Calculations of Mean Escape Depths of Photoelectrons in Elemental Solids Excited by Linearly Polarized X-rays for High-Energy Photoelectron Spectroscopy

We have calculated mean escape depths (MEDs, D) of photoelectrons from Si, Cu, and Au excited by linearly polarized X-rays over the 50 to 10,000 eV energy range for high -energy photoelectron spectroscopy. These calculations were done with Monte Carlo methods using the values of electron inelastic mean free paths λ that were calculated by the relativistic full Penn algorithm and the Dirac-Hartree-Fock atomic potential for elastic scattering of electrons. In order to know the dependence of MED on the asymmetry parameter β and the emission angle θ, we calculated MEDs for β= -1 to β= 2 (by 0.5 steps) andθ=0° to θ=80° (with respect to the surface normal). The resulting MED values increase as the β values decrease over the 50 to 10,000 eV energy range. We also found that the values of D/λcosθ are approximately constant to within 10% for a given value of θ and for energies over 1000 eV (except for the condition of β=-1) over a range of emission angles (typically 0° - 40° or 60°). We also found that the energy dependence of the ratios D/λcosθ at emission angleθ=0° can be expressed by the Jablonski-Powell predictive equation over the 50 to 10,000 eV energy range. Finally, we have obtained a predictive MED equation that could be applied to the wide range of experimental conditions that are used in high-energy XPS with synchrotron radiation.