The electron attenuation length revisited

Abstract

The electron attenuation length (AL) is commonly understood to be a measure of the opacity of a solid for a given electron energy in surface-sensitive spectroscopies such as Auger-electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). Initially, the term attenuation length was used interchangeably with the term inelastic mean free path (IMFP), the latter being defined as the mean distance between inelastic collisions. However, about 20 years ago, it was realized that elastic-scattering of signal electrons in the solid may considerably influence their trajectories. The projection of a trajectory on a given direction could then have a significantly different length than the length actually traveled, and thus the AL could differ from the IMFP. In addition, calculations showed that the difference between the AL and the IMFP depended on the experimental configuration. It has been generally difficult to measure differences between the AL and the IMFP. Most measurements of the AL, or the recently preferred replacement term effective attenuation length (EAL), have been made from changes of AES or XPS peak intensities as overlayer films of various thicknesses were deposited on a substrate. Unfortunately, the derived EALs generally have large uncertainties because of inadequate knowledge of film morphology and thickness. As a result, EAL values deduced from “universal curves” should be regarded only as rough guides. Furthermore, it has been realized recently that the present formal definition of the EAL is relevant to the determination of the depth of thin marker layers while measurements of AES or XPS intensities have been used to determine EALs (or equivalently, overlayer-film thicknesses have been obtained from AES or XPS intensities and EAL values from the literature). These two approaches would give identical EALs if elastic-scattering effects were negligible but, as we show here, numerical differences arise in situations of practical relevance. We make a further distinction between “local” EALs (based on definitions for a narrow range of overlayer-film thicknesses or marker-layer depths) and “practical” EALs (based on definitions for a specific thickness or depth). We report comparisons of calculated local and practical EALs for XPS with Mg Kα X-rays in a range of measurement configurations for two illustrative cases: Si 2s photoelectrons in Si (for which elastic-electron scattering effects are relatively weak) and Au 4s photoelectrons in Au (for which the elastic-scattering effects are relatively strong). The practical EALs for overlayer-film thickness measurements in conventional XPS experiments are found not to vary appreciably with emission angle for emission angles between 0° and 65°. For this range of emission angles, the practical EALs do not vary significantly with film thickness for a useful range of overlayer-film thicknesses, and it is then useful to make use of average practical EALs for film-thickness measurements. The ratio of the average practical EAL to the corresponding IMFP for these conditions is 0.91 for Si 2s photoelectrons and 0.76 for Au 4s photoelectrons. Practical EALs were also calculated for the N 7VV, N 5N 67V, and M 5N 67N 67 Auger transitions in Au. We found qualitatively similar variations of these practical EALs on film thickness and emission angle as in XPS. It is recommended that overlayer-film thicknesses be determined in AES and XPS using EALs for the particular materials and measurement conditions.