Abstract
AES and XPS are quantitative analytical tools. The basis of their quantification is the determination of the intensity of a characteristic signal from a measured spectrum. Mainly depending on the tolerable uncertainty in the respective analytical task, the signal intensity is obtained by application of more or less elaborate procedures to the raw data, as outlined in the next paragraph (Sect.4.1). Section 4.2 presents the basic tools for quantification such as relative sensitivity factors and electron attenuation length in electron spectroscopies. As shown in Sect. 4.3 for XPS and in Sect. 4.4 for AES, quantification of intensities in terms of atomic concentrations is only possible by knowledge of the in-depth distribution of composition, with the limiting cases of homogeneous distribution and of thin atomic layer(s) on a substrate.
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Notes
- 1.
- 2.
- 3.
- 4.
Note that it has become customary to express the product \({\sigma }_{A,\ i}\ W({\beta }_{A,i},\psi )\) by the differential cross section \(\mathrm{d}{\sigma }_{A,i}/\mathrm{d}\Omega \,=\,(1/4\pi ){\sigma }_{A,i}\ W({\beta }_{A,i},\psi )\) [4.29]. Furthermore, in solids β A, i has to be replaced by the modified parameter β A, ieff (see Sect. 4.3.1.2).
- 5.
The exponent 0.75 applies only for E > 200 eV, and for elements and inorganic compounds. For organic compounds, the exponent is 0.79 [4.39].
- 6.
In principle, the dependence of the elastic scattering correction factor Q on the emission angle has to be considered in the attenuation length \(\lambda \,=\,{\lambda }_{\mathit{in}}Q(\theta ,\omega )\) (4.20). Because after (4.24) the dependence of Q on θ is proportional to Q(0, ω), the angular dependence cancels in (4.84a)–(4.84c). The slight effect of the angular dependence of ω is again similar for both elements [4.68] and practically cancels in the ratio. With the matrix correction factor \({F}_{A,B}^{m}(\psi )\) inserted in (4.57), (4.58a), and (4.58b), quantification to obtain \({X}_{A},\ {X}_{B}\) can be accomplished for \(\psi \neq 54.{7}^{\circ }\) with (4.50), (4.52), and (4.54).
- 7.
- 8.
Note that the inelastic mean free path is exactly the same for Auger- and photoelectrons of the same kinetic energy. However, attenuation lengths between AES and XPS may differ slightly because of the different effects of elastic scattering for symmetric and asymmetric emission (see Sects. 4.2.2 and 4.3.1).
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Hofmann, S. (2013). Quantitative Analysis (Data Evaluation). In: Auger- and X-Ray Photoelectron Spectroscopy in Materials Science. Springer Series in Surface Sciences, vol 49. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27381-0_4
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