Depth of Analysis, Inelastic Mean Free Path

The inelastic mean free path, or IMFP (λ), is defined as the average distance that an electron with a given energy travels between successive inelastic collisions. One sigma (σ) (or 68 %) of all photoelectrons will come from within one λ of depth, while the majority (3σ or 99.7 %) of photoelectrons will come from 3λ. For most core electrons excited by Al Kα X-rays this depth is on the order of a few nm. Denser elements/compounds will have shallower IMFPs as will core electrons with greater binding energies (i.e. smaller kinetic energies). With the appropriate equations, as defined in references[1,2] the IMFP can be used to calculate the thickness of oxide films and thin overlayers. By tilting the sample with respect to the analyzer one can change the effective IMFP. This is known as angle resolved XPS and it is useful for gaining an understanding of thin surface layers. This type of analysis can also be achieved using synchrotron radiation through manipulation of the incident X-ray energy. 

[1] T.A. Carlson, G.E. McGuire, J. Electron Spectrosc. Relat. Phenom. 1 (1972/73) 161.
[2] B.R. Strohmeier, Surf. Interface Anal. 15 (1990) 51.