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,

A new method for quantitative analysis of EELS

1994 ◽  
Vol 52 ◽  
pp. 950-951
Author(s):  
Suichu Luo ◽  
David C. Joy
Keyword(s):  
Quantitative Analysis ◽  
Energy Loss ◽  
Single Scattering ◽  
New Method ◽  
Three Dimension ◽  
Angular Correction ◽  
Accurate Quantitative Analysis ◽  
Angular Scattering ◽  
Electron Intensity ◽  
Image Position

Techniques to remove plural scattering from electron energy loss spectra (EELS) are important in bot hmicroanalysis and other quantitative applications of electron spectroscopy. The techniques used are either based on convolution, or Fourier transform deconvolution, methods, in which either the elastic scattering angular correction or both elastic and inelastic angular corrections are not included. In this work we propose a new method based on both angular and energy loss three-dimension Poisson statistics which includes elastic and inelastic mixed angular scattering correction in order to obtain more accurate quantitative analysis for EELS.The electron scattering distribution determined by angular and energy loss three-dimension Poissonstatistics is given by:where IT is the total incident electron intensity; t is the sample thickness; λi, λe and λT are inelastic , elastic and total 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.

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.

Thickness measurements by Electron Energy Loss Spectroscopy (EELS)

1993 ◽  
Vol 51 ◽  
pp. 434-435
Author(s):  
Ruoya Ho ◽  
Lijie Zhao ◽  
Yun-Yu Wang ◽  
Zhifeng Shao ◽  
Andrew P. Somlyo
Keyword(s):  
Energy Loss ◽  
Mean Free Path ◽  
Finite Energy ◽  
Specimen Thickness ◽  
Essential Requirement ◽  
High Loss ◽  
Image Position ◽  
Inelastic Mean Free Path ◽  
Thickness Measurements ◽  
Electron Energy Loss

An estimate of specimen mass-thickness is an essential requirement for evaluate with EELS the absolute elemental concentration in biological specimens. 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 count in an EELS spectrum and I0 is the count in the zero loss peak. This equation is rigorously correct, only if the electrons are collected over all scattering angles and the spectrum covers all energy losses. But in most experiments with a finite energy loss region, because of the limited collection semi-angle, we can only collect a fraction of scattered electrons. Omitting the high loss electrons will result in a cut-off error that is usually less than 5%, if we use an energy window from 0 eV to 150 eV or above. But the effect of the limited semi-angle is more serious. Fig. 1 shows the ln(It/I0) measured on the same specimen in both TEM and STEM mode at 80 keV with a magnetic sector spectrometer equipped with a parallel detector on Philips 400 FEG.

Measurement of the Inelastic Mean Free Path by EELS Analyses of Submicron Spheres

1990 ◽  
Vol 48 (2) ◽  
pp. 74-75
Author(s):  
Laura A. Bonney
Keyword(s):  
Energy Loss ◽  
Free Path ◽  
Analytical Electron Microscopy ◽  
Mean Free Path ◽  
Thickness Measurement ◽  
Crystal Defects ◽  
Sample Thickness ◽  
Area Of Interest ◽  
Image Position ◽  
Inelastic Mean Free Path

Accurate measurement of sample thickness is important for analytical electron microscopy (AEM) but is often difficult and tedious. Unlike other thickness measurement methods, with electron energy loss spectroscopy (EELS) thickness may be measured in both amorphous and crystalline specimens and at the same location and orientation at which other data is collected in the electron microscope. Thickness values may be obtained from convergent-beam electron diffraction (CBED) data only if the sample is crystalline with large grains of uniform thickness. Sample thickness may be measured from crystal defects projected through the entire foil, but such defects are not always conveniently located in the area of interest. The distance between contamination spots on the upper and lower surfaces of the specimen may be measured, but this is not considered accurate and contamination is not desirable in microanalysis.Sample thickness t may be determined with EELS by the relation:(1)where It is the total intensity in the EEL spectrum, Iz is the intensity in the zero loss peak, and λ is the inelastic mean free path for energy loss of an incident electron in the sample.

Developments in the processing of electron energy-loss spectra

1987 ◽  
Vol 45 ◽  
pp. 80-83
Author(s):  
R.F. Egerton
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Fourier Transforms ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Additional Information ◽  
Scattering Spectrum ◽  
Characteristic Features ◽  
The Fourier Transform

Because the total-inelastic mean free path is generally comparable to the specimen thickness, energy-loss spectra recorded in a TEM contain appreciable contributions from plural (or multiple) scattering, which imparts no additional information but may distort or submerge characteristic features. Happily, the single-scattering spectrum S(E) can be derived from a recorded spectrum by the method of Fourier-log deconvolution; if j(f) and z(f) are the Fourier transforms of the recorded data J(E) and of the zero-loss peak Z(E), the Fourier transform s(f) of the single-scattering distribution S(E) is given by:s(f) = r(f) loge [j(f)/z(f)] (1)Here, r(f) is the Fourier transform of a bell-shaped reconvolution function R(E); if r(f) were omitted from Eq.(l), s(f) would correspond to an ‘ideal’ single-scattering distribution, unbroadened by the instrumental resolution △E.

