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.

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,

The influence of specimen thickness in quantitative electron energy loss spectroscopy: II

1983 ◽  
Vol 41 ◽  
pp. 388-389
Author(s):  
Nestor J. Zaluzec
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Intensity Ratio ◽  
Mean Free Path ◽  
Specimen Thickness ◽  
Subsequent Work ◽  
The Mean ◽  
Plasmon Loss ◽  
Electron Energy Loss

In a previous paper it was shown that the influence of specimen thickness on quantitative electron energy loss spectroscopy (EELS) can be judged by measuring the intensity ratio of any two characteristic EEL edges as a function of thickness. If the specimen is homogeneous and thickness effects are neglegible then, one can show from Egerton’s formulation that this intensity ratio should be a constant. Any departure from a constant value indicates a breakdown of the quantitative theory due to thickness related effects. It was shown that if the ratio of Ip/IO (Ip = intensity of plasmon loss, IO = intensity of zero loss) exceeds ∼ 0.3 then quantitative analysis can be in significant error. In subsequent work Egerton showed that a better measure is the ratio of ℓn(It/IO) which is related to the ratio of t/λ. Here It is the total energy loss intensity, t the specimen thickness and λ the mean-free path for total inelastic scattering.

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.

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.

Some problems and solutions in electron energy loss spectroscopy of cryosections

1993 ◽  
Vol 51 ◽  
pp. 566-567
Author(s):  
Zhifeng Shao ◽  
Ruoya Ho ◽  
Andrew P. Somlyo
Keyword(s):  
High Resolution ◽  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Biological Research ◽  
Specimen Thickness ◽  
Elemental Distribution ◽  
Electron Dose ◽  
Simple Assumption ◽  
Electron Energy Loss

Electron energy loss spectroscopy (EELS) has been a powerful tool for high resolution studies of elemental distribution, as well as electronic structure, in thin samples. Its foundation for biological research has been laid out nearly two decades ago, and in the subsequent years it has been subjected to rigorous, but by no means extensive research. In particular, some problems unique to EELS of biological samples, have not been fully resolved. In this article we present a brief summary of recent methodological developments, related to biological applications of EELS, in our laboratory. The main purpose of this work was to maximize the signal to noise ratio (S/N) for trace elemental analysis at a minimum dose, in order to reduce the electron dose and/or time required for the acquisition of high resolution elemental maps of radiation sensitive biological materials.Based on the simple assumption of Poisson distribution of independently scattered electrons, it had been generally assumed that the optimum specimen thickness, at which the S/N is a maximum, must be the total inelastic mean free path of the beam electron in the sample.

The Influence of Specimen Thickness in Quantitative Electron Energy Loss Spectroscopy

1980 ◽  
Vol 38 ◽  
pp. 112-113
Author(s):  
Nestor J. Zaluzec
Keyword(s):  
Quantitative Analysis ◽  
Adverse Effects ◽  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Materials Science ◽  
Light Element ◽  
Specimen Thickness ◽  
Element Analysis ◽  
Electron Energy Loss

The application of electron energy loss spectroscopy (EELS) to light element analysis is rapidly becoming an important aspect of the microcharacterization of solids in materials science, however relatively stringent requirements exist on the specimen thickness under which one can obtain EELS data due to the adverse effects of multiple inelastic scattering.1,2 This study was initiated to determine the limitations on quantitative analysis of EELS data due to specimen thickness.

A Poor Man’s Approach to Semi-Quantitative Analysis with Electron Energy Loss Spectroscopy

1980 ◽  
Vol 38 ◽  
pp. 110-111
Author(s):  
M. Isaacson
Keyword(s):  
Quantitative Analysis ◽  
Energy Loss ◽  
Electron Energy ◽  
Cross Section ◽  
Electron Energy Loss Spectroscopy ◽  
Excitation Cross Section ◽  
Incident Electron ◽  
Integral Cross Section ◽  
Image Position ◽  
Electron Energy Loss

In an earlier paper1 it was found that to a good approximation, the efficiency of collection of electrons that had lost energy due to an inner shell excitation could be written as where σE was the total excitation cross-section and σE(θ, Δ) was the integral cross-section for scattering within an angle θ and with an energy loss up to an energy Δ from the excitation edge, EE. We then obtained: where , with P being the momentum of the incident electron of velocity v. The parameter r was due to the assumption that d2σ/dEdΩ∞E−r for energy loss E. In reference 1 it was assumed that r was a constant.

Can the Number of D Electrons in Transition Metals be Measured from White Lines?

1997 ◽  
Vol 3 (S2) ◽  
pp. 957-958 ◽  
Author(s):  
P. Rez
Keyword(s):  
Transition Metals ◽  
Energy Loss ◽  
Electron Energy ◽  
Transition Elements ◽  
White Line ◽  
Line Intensities ◽  
Continuum Region ◽  
The Matrix ◽  
Image Position ◽  
Electron Energy Loss

Sharp peaks at threshold are a prominent feature of the L23 electron energy loss edges of both first and second row transition elements. Their intensity decreases monotonically as the atomic number increases across the period. It would therefore seem likely that the number of d electrons at a transition metal atom site and any variation with alloying could be measured from the L23 electron energy loss spectrum. Pearson measured the white line intensities for a series of both 3d and 4d transition metals. He normalised the white line intensity to the intensity in a continuum region 50eV wide starting 50eV above threshold. When this normalised intensity was plotted against the number of d electrons assumed for each elements he obtained a monotonie but non linear variation. The energy loss spectrum is given bywhich is a product of p<,the density of d states, and the matrix elements for transitions between 2p and d states.

scholarly journals Chemical identification through two-dimensional electron energy-loss spectroscopy

2020 ◽  
Vol 6 (28) ◽  
pp. eabb4713
Author(s):  
Renwen Yu ◽  
F. Javier García de Abajo
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Electronic Device ◽  
Theoretical Calculations ◽  
Chemical Species ◽  
High Sensitivity ◽  
Two Dimensional ◽  
Excitation Spectra ◽  
Electron Energy Loss

We explore a disruptive approach to nanoscale sensing by performing electron energy loss spectroscopy through the use of low-energy ballistic electrons that propagate on a two-dimensional semiconductor. In analogy to free-space electron microscopy, we show that the presence of analyte molecules in the vicinity of the semiconductor produces substantial energy losses in the electrons, which can be resolved by energy-selective electron injection and detection through actively controlled potential gates. The infrared excitation spectra of the molecules are thereby gathered in this electronic device, enabling the identification of chemical species with high sensitivity. Our realistic theoretical calculations demonstrate the superiority of this technique for molecular sensing, capable of performing spectral identification at the zeptomol level within a microscopic all-electrical device.

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