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

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.