scholarly journals Determining On-Axis Crystal Thickness with Quantitative Position-Averaged Incoherent Bright-Field Signal in an Aberration-Corrected STEM

2012 ◽  
Vol 18 (4) ◽  
pp. 720-727 ◽  
Author(s):  
Huolin L. Xin ◽  
Ye Zhu ◽  
David A. Muller
Keyword(s):  
Accurate Determination ◽  
Analytical Electron Microscopy ◽  
Mean Free Path ◽  
Specimen Thickness ◽  
Crystal Thickness ◽  
Bright Field ◽  
Analytical Electron ◽  
Inelastic Mean Free Path ◽  
Electron Energy Loss

AbstractAn accurate determination of specimen thickness is essential for quantitative analytical electron microscopy. Here we demonstrate that a position-averaged incoherent bright-field signal recorded on an absolute scale can be used to determine the thickness of on-axis crystals with a precision of ±1.6 nm. This method measures both the crystalline and the noncrystalline parts (surface amorphous layers) of the sample. However, it avoids the systematic error resulting from surface plasmon contributions to the inelastic mean-free-path thickness estimated by electron energy loss spectroscopy.

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.

Determination of Mean Free Path for Inelastic Scattering in Poly(2-Vinyl Pyridine) by Low-Loss Spectrum Imaging

2000 ◽  
Vol 6 (S2) ◽  
pp. 224-225
Author(s):  
A. Aitouchen ◽  
T. Chou ◽  
M. Libera ◽  
M. Misra
Keyword(s):  
Free Path ◽  
Free Fall ◽  
Mean Free Path ◽  
Specimen Thickness ◽  
Thickness Determination ◽  
Vinyl Pyridine ◽  
Integrated Intensity ◽  
Inelastic Mean Free Path ◽  
Electron Energy Loss

The common experimental method to determine the total inelastic mean free path i by electron energy-loss spectroscopy (EELS) is by the relation : t/λi= ln(It/IO) [1] where t is the specimen thickness, It, is the total integrated intensity, and Io is the intensity of the zero-loss peak. The accuracy of this measurement depends on the thickness determination. Model geometries like cubes, wedges, and spheres enable accurate thickness determination from transmission images.Spherical polymers with diameters of order 10-200nm can be made from a number of high-Tg polymers by solvent atomization. This research studied atomized spheres of poly(2-vinyl pyridine) [PVP]. A solution of 0.1% PVP in THF was nebulized. After solvent evaporation during free fall within the chamber atmosphere, solid spherical polymer particles with a range of diameters were collected on holey-carbon TEM grids at the bottom of the atomization chamber.

Quantitative Composition Maps of Magnetic Recording Media by EFTEM

1999 ◽  
Vol 5 (S2) ◽  
pp. 634-635 ◽  
Author(s):  
J. Bentley ◽  
J.E. Wittig ◽  
T.P. Nolan
Keyword(s):  
Magnetic Recording ◽  
Core Loss ◽  
Mean Free Path ◽  
Model Material ◽  
Quantitative Composition ◽  
Specimen Thickness ◽  
Recording Media ◽  
Magnetic Recording Media ◽  
Plan View ◽  
Inelastic Mean Free Path

Elemental mapping of Co-Cr-X based magnetic recording media at resolutions approaching 1 nm by energy-filtered transmission electron microscopy (EFTEM) can provide quantitative measurements of intergranular Cr segregation for correlation with magnetic properties and materials processing. The thin-film media present many challenges for EFTEM methods, such as diffraction contrast and closelyspaced edges. The goal of this work was to provide robust methods for mapping quantitative compositions in such materials. Results presented here are for a model material of 60 nm of Co84Cr12Ta4 on a 75 nm Cr underlayer; both films were d.c. magnetron sputtered onto a NiP-plated Al substrate pre-heated to 250°C. Other compositions and thinner layers (∼30 nm) have also been studied. EFTEM was performed on back-thinned, plan-view specimens with a Gatan Imaging Filter (GIF) interfaced to a 300 kV LaB6 Philips CM30. Optimized acquisition conditions have been detailed elsewhere. Besides core-loss image series, zero-loss I0 (slit width Δ=10eV), low-loss Ik (Δ=30eV), and unfiltered IT images were recorded, and maps of t/λ. = ln(IT / I0), where t is specimen thickness and λ. is the total inelastic mean free path, were produced.

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