Angular distribution of photoelectrons emitted by the laboratory soft and hard X-ray radiation sources

Highlights: •Applicability of the dipole approximation in quantitative XPS. •Necessity to use the non-dipole approximation for high kinetic energy photoelectrons. •Influence of photoelectron elastic scattering on the signal intensity. •Correction parameters for the elastic scattering effects. -- Abstract: XPS spectrometers are typically equipped with the Mg Kα radiation and/or Al Kα radiation sources. However, for some analyses, it is convenient to use the laboratory sources emitting high energy X-rays, e.g. to avoid coincidence of peaks due to photoelectrons and Auger electrons, or to increase the information depth. On the other hand, the mathematical formalism of quantitative XPS analysis is based on the theoretical photoemission cross section that is valid for photoelectrons emitted with a relatively low kinetic energy (the so-called dipole approximation – DA). For high kinetic energy photoelectrons, the photoemission cross section needs to be modified with nondipolar parameters. An important issue for an analyst is the correction of the formalism of quantitative analysis for the photoelectron elastic scattering effects. The Monte Carlo program has been developed for simulation of transport of photoelectrons emitted from polycrystalline or amorphous solids by four X-ray radiation sources: Mg Kα, Al Kα, Zr Lα and Ti Kα. Calculations were performed for photoelectrons emitted in elemental solids with a wide range of atomic numbers: Al, Cu, Ag and Au. The photoelectron emission event was described within the DA and the model modified with the multipole correction (non-dipole approximation – NDA). It has been found that, in a typical XPS configuration, the dipole approximation is of sufficient accuracy for the Mg Kα and Al Kα radiation sources. The difference between photoelectron signal intensities calculated within the DA and NDA did not exceed 8% when elastic photoelectron elastic scattering is neglected. For high-energy radiation sources, Zr Lα and Ti Kα, the difference may reach 25% in this geometry, and thus the NDA model is recommended for calculations. The photoelectron elastic collisions are found to decrease the difference between the DA and NDA models. An important result of the present analysis is the observation that the NDA formalism can be corrected for elastic scattering effects in the same way as the DA formalism, i.e. with two parameters, Qx and βx. Furthermore, the expressions for calculating these parameters derived for the DA model and for the Mg Kα and Al Kα sources are found to be also applicable to photoelectron emitted by the Zr Lα and Ti Kα sources. However, new expressions valid for all four radiation sources have been tentatively derived in the present work