PART I. Quantitative Analysis of Electron Spectra

Inelastic Scattering Cross Section. The inelastic scattering cross section that defines the probability that an electron loses energy T per unit energy loss and per unit path length traveled is one of the key parameters in quantitative peak shape analysis. In the dielectric response formalism of solid electron interaction, the cross section may be evaluated from the wave vector and frequency dependent complex dielectric function ( , u) [105,106] 

The term 3(— l/e q, co)) is referred to as the dielectric loss function. Structures in this function can be correlated to bulk plasmon excitations. In the vicinity of a surface the differential cross section for inelastic scattering has to be modified to describe the excitation of surface plasmons. The surface energy loss function is proportional to 3(—l/e(, cu) + 1). In general, the dielectric function is not known with respect to energy and momentum transfer. Theoretical approaches to determine the cross section therefore have to rely on model dielectric functions. Experimentally, cross sections are determined by either optical absorption experiments or analysis of reflection energy loss spectra [107,108] (see Section 4.3). 

In a systematic study applying the latter method to several materials, it was found that the inelastic electron scattering losses of solid materials exhibit common characteristic features [109]. Therefore, the inelastic scattering cross section 

The analysis of a given nanostructure proceeds as follows Let us assume that the sample to be analyzed consists of a substrate material S and a deposited material D that is distributed in some way, described by the unknown emitter profile From a reference sample, consisting of the pure material D ex- 

For the deposit/substrate system the total measured spectrum is simply the sum of the substrate spectrum and the deposit spectrum (noninterfering peaks are of course best suited for the analysis). As the two distribution functions are com- 

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