Role of the emission depth distribution function in quantification of electron spectroscopies

Abstract

Quantitative analysis by Auger electron spectroscopy or photoelectron spectroscopy should be founded on a reliable relation between the measured signal intensity and composition of the surface region. In this relation, the signal electron elastic scattering effects are conveniently described by the emission depth distribution function (DDF). This function is the distribution of depths of origin for signal electrons emitted from a solid in a given direction without energy loss. Numerous parameters needed for quantification of electron spectroscopies can be derived from the DDF, e.g. the mean escape depth, the information depth, the effective attenuation length, etc. Generally, knowledge of the accurate DDF facilitates the procedure of including the elastic scattering effects into the formalism of quantitative analysis. The function called the partial escape distribution (PED) defining the probability of emission in a given direction after a certain number of inelastic interactions can be considered as a generalization of the DDF. The PED becomes equivalent to the DDF in the case of no inelastic interactions. A series of the PED functions is needed for quantification of the recorded spectra, especially when the elastic collisions need to be taken into account. It has been shown that the PED for any number of inelastic collisions can be derived from the DDF. Reliability of the obtained PED functions was checked for different analytical expressions for the DDF. It has been shown that the expression published by Tilinin et al. is the most accurate, and can be recommended for calculations of the PED.