Inelastic mean-free path 1

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... 

Xps is a surface sensitive technique as opposed to a bulk technique because electrons caimot travel very far in soHds without undergoing energy loss. Thus, even though the incident x-rays penetrate the sample up to relatively large depths, the depth from which the electron information is obtained is limited by the "escape depth" of the photoemitted electrons. This surface sensitivity of xps is quantitatively defined by the inelastic mean free path parameter which is given the symbol X. This parameter is defined to be the distance an electron travels before engaging in an interaction in which it experiences an energy loss. 

Fig. 11. "Universal curve" of inelastic mean free path, X, as a function of electron kinetic energy. Solid line is universal curve, points are experimental data...

The inelastic collision process is characterized by an inelastic mean free path, which is the distance traveled after which only 1/e of the Auger electrons maintain their initial energy. This is very important because only the electrons that escape the sample with their characteristic Auger energy are usefrd in identifying the atoms in... 

Values of the total cross-section a a for A1 Ka, radiation, relative to the carbon Is level, have been calculated by Scofield [2.7], and of the asymmetry parameter /Ja by Redman et al. [2.8]. Seah and Dench [2.3] have compiled many measurements of the inelastic mean free path, and for elements the best-fit relationship they found was ... 

The reasons AES is a surface-specific technique have been given in Sect. 2.1.1, with reference to Fig. 2.2. The normal range of kinetic energies recorded in an AES spectrum would typically be from 20 to 1000 eV, corresponding to inelastic mean free path values of 2 to 6 monolayers. 

For the inelastic mean free path, Eq. (2.10) given for XPS also applies. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

Using the Ashley approximation, the inverse inelastic mean free path is given, in congruity with the stopping power (see Sect. 2.5.2), as follows ... 

Integration of these component peaks, with appropriate corrections applied for different photoionization cross-sections and inelastic mean free paths, gives the electron populations listed in Table 4. The atomic charges obtained are consistent... 

One can go a step further and use the /P//s ratio for a quantitative estimate of the dispersion. Through the years, several methods have been proposed to predict XPS intensity ratios for supported catalysts. Angevine et al. [29] modeled their catalyst with crystallites on top of a semi-infinite support, as sketched in Fig. 3.9a. However, as the inelastic mean free path of, for example, Si02 is 3.7 nm, photoelectrons coming from particles inside pores as deep as 10 nm below the surface still contribute to the XPS signal and the assumption of a semi-infinite support is probably too simple. Indeed, the model predicts /P//s ratios that may be a factor of 3 too high [30],... 

Note that /lo(Es) is the inelastic mean free path of electrons formed in the substrate travelling through the overlayer. In the case that the overlayer is a film of Si02 on a silicon crystal, as in Fig. 3.13, Expression (3-9) reduces to... 

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