Determination of ionization cross section by electron spectroscopic imaging

1988 ◽  
Vol 46 ◽  
pp. 536-537
Author(s):  
G.T. Simon ◽  
Y.M. Heng ◽  
F.P. Ottensmeyer
Keyword(s):  
Energy Loss ◽  
Cross Section ◽  
Ionization Cross Section ◽  
Unit Area ◽  
Core Loss ◽  
Ionization Cross ◽  
Image Position ◽  
Electron Energy Loss ◽  
Ionization Edge

Electron energy loss spectroscopy (EELS) has become a significant technique for high resolution elemental microanalysis and mapping. Theoretically, quantitative analysis requires only one simple equation:Eqn.(1)where N is the number of atoms per unit area analysed; I(net)(a,δ) is the core loss intensity integrated over an energy range δ beyond the ionization edge and with a collection angle a; I(total) is the total intensity integrated beneath the whole spectrum; σ(a,δ) is the corresponding ionization cross section.To obtain I(net) according to current convention and some theoretical justification, the simplest way of removing the background beneath an ionization edge is simply fitting at least two pre-edge measurements to the equation of I=AE-r, where I is the intensity of electrons that have energy loss E; A and r are constants to be determined from the fitted pre-edge region. Several other methods have also been derived for better accuracy in specific applications.

Correcting channeling and diffraction effects in quantitative REELS surface microanalysis

1991 ◽  
Vol 49 ◽  
pp. 708-709
Author(s):  
Z. L. Wang ◽  
J. Bentley
Keyword(s):  
Cross Section ◽  
Ionization Cross Section ◽  
Core Loss ◽  
Single Atom ◽  
Inelastic Electron ◽  
Ionization Cross ◽  
Reflection Electron Microscopy ◽  
Image Position ◽  
Diffraction Effects ◽  
Electron Energy Loss

Channeling conditions or resonance conditions have to be satisfied in order to enhance image contrast in reflection electron microscopy (REM) and the signal-to-background ratio in reflection electron energy-loss spectroscopy (REELS). The introduction of the channeling and diffraction effects can complicate surface microanalysis (Fig. 1). In REELS, the composition ratio for two elements may be determined by(1)where σ(A,β,Δ) is the single-atom ionization cross-section of element A for collection semi-angle β and energy window Δ; iA is the average local (channeling) current density at A atom sites; NA is the average atomic concentration of A atoms; σeff(A,β,Δ) is defined as an effective ionization cross-section (EICS) of element A; IA(β,Δ) is the integrated core-loss intensity for element A; and KA is introduced to take into account the deviation of the final inelastic electron angular distribution from the Lorentzian function due to dynamical diffraction effects. Equivalent symbols apply to element B.

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.

The Influence of Diffracting Conditions on Quantitative Electron Energy Loss Spectroscopy

1980 ◽  
Vol 38 ◽  
pp. 114-115
Author(s):  
N. J. Zaluzec ◽  
J. Hren ◽  
R. W. Carpenter
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Cross Section ◽  
Electron Energy Loss Spectroscopy ◽  
Ionization Cross ◽  
Crystalline Materials ◽  
X Ray ◽  
Scattering Effects ◽  
Electron Energy Loss ◽  
Multiple Scattering Effects

Since many applications of electron energy loss spectroscopy (EELS) deal with microanalysis of crystalline materials it is relevant to consider the effects of diffracting conditions on an EELS measurement. It is well known that anamolous effects can be observed during thin film x-ray microanalysis when crystalline materials are oriented under diffracting conditions near S = 0.1-4 It is not surprizing, therefore, that similar effects will be present in EELS, since this anamolous x-ray generation is a result of variations in the ionization cross-section with crystalline orientation2,3. Furthermore since multiple scattering effects quickly average out these perturbations2 one expects the most pronounced effects under conditions appropriate to EELS.5

Determination of the absolute two-photon ionization cross section of He by an XUV free electron laser

2011 ◽  
Vol 44 (16) ◽  
pp. 161001 ◽  
Author(s):  
Takahiro Sato ◽  
Atsushi Iwasaki ◽  
Kazuki Ishibashi ◽  
Tomoya Okino ◽  
Kaoru Yamanouchi ◽  
...  
Keyword(s):  
Cross Section ◽  
Free Electron ◽  
Free Electron Laser ◽  
Ionization Cross Section ◽  
Ionization Cross ◽  
Two Photon ◽  
Photon Ionization ◽  
The Absolute

Background modeling alternatives in EELS and their implications on microanalysis

1988 ◽  
Vol 46 ◽  
pp. 538-539
Author(s):  
Kannan M. Krishnan ◽  
M. T. Stampfer
Keyword(s):  
Cross Sections ◽  
Core Loss ◽  
Energy Window ◽  
Ionization Cross ◽  
Inverse Power Law ◽  
Power Law Function ◽  
Edge Based ◽  
Electron Energy Loss ◽  
Source Of Error ◽  
Ionization Edge

With the advent of parallel detectors, electron energy-loss spectroscopy (EELS) is expected to be employed increasingly in the routine microanalysis of light elements. The quantitation formulae that are used are relatively simple and straightforward and require only a measurement of the integrated core-loss intensity over a particular energy window beyond the ionization edge (Δi) and most often, a calculated ionization cross-section. Even though the hydrogenic cross-sections that are used routinely for microanalysis can be a source of error, it is observed that the procedure that largely determines the accuracy of quantification is the removal of the contribution of the background below the ionization edge. Based on empirical observations, an inverse power law function of the form I = AE-r, where the exponent ‘r’ takes values from 2 to 6, is now commonly used for the background. A background fitting region preceding the ionization edge (Δb) is chosen, the constants A and r determined by least squares refinement and the background extrapolated beyond the ionization edge for the required energy window (Δi).

A simple parameterization scheme for inner-shell cross sections

1988 ◽  
Vol 46 ◽  
pp. 532-533
Author(s):  
R.F. Egerton
Keyword(s):  
Solid State ◽  
Energy Loss ◽  
Cross Section ◽  
Cross Sections ◽  
Elemental Analysis ◽  
Incident Energy ◽  
Core Loss ◽  
Dipole Oscillator ◽  
Electron Energy Loss ◽  
Hand Calculator

Quantitative elemental analysis by electron energy-loss spectroscopy requires values of core-loss cross section σ(β,Δ) integrated up to a scattering angle β and over an energy range Δ above the ionization threshold. Such cross sections can be calculated using atomic models [1-3], neglecting solid-state effects. They can also be determined experimentally [4,5], but only for particular values of β,Δ and incident energy E0. By representing σ(β,Δ) in terms of an integrated dipole oscillator strength f(Δ) which is independent of β and E0, we realize two advantages: (1) measurements on solids can be directly compared with one another and with theory, and (2) values of σ(β,Δ) for K, L and M edges can be derived from tabulated values of f(Δ) by use of a hand calculator or a very short computer program.

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