Inelastic background signal in x-ray photoelectron spectroscopy.

Abstract

An inversion formula, derived previously by Tougaard and the author to extract a primary excitation spectrum from the measured photoelectron spectrum of a semi-infinite solid, has been generalized to cover the entire energy range from the highest spectral energy to zero. In the absence of elastic electron scattering, the original expression retains its form, but the full energy dependence of the mean free path and the differential energy-loss cross section need to be incorporated. Elastic scattering can be included, either qualitatively within an infinite-medium model, or rigorously on the basis of an invariant-embedding approach. Apart from measurable quantities, the elastic-scattering correction contains an integral over the primary excitation rate, i.e., the quantity looked for. Therefore, iterative solution may be required in the presence of pronounced elastic scattering.