How Is the Signal Attenuation in Surface Electron Spectroscopy Described? VII. Calculations of electron inelastic mean free paths in solids by the single pole approximation in Penn algorithm

• Published in: Journal of Surface Analysis 2024, Vol.31(1), pp.29-55
• Main Authors: Shigeo, Tanuma, Shinotsuka, Hiroshi
• Format: Article
• Language: eng ; jpn
• ISSN: 1341-1756; 1347-8400
• DOI: 10.1384/jsa.31.29

In this article, we will describe the method for calculating the electron inelastic mean free path (IMFP) in solids using the single pole approximation (SPA) proposed by Penn. The SPA is relatively straightforward to compute, easy to program, and simple to use. In surface quantitative analyses employing Auger Electron Spectroscopy (AES) and X-ray Photoelectron Spectroscopy (XPS) with relative sensitivity factors, the energy ranges targeted are often above 150 eV or 200 eV. The SPA-derived IMFP results (SPA-IMFP) are reported in Penn's original paper to coincide with those calculated by the Full Penn Algorithm (FPA-IMFP) within a 3 % error for energy regions above 200 eV; however, a detailed comparison has not been conducted. The practicality of SPA-IMFP will significantly increase once its applicable energy range and the error range relative to FPA-IMFP are established. To this end, separate computation programs were developed for the two algorithms to verify the consistency between SPA and FPA calculations across 41 types of elemental solids (Li, Be, C (graphite), C (diamond), C(glassy), Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au, Bi). If a 5 % discrepancy relative to FPA is acceptable, then the SPA can be used to calculate IMFP in the energy range of 200 eV to 10 keV. In this energy range, the third quartile for the 41 elemental solids was below 4 %.