Mean free path for inelastic

Surface sensitivity in LEED is provided by the limited mean free path for inelastic scattering of slow electrons. This mean fi-ee path is the distance traveled by an electron in the solid before it collides inelastically, loses energy, and thus becomes... 

Fig. 1. Mean free path for inelastic scattering, A, for aluminium [after Refs. (6) and (7)]. Experimental points measured mean attenuation lengths taken from the compilation by Powell (5)...

Fig. I. Photoelectron mean free path for inelastic scattering in Si and Au in the energy range of interest for XANES spectra. The data were obtained from the measurement of electron escape depth in photoemission experiments...

We see that for EELS analysis, the resolution is degraded only linearly with foil thickness. Comparison with the values in Table 3.1 shows that if the collector aperture is about 10 mrad, and the energy losses are 200 eV or more, nanometer resolution can be maintained for foils up to about 100 nm thick. This thickness coincides approximately with the mean free path for inelastic scattering, so that spectra from thicker foils suffer degradation of energy resolution anyway. 

Tn transmission experiments the relative importance of bulk and surface loss components will be a function of film thickness, but bulk response will generally dominate. In reflection geometry the bulk/surface balance depends sensitively on incident energy and angle and the mean free path for inelastic loss within the solid, but at low p( 200 eV) the contributions are likely to be comparable, with surface response becoming increasingly important near glancing incidence. 

Here denotes the mean free path for inelastic scattering given as... 

Vji, is the drift velocity in the solution at field strength E, AWi is the average inelastic loss, and Aj denotes the mean free path for inelastic scattering (see Equation 10). From Equations 13 and 14 it follows that... 

The Auger and photoemitted electrons of interest have relatively low KE (50 to 2000 eV) and have a high probability of undergoing inelastic collision with an atom in the matrix. Thus, only those photoelectrons generated near the sample surface (< 10 nm) will contribute to XPS signals. Detailed experimental values of the inelastic mean free path for electrons having the energies important in XPS have been reported [7]. Furthermore, detailed descriptions of the hardware and instrumentation involved in the XPS technique are also available [8]. 

Up to now we have discussed two extreme limits, the band picture on the one hand, and strong localization associated with interruptions in the metallic chains on the other. In fact, from work on thin metallic films and metallic glasses it is known that there is an intermediate region, that of weak localization. This occurs when the mean free path for elastic scattering (Lel) is only somewhat larger than, or comparable with, that for inelastic processes (Lin). In the first approximation there are corrections to the Boltzmann transport formula which depend on the ratio Lin/Lel in different ways for one-, two-, and three-dimensional materials. Weak localization... 

In the interpretation of the x-ray absorption spectra the inelastic interaction between the photoelectron and the valence electrons is an important process. The mean free paths for Au and Si are shown in Fig. 1 Therefore, in x-ray absorption... 

The outcome of the analysis of the integrated peak intensities shown in Fig. 6 is shown in Table 1 after corrections for different photoelectron cross sections and for the different inelastic mean free paths for the photoelectrons. The C l.s peak was not included in the quantitative balance since it was felt to represent a contamination overlayer which was not an integral part of the corrosion film. Previous XPS intensity studies of reference oxides showed reasonably good agreement with expected stoichiometries [9]. From the analysis, it can be seen that this film contained more oxygen than was accountable by stoichiometry the balance is believed to be water of hydration. 

The measurement of film thicknesses in the range 1-6 nm is often possible with XPS. This results from the ability to distinguish oxide and metal peaks for an element, often at an intensity ratio of 20 1, coupled with the fact that the inelastic mean free paths for many photoelectron lines are in the range of 2-. nm. Recently it has been possible to measure the growth of oxide on A1 and Mg metals in the presence of water vapor over an exposure range of 12 orders of magnitude [10]. 

A vacuum environment is necessary for XPS experiments to be undertaken for three reasons. First, low pressure is required to insure a sufficient inelastic mean free path for the photoelectrons to escape the solid and reach the electron detector without being dissipated via inelastic collisions. From the kinetic theory of gases, the mean free path of the gas molecule (analogous to the IMFP concept of photoelectrons traveling through a solid), X, can be determined from... 

Seah M P and Dench W A 1979 Quantitative electron spectroscopy of surfaces a standard data base for electron inelastic mean free paths in solids Surf, interface Anai. 1 2... 

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