Unless otherwise stated this page contains Version 1.0 content (Read more about versions)
4.5.2 Attenuation length of electrons in solids
The electron attenuation length (AL), λ, is defined as the thickness of material through which electrons may pass with a probability e−1 that they survive without inelastic scattering. Conventionally the inelastic scattering is considered to be significant only for energy losses 1 eV, phonon excitations being ignored. (The AL should not be confused with the total electron range which may be 10 to 100 times greater.) The value of λ depends on both the material and electron energy. For electrons emitted at an angle θ to the normal from a solid surface, the unscattered intensity from a source at a depth z below the surface follows the approximate relation
Thus, in Auger and X-ray photoelectron spectra from solid surfaces, the average information depth is characterized by λ cos θ.
For elements, an empirical and approximate description of λ in nm is given by Seah and Dench (1979)
where E eV is the electron energy and a3
nm3 is the volume of one atom of the element in the solid state.
This description fits the experimental data on average to a standard deviation
More recent studies of the theoretical parameter, the inelastic mean free path (IMFP), show an energy dependence closer to that of Wagner et al. (1980). The IMFP, λi, is the average total distance that the electrons traverse between inelastic scattering whereas the AL reflects the average net distance travelled. The AL is some 20% less than the IMFP due to the elastic scatterings which deflect the electron trajectories. The general form of the IMFP relation (Tanuma et al., 1993) is
where the various constants may be calculated from tables of values of
basic materials constants.
M. P. Seah and W. A. Dench (1979) Surface and Interface Analysis,
This site is hosted and maintained by the National Physical Laboratory