Influence of elastic-electron scattering on measurements of silicon dioxide film thicknesses by x-ray photoelectron spectroscopy

Abstract

We investigate the systematic error due to neglect of elastic scattering of photoelectrons in measurements of the thicknesses of thin films of ${\mathrm{SiO}}_{\mathrm{2}}$ on Si by x-ray photoelectron spectroscopy (XPS). Calculations were made of substrate Si $\text{2p}$ photoelectron currents excited by Mg and Al $\mathrm{K\alpha }$ x rays for different ${\mathrm{SiO}}_{\mathrm{2}}$ thicknesses, different angles of photoelectron emission, and three representative XPS configurations using an algorithm based on the transport approximation. We calculated practical effective attenuation lengths (EALs) from changes of the computed Si $\text{2p}$ photoelectron currents. These EALs were less than the corresponding inelastic mean free paths by between 6.5% and 9.4%, with the difference depending on the x-ray source, the specific range of ${\mathrm{SiO}}_{\mathrm{2}}$ film thicknesses under consideration, the XPS configuration, and the range of photoelectron emission angles. Useful average values of the EAL were found for emission angles between 0° and about 60° (with respect to the surface normal) and for silicon dioxide thicknesses such that the substrate signal was attenuated to not more than 1% and 10% of its original value. Our calculated EALs are in satisfactory agreement with measured EALs. For larger emission angles, the calculated EALs change rapidly with ${\mathrm{SiO}}_{\mathrm{2}}$ thickness, and specific values should be found for the conditions of interest.