Effective Attenuation Lengths for Different Quantitative Applications of X-ray Photoelectron Spectroscopy

The effective attenuation length (EAL) is a useful parameter in quantitative applications of x-ray photoelectron spectroscopy (XPS). This parameter is used in place of the inelastic mean free path (IMFP) in expressions for different XPS applications to correct those expressions for elastic scattering of the photoelectrons. We consider expressions used to determine (i) the thickness of an overlayer film on a planar substrate, (ii) the surface composition, (iii) the depth of a thin marker or delta layer, and (iv) the shell thickness of a core–shell nanoparticle. An EAL can be used for each of these applications. In general, the EAL depends on the particular defining equation as well as on the XPS configuration. Many attempts were made in the 1970s and 1980s to measure EALs for the determination of overlayer-film thicknesses, but there were often wide scatters in the reported results due to the difficulty in preparing uniform films with known thicknesses. We have therefore been motivated to calculate EALs for each application. The SRD 82 database from the National Institute of Standards and Technology (NIST) provides EALs for the measurement of overlayer-film thicknesses and of marker-layer depths. These EALs can be determined for photoelectron energies between 50 eV and 2 keV and for user-specified XPS configurations. We review EAL predictive equations for the determination of overlayer-film thicknesses on a planar substrate for XPS with unpolarized x rays and with linearly polarized x rays as well as an EAL predictive equation for quantitative analysis by XPS. These equations are simple analytical expressions that are valid for well-defined ranges of experimental conditions and for useful ranges of electron energies. We also point out that EALs for the determination of overlayer-film thicknesses can be derived from the simulated photoelectron intensities obtained from the NIST Database for the Simulation of Electron Spectra for Surface Analysis (SRD 100). Where possible, we make comparisons of the calculated EALs with illustrative experimental results. A key parameter in the EAL predictive equations is the so-called albedo, a useful measure of the strength of elastic-scattering effects in a material. The albedo is a simple function of the IMFP and the transport mean free path (TRMFP). We provide a tabulation of albedo and TRMFP values in the supplementary material for 41 elemental solids and 42 inorganic compounds for photoelectron energies between 50 eV and 30 keV. For other materials, albedo values can be determined from IMFP and TRMFP data available in the NIST SRD 82 and SRD 100 databases.