Comparisons of practical attenuation lengths obtained from different algorithms for application in XPS

Practical effective attenuation lengths (EALs) are needed for the determination of overlayer-film thicknesses by X-ray photoelectron spectroscopy (XPS). We have investigated the reliability of calculations of practical EALs from four analytical formulae, three proposed by Nefedov and Federova and one proposed by Tilinin et al. for the signal–electron depth distribution function in XPS. Comparisons were made between practical EALs from these formulae and practical EALs obtained from Monte Carlo (MC) simulations for Si 2s, Si 2p3/2, Cu 2s, Cu 2p3/2, Au 4s, and Au 4f7/2 photoelectrons excited by Mg Kα X-rays. For a common XPS configuration in which the angle between the X-ray source and the analyzer axis was 54°, practical EALs were calculated for electron emission angles between 0° and 80° (with respect to the surface normal) and for overlayer-film thicknesses such that the substrate signal intensities were reduced to 10% of their values for an uncovered substrate at each emission angle. The average deviations between practical EALs from the four formulae and from MC simulations were 4.97% for the Tilinin et al. algorithm and 8.99%, 7.02%, and 5.79% for the three Nefedov and Federova algorithms. Practical EALs from the Tilinin et al. formula are thus generally more reliable that those from the Nefedov and Federova formulae. For a less-common XPS configuration in which the angle between the X-ray source and the analyzer axis was less than 10° and the emission angle is 0°, practical EALs from one of the Nefedov and Federova formulae were found to be more reliable than those from the Tilinin et al. formula.