Single Scattering and Applications

2002 ◽  
pp. 231-258
Keyword(s):  
Single Scattering

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

Background Fitting in the Low-Loss Region of Electron Energy Loss Spectra

1990 ◽  
Vol 48 (2) ◽  
pp. 56-57
Author(s):  
C P Scott ◽  
A J Craven ◽  
C J Gilmore ◽  
A W Bowen
Keyword(s):  
Energy Loss ◽  
Multiple Scattering ◽  
Simple Form ◽  
Single Scattering ◽  
Low Loss ◽  
Characteristic Energy ◽  
Normal Method ◽  
Fitting In ◽  
Electron Energy Loss ◽  
Electron Energy Loss Spectra

The normal method of background subtraction in quantitative EELS analysis involves fitting an expression of the form I=AE-r to an energy window preceding the edge of interest; E is energy loss, A and r are fitting parameters. The calculated fit is then extrapolated under the edge, allowing the required signal to be extracted. In the case where the characteristic energy loss is small (E < 100eV), the background does not approximate to this simple form. One cause of this is multiple scattering. Even if the effects of multiple scattering are removed by deconvolution, it is not clear that the background from the recovered single scattering distribution follows this simple form, and, in any case, deconvolution can introduce artefacts.The above difficulties are particularly severe in the case of Al-Li alloys, where the Li K edge at ~52eV overlaps the Al L2,3 edge at ~72eV, and sharp plasmon peaks occur at intervals of ~15eV in the low loss region. An alternative background fitting technique, based on the work of Zanchi et al, has been tested on spectra taken from pure Al films, with a view to extending the analysis to Al-Li alloys.

Local thickness determination by Electron Energy Loss Spectroscopy

1994 ◽  
Vol 52 ◽  
pp. 944-945
Author(s):  
Suichu Luo ◽  
John R. Dunlap ◽  
Richard W. Williams ◽  
David C. Joy
Keyword(s):  
Energy Loss ◽  
Analytical Electron Microscopy ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Three Dimension ◽  
Angular Correction ◽  
Electron Intensity ◽  
Image Position ◽  
Inelastic Mean Free Path

In analytical electron microscopy, it is often important to know the local thickness of a sample. The conventional method used for measuring specimen thickness by EELS is:where t is the specimen thickness, λi is the total inelastic mean free path, IT is the total intensity in an EEL spectrum, and I0 is the zero loss peak intensity. This is rigorouslycorrect only if the electrons are collected over all scattering angles and all energy losses. However, in most experiments only a fraction of the scattered electrons are collected due to a limited collection semi-angle. To overcome this problem we present a method based on three-dimension Poisson statistics, which takes into account both the inelastic and elastic mixed angular correction.The three-dimension Poisson formula is given by:where I is the unscattered electron intensity; t is the sample thickness; λi and λe are the inelastic and elastic scattering mean free paths; Si (θ) and Se(θ) are normalized single inelastic and elastic angular scattering distributions respectively ; F(E) is the single scattering normalized energy loss distribution; D(E,θ) is the plural scattering distribution,

Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 422-423
Author(s):  
John C. Russ
Keyword(s):  
Monte Carlo ◽  
Energy Loss ◽  
Secondary Electron ◽  
Secondary Electron Emission ◽  
Analytical Calculation ◽  
Mean Free Path ◽  
Single Scattering ◽  
High Energy ◽  
Secondary Electron Yield ◽  
Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

Scattering of Electrons at High - Pressure and Restoration of Image Contrast in High Pressure Scanning Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 384-385
Author(s):  
J. S. Shah ◽  
R. Durkin ◽  
A. N. Farley
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
High Pressure ◽  
Cross Sections ◽  
Single Scattering ◽  
Image Contrast ◽  
Experimental Scheme ◽  
Medium Resolution ◽  
Scattering Approximation ◽  
Scanning Electron

It is now possible to perform High Pressure Scanning Electron Microscopy (HPSEM) in the range 10 to 2000 Pa. Here the effect of scattering on resolution has been evaluated by calculating the profile of the beam in high pressure and assessing its effect on the image contrast . An experimental scheme is presented to show that the effect of the primary beam ionization is to reduce image contrast but this effect can be eliminated by a novel use of specimen current detection in the presence of an electric field. The mechanism of image enhancement is discussed in terms of collection of additional carriers generated by the emissive components.High Pressure SEM (HPSEM) instrumentation is establishing itself as commercially viable. There are now a number of manufacturers, such as JEOL, ABT, ESCAN, DEBEN RESEARCH, selling microscopes and accessories for HPSEM. This is because high pressure techniques have begun to yield high quality micrographs at medium resolution.To study the effect of scattering on the incident electron beam, its profile - in a high pressure environment - was evaluated by calculating the elastic and inelastic scattering cross sections for nitrogen in the energy range 5-25 keV. To assess the effect of the scattered beam on the image contrast, the modification of a sharp step contrast function due to scattering was calculated by single scattering approximation and experimentally confirmed for a 20kV accelerated beam.

Information and Dose in the Scanning Transmission Ion Microscope

1980 ◽  
Vol 38 ◽  
pp. 232-233
Author(s):  
Fox T. R. ◽  
R. Levi-Setti
Keyword(s):  
Information Retrieval ◽  
Electron Microscope ◽  
Elastic Scattering ◽  
Energy Loss ◽  
Cross Sections ◽  
Previous Analysis ◽  
Single Scattering ◽  
Screening Length ◽  
Relative Damage ◽  
Scanning Transmission

At an earlier meeting [1], we discussed information retrieval in the scanning transmission ion microscope (STIM) compared with the electron microscope at the same energy. We treated elastic scattering contrast, using total elastic cross sections; relative damage was estimated from energy loss data. This treatment is valid for “thin” specimens, where the incident particles suffer only single scattering. Since proton cross sections exceed electron cross sections, a given specimen (e.g., 1 μg/cm2 of carbon at 25 keV) may be thin for electrons but “thick” for protons. Therefore, we now extend our previous analysis to include multiple scattering. Our proton results are based on the calculations of Sigmund and Winterbon [2], for 25 keV protons on carbon, using a Thomas-Fermi screened potential with a screening length of 0.0226 nm. The electron results are from Crewe and Groves [3] at 30 keV.

scholarly journals Directional Plasmonic Excitation by Helical Nanotips

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1333
Author(s):  
Leeju Singh ◽  
Nicolò Maccaferri ◽  
Denis Garoli ◽  
Yuri Gorodetski
Keyword(s):  
Surface Plasmon ◽  
Single Scattering ◽  
Coupling Factor ◽  
Metallic Surface ◽  
Phase Matching ◽  
Plasmon Excitation ◽  
Surface Plasmon Excitation ◽  
Specific Momentum ◽  
Plasmon Polaritons ◽  
Strong Spin

The phenomenon of coupling between light and surface plasmon polaritons requires specific momentum matching conditions. In the case of a single scattering object on a metallic surface, such as a nanoparticle or a nanohole, the coupling between a broadband effect, i.e., scattering, and a discrete one, such as surface plasmon excitation, leads to Fano-like resonance lineshapes. The necessary phase matching requirements can be used to engineer the light–plasmon coupling and to achieve a directional plasmonic excitation. Here, we investigate this effect by using a chiral nanotip to excite surface plasmons with a strong spin-dependent azimuthal variation. This effect can be described by a Fano-like interference with a complex coupling factor that can be modified thanks to a symmetry breaking of the nanostructure.

scholarly journals Fast Hyper-Spectral Radiative Transfer Model Based on the Double Cluster Low-Streams Regression Method

2021 ◽  
Vol 13 (3) ◽  
pp. 434
Author(s):  
Ana del Águila ◽  
Dmitry S. Efremenko
Keyword(s):  
Radiative Transfer ◽  
Single Scattering ◽  
Atmospheric Composition ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Absorption Bands ◽  
Acceleration Techniques ◽  
Scattering Approximation ◽  
Fine Resolution ◽  
Single Scattering Approximation

Fast radiative transfer models (RTMs) are required to process a great amount of satellite-based atmospheric composition data. Specifically designed acceleration techniques can be incorporated in RTMs to simulate the reflected radiances with a fine spectral resolution, avoiding time-consuming computations on a fine resolution grid. In particular, in the cluster low-streams regression (CLSR) method, the computations on a fine resolution grid are performed by using the fast two-stream RTM, and then the spectra are corrected by using regression models between the two-stream and multi-stream RTMs. The performance enhancement due to such a scheme can be of about two orders of magnitude. In this paper, we consider a modification of the CLSR method (which is referred to as the double CLSR method), in which the single-scattering approximation is used for the computations on a fine resolution grid, while the two-stream spectra are computed by using the regression model between the two-stream RTM and the single-scattering approximation. Once the two-stream spectra are known, the CLSR method is applied the second time to restore the multi-stream spectra. Through a numerical analysis, it is shown that the double CLSR method yields an acceleration factor of about three orders of magnitude as compared to the reference multi-stream fine-resolution computations. The error of such an approach is below 0.05%. In addition, it is analysed how the CLSR method can be adopted for efficient computations for atmospheric scenarios containing aerosols. In particular, it is discussed how the precomputed data for clear sky conditions can be reused for computing the aerosol spectra in the framework of the CLSR method. The simulations are performed for the Hartley–Huggins, O2 A-, water vapour and CO2 weak absorption bands and five aerosol models from the optical properties of aerosols and clouds (OPAC) database.

Sign in / Sign up

Export Citation Format

Share Document