Editing X-ray photoelectron spectroscopy (section)

====Inelastic mean free path====

In a solid, inelastic scattering events also contribute to the photoemission process, generating electron-hole pairs which show up as a tail on the high energy side of the main photoemission peak. Due to scattering, the electron intensity can be written in the [[Beer–Lambert law|Beer–Lambert form]]
:<math>
I(z) = I_0 e^{-z/\lambda}
</math>
where <math>\lambda</math> is the electronic '''[[inelastic mean free path]]''' ('''IMFP'''). Here, <math>z</math> is the distance to the sample surface. The IMFP generally depends rather weakly on material, but strongly on the photoelectron kinetic energy <math>E_\text{kin}</math>. Quantitatively we can fit the IMFP by<ref>{{cite book |last1=Attard |first1=Gary |last2=Barnes |first2=Colin |date=1998 |title=Surfaces |publisher=Oxford Chemistry Primers |page=27 |isbn=978-0198556862 }}</ref><ref>{{cite journal|last1=Seah|first1=M. P.|last2=Dench|first2=W. A.|date=1979|title=Quantitative Electron Spectroscopy of Surfaces: A Standard Data Base for Electron Inelastic Mean Free Paths in Solids|journal=Surf. Interf. Anal.|volume=1|number=1|page=2{{hyphen}}10|doi=10.1002/sia.740010103}}</ref><ref>{{cite web|url = http://www.lasurface.com/xps/imfp.php |title = XPS: The Mean Free Path|website = lasurface.com}}</ref>
:<math>
\lambda = 538\,\text{nm}\,\left( E_\text{kin}/\text{eV}\right)^{-2} + 0.41\,\text{nm}\,\left(a / \text{nm}\right)^{1/2} \left(E_\text{kin} / \text{eV}\right)^{1/2}
</math>
where <math>a</math> is the thickness of one monolayer, as given by the number density <math>\rho</math> as <math>a = \rho^{-1/3}</math>. The above formula is a fit to a compilation of experimental data for pure elements. For anorganic and organic compounds, its numerical factors are different, see the paper by Seah and Dench (1979).