Attenuation length, electrons

The total contribution to the Auger electron signal is then dependent upon the attenuation length (kM) in the matrix before being inelastically scattered, and upon the transmission efficiency of the electron spectrometer as well as the efficiency of the electron detector. Calculated intensities of Auger peaks rarely give an accuracy better than 50%, and it is more reliable to adopt an approach which utilises standards, preferably obtained in the same instrument. 

Figure 8 shows the attenuation length of electrons in solids as a function of their kinetic energy. The few theoretical calculations available cire in good agreement with these empirical data Only unscattered electrons convey useful information, while scattered electrons contribute to a structureless background (secondary electrons). From Fig. 8, it is clear that photoelectron spectroscopy probes at most a few tens of Angstroms. 

Fig. 8. A universal curve (or band) of electron attenuation length vs. electron kinetic energy, as resulting from an inspection of many experimental results on heavy metals. The energy of different laboratory sources, representing the maximal kinetic energy of the electron, is drawn for comparison in the figure (from Ref. 5)...

Mean free path values are often approximated by a calculating them from a general formula [24], but data which take material properties into account are available also [25]. That this is important is illustrated by the mean free path of Si 2p photoelectrons in SiC>2 (3.7 nm) and in pure silicon (3.2 nm, valid when using A1 Ka radiation) the 2-values differ considerably, although the kinetic energies of the electrons are the same. In a recent review, Jablonski and Powell discussed developments in the understanding of electron attenuation lengths [26]. 

In this formula A and Aj are the spin-dependent hot electron attenuation lengths, which have been measured by various experimental techniques for different ferromagnetic materials [135-145]. The SVT and MTT have also successfully been used to measure Af and for 3d transition metal alloys [146-148], In these experiments the collector current is measured as a function of the ferromagnetic base layer thickness. 

The results show that the attenuation length of minority electrons in NiFe and CoFe is only about 1 nm, while that of majority electrons is a factor 4 to 6 larger. Consequently, thin ferromagnetic films act as efficient spin filters for hot electron currents. For example, the calculated transmission polarization of a 4 nm thick ferromagnetic film with Ai = 1 nm and At = 5 nm amounts already 92%. 

It is not strictly correct to equate the inelastic mean free path with the attenuation length, as we do so essentially in Fig. 1. One would have to assume in the experiment that as many electrons are scattered elastically into as out of the direction of the analyser slits. Because of the net loss due to back scattering this can never be the case in practice. 

Due to the bonding selectivity of chemisorption, SAM of DNA can be prepared without significant amounts of impurities. Furthermore, molecular orientation within the layer is fairly well defined [19]. Owing to these characteristics, SAM films of DNA have been particularly useful in the determination of absolute yields and cross sections for specific damages. When extracting attenuation lengths (AL) or cross sections from electron-scattering experiments on thin molecular films, by far the most difficult parameter to determine and control, is the film thickness and its... 

Figure 19-10. Dependence of yield of LEE-induced 5 -oligonucleotide fragments on their length for electron energies of 8 ( A), 28 (O), and 68 eV ( ). The curves represent decaying exponential fits. The inset shows the dependence of the attenuation length (AL) on LEE energy. The error bars represent the uncertainty range of the fitting parameter in the exponential...

Table 19-1. Attenuation length and effective cross section for strand breaks (SB) in SAM of oligonu-cleotides chemisorbed on gold as a function of electron energy...

Incident electron energy (eV) Attenuation length (nm) Effective cross section for SB (x 10 17 cm2)1 ... 

Fig. 5.1 Spin resolved intensities of Co/W(110) after excitation with Ne I radiation hv = 16.85 eV). Filled upward triangle denote majority and filled downward triangle minraity electrons. The tungsten structure at a binding energy of 2.9 eV shows significantly different peak areas in both spin channels (light and dark gray shaded) indicating a spin dependence of the particular attenuation lengths...

Fig. 5.2 Left attenuation of the tungsten feature as a function of cobalt thickness in monolayers (ML) for the spin integrated measurement (filled dianwnd), for majority (filled square) and minority (open circle) electrons. Right universal curve of the inelastic mean firee path [4] included are the different attenuation lengths for majority (filled square) and minority (open circle) electrons being 4.4 and 3.2 ML, respectively, at a kinetic energy of 10 eV...

It seems to be possible to explain the polarization enhancement of secondary electrons by the spin dependence of the IMFP. This means, the different attenuation lengths act as a spin filter, majority electrons preferentially allowing to be transmitted. The spin asymmetry of the IMFP, given by A = (2+ — 2 )/(2+ + 2 ), amounts to about 20% for both systems and is confirmed by an investigation of Fe/Cu(100) [8] leading to the same value of A. A very effective spin filter can be realized by a graphene layer which was theoretically predicted [11] and experimentally verified for graphene on Ni(lll) [12]. 

The effective attenuation length is a function of electron kinetic energy and of the medium density. However, when we represent A. in number of monolayers, an approximately universal curve is obtained [32] as displayed in Figure 12. 

Fig. 12. Schematic representation of electron effective attenuation length as a function of electron energy.

Since the attenuation length for X-rays is much larger than for electrons, X-ray intensity is con-... 

Quantification is simple if the atoms are homogeneously distributed with depth since the intensity of each XPS peak is then directly related to the abundance of that particular element at the specimen surface. The peak intensity will usually be reported as a peak area and this will be normalized using atomic sensitivity factors (the intensity of the photoelectron transition of interest, I, is related to the concentration of that element within the XPS analysis volume, and the sensitivity factor, S, in the following way F= concentrationxS). Such atomic sensitivity factors are a function of the basic physical parameters, such as the relative photoelectron cross-sections of the different elements, electron attenuation lengths, and instrumental parameters, such as analyzer transmission functions, of the XPS experiment. The ratio of normalized peak area to the sum of normalized peak areas for the major peaks of all elements detected in the spectrum provides an analysis as an atomic fraction (or when multiplied by 100, atomic %). 

Table 3. Photoelectron Ionization Cross Sections a and Electron Attenuation Length X of Self-Assembled ODP Monolayer on Ta205, from Data Given in Refs 15 and 16...

The electron attenuation length (mean free path length X) in the various layers was calculated using the general expressions given by Seah ... 

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