frozen lattice model and the scattering factor model, and explain how they may be combined with the mixed dynamic form factor approach.     

Spatial charge cloud size of microchannel plates

We examine the spatial evolution of charge clouds emitted by microchannel plates (MCPs). A model of this evolution is presented, along with a comparison to experimental results. We also present an experimental method to measure the charge cloud radius in which the radial charge cloud distribution is assumed to be Gaussian. When a charge cloud is released from the MCP, its initial size is determined by the number and distribution of excited channels. The size of the charge cloud is examined as a function acceleration voltage, distance between MCP and anode, and MCP bias voltage. Since electrons released from the MCP have various initial energies and angular divergence, the charge cloud size increases as it travels away from the MCP. Space charge effects also contribute to the growth of the charge cloud. The experimental results are in close agreement with our model, which includes these effects. From experiment, we also derive an approximate expression for charge cloud radius as a function of acceleration voltage and distance between MCP and anode. This expression can be used for the practical design and optimization of a position sensing system comprised of multiple anodes.     

Coherent inelastic scattering in Si and TiAl

An image filter has been used to test a simple model describing the dynamical scattering of electrons that have suffered multiple interactions with plasmons. Semi-quantitative agreement is observed in both Si and TiAl under quasi two-beam conditions. In the latter material it is shown that the classical Hirsch, Howie, Whelan analysis of contrast due to dislocations can be carried out in images produced by electrons that have suffered as many as five interactions with plasmons and at thicknesses at which the unfiltered and zero loss images show no contrast.     

Deconvolution of core electron energy loss spectra

Different deconvolution methods for removing multiple scattering and instrumental broadening from core loss electron energy loss spectra are compared with special attention to the artefacts they introduce. The Gaussian modifier method, Wiener filter, maximum entropy, and model based methods are described. Their performance is compared on virtual spectra where the true single scattering distribution is known. A test on experimental spectra confirms the good performance of model based deconvolution in comparison to maximum entropy methods and shows the advantage of knowing the estimated error bars from a single spectrum acquisition.     

New magnetic electron spectrometer with directional sensitivity for a satellite application

Design and test of a new magnetic electron spectrometer with excellent angular and rather small energy resolution is described. The system is specifically designed for a space flight application to analyze the angular distribution of energetic electrons. Incident electrons with energies between 15 and 270 keV are focused with respect to the direction of incidence. Reasonable directional focusing is obtained over an angular range of 60 degrees with a resolution of 5 degrees. This magnetic electron spectrometer is part of the energetic particle instrument (EPI) developed for the European Space Agency (ESA) GEOS program. GEOS-1 was launched on April 20, 1977, and injected into a 12-h orbit. The instrument has worked successfully since the switch-on-phase in the beginning of May 1977.     

A computational test for the removal of plural scattering from angle-resolved energy loss spectra

A recently developed method based on matrix analysis for the removal of plural scattering from angle-resolved energy loss spectra is tested. A single loss function, Lorentzian in the energy and Gaussian in the angular variable is assumed as input for the test. Multiple scattering probabilities are simulated by summing up n-fold self-convolutions of the input function according to the Poisson distribution for incoherent n-fold scattering. The simulated profile serves as input for the retrieval algorithm, the result of which is compared with the original single-loss probability. It is concluded that the method is feasible, but not likely to be suited for routine investigations.     

Long-time stability of a low-energy electron diffraction spin polarization analyzer for magnetic imaging

The time stability of a polarization analyzer that is used for imaging of magnetic structures in a scanning electron microscope with spin polarization analysis (spin-SEM or SEMPA) is investigated. The detector is based on the diffraction of low-energy electrons at a W(100) crystal at 104.5 eV (LEED detector). Due to the adsorption of hydrogen from residual gas, a change of the scattering conditions is found that causes an angular shift of the LEED beams as well as changes of intensity. The quality factor, which describes the efficiency of the detector in SEMPA application, however, is found to be almost constant up to a hydrogen coverage of θ ≈ 0.25. This gives stable working conditions within roughly 1 h at vacuum conditions of 10(-10) mbar.     

Effects of the introduction of the discrete energy loss process into Monte Carlo simulation of electron scattering

First, the single scattering model is briefly described. Next, the hybrid model is explained, which takes into consideration a part of the discrete energy loss processes. The Vriens or the Gryzinski cross section is used for core electron ionizations, and the Moller cross section for free electron excitations. The model is applied to the calculations of the energy distribution of transmitted electrons through a thin film and the depth distribution of generated x-rays. From comparisons among the calculated results with and without energy straggling and experimental data, it is found that the Gryzinski cross section shows the best result.     

An improved model for gaseous amplification in the environmental SEM

We present a new model for the gas amplification effect used in many environmental scanning electron microscopes, wherein molecular complexity is shown to be the critical factor. Monte Carlo simulations, based on experimental electron scattering cross-sections, are used to deduce a predictive model for the amplification process that is superior to the Townsend gas capacitor model. These predictions are compared with experimentally obtained amplification curves. Significantly, it is shown that the ionization efficiency of the electrons changes dramatically over the gap distance, and a constant value cannot be assumed. Atomic and molecular excitations affect the amplification process in two ways: first, they serve to lower the average kinetic energy of the imaging electrons, thereby keeping a greater fraction near the ionization threshold energy. Second, molecular normal modes determine the effectiveness of positive gas ions in producing additional secondaries upon surface impact. Practical implications such as signal gain and fraction of useful signal as a function of operating conditions are discussed in the light of the new model. Finally, we speculate on potential new contrast mechanisms brought about by the presence of an imaging gas.     

Validity of the dipole approximation in TEM‐EELS studies

Nondipole effects in electron energy‐loss spectroscopy are evaluated in terms of deviation of the inelastic scattering from a Lorentzian angular distribution, which is assumed in established procedures for plural‐scattering deconvolution, thickness measurement, and Kramers‐Kronig analysis. The deviation appears to be small and may be outweighed by the effect of plural (elastic + inelastic) scattering, which is not removed by conventional deconvolution methods. In the core‐loss region of the spectrum, non‐Lorentzian behaviour stems from a reduction of the generalized oscillator strength from its optical value and (for energies far above an ionization threshold) formation of a Bethe‐ridge angular distribution. At incident energies above 200 keV, retardation effects further distort the angular dependence, even for core losses just above threshold. With an on‐axis collection aperture, non‐dipole effects are masked by the rapid falloff of intensity with scattering angle, but they may become important for off‐axis measurements. Near‐edge fine structure is sensitive to nondipole effects but these can be minimized by use of an angle‐limiting collection aperture. Microsc. Res. Tech. 77:773–778, 2014. © 2014 Wiley Periodicals, Inc.