Relationships between electron inelastic mean free paths, effective attenuation lengths, and mean escape depths

The terms inelastic mean free path (IMFP), effective attenuation length (EAL), and mean escape depth (MED) are frequently used to specify the surface sensitivity of Auger-electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). These terms are different conceptually because of the effects of elastic-electron scattering, and generally have different numerical values for a specified material and electron energy. In addition, values of the EAL and MED depend on the instrumental configuration. We give an historical overview of efforts to measure EALs by the overlayer method and of work to investigate elastic-scattering effects in AES and XPS. We then apply an analytical formalism developed from a solution of the kinetic Boltzmann equation within the transport approximation to demonstrate the relationships between the IMFP, EAL, and MED for selected elemental solids and for common measurement conditions. Examples are given to show the magnitude of elastic-scattering effects on MED values for angle-resolved XPS and AES. If XPS or AES data are acquired for emission angles between zero and 60°, the ratio of the MED to that found with elastic scattering neglected is approximately constant (to within 10%), and this ratio can be used to determine an average value for the EAL. This EAL value can then be used to establish the depth scale in the data analysis. Finally, we show ratios of the EAL to the IMFP for XPS from the Au 4s subshell with Mg K X-rays as a function of emission angle and depth; this ratio has a weak dependence on emission angle from zero to 40° but a more pronounced dependence for larger emission angles.