Simple universal curve for the energy‐dependent electron attenuation length for all materials

An analysis is presented for a simple, universal equation for the computation of attenuation lengths (L) for any material, necessary for quantifying layer thicknesses in Auger electron spectroscopy (AES) and X‐ray photoelectron spectroscopy (XPS). Attenuation lengths for selected materials may be computed from the inelastic mean free path (λ_Opt) computed, in turn, from optical data. The computation of L involves the transport mean free path and gives good L values where values of λ_Opt are available. However, λ_Opt values are not available for all materials. Instead, λ may be calculated from the TPP‐2M relation, but this requires the accurate estimation of a number of materials parameters that vary over a wide range. Although these procedures are all soundly based, they are impractical in many analytical situations. L is therefore simply reexpressed, here, in terms of the average Z of the layer which may be deduced from the AES or XPS analysis, the average atomic size a (varies in a small range) and the kinetic energy E of the emitted electron. For strongly bonded materials, such as oxides and alkali halides, a small extra term is included for the heat of formation. A new equation, S3, is established with a root mean square (RMS) deviation of 8% compared with the values of attenuation length calculated from λ_Opt available for elements, inorganic compounds, and organic compounds. This excellent result is suitable for practical analysis. In many films, an average value of a of 0.25 nm is appropriate, and then L may be expressed only in terms of the average Z and E. Then, L expressed in monolayers, equation S4, exhibits an RMS deviation of 9% for many elements. These results are valid for the energy range 100 to 30 000 eV and for angles of emission up to 65°. Copyright © 2012 Crown copyright